U.S. patent application number 11/193654 was filed with the patent office on 2006-01-26 for apparatus and method for automated protein design.
Invention is credited to Bassil I. Dahiyat, D. Benjamin Gordon, Stephen L. Mayo, Arthur Street, Yaoying Su.
Application Number | 20060019316 11/193654 |
Document ID | / |
Family ID | 27366337 |
Filed Date | 2006-01-26 |
United States Patent
Application |
20060019316 |
Kind Code |
A1 |
Mayo; Stephen L. ; et
al. |
January 26, 2006 |
Apparatus and method for automated protein design
Abstract
The present invention relates to apparatus and methods for
quantitative protein design and optimization.
Inventors: |
Mayo; Stephen L.; (Pasadena,
CA) ; Dahiyat; Bassil I.; (Los Angeles, CA) ;
Gordon; D. Benjamin; (Pasadena, CA) ; Street;
Arthur; (Los Angeles, CA) ; Su; Yaoying;
(Newport Beach, CA) |
Correspondence
Address: |
DORSEY & WHITNEY LLP
555 CALIFORNIA STREET, SUITE 1000
SUITE 1000
SAN FRANCISCO
CA
94104
US
|
Family ID: |
27366337 |
Appl. No.: |
11/193654 |
Filed: |
July 28, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09812034 |
Mar 19, 2001 |
6950754 |
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11193654 |
Jul 28, 2005 |
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09127926 |
Jul 31, 1998 |
6269312 |
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11193654 |
Jul 28, 2005 |
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09058459 |
Apr 10, 1998 |
6188965 |
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11193654 |
Jul 28, 2005 |
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60043464 |
Apr 11, 1997 |
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60054678 |
Aug 4, 1997 |
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60061097 |
Oct 3, 1997 |
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60087561 |
Jun 1, 1998 |
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Current U.S.
Class: |
435/7.1 ;
702/19 |
Current CPC
Class: |
C12N 15/1034 20130101;
G16B 15/00 20190201; G16B 30/00 20190201; C07K 1/00 20130101; C07K
14/001 20130101; C07K 1/003 20130101; G16B 20/00 20190201; C12N
15/1089 20130101 |
Class at
Publication: |
435/007.1 ;
702/019 |
International
Class: |
G06K 9/00 20060101
G06K009/00; G01N 35/00 20060101 G01N035/00 |
Claims
1-29. (canceled)
30. A method executed by a computer under the control of a program,
said computer including a memory for storing said program, said
method comprising the steps of: a) receiving a set of three
dimensional coordinates for a target protein having a protein
backbone structure and a plurality of variable residue positions;
b) altering the coordinates of a plurality of atoms of said
backbone structure of said target protein; and c) computationally
generating a set of rank ordered optimized variant sequences using
at least one scoring function, wherein said variant sequences
comprise at least one variant amino acid at least one variant
residue position.
31. The method according to claim 30 wherein said set comprises the
global minimum using said scoring function.
32. The method according to claim 30 wherein said set consists of
the global minimum using said scoring function.
33. The method according to claim 30 wherein said variable residue
positions are classified as core, surface or boundary residues.
34. The method according to claim 30 wherein said scoring function
is selected from the group consisting of a van der Waals potential
scoring function, a hydrogen bond potential scoring function, an
atomic solvation scoring function, an electrostatic scoring
function and a secondary structure propensity scoring function.
35. The method according to claim 30 wherein said computational
generation of said set utilizes at least two scoring functions.
36. The method according to claim 30 wherein said computational
generation of said set utilizes at least three scoring
functions.
37. The method according to claim 30 wherein said computational
generation of said set utilizes at least four scoring
functions.
38. The method of claim 30 wherein said altering is by altering at
least one supersecondary structure parameter of said backbone
structure.
39. A computer readable memory that upon execution by a computer
processor performs the method of claim 30.
40. The computer readable memory according to claim 39 wherein said
set comprises the global minimum using said scoring function.
41. The computer readable memory according to claim 39 wherein said
set consists of the global minimum using said scoring function.
42. The computer readable memory according to claim 39 wherein said
variable residue positions are classified as core, surface or
boundary residues.
43. The computer readable memory according to claim 39 wherein said
scoring function is selected from the group consisting of a van der
Waals potential scoring function, a hydrogen bond potential scoring
function, an atomic solvation scoring function, an electrostatic
scoring function and a secondary structure propensity scoring
function.
42. The computer readable memory according to claim 39 wherein said
computational generation of said set utilizes at least two scoring
functions.
43. The computer readable memory according to claim 39 wherein said
computational generation of said set utilizes at least three
scoring functions.
44. The computer readable memory according to claim 39 wherein said
computational generation of said set utilizes at least four scoring
functions.
45. The computer readable memory of claim 39, wherein said altering
is by altering at least one super secondary structure parameter of
said backbone structure.
46. A computer processor that executes the computer readable memory
of claim 39.
Description
[0001] This application is a continuation of U.S. Ser. No.
09/812,034, filed Mar. 19, 2001, which is a continuation of U.S.
Ser. No. 09/127,926, filed Jul. 7, 1998, now U.S. Pat. No.
6,269,312, which is a continuation of U.S. Ser. No. 09/058,459,
filed Apr. 10, 1998, now U.S. Pat. No. 6,188,965, which claims the
benefit of U.S. Provisional Application No. 60/043,464, filed Apr.
11, 1997, U.S. Provisional Application No. 60/054,678, filed Aug.
4, 1997, U.S. Provisional Application No. 60/061,097, filed Oct. 3,
1997, and U.S. Provisional Application No. 60/087,561, filed Jun.
1, 1998.
FIELD OF THE INVENTION
[0002] The present invention relates to an apparatus and method for
quantitative protein design and optimization.
BACKGROUND OF THE INVENTION
[0003] De novo protein design has received considerable attention
recently, and significant advances have been made toward the goal
of producing stable, well-folded proteins with novel sequences.
Efforts to design proteins rely on knowledge of the physical
properties that determine protein structure, such as the patterns
of hydrophobic and hydrophilic residues in the sequence, salt
bridges and hydrogen bonds, and secondary structural preferences of
amino acids. Various approaches to apply these principles have been
attempted. For example, the construction of .alpha.-helical and
.beta.-sheet proteins with native-like sequences was attempted by
individually selecting the residue required at every position in
the target fold (Hecht, et al., Science 249:884-891 (1990); Quinn,
et al., Proc. Natl. Acad. Sci USA 91:8747-8751 (1994)).
Alternatively, a minimalist approach was used to design helical
proteins, where the simplest possible sequence believed to be
consistent with the folded structure was generated (Regan, et al.,
Science 241:976-978 (1988); DeGrado, et al., Science 243:622-628
(1989); Handel, et al., Science 261:879-885 (1993)), with varying
degrees of success. An experimental method that relies on the
hydrophobic and polar (HP) pattern of a sequence was developed
where a library of sequences with the correct pattern for a four
helix bundle was generated by random mutagenesis (Kamtekar, et al.,
Science 262:1680-1685 (1993)). Among non de novo approaches,
domains of naturally occurring proteins have been modified or
coupled together to achieve a desired tertiary organization (Pessi,
et al., Nature 362:367-369 (1993); Pomerantz, et al., Science
267:93-96 (1995)).
[0004] Though the correct secondary structure and overall tertiary
organization seem to have been attained by several of the above
techniques, many designed proteins appear to lack the structural
specificity of native proteins. The complementary geometric
arrangement of amino acids in the folded protein is the root of
this specificity and is encoded in the sequence.
[0005] Several groups have applied and experimentally tested
systematic, quantitative methods to protein design with the goal of
developing general design algorithms (Hellinga, et al., J. Mol.
Biol. 222: 763-785 (1991); Hurley, et al., J. Mol. Biol.
224:1143-1154 (1992); Desjarlaisl, et al., Protein Science
4:2006-2018 (1995); Harbury, et al., Proc. Natl. Acad. Sci. USA
92:8408-8412 (1995); Klemba, et al., Nat. Struc. Biol. 2:368-373
(1995); Nautiyal, et al., Biochemistry 34:11645-11651 (1995);
Betzo, et al., Biochemistry 35:6955-6962 (1996); Dahiyat, et al.,
Protein Science 5:895-903 (1996); Jones, Protein Science 3:567-574
(1994); Konoi, et al., Proteins: Structure, Function and Genetics
19:244-255 (1994)). These algorithms consider the spatial
positioning and steric complementarity of side chains by explicitly
modeling the atoms of sequences under consideration. To date, such
techniques have typically focused on designing the cores of
proteins and have scored sequences with van der Waals and sometimes
hydrophobic solvation potentials.
[0006] Recent studies using coiled coils have demonstrated that
core side-chain packing can be combined with explicit backbone
flexibility (Harbury et al., PNAS USA 92:8408-8412 (1995); Offer
& Sessions, J. Mol. Biol. 249:967-987 (1995). In these cases,
the goal was to search for backbone coordinates that satisfied a
fixed amino acid sequence.
[0007] In addition, the qualitative nature of many design
approaches has hampered the development of improved, second
generation, proteins because there are no objective methods for
learning from past design successes and failures.
[0008] Thus, it is an object of the invention to provide
computational protein design and optimization via an objective,
quantitative design technique implemented in connection with a
general purpose computer.
SUMMARY OF THE INVENTION
[0009] In accordance with the objects outlined above, the present
invention provides methods executed by a computer under the control
of a program, the computer including a memory for storing the
program. The method comprising the steps of receiving a protein
backbone structure with variable residue positions, establishing a
group of potential rotamers for each of the variable residue
positions, wherein at least one variable residue position has
rotamers from at least two different amino acid side chains, and
analyzing the interaction of each of the rotamers with all or part
of the remainder of the protein backbone structure to generate a
set of optimized protein sequences. The methods further comprise
classifying each variable residue position as either a core,
surface or boundary residue. The analyzing step may include a
Dead-End Elimination (DEE) computation. Generally, the analyzing
step includes the use of at least one scoring function selected
from the group consisting of a Van der Waals potential scoring
function, a hydrogen bond potential scoring function, an atomic
salvation scoring function, a secondary structure propensity
scoring function and an electrostatic scoring function. The methods
further comprise altering the protein backbone prior to the
analysis, comprising altering at least one supersecondary structure
parameter value. The methods may further comprise generating a rank
ordered list of additional optimal sequences from the globally
optimal protein sequence. Some or all of the protein sequences from
the ordered list may be tested to produce potential energy test
results.
[0010] In an additional aspect, the invention provides nucleic acid
sequences encoding a protein sequence generated by the present
methods, and expression vectors and host cells containing the
nucleic acids.
[0011] In a further aspect, the invention provides a computer
readable memory to direct a computer to function in a specified
manner, comprising a side chain module to correlate a group of
potential rotamers for residue positions of a protein backbone
model, and a ranking module to analyze the interaction of each of
said rotamers with all or part of the remainder of said protein to
generate a set of optimized protein sequences. The memory may
further comprise an assessment module to assess the correspondence
between potential energy test results and theoretical potential
energy data.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 illustrates a general purpose computer configured in
accordance with an embodiment of the invention.
[0013] FIG. 2 illustrates processing steps associated with an
embodiment of the invention.
[0014] FIG. 3 illustrates processing steps associated with a
ranking module used in accordance with an embodiment of the
invention. After any DEE step, any one of the previous DEE steps
may be repeated. In addition, any one of the DEE steps may be
eliminated; for example, original singles DEE (step 74) need not be
run.
[0015] FIG. 4 depicts the protein design automation cycle.
[0016] FIG. 5 depicts the helical wheel diagram of a coiled coil.
One heptad repeat is shown viewed down the major axes of the
helices. The a and d positions define the solvent-inaccessible core
of the molecule (Cohen & Parry, 1990, Proteins, Structure,
Function and Genetics 7:1-15).
[0017] FIGS. 6A and 6B depict the comparison of simulation cost
functions to experimental Tm's. FIG. 6A depicts the initial cost
function, which contains only a van der Waals term for the eight
PDA peptides. FIG. 6B depicts the improved cost function containing
polar and nonpolar surface area terms weighted by atomic solvation
parameters derived from QSAR analysis; 16 cal/mol/.ANG..sup.2
favors hydrophobic surface burial.
[0018] FIG. 7 shows the rank correlation of energy predicted by the
simulation module versus the combined activity score of .lamda.
repressor mutants (Lim, et al., J. Mol. Biol. 219:359-376 (1991);
Hellinga, et al., Proc. Natl. Acad. Sci. USA 91:5803-5807
(1994)).
[0019] FIG. 8 shows the sequence of pda8d (SEQ ID NO:2) aligned
with the second zinc finger of Zif268 (SEQ D NO:1). The boxed
ositions were designed using the sequence selection algorithm. The
coordinates of PDB record 1zaa (Paveletch, et al., Science
252:809-817 (1991)) from residues 33-60 were used as the structure
template. In our numbering, position 1 corresponds to 1zaa position
33.
[0020] FIGS. 9A and 9B shows the NMR spectra and solution secondary
structure of pda8d from Example 3. FIG. 9A is the TOCSY H.alpha.-HN
fingerprint region of pda8d. FIG. 9B is the NMR NOE connectivities
of pda8d. Bars represent unambiguous connectivities and the bar
thickness of the sequential connections is indexed to the intensity
of the resonance.
[0021] FIGS. 10A and 10B depict the secondary structure content and
thermal stability of .alpha.90, .alpha.85, .alpha.70 and
.alpha.107. FIG. 10A depicts the far UV spectra (circular
dichroism). FIG. 10B depicts the thermal denaturation monitored by
CD.
[0022] FIG. 11 depicts the sequence of FSD-1 (SEQ ID NO:3) of
Example 5 aligned with the second zinc finger of Zif268 (SEQ ID
NO:1). The bar at the top of the figure shows the residue position
classifications: solid bars indicate core positions, hatched bars
indicate boundary positions and open bars indicate surface
positions. The alignment matches positions of FSD-1 (SEQ ID NO:3)
to the corresponding backbone template positions of Zif268 (SEQ ID
NO:1). Of the six identical positions (21%) between FSD-1 (SEQ ID
NO:3) and Zif268 (SEQ ID NO:1), four are buried (Ile7, Phe12, Leu18
and Ile22). The zinc binding residues of Zif268 are boxed.
Representative non-optimal sequence solutions (SEQ ID NOS:4-22)
determined using a Monte Carlo simulated annealing protocol are
shown with their rank. Vertical lines indicate identity with FSD-1
(SEQ ID NO:3). The symbols at the bottom the figure show the degee
of sequence conservation for each residue position computed across
the top 1000 sequences: filled circles indicate greater than 99%
conservation, half-filled circles indicate conservation between 90
and 99%, open circles indicate conservation between 50 and 90%, and
the absence of symbol indicates less than 50% conservation. The
consensus sequence determined by choosing the amino acid with the
highest occurrence at each position is identical to the sequence of
FSD-1 (SEQ ID NO:3).
[0023] FIG. 12 is a schematic representation of the minimum and
maximum quantities (defined in Eq. 24 to 27) that are used to
construct speed enhancements. The minima and maxima are utilized
directly to find the |i.sub.uj.sub.v|.sub.mb pair and for the
comparison of extrema. The differences between the quantities,
denoted with arrows, are used to construct the q.sub.rs and
q.sub.uv metrics.
[0024] FIGS. 13A, 13B, 13C, 13D, 13E and 13F depicts the areas
involved in calculating the buried and exposed areas of Equations
18 and 19. The dashed box is the protein template, the heavy solid
lines correspond to three rotamers at three different residue
positions, and the lighter solid lines correspond to surface areas.
a) A.sup.0.sub.i.sub.r.sub.t3 for each rotamer. b)
A.sub.i.sub.r.sub.t for each rotamer. c)
(A.sup.0.sub.i.sub.r.sub.t3-A.sub.i.sub.r.sub.t) summed over the
three residues. The upper residue does not bury any area against
the template except that buried in the tri-peptide state
A.sup.0.sub.i.sub.r.sub.t3. d) A.sub.i.sub.r.sub.j.sub.s.sub.t for
one pair of rotamers. e) The area buried between rotamers,
(A.sub.i.sub.r.sub.t+A.sub.j.sub.s.sub.t-A.sub.i.sub.r.sub.j.sub.s.sub.t)-
, for the same pair of rotamers as in (d). f) The area buried
between rotamers,
(A.sub.i.sub.r.sub.t+A.sub.j.sub.s.sub.t-A.sub.i.sub.r.sub.j.su-
b.s.sub.t), summed over the three pairs of rotamers. The area b
intersected by all three rotamers is counted twice and is indicated
by the double lines. The buried area calculated by Equation 18 is
the area buried by the template, represented in (c), plus s times
the area buried between rotamers, represented in (f). The scaling
factor s accounts for the over-counting shown by the double lines
in (f). The exposed area calculated by Equation 19 is the exposed
are in the presence of the template, represented in (b), minus s
times the area buried between rotamers, represented in (f).
[0025] FIGS. 14A, 14B, 14C and 14D depict several super-secondary
structure parameters for .alpha./.beta. proteins. The definitions
are similar to those previously developed for .alpha./.beta.
proteins (Janin & Chothia, J Mol Biol 143:95-128 (1980); Cohen
et al., J Mol Biol 156:821862 (1982)). The helix center is defined
as the average C.sub..alpha. position of the residues in the helix.
The helix axis is defined as the principal moment of the
C.sub..alpha. atoms of the residues in the helix. (Chothia et al.,
Proc Natl Acad Sci USA 78:4146-4150 (1981); J Mol Biol 145:215-250
(1981). The strand axis is defined as the average of the
least-squares lines fit through the midpoints of sequential
C.sub..alpha. positions of two central .beta.-strands. The sheet
plane is defined as the least-squares plane fit through the
C.sub..alpha. positions of the residues of the sheet. The sheet
axis is defined as the vector perpendicular to the sheet plane that
passes through the helix center. .OMEGA. is the angle between the
strand axis and the helix axis after projection onto the sheet
plane; .theta. is the angle between the helix axis and the sheet
plane; h is the distance between the helix center and the sheet
plane; .sigma. is the rotation angle about the helix axis. The
super-secondary structure parameter values for native G.beta.1 are
.OMEGA.=-26.49.degree., .theta.=3.20.degree., h=10.04 .ANG. and
.sigma.=0.degree..
[0026] FIG. 15 depicts the Far-UV CD spectra of G.beta.1 and the
most perturbed of the Ah-series mutants, .DELTA.h.sub.0.9[+1.50
.ANG.]. .DELTA.h.sub.0.9[-1.50 .ANG.] and .DELTA.h.sub.1.0[+1.50
.ANG.] have CD spectra similar to .DELTA.h.sub.0.9[+1.50 .ANG.],
while the remaining mutants have CD spectra similar to
G.beta.1.
[0027] FIG. 16 depicts the thermal denaturation of G.beta.1 and the
Ah-series mutants monitored by CD at 218 nm.
[0028] FIGS. 17A, 17B, 17C and 17D depict four supersecondary
structure parameters for .beta./.beta. protein interactions. FIGS.
17A and 17B are relevant to .beta. barrel proteins; FIG. 17C is
relevant to .beta.-sheet interactions. FIG. 17A shows only three
strands, and depicts R, the barrel radius; .alpha., the tilt of the
strands relative to the barrel axis; .alpha., the distance from
C.sup..alpha. to C.sup..alpha. along the strands; and b, the
interstrand distance. FIG. 17B shows the twist and coiling angles
of the .beta.-sheet, with residues A, B and C from one strand,
residues D, E and F in strand 2, and residues G, H and I from
strand 3. The circles represent the positions of the residues when
projected onto the surface of the barrel. In this case, .theta. is
the mean twist of the .beta.-sheet about an axis perpendicular to
the strand direction. .tau. is the mean twist of the .beta.-sheet
about an axis parallel to the strand direction. .beta. is the mean
coiling of the .beta.-sheet along the strands. .eta. is the mean
coiling of the .beta.-sheet along a line perpendicular to the
strands. FIG. 17C depicts two .beta.-sheets, with the chain
direction being shown with arrows. FIG. 17D depicts two
.beta.-sheets of distance h with angle .theta. between the average
strand vectors. There is also .phi., perpendicular to vectors
defining .theta..
[0029] FIGS. 18A, 18B, 18C and 18D depict four supersecondary
structure parameters .alpha./.alpha. supersecondary structure
parameters for .alpha./.alpha. interactions. d is the distance
between the helices and .theta. is the angle between the axes of
the helices. .sigma. is defined as the rotation around the helix
axis. .OMEGA. is the angle between two strand axes after projection
onto a plane. In FIGS. 18C and 18D, the dark circle represents a
view of the helix from the end.
DETAILED DESCRIPTION OF THE INVENTION
[0030] The present invention is directed to the quantitative design
and optimization of amino acid sequences, using an "inverse protein
folding" approach, which seeks the optimal sequence for a desired
structure. Inverse folding is similar to protein design, which
seeks to find a sequence or set of sequences that will fold into a
desired structure. These approaches can be contrasted with a
"protein folding" approach which attempts to predict a structure
taken by a given sequence.
[0031] The general preferred approach of the present invention is
as follows, although alternate embodiments are discussed below. A
known protein structure is used as the starting point. The residues
to be optimized are then identified, which may be the entire
sequence or subset(s) thereof. The side chains of any positions to
be varied are then removed. The resulting structure consisting of
the protein backbone and the remaining sidechains is called the
template. Each variable residue position is then preferably
classified as a core residue, a surface residue, or a boundary
residue; each classification defines a subset of possible amino
acid residues for the position (for example, core residues
generally will be selected from the set of hydrophobic residues,
surface residues generally will be selected from the hydrophilic
residues, and boundary residues may be either). Each amino acid can
be represented by a discrete set of all allowed conformers of each
side chain, called rotamers. Thus, to arrive at an optimal sequence
for a backbone, all possible sequences of rotamers must be
screened, where each backbone position can be occupied either by
each amino acid in all its possible rotameric states, or a subset
of amino acids, and thus a subset of rotamers.
[0032] Two sets of interactions are then calculated for each
rotamer at every position: the interaction of the rotamer side
chain with all or part of the backbone (the "singles" energy, also
called the rotamer/template or rotamer/backbone energy), and the
interaction of the rotamer side chain with all other possible
rotamers at every other position or a subset of the other positions
(the "doubles" energy, also called the rotamer/rotamer energy). The
energy of each of these interactions is calculated through the use
of a variety of scoring functions, which include the energy of van
der Waal's forces, the energy of hydrogen bonding, the energy of
secondary structure propensity, the energy of surface area
solvation and the electrostatics. Thus, the total energy of each
rotamer interaction, both with the backbone and other rotamers, is
calculated, and stored in a matrix form.
[0033] The discrete nature of rotamer sets allows a simple
calculation of the number of rotamer sequences to be tested. A
backbone of length n with m possible rotamers per position will
have m.sup.n possible rotamer sequences, a number which grows
exponentially with sequence length and renders the calculations
either unwieldy or impossible in real time. Accordingly, to solve
this combinatorial search problem, a "Dead End Elimination" (DEE)
calculation is performed. The DEE calculation is based on the fact
that if the worst total interaction of a first rotamer is still
better than the best total interaction of a second rotamer, then
the second rotamer cannot be part of the global optimum solution.
Since the energies of all rotamers have already been calculated,
the DEE approach only requires sums over the sequence length to
test and eliminate rotamers, which speeds up the calculations
considerably. DEE can be rerun comparing pairs of rotamers, or
combinations of rotamers, which will eventually result in the
determination of a single sequence which represents the global
optimum energy.
[0034] Once the global solution has been found, a Monte Carlo
search may be done to generate a rank-ordered list of sequences in
the neighborhood of the DEE solution. Starting at the DEE solution,
random positions are changed to other rotamers, and the new
sequence energy is calculated. If the new sequence meets the
criteria for acceptance, it is used as a starting point for another
jump. After a predetermined number of jumps, a rank-ordered list of
sequences is generated.
[0035] The results may then be experimentally verified by
physically generating one or more of the protein sequences followed
by experimental testing. The information obtained from the testing
can then be fed back into the analysis, to modify the procedure if
necessary.
[0036] Thus, the present invention provides a computer-assisted
method of designing a protein. The method comprises providing a
protein backbone structure with variable residue positions, and
then establishing a group of potential rotamers for each of the
residue positions. As used herein, the backbone, or template,
includes the backbone atoms and any fixed side chains. The
interactions between the protein backbone and the potential
rotamers, and between pairs of the potential rotamers, are then
processed to generate a set of optimized protein sequences,
preferably a single global optimum, which then may be used to
generate other related sequences.
[0037] FIG. 1 illustrates an automated protein design apparatus 20
in accordance with an embodiment of the invention. The apparatus 20
includes a central processing unit 22 which communicates with a
memory 24 and a set of input/output devices (e.g., keyboard, mouse,
monitor, printer, etc.) 26 through a bus 28. The general
interaction between a central processing unit 22, a memory 24,
input/output devices 26, and a bus 28 is known in the art. The
present invention is directed toward the automated protein design
program 30 stored in the memory 24.
[0038] The automated protein design program 30 may be implemented
with a side chain module 32. As discussed in detail below, the side
chain module establishes a group of potential rotamers for a
selected protein backbone structure. The protein design program 30
may also be implemented with a ranking module 34. As discussed in
detail below, the ranking module 34 analyzes the interaction of
rotamers with the protein backbone structure to generate optimized
protein sequences. The protein design program 30 may also include a
search module 36 to execute a search, for example a Monte Carlo
search as described below, in relation to the optimized protein
sequences. Finally, an assessment module 38 may also be used to
assess physical parameters associated with the derived proteins, as
discussed further below.
[0039] The memory 24 also stores a protein backbone structure 40,
which is downloaded by a user through the input/output devices 26.
The memory 24 also stores information on potential rotamers derived
by the side chain module 32. In addition, the memory 24 stores
protein sequences 44 generated by the ranking module 34. The
protein sequences 44 may be passed as output to the input/output
devices 26.
[0040] The operation of the automated protein design apparatus 20
is more fully appreciated with reference to FIG. 2. FIG. 2
illustrates processing steps executed in accordance with the method
of the invention. As described below, many of the processing steps
are executed by the protein design program 30. The first processing
step illustrated in FIG. 2 is to provide a protein backbone
structure (step 50). As previously indicated, the protein backbone
structure is downloaded through the input/output devices 26 using
standard techniques.
[0041] The protein backbone structure corresponds to a selected
protein. By "protein" herein is meant at least two amino acids
linked together by a peptide bond. As used herein, protein includes
proteins, oligopeptides and peptides. The peptidyl group may
comprise naturally occurring amino acids and peptide bonds, or
synthetic peptidomimetic structures, i.e. "analogs", such as
peptoids (see Simon et al., PNAS USA 89(20):9367 (1992)). The amino
acids may either be naturally occuring or non-naturally occuring;
as will be appreciated by those in the art, any structure for which
a set of rotamers is known or can be generated can be used as an
amino acid. The side chains may be in either the (R) or the (S)
configuration. In a preferred embodiment, the amino acids are in
the (S) or L-configuration.
[0042] The chosen protein may be any protein for which a three
dimensional structure is known or can be generated; that is, for
which there are three dimensional coordinates for each atom of the
protein. Generally this can be determined using X-ray
crystallographic techniques, NMR techniques, de novo modelling,
homology modelling, etc. In general, if X-ray structures are used,
structures at 2 .ANG. resolution or better are preferred, but not
required.
[0043] The proteins may be from any organism, including prokaryotes
and eukaryotes, with enzymes from bacteria, fungi, extremeophiles
such as the archebacteria, insects, fish, animals (particularly
mammals and particularly human) and birds all possible.
[0044] Suitable proteins include, but are not limited to,
industrial and pharmaceutical proteins, including ligands, cell
surface receptors, antigens, antibodies, cytokines, hormones, and
enzymes. Suitable classes of enzymes include, but are not limited
to, hydrolases such as proteases, carbohydrases, lipases;
isomerases such as racemases, epimerases, tautomerases, or mutases;
transferases, kinases, oxidoreductases, and phophatases. Suitable
enzymes are listed in the Swiss-Prot enzyme database.
[0045] Suitable protein backbones include, but are not limited to,
all of those found in the protein data base compiled and serviced
by the Brookhaven National Lab.
[0046] Specifically included within "protein" are fragments and
domains of known proteins, including functional domains such as
enzymatic domains, binding domains, etc., and smaller fragments,
such as turns, loops, etc. That is, portions of proteins may be
used as well. In addition, protein variants, i.e. non-naturally
occuring variants, may be used.
[0047] Once the protein is chosen, the protein backbone structure
is input into the computer. By "protein backbone structure" or
grammatical equivalents herein is meant the three dimensional
coordinates that define the three dimensional structure of a
particular protein. The structures which comprise a protein
backbone structure (of a naturally occuring protein) are the
nitrogen, the carbonyl carbon, the .alpha.-carbon, and the carbonyl
oxygen, along with the direction of the vector from the
.alpha.-carbon to the .beta.-carbon.
[0048] The protein backbone structure which is input into the
computer can either include the coordinates for both the backbone
and the amino acid side chains, or just the backbone, i.e. with the
coordinates for the amino acid side chains removed. If the former
is done, the side chain atoms of each amino acid of the protein
structure may be "stripped" or removed from the structure of a
protein, as is known in the art, leaving only the coordinates for
the "backbone" atoms (the nitrogen, carbonyl carbon and oxygen, and
the .alpha.-carbon, and the hydrogens attached to the nitrogen and
.alpha.-carbon).
[0049] In a preferred embodiment, the protein backbone structure is
altered prior to the analysis outlined below. In this embodiment,
the representation of the starting protein backbone structure is
reduced to a description of the spatial arrangement of its
secondary structural elements. The relative positions of the
secondary structural elements are defined by a set of parameters
called supersecondary structure parameters. These parameters are
assigned values that can be systematically or randomly varied to
alter the arrangement of the secondary structure elements to
introduce explicit backbone flexibility. The atomic coordinates of
the backbone are then changed to reflect the altered supersecondary
structural parameters, and these new coordinates are input into the
system for use in the subsequent protein design automation.
[0050] Basically, a protein is first parsed into a collection of
secondary structural elements which are then abstracted into
geometrical objects. For example, as more fully outlined below, an
.alpha.-helix is represented by its helical axis and geometric
center. The relative orientation and distance between these objects
are summarized as super-secondary structure parameters. Concerted
backbone motion can be introduced by simply modulating a protein's
super-secondary structure parameter values. Accordingly, when all
or part of the backbone is to be altered, the portion to be altered
is classified as belonging to a particular supersecondary structure
element, i.e. .alpha./.beta., .alpha./.alpha. or .beta./.beta., and
then the supersecondary structural elements as outlined below are
altered. As will be appreciated by those in the art, these elements
need not be covalently linked, i.e. part of the same protein; for
example, this can be done to evaluate protein-protein
interactions.
[0051] As will be appreciated by those in the art, it is possible
to alter the backbone of certain positions, while retaining either
a particular amino acid (which can be "floated", as outlined below)
or a particular rotamer at the position; alternatively, both the
backbone can be moved and the amino acid side chain can be
optimized as outlined herein. Similarly, the backbone can be held
constant and only the amino acid side chains are optimized.
Combinations of any of these at any position may be done. In
general, when supersecondary structural parameters are altered,
this is done on more than one amino acid, i.e. the backbone atoms
of a plurality of amino acids that contribute to the secondary
structure are moved.
[0052] As will be appreciated by those in the art, there are a wide
variety of different supersecondary structure parameters that can
be used. Super-secondary structure parameterization has been
described for fold classes that include .alpha./.alpha. (Crick F H
C The Fourier transform of a coiled-coil. Acta Crystallogr
6:685-689 (1953a); Crick F H C. The packing of .alpha.-helices.
Acta Crystallogr 6:689-697 (1953b); Chothia et al., Proc Natl Acad
Sci USA 78:4146-4150 (1981) "Relative orientation of close-packed
.beta.-pleated sheets in proteins" and Chothia et al., J Mol Biol
145:215-250 (1981) "Helix to helix packing in proteins"; Chou, et
al. Energetics of the structure of the four-.alpha.-helix bundle in
proteins. Proc Natl Acad Sci USA 85:4295-4299 (1988); Murzin A G,
Finkelstein A V. General architecture of the .alpha.-helical
globule. J Mol Biol 204:749-769 (1988); Presnell S R, Cohen F E.
Topological distribution of four-.alpha.-helix bundles. Proc Nat
Acad Sci USA 86:6592-6596 (1989); Harris et al. Four helix bundle
diversity in globular proteins. J Mol Biol 236:1356-1368 (1994),
.alpha./.beta. (Chothia et al., Structure of proteins: packing of
.alpha.-helices and pleated sheets. Proc Natl Acad Sci USA
74:4130-4134 (1977); Janin & Chothia, 1980 Packing of
.alpha.-helices onto .beta.-pleated sheets and the anatomy of
.alpha./.beta. proteins. J Mol Biol 143:95-128; Cohen et al., 1982,
Analysis and prediction of the packing of .alpha.-helices against a
.beta.-sheet in the tertiary structure of globular proteins. J Mol
Biol 156:821-862; Chou et al., 1985, Interactions between an
.alpha.-helix and .beta.-sheet energetics of .alpha./.beta. packing
in proteins. J Mol Biol 186:591-609, and .beta./.beta. (Cohen et
al., Analysis and prediction of protein .delta.-sheet structures by
a combinatorial approach. Nature 285:378-382 (1980); Cohen et al.,
Analysis of the tertiary structure of protein .beta.-sheet
sandwiches. J Mol Biol 148:253-272 (1981); Chothia & Janin,
Relative orientation of close-packed .beta.-pleated sheets in
proteins. Proc Natl Acad Sci USA 78:4146-4150 (1981); Chothia &
Janin, Proc Natl Acad Sci USA 78:3955-3965 (1982) Orthogonal
packing of 8-pleated sheets in proteins; Chou et al., J Mol Biol
188:641-649 (1986) "Interactions between two .beta.-sheets
energetics of .beta./.beta. packing in proteins"; Laster et al.,
Proc Natl Acad Sci USA 85:3338-3342 (1988) "Structure principles of
parallel .beta.-barrels in proteins"; Murzin et al., J Mol Biol
236:1369-1381 (1994a), "Principles determining the structure of
.beta.-sheet barrels. I. A theoretical analysis"; Murzin et al. J
Mol Biol 236:1382-1400 (1994b) "Principles determining the
structure of .beta.-sheet barrels. II. The observed structures";
all of these references are explicitly incorporated by reference
herein in their entireity).
[0053] Four different supersecondary structure parameters useful
for .alpha./.beta. proteins are shown in FIG. 14. In a preferred
embodiment, as for all the supersecondary structure parameters, at
least one of these parameter values is altered; other embodiments
utilize simultaneous or sequential alteration of two, three or four
of these parameter values.
[0054] For the .alpha./.beta. protein interactions, the helix
center is defined as the average C.sub..alpha. position of the
residues chosen for backbone movement. The helix axis is defined as
the principal moment of the C.sub..alpha. atoms of these residues
(see Chothia et al., 1981, supra). The strand axis is defined as
the average of the least-squares lines fit through the midpoints of
sequential C.sub..alpha. positions of the two central 8-strands.
The sheet plane is defined as the least-squares plane fit through
the C.sub..alpha. positions of the two central 6-strands. The sheet
axis is defined as the vector perpendicular to the sheet plane that
passes through the helix center. .OMEGA. is the angle between the
strand axis and the helix axis after projection onto the sheet
plane; .theta. is the angle between the helix axis and the sheet
plane; h is the distance between the helix center and the sheet
plane; .sigma. is the rotation angle about the helix axis. Backbone
alteration requires altering at least one of these parameter
values. In a preferred embodiment, the supersecondary structure
parameter value .OMEGA. is altered by changing the angle degree
(either positively or negatively) of up to about 25 degrees, with
changes of .+-.1.degree., 2.5.degree., 5.degree., 7.5.degree., and
10.degree. being particularly preferred. In a preferred embodiment,
the supersecondary structure parameter value 0 is altered by
changing the angle degree (either positively or negatively) of up
to about 25 degrees, with changes of .+-.1.degree., 2.5.degree.,
5.degree., 7.5.degree., and 10.degree. being particularly
preferred. the supersecondary structure parameter value .sigma. is
altered by changing the angle degree (either positively or
negatively) of up to about 25 degrees, with changes of
.+-.1.degree., 2.5.degree., 5.degree., 7.5.degree., and 10.degree.
being particularly preferred. In a preferred embodiment, the
supersecondary structure parameter value h is altered by changes
(either positive or negative) of up to about 8 .ANG., with changes
of .+-.0.25, 0.50, 0.75, 1.00, 1.25 and 1.5 being particularly
preferred. However, as will be appreciated by those in the art, as
for all the parameter values outlined herein, larger changes can be
made, depending on the protein (i.e. how close or far other
secondary structure elements are) and whether other parameter
values are made; for example, larger changes in .OMEGA. can be made
if the helix is also moved away from the sheet (i.e. h is
increased).
[0055] Four different supersecondary structure parameters useful
for .alpha./.alpha. proteins are shown in FIG. 18. As for
.alpha./.beta. parameters, the helix center is defined as the
average C.sub..alpha. position of the residues in the helix. The
helix axis is defined as the principal moment of the C.sub..alpha.
atoms of the residues in the helix. .sigma. is defined as the
rotation around the helix axis. .OMEGA. is the angle between two
strand axes after projection onto a plane. Thus, d, the distance
between the helices, can be altered, generally as outlined above
for h. Similarly, .theta., .sigma. and .OMEGA. can be altered as
above.
[0056] There are a number of different supersecondary structure
parameters useful for .beta./.beta. proteins. .beta.-barrel
configurations contain a number of different parameters that can be
altered, as shown in FIG. 17. These include: (see FIG. 17A) R, the
barrel radius; .alpha., the angle of tilt of the strands relative
to the barrel axis; and b, the interstrand distance; (see FIG. 17B)
.theta., the mean twist of the .beta.-sheet about an axis
perpendicular to the strand direction; .tau., the mean twist of the
.beta.-sheet about an axis parallel to the strand direction;
.epsilon. the mean coiling of the .beta.-sheet along the strands;
.eta., the mean coiling of the .beta.-sheet along a line
perpendicular to the strands; and (FIG. 17C) .OMEGA. is angle
between the two .beta.-sheet axes. As for the .alpha./.beta.
parameter values, each of these may be altered, either positively
or negatively. Generally, changes are made in at least one of these
parameter values, by changing the angle degree (either positively
or negatively) of up to about 25 degrees, with changes of .+-.10,
2.5.degree., 5.degree., 7.5.degree., and 10.degree. being
particularly preferred. b can be changed up to .+-.1 .ANG.. Fore
sandwich structures (FIGS. 17C and 17D), 0 can be altered up to
.+-.45.degree., with changes of .+-.1.degree., 2.5.degree.,
5.degree., 7.5.degree., and 10.degree. being particularly
preferred. Similarly, h can be altered as outlined above for
.alpha./.beta. proteins, and .theta. and .phi. can be altered up to
.+-.30.degree..
[0057] Once the desired value changes are selected, the coordinate
positions for the positions chosen are altered to reflect the
change, to form a "new" or "altered" backbone protein structure,
i.e. one that has all or part of the backbone atoms in a different
position relative to the starting structure. It should be noted
that this process can be repeated, i.e. additional backbone changes
can be made, on the same or different residues. In addition, after
optimization, the backbone of one or more optimal sequences can
altered and an optimization can be run.
[0058] Alternatively, movement of the backbone can be done
manually, i.e. sections of the protein backbone can be randomly or
arbitrarily moved. In this embodiment, the backbone atoms of one or
more amino acids can be moved some distance, generally an angstrom
or more, in any direction. This can be done using standard modeling
programs; for example, Molecular Dynamics minimization, Monte Carlo
dynamics, or random backbone coordinate/angle motion. It is also
possible to move the backbone atoms of single residues, that are
either components of secondary structural elements or not.
[0059] Once a protein structure backbone is generated (with
alterations, as outlined above) and input into the computer,
explicit hydrogens are added if not included within the structure
(for example, if the structure was generated by X-ray
crystallography, hydrogens must be added). After hydrogen addition,
energy minimization of the structure is run, to relax the hydrogens
as well as the other atoms, bond angles and bond lengths. In a
preferred embodiment, this is done by doing a number of steps of
conjugate gradient minimization (Mayo et al., J. Phys. Chem.
94:8897 (1990)) of atomic coordinate positions to minimize the
Dreiding force field with no electrostatics. Generally from about
10 to about 250 steps is preferred, with about 50 being most
preferred.
[0060] The protein backbone structure contains at least one
variable residue position. As is known in the art, the residues, or
amino acids, of proteins are generally sequentially numbered
starting with the N-terminus of the protein. Thus a protein having
a methionine at it's N-terminus is said to have a methionine at
residue or amino acid position 1, with the next residues as 2, 3,
4, etc. At each position, the wild type (i.e. naturally occuring)
protein may have one of at least 20 amino acids, in any number of
rotamers. By "variable residue position" herein is meant an amino
acid position of the protein to be designed that is not fixed in
the design method as a specific residue or rotamer, generally the
wild-type residue or rotamer.
[0061] In a preferred embodiment, all of the residue positions of
the protein are variable. That is, every amino acid side chain may
be altered in the methods of the present invention. This is
particularly desirable for smaller proteins, although the present
methods allow the design of larger proteins as well. While there is
no theoretical limit to the length of the protein which may be
designed this way, there is a practical computational limit.
[0062] In an alternate preferred embodiment, only some of the
residue positions of the protein are variable, and the remainder
are "fixed", that is, they are identified in the three dimensional
structure as being in a set conformation. In some embodiments, a
fixed position is left in its original conformation (which may or
may not correlate to a specific rotamer of the rotamer library
being used). Alternatively, residues may be fixed as a non-wild
type residue; for example, when known site-directed mutagenesis
techniques have shown that a particular residue is desirable (for
example, to eliminate a proteolytic site or alter the substrate
specificity of an enzyme), the residue may be fixed as a particular
amino acid. Alternatively, the methods of the present invention may
be used to evaluate mutations de novo, as is discussed below. In an
alternate preferred embodiment, a fixed position may be "floated";
the amino acid at that position is fixed, but different rotamers of
that amino acid are tested. In this embodiment, the variable
residues may be at least one, or anywhere from 0.1% to 99.9% of the
total number of residues. Thus, for example, it may be possible to
change only a few (or one) residues, or most of the residues, with
all possibilities in between.
[0063] In a preferred embodiment, residues which can be fixed
include, but are not limited to, structurally or biologically
functional residues. For example, residues which are known to be
important for biological activity, such as the residues which form
the active site of an enzyme, the substrate binding site of an
enzyme, the binding site for a binding partner (ligand/receptor,
antigen/antibody, etc.), phosphorylation or glycosylation sites
which are crucial to biological function, or structurally important
residues, such as disulfide bridges, metal binding sites, critical
hydrogen bonding residues, residues critical for backbone
conformation such as proline or glycine, residues critical for
packing interactions, etc. may all be fixed in a conformation or as
a single rotamer, or "floated".
[0064] Similarly, residues which may be chosen as variable residues
may be those that confer undesirable biological attributes, such as
susceptibility to proteolytic degradation, dimerization or
aggregation sites, glycosylation sites which may lead to immune
responses, unwanted binding activity, unwanted allostery,
undesirable enzyme activity but with a preservation of binding,
etc.
[0065] As will be appreciated by those in the art, the methods of
the present invention allow computational testing of "site-directed
mutagenesis" targets without actually making the mutants, or prior
to making the mutants. That is, quick analysis of sequences in
which a small number of residues are changed can be done to
evaluate whether a proposed change is desirable. In addition, this
may be done on a known protein, or on an protein optimized as
described herein.
[0066] As will be appreciated by those in the art, a domain of a
larger protein may essentially be treated as a small independent
protein; that is, a structural or functional domain of a large
protein may have minimal interactions with the remainder of the
protein and may essentially be treated as if it were autonomous. In
this embodiment, all or part of the residues of the domain may be
variable.
[0067] It should be noted that even if a position is chosen as a
variable position, it is possible that the methods of the invention
will optimize the sequence in such a way as to select the wild type
residue at the variable position. This generally occurs more
frequently for core residues, and less regularly for surface
residues. In addition, it is possible to fix residues as non-wild
type amino acids as well.
[0068] Once the protein backbone structure has been selected and
input, and the variable residue positions chosen, a group of
potential rotamers for each of the variable residue positions is
established. This operation is shown as step 52 in FIG. 2. This
step may be implemented using the side chain module 32. In one
embodiment of the invention, the side chain module 32 includes at
least one rotamer library, as described below, and program code
that correlates the selected protein backbone structure with
corresponding information in the rotamer library. Alternatively,
the side chain module 32 may be omitted and the potential rotamers
42 for the selected protein backbone structure may be downloaded
through the input/output devices 26.
[0069] As is known in the art, each amino acid side chain has a set
of possible conformers, called rotamers. See Ponder, et al., Acad.
Press Inc. (London) Ltd. pp. 775-791 (1987); Dunbrack, et al.,
Struc. Biol. 1(5):334-340 (1994); Desmet, et al., Nature
356:539-542 (1992), all of which are hereby expressly incorporated
by reference in their entireity. Thus, a set of discrete rotamers
for every amino acid side chain is used. There are two general
types of rotamer libraries: backbone dependent and backbone
independent. A backbone dependent rotamer library allows different
rotamers depending on the position of the residue in the backbone;
thus for example, certain leucine rotamers are allowed if the
position is within an a helix, and different leucine rotamers are
allowed if the position is not in a .alpha.-helix. A backbone
independent rotamer library utilizes all rotamers of an amino acid
at every position. In general, a backbone independent library is
preferred in the consideration of core residues, since flexibility
in the core is important. However, backbone independent libraries
are computationally more expensive, and thus for surface and
boundary positions, a backbone dependent library is preferred.
However, either type of library can be used at any position.
[0070] In addition, a preferred embodiment does a type of "fine
tuning" of the rotamer library by expanding the possible .chi.
(chi) angle values of the rotamers by plus and minus one standard
deviation (or more) about the mean value, in order to minimize
possible errors that might arise from the discreteness of the
library. This is particularly important for aromatic residues, and
fairly important for hydrophobic residues, due to the increased
requirements for flexibility in the core and the rigidity of
aromatic rings; it is not as important for the other residues. Thus
a preferred embodiment expands the .chi..sub.1 and .chi..sub.2
angles for all amino acids except Met, Arg and Lys.
[0071] To roughly illustrate the numbers of rotamers, in one
version of the Dunbrack & Karplus backbone-dependent rotamer
library, alanine has 1 rotamer, glycine has 1 rotamer, arginine has
55 rotamers, threonine has 9 rotamers, lysine has 57 rotamers,
glutamic acid has 69 rotamers, asparagine has 54 rotamers, aspartic
acid has 27 rotamers, tryptophan has 54 rotamers, tyrosine has 36
rotamers, cysteine has 9 rotamers, glutamine has 69 rotamers,
histidine has 54 rotamers, valine has 9 rotamers, isoleucine has 45
rotamers, leucine has 36 rotamers, methionine has 21 rotamers,
serine has 9 rotamers, and phenylalanine has 36 rotamers.
[0072] In general, proline is not generally used, since it will
rarely be chosen for any position, although it can be included if
desired. Similarly, a preferred embodiment omits cysteine as a
consideration, only to avoid potential disulfide problems, although
it can be included if desired.
[0073] As will be appreciated by those in the art, other rotamer
libraries with all dihedral angles staggered can be used or
generated.
[0074] In a preferred embodiment, at a minimum, at least one
variable position has rotamers from at least two different amino
acid side chains; that is, a sequence is being optimized, rather
than a structure.
[0075] In a preferred embodiment, rotamers from all of the amino
acids (or all of them except cysteine, glycine and proline) are
used for each variable residue position; that is, the group or set
of potential rotamers at each variable position is every possible
rotamer of each amino acid. This is especially preferred when the
number of variable positions is not high as this type of analysis
can be computationally expensive.
[0076] In a preferred embodiment, each variable position is
classified as either a core, surface or boundary residue position,
although in some cases, as explained below, the variable position
may be set to glycine to minimize backbone strain.
[0077] It should be understood that quantitative protein design or
optimization studies prior to the present invention focused almost
exclusively on core residues. The present invention, however,
provides methods for designing proteins containing core, surface
and boundary positions. Alternate embodiments utilize methods for
designing proteins containing core and surface residues, core and
boundary residues, and surface and boundary residues, as well as
core residues alone (using the scoring functions of the present
invention), surface residues alone, or boundary residues alone.
[0078] The classification of residue positions as core, surface or
boundary may be done in several ways, as will be appreciated by
those in the art. In a preferred embodiment, the classification is
done via a visual scan of the original protein backbone structure,
including the side chains, and assigning a classification based on
a subjective evaluation of one skilled in the art of protein
modelling. Alternatively, a preferred embodiment utilizes an
assessment of the orientation of the C.alpha.-C.beta. vectors
relative to a solvent accessible surface computed using only the
template C.alpha. atoms. In a preferred embodiment, the solvent
accessible surface for only the C.alpha. atoms of the target fold
is generated using the Connolly algorithm with a probe radius
ranging from about 4 to about 12 .ANG., with from about 6 to about
10 .ANG. being preferred, and 8 .ANG. being particularly preferred.
The C.alpha. radius used ranges from about 1.6 .ANG. to about 2.3
.ANG., with from about 1.8 to about 2.1 .ANG. being preferred, and
1.95 .ANG. being especially preferred. A residue is classified as a
core position if a) the distance for its C.alpha., along its
C.alpha.-C.beta. vector, to the solvent accessible surface is
greater than about 4-6 .ANG., with greater than about 5.0 .ANG.
being especially preferred, and b) the distance for its C.beta. to
the nearest surface point is greater than about 1.5-3 .ANG., with
greater than about 2.0 .ANG. being especially preferred. The
remaining residues are classified as surface positions if the sum
of the distances from their C.alpha., along their C.alpha.-C.beta.
vector, to the solvent accessible surface, plus the distance from
their C.beta. to the closest surface point was less than about
2.5-4 .ANG., with less than about 2.7 .ANG. being especially
preferred. All remaining residues are classified as boundary
positions.
[0079] Once each variable position is classified as either core,
surface or boundary, a set of amino acid side chains, and thus a
set of rotamers, is assigned to each position. That is, the set of
possible amino acid side chains that the program will allow to be
considered at any particular position is chosen. Subsequently, once
the possible amino acid side chains are chosen, the set of rotamers
that will be evaluated at a particular position can be determined.
Thus, a core residue will generally be selected from the group of
hydrophobic residues consisting of alanine, valine, isoleucine,
leucine, phenylalanine, tyrosine, tryptophan, and methionine (in
some embodiments, when the a scaling factor of the van der Waals
scoring function, described below, is low, methionine is removed
from the set), and the rotamer set for each core position
potentially includes rotamers for these eight amino acid side
chains (all the rotamers if a backbone independent library is used,
and subsets if a rotamer dependent backbone is used). Similarly,
surface positions are generally selected from the group of
hydrophilic residues consisting of alanine, serine, threonine,
aspartic acid, asparagine, glutamine, glutamic acid, arginine,
lysine and histidine. The rotamer set for each surface position
thus includes rotamers for these ten residues. Finally, boundary
positions are generally chosen from alanine, serine, threonine,
aspartic acid, asparagine, glutamine, glutamic acid, arginine,
lysine histidine, valine, isoleucine, leucine, phenylalanine,
tyrosine, tryptophan, and methionine. The rotamer set for each
boundary position thus potentially includes every rotamer for these
seventeen residues (assuming cysteine, glycine and proline are not
used, although they can be).
[0080] Thus, as will be appreciated by those in the art, there is a
computational benefit to classifying the residue positions, as it
decreases the number of calculations. It should also be noted that
there may be situations where the sets of core, boundary and
surface residues are altered from those described above; for
example, under some circumstances, one or more amino acids is
either added or subtracted from the set of allowed amino acids. For
example, some proteins which dimerize or multimerize, or have
ligand binding sites, may contain hydrophobic surface residues,
etc. In addition, residues that do not allow helix "capping" or the
favorable interaction with an .alpha.-helix dipole may be
subtracted from a set of allowed residues. This modification of
amino acid groups is done on a residue by residue basis.
[0081] In a preferred embodiment, proline, cysteine and glycine are
not included in the list of possible amino acid side chains, and
thus the rotamers for these side chains are not used. However, in a
preferred embodiment, when the variable residue position has a
.phi. angle (that is, the dihedral angle defined by 1) the carbonyl
carbon of the preceding amino acid; 2) the nitrogen atom of the
current residue; 3) the .alpha.-carbon of the current residue; and
4) the carbonyl carbon of the current residue) greater than
0.degree., the position is set to glycine to minimize backbone
strain.
[0082] Once the group of potential rotamers is assigned for each
variable residue position, processing proceeds to step 54 of FIG.
2. This processing step entails analyzing interactions of the
rotamers with each other and with the protein backbone to generate
optimized protein sequences. The ranking module 34 may be used to
perform these operations. That is, computer code is written to
implement the following functions. Simplistically, as is generally
outlined above, the processing initially comprises the use of a
number of scoring functions, described below, to calculate energies
of interactions of the rotamers, either to the backbone itself or
other rotamers.
[0083] The scoring functions include a Van der Waals potential
scoring function, a hydrogen bond potential scoring function, an
atomic solvation scoring function, a secondary structure propensity
scoring function and an electrostatic scoring function. As is
further described below, at least one scoring function is used to
score each position, although the scoring functions may differ
depending on the position classification or other considerations,
like favorable interaction with an .alpha.-helix dipole. As
outlined below, the total energy which is used in the calculations
is the sum of the energy of each scoring function used at a
particular position, as is generally shown in Equation 1:
E.sub.total=nE.sub.vdw+nE.sub.as+nE.sub.h-bonding+nE.sub.ss+nE.sub.elec
[0084] In Equation 1, the total energy is the sum of the energy of
the van der Waals potential (E.sub.vdw), the energy of atomic
salvation (E.sub.ss), the energy of hydrogen bonding
(E.sub.h-bonding), the energy of secondary structure (E.sub.ss) and
the energy of electrostatic interaction (E.sub.elec). The term n is
either 0 or 1, depending on whether the term is to be considered
for the particular residue position, as is more fully outlined
below.
[0085] In a preferred embodiment, a van der Waals' scoring function
is used. As is known in the art, van der Waals' forces are the
weak, non-covalent and non-ionic forces between atoms and
molecules, that is, the induced dipole and electron repulsion
(Pauli principle) forces.
[0086] The van der Waals scoring function is based on a van der
Waals potential energy. There are a number of van der Waals
potential energy calculations, including a Lennard-Jones 12/6
potential with radii and well depth parameters from the Dreiding
force field, Mayo et al., J. Prot. Chem., 1990, expressly
incorporated herein by reference, or the exponential 6 potential.
Equation 2, shown below, is the preferred Lennard-Jones potential:
E vdw = D 0 .times. { ( R 0 R ) 12 - 2 .times. ( R 0 R ) 6 }
Equation .times. .times. 2 ##EQU1## R.sub.0 is the geometric mean
of the van der Waals radii of the two atoms under consideration,
and D.sub.0 is the geometric mean of the well depth of the two
atoms under consideration. E.sub.vdw and R are the energy and
interatomic distance between the two atoms under consideration, as
is more fully described below.
[0087] In a preferred embodiment, the van der Waals forces are
scaled using a scaling factor, .alpha., as is generally discussed
in Example 4. Equation 3 shows the use of a in the van der Waals
Lennard-Jones potential equation: E vdw = D 0 .times. { ( .alpha.
.times. .times. R 0 R ) 12 - 2 .times. ( .alpha. .times. .times. R
0 R ) 6 } Equation .times. .times. 3 ##EQU2##
[0088] The role of the .alpha. scaling factor is to change the
importance of packing effects in the optimization and design of any
particular protein. As discussed in the Examples, different values
for .alpha. result in different sequences being generated by the
present methods. Specifically, a reduced van der Waals steric
constraint can compensate for the restrictive effect of a fixed
backbone and discrete side-chain rotamers in the simulation and can
allow a broader sampling of sequences compatible with a desired
fold. In a preferred embodiment, .alpha. values ranging from about
0.70 to about 1.10 can be used, with .alpha. values from about 0.8
to about 1.05 being preferred, and from about 0.85 to about 1.0
being especially preferred. Specific .alpha. values which are
preferred are 0.80, 0.85, 0.90, 0.95, 1.00, and 1.05.
[0089] Generally speaking, variation of the van der Waals scale
factor .alpha. results in four regimes of packing specificity:
regime 1 where 0.9.ltoreq..alpha..ltoreq.1.05 and packing
constraints dominate the sequence selection; regime 2 where
0.8.ltoreq..alpha.<0.9 and the hydrophobic solvation potential
begins to compete with packing forces; regime 3 where
.alpha.<0.8 and hydrophobic solvation dominates the design; and,
regime 4 where .alpha.>1.05 and van der Waals repulsions appear
to be too severe to allow meaningful sequence selection. In
particular, different .alpha. values may be used for core, surface
and boundary positions, with regimes 1 and 2 being preferred for
core residues, regime 1 being preferred for surface residues, and
regime 1 and 2 being preferred for boundary residues.
[0090] In a preferred embodiment, the van der Waals scaling factor
is used in the total energy calculations for each variable residue
position, including core, surface and boundary positions.
[0091] In a preferred embodiment, an atomic solvation potential
scoring function is used. As is appreciated by those in the art,
solvent interactions of a protein are a significant factor in
protein stability, and residue/protein hydrophobicity has been
shown to be the major driving force in protein folding. Thus, there
is an entropic cost to solvating hydrophobic surfaces, in addition
to the potential for misfolding or aggregation. Accordingly, the
burial of hydrophobic surfaces within a protein structure is
beneficial to both folding and stability. Similarly, there can be a
disadvantage for burying hydrophilic residues. The accessible
surface area of a protein atom is generally defined as the area of
the surface over which a water molecule can be placed while making
van der Waals contact with this atom and not penetrating any other
protein atom. Thus, in a preferred embodiment, the solvation
potential is generally scored by taking the total possible exposed
surface area of the moiety or two independent moieties (either a
rotamer or the first rotamer and the second rotamer), which is the
reference, and subtracting out the "buried" area, i.e. the area
which is not solvent exposed due to interactions either with the
backbone or with other rotamers. This thus gives the exposed
surface area.
[0092] Alternatively, a preferred embodiment calculates the scoring
function on the basis of the "buried" portion; i.e. the total
possible exposed surface area is calculated, and then the
calculated surface area after the interaction of the moieties is
subtracted, leaving the buried surface area. A particularly
preferred method does both of these calculations.
[0093] As is more fully described below, both of these methods can
be done in a variety of ways. See Eisenberg et al., Nature
319:199-203 (1986); Connolly, Science 221:709-713 (1983); and
Wodak, et al., Proc. Natl. Acad. Sci. USA 77(4):1736-1740 (1980),
all of which are expressly incorporated herein by reference. As
will be appreciated by those in the art, this solvation potential
scoring function is conformation dependent, rather than
conformation independent.
[0094] In a preferred embodiment, the pairwise solvation potential
is implemented in two components, "singles" (rotamer/template) and
"doubles" (rotamer/rotamer), as is more fully described below. For
the rotamer/template buried area, the reference state is defined as
the rotamer in question at residue position i with the backbone
atoms only of residues i-1, i and i+1, although in some instances
just i may be used. Thus, in a preferred embodiment, the solvation
potential is not calculated for the interaction of each backbone
atom with a particular rotamer, although more may be done as
required. The area of the side chain is calculated with the
backbone atoms excluding solvent but not counted in the area. The
folded state is defined as the area of the rotamer in question at
residue i, but now in the context of the entire template structure
including non-optimized side chains, i.e. every other foxed
position residue. The rotamer/template buried area is the
difference between the reference and the folded states. The
rotamer/rotamer reference area can be done in two ways; one by
using simply the sum of the areas of the isolated rotamers; the
second includes the full backbone. The folded state is the area of
the two rotamers placed in their relative positions on the protein
scaffold but with no template atoms present. In a preferred
embodiment, the Richards definition of solvent accessible surface
area (Lee and Richards, J. Mol. Biol. 55:379-400, 1971, hereby
incorporated by reference) is used, with a probe radius ranging
from 0.8 to 1.6 .ANG., with 1.4 .ANG. being preferred, and Drieding
van der Waals radii, scaled from 0.8 to 1.0. Carbon and sulfur, and
all attached hydrogens, are considered nonpolar. Nitrogen and
oxygen, and all attached hydrogens, are considered polar. Surface
areas are calculated with the Connolly algorithm using a dot
density of 10 .ANG.-2 (Connolly, (1983) (supra), hereby
incorporated by reference).
[0095] In a preferred embodiment, there is a correction for a
possible overestimation of buried surface area which may exist in
the calculation of the energy of interaction between two rotamers
(but not the interaction of a rotamer with the backbone). Since, as
is generally outlined below, rotamers are only considered in pairs,
that is, a first rotamer is only compared to a second rotamer
during the "doubles" calculations, this may overestimate the amount
of buried surface area in locations where more than two rotamers
interact, that is, where rotamers from three or more residue
positions come together. Thus, a correction or scaling factor is
used as outlined below.
[0096] The general energy of solvation is shown in Equation 4:
E.sub.sa=f(SA) Equation 4 where E.sub.sa is the energy of
solvation, f is a constant used to correlate surface area and
energy, and SA is the surface area. This equation can be broken
down, depending on which parameter is being evaluated. Thus, when
the hydrophobic buried surface area is used, Equation 5 is
appropriate: E.sub.sa=f.sub.1(SA.sub.buried hydrophobic) Equation 5
where f.sub.1 is a constant which ranges from about 10 to about 50
cal/mol/.ANG..sup.2, with 23 or 26 cal/mol/.ANG..sup.2 being
preferred. When a penalty for hydrophilic burial is being
considered, the equation is shown in Equation 6:
E.sub.sa=f.sub.1(SA.sub.buried hydrophobic)+f.sub.2(SA.sub.buried
hydrophilic) Equation 6 where f.sub.2 is a constant which ranges
from -50 to -250 cal/mol/.ANG..sup.2, with -86 or -100
cal/mol/.ANG..sup.2 being preferred. Similarly, if a penalty for
hydrophobic exposure is used, equation 7 or 8 may be used:
E.sub.sa=f.sub.1(SA.sub.buried hydrophobic)+f.sub.3(SA.sub.exposed
hydrophobic) Equation 7 E.sub.sa=f.sub.1(SA.sub.buried
hydrophobic)+f.sub.2(SA.sub.buried
hydrophilic)+f.sub.3(SA.sub.exposed
hydrophobic)+f.sub.4(SA.sub.exposed hydrophilic) Equation 8
[0097] In a preferred embodiment, f.sub.3=-f.sub.1.
[0098] In one embodiment, backbone atoms are not included in the
calculation of surface areas, and values of 23 cal/mol/.ANG..sup.2
(f.sub.1) and -86 cal/mol/.ANG..sup.2 (f.sub.2) are determined.
[0099] In a preferred embodiment, this overcounting problem is
addressed using a scaling factor that compensates for only the
portion of the expression for pairwise area that is subject to
over-counting. In this embodiment, values of -26
cal/mol/.ANG..sup.2 (f.sub.1) and 100 cal/mol/.ANG..sup.2 (f.sub.2)
are determined.
[0100] Atomic solvation energy is expensive, in terms of
computational time and resources. Accordingly, in a preferred
embodiment, the solvation energy is calculated for core and/or
boundary residues, but not surface residues, with both a
calculation for core and boundary residues being preferred,
although any combination of the three is possible.
[0101] In a preferred embodiment, a hydrogen bond potential scoring
function is used. A hydrogen bond potential is used as predicted
hydrogen bonds do contribute to designed protein stability (see
Stickle et al., J. Mol. Biol. 226:1143 (1992); Huyghues-Despointes
et al., Biochem. 34:13267 (1995), both of which are expressly
incorporated herein by reference). As outlined previously, explicit
hydrogens are generated on the protein backbone structure.
[0102] In a preferred embodiment, the hydrogen bond potential
consists of a distance-dependent term and an angle-dependent term,
as shown in Equation 9: E H - Bonding = D 0 .times. { 5 .times. ( R
0 R ) 12 - 6 .times. ( R 0 R ) 10 } .times. F .function. ( .theta.
, .0. , .phi. ) Equation .times. .times. 9 ##EQU3## where R.sub.0
(2.8 .ANG.) and D.sub.0 (8 kcal/mol) are the hydrogen-bond
equilibrium distance and well-depth, respectively, and R is the
donor to acceptor distance. This hydrogen bond potential is based
on the potential used in DREIDING with more restrictive
angle-dependent terms to limit the occurrence of unfavorable
hydrogen bond geometries. The angle term varies depending on the
hybridization state of the donor and acceptor, as shown in
Equations 10, 11, 12 and 13. Equation 10 is used for sp.sup.3 donor
to sp acceptor; Equation 11 is used for sp.sup.3 donor to sp.sup.2
acceptor, Equation 12 is used for sp.sup.2 donor to sp.sup.3
acceptor, and Equation 13 is used for sp.sup.2 donor to sp.sup.2
acceptor: F.dbd.cos.sup.2.theta. cos.sup.2(O-109.5) Equation 10
F=cos.sup.2.theta. cos.sup.2O Equation 11 F=cos.sup.4.theta.
Equation 12 F=cos.sup.2.theta. cos.sup.2(max[.phi., .phi.])
[0103] In Equations 10-13, .theta. is the donor-hydrogen-acceptor
angle, .phi. is the hydrogen-acceptor-base angle (the base is the
atom attached to the acceptor, for example the carbonyl carbon is
the base for a carbonyl oxygen acceptor), and .phi. is the angle
between the normals of the planes defined by the six atoms attached
to the sp.sup.2 centers (the supplement of .phi. is used when .phi.
is less than 90.degree.). The hydrogen-bond function is only
evaluated when 2.6 .ANG..ltoreq.R.ltoreq.3.2 .ANG.,
.theta.>90.degree., .phi.-109.5.degree.<90.degree. for the
sp.sup.3 donor--sp.sup.3 acceptor case, and, .phi.>90.degree.
for the sp.sup.3 donor--sp.sup.2 acceptor case; preferably, no
switching functions are used. Template donors and acceptors that
are involved in template-template hydrogen bonds are preferably not
included in the donor and acceptor lists. For the purpose of
exclusion, a template-template hydrogen bond is considered to exist
when 2.5 .ANG..ltoreq.R.ltoreq.3.3 .ANG. and
.theta..gtoreq.135.degree..
[0104] The hydrogen-bond potential may also be combined or used
with a weak coulombic term that includes a distance-dependent
dielectric constant of 40R, where R is the interatomic distance.
Partial atomic charges are preferably only applied to polar
functional groups. A net formal charge of +1 is used for Arg and
Lys and a net formal charge of -1 is used for Asp and Glu; see
Gasteiger, et al., Tetrahedron 36:3219-3288 (1980); Rappe, et al.,
J. Phys. Chem. 95:3358-3363 (1991).
[0105] In a preferred embodiment, an explicit penalty is given for
buried polar hydrogen atoms which are not hydrogen bonded to
another atom. See Eisenberg, et al., (1986) (supra), hereby
expressly incorporated by reference. In a preferred embodiment,
this penalty for polar hydrogen burial, is from about 0 to about 3
kcal/mol, with from about 1 to about 3 being preferred and 2
kcal/mol being particularly preferred. This penalty is only applied
to buried polar hydrogens not involved in hydrogen bonds. A
hydrogen bond is considered to exist when E.sub.HB ranges from
about 1 to about 4 kcal/mol, with E.sub.HB of less than -2 kcal/mol
being preferred. In addition, in a preferred embodiment, the
penalty is not applied to template hydrogens, i.e. unpaired buried
hydrogens of the backbone.
[0106] In a preferred embodiment, only hydrogen bonds between a
first rotamer and the backbone are scored, and rotamer-rotamer
hydrogen bonds are not scored. In an alternative embodiment,
hydrogen bonds between a first rotamer and the backbone are scored,
and rotamer-rotamer hydrogen bonds are scaled by 0.5.
[0107] In a preferred embodiment, the hydrogen bonding scoring
function is used for all positions, including core, surface and
boundary positions. In alternate embodiments, the hydrogen bonding
scoring function may be used on only one or two of these.
[0108] In a preferred embodiment, a secondary structure propensity
scoring function is used. This is based on the specific amino acid
side chain, and is conformation independent. That is, each amino
acid has a certain propensity to take on a secondary structure,
either .alpha.-helix or .beta.-sheet, based on its .phi. and .psi.
angles. See Mufnoz et al., Current Op. in Biotech. 6:382 (1995);
Minor, et al., Nature 367:660-663 (1994); Padmanabhan, et al.,
Nature 344:268-270 (1990); Munoz, et al., Foldinq & Design
1(3):167-178 (1996); and Chakrabartty, et al., Protein Sci. 3:843
(1994), all of which are expressly incorporated herein by
reference. Thus, for variable residue positions that are in
recognizable secondary structure in the backbone, a secondary
structure propensity scoring function is preferably used. That is,
when a variable residue position is in an .alpha.-helical area of
the backbone, the .alpha.-helical propensity scoring function
described below is calculated. Whether or not a position is in a
.alpha.-helical area of the backbone is determined as will be
appreciated by those in the art, generally on the basis of .phi.
and .psi. angles; for .alpha.-helix, .phi. angles from -2 to -70
and .psi. angles from -30 to -100 generally describe an
.alpha.-helical area of the backbone.
[0109] Similarly, when a variable residue position is in a
.beta.-sheet backbone conformation, the .beta.-sheet propensity
scoring function is used. .delta.-sheet backbone conformation is
generally described by .phi. angles from -30 to -100 and .chi.
angles from +40 to +180. In alternate preferred embodiments,
variable residue positions which are within areas of the backbone
which are not assignable to either .beta.-sheet or .alpha.-helix
structure may also be subjected to secondary structure propensity
calculations.
[0110] In a preferred embodiment, energies associated with
secondary propensities are calculated using Equation 14:
E.sub..varies.=10.sup.N.sup.ss.sup.(.DELTA.G.degree..sup.aa.sup.-.DELTA.G-
.degree..sup.ala.sup.)-1 Equation 14
[0111] In Equation 14, E.sub..alpha., (or E.beta.) is the energy of
.alpha.-helical propensity, .DELTA.G.degree..sub.aa is the standard
free energy of helix propagation of the amino acid, and
.DELTA.G.degree..sub.ala is the standard free energy of helix
propagation of alanine used as a standard, or standard free energy
of .beta.-sheet formation of the amino acid, both of which are
available in the literature (see Chakrabartty, et al., (1994)
(supra), and Munoz, et al., Folding & Design 1(3):167-178
(1996)), both of which are expressly incorporated herein by
reference), and N.sub.ss is the propensity scale factor which is
set to range from 1 to 4, with 3.0 being preferred. This potential
is preferably selected in order to scale the propensity energies to
a similar range as the other terms in the scoring function.
[0112] In a preferred embodiment, .beta.-sheet propensities are
preferably calculated only where the i-1 and i+1 residues are also
in .beta.-sheet conformation.
[0113] In a preferred embodiment, the secondary structure
propensity scoring function is used only in the energy calculations
for surface variable residue positions. In alternate embodiments,
the secondary structure propensity scoring function is used in the
calculations for core and boundary regions as well.
[0114] In a preferred embodiment, an electrostatic scoring function
is used, as shown below in Equation 15: E elec = qq ' .epsilon.
.times. .times. r 2 Equation .times. .times. 15 ##EQU4##
[0115] In this Equation, q is the charge on atom 1, q' is charge on
atom 2, and r is the interaction distance.
[0116] In a preferred embodiment, at least one scoring function is
used for each variable residue position; in preferred embodiments,
two, three or four scoring functions are used for each variable
residue position.
[0117] Once the scoring functions to be used are identified for
each variable position, the preferred first step in the
computational analysis comprises the determination of the
interaction of each possible rotamer with all or part of the
remainder of the protein. That is, the energy of interaction, as
measured by one or more of the scoring functions, of each possible
rotamer at each variable residue position with either the backbone
or other rotamers, is calculated. In a preferred embodiment, the
interaction of each rotamer with the entire remainder of the
protein, i.e. both the entire template and all other rotamers, is
done. However, as outlined above, it is possible to only model a
portion of a protein, for example a domain of a larger protein, and
thus in some cases, not all of the protein need be considered.
[0118] In a preferred embodiment, the first step of the
computational processing is done by calculating two sets of
interactions for each rotamer at every position (step 70 of FIG.
3): the interaction of the rotamer side chain with the template or
backbone (the "singles" energy), and the interaction of the rotamer
side chain with all other possible rotamers at every other position
(the "doubles" energy), whether that position is varied or floated.
It should be understood that the backbone in this case includes
both the atoms of the protein structure backbone, as well as the
atoms of any fixed residues, wherein the fixed residues are defined
as a particular conformation of an amino acid.
[0119] Thus, "singles" (rotamer/template) energies are calculated
for the interaction of every possible rotamer at every variable
residue position with the backbone, using some or all of the
scoring functions. Thus, for the hydrogen bonding scoring function,
every hydrogen bonding atom of the rotamer and every hydrogen
bonding atom of the backbone is evaluated, and the E.sub.HB is
calculated for each possible rotamer at every variable position.
Similarly, for the van der Waals scoring function, every atom of
the rotamer is compared to every atom of the template (generally
excluding the backbone atoms of its own residue), and the E.sub.vdW
is calculated for each possible rotamer at every variable residue
position. In addition, generally no van der Waals energy is
calculated if the atoms are connected by three bonds or less. For
the atomic solvation scoring function, the surface of the rotamer
is measured against the surface of the template, and the E.sub.as
for each possible rotamer at every variable residue position is
calculated. The secondary structure propensity scoring function is
also considered as a singles energy, and thus the total singles
energy may contain an E.sub.ss term. As will be appreciated by
those in the art, many of these energy terms will be close to zero,
depending on the physical distance between the rotamer and the
template position; that is, the farther apart the two moieties, the
lower the energy.
[0120] Accordingly, as outlined above, the total singles energy is
the sum of the energy of each scoring function used at a particular
position, as shown in Equation 1, wherein n is either 1 or zero,
depending on whether that particular scoring function was used at
the rotamer position:
E.sub.total=nE.sub.vdw+nE.sub.as+nE.sub.h-bonding+nE.sub.ss+nE.sub.elec
Equation 1
[0121] Once calculated, each singles E.sub.total for each possible
rotamer is stored in the memory 24 within the computer, such that
it may be used in subsequent calculations, as outlined below.
[0122] For the calculation of "doubles" energy (rotamer/rotamer),
the interaction energy of each possible rotamer is compared with
every possible rotamer at all other variable residue positions.
Thus, "doubles" energies are calculated for the interaction of
every possible rotamer at every variable residue position with
every possible rotamer at every other variable residue position,
using some or all of the scoring functions. Thus, for the hydrogen
bonding scoring function, every hydrogen bonding atom of the first
rotamer and every hydrogen bonding atom of every possible second
rotamer is evaluated, and the E.sub.HB is calculated for each
possible rotamer pair for any two variable positions. Similarly,
for the van der Waals scoring function, every atom of the first
rotamer is compared to every atom of every possible second rotamer,
and the E.sub.vdW is calculated for each possible rotamer pair at
every two variable residue positions. For the atomic solvation
scoring function, the surface of the first rotamer is measured
against the surface of every possible second rotamer, and the
E.sub.as for each possible rotamer pair at every two variable
residue positions is calculated. The secondary structure propensity
scoring function need not be run as a "doubles" energy, as it is
considered as a component of the "singles" energy. As will be
appreciated by those in the art, many of these double energy terms
will be close to zero, depending on the physical distance between
the first rotamer and the second rotamer; that is, the farther
apart the two moieties, the lower the energy.
[0123] Accordingly, as outlined above, the total doubles energy is
the sum of the energy of each scoring function used to evaluate
every possible pair of rotamers, as shown in Equation 16, wherein n
is either 1 or zero, depending on whether that particular scoring
function was used at the rotamer position:
E.sub.total=nE.sub.vdw+nE.sub.as+nE.sub.h-bonding+E.sub.elec
Equation 16
[0124] An example is illuminating. A first variable position, i,
has three (an unrealistically low number) possible rotamers (which
may be either from a single amino acid or different amino acids)
which are labelled ia, ib, and ic. A second variable position, j,
also has three possible rotamers, labelled jd, je, and jf. Thus,
nine doubles energies (E.sub.total) are calculated in all:
E.sub.total(ia, jd), E.sub.total(ia, je), E.sub.total(ia, jf),
E.sub.total(ib, jd), E.sub.total(ib, je), E.sub.total(ib, jf),
E.sub.total(ic, jd), E.sub.total(ic, je), and E.sub.total(ic,
jf).
[0125] Once calculated, each doubles E.sub.total for each possible
rotamer pair is stored in memory 24 within the computer, such that
it may be used in subsequent calculations, as outlined below.
[0126] Once the singles and doubles energies are calculated and
stored, the next step of the computational processing may occur.
Generally speaking, the goal of the computational processing is to
determine a set of optimized protein sequences. By "optimized
protein sequence" herein is meant a sequence that best fits the
mathematical equations herein. As will be appreciated by those in
the art, a global optimized sequence is the one sequence that best
fits Equation 1, i.e. the sequence that has the lowest energy of
any possible sequence. However, there are any number of sequences
that are not the global minimum but that have low energies.
[0127] In a preferred embodiment, the set comprises the globally
optimal sequence in its optimal conformation, i.e. the optimum
rotamer at each variable position. That is, computational
processing is run until the simulation program converges on a
single sequence which is the global optimum.
[0128] In a preferred embodiment, the set comprises at least two
optimized protein sequences. Thus for example, the computational
processing step may eliminate a number of disfavored combinations
but be stopped prior to convergence, providing a set of sequences
of which the global optimum is one. In addition, further
computational analysis, for example using a different method, may
be run on the set, to further eliminate sequences or rank them
differently. Alternatively, as is more fully described below, the
global optimum may be reached, and then further computational
processing may occur, which generates additional optimized
sequences in the neighborhood of the global optimum.
[0129] If a set comprising more than one optimized protein
sequences is generated, they may be rank ordered in terms of
theoretical quantitative stability, as is more fully described
below.
[0130] In a preferred embodiment, the computational processing step
first comprises an elimination step, sometimes referred to as
"applying a cutoff", either a singles elimination or a doubles
elimination. Singles elimination comprises the elimination of all
rotamers with template interaction energies of greater than about
10 kcal/mol prior to any computation, with elimination energies of
greater than about 15 kcal/mol being preferred and greater than
about 25 kcal/mol being especially preferred. Similarly, doubles
elimination is done when a rotamer has interaction energies greater
than about 10 kcal/mol with all rotamers at a second residue
position, with energies greater than about 15 being preferred and
greater than about 25 kcal/mol being especially preferred.
[0131] In a preferred embodiment, the computational processing
comprises direct determination of total sequence energies, followed
by comparison of the total sequence energies to ascertain the
global optimum and rank order the other possible sequences, if
desired. The energy of a total sequence is shown below in Equation
17: E total .times. .times. protein = E ( b - b ) + all .times.
.times. i .times. E ( ia ) + all .times. .times. i .times. + all
.times. .times. j .times. .times. pairs .times. E ( ia , ja )
Equation .times. .times. 17 ##EQU5##
[0132] Thus every possible combination of rotamers may be directly
evaluated by adding the backbone-backbone (sometimes referred to
herein as template-template) energy (E.sub.(b-b) which is constant
over all sequences herein since the backbone is kept constant), the
singles energy for each rotamer (which has already been calculated
and stored), and the doubles energy for each rotamer pair (which
has already been calculated and stored). Each total sequence energy
of each possible rotamer sequence can then be ranked, either from
best to worst or worst to best. This is obviously computationally
expensive and becomes unwieldy as the length of the protein
increases.
[0133] In a preferred embodiment, the computational processing
includes one or more Dead-End Elimination (DEE) computational
steps. The DEE theorem is the basis for a very fast discrete search
program that was designed to pack protein side chains on a fixed
backbone with a known sequence. See Desmet, et al., Nature
356:539-542 (1992); Desmet, et al., The Protein Folding Problem and
Tertiary Structure Prediction, Ch. 10:1-49 (1994); Goldstein,
Biophys. Jour. 66:1335-1340 (1994), all of which are incorporated
herein by reference. DEE is based on the observation that if a
rotamer can be eliminated from consideration at a particular
position, i.e. make a determination that a particular rotamer is
definitely not part of the global optimal conformation, the size of
the search is reduced. This is done by comparing the worst
interaction (i.e. energy or E.sub.total) of a first rotamer at a
single variable position with the best interaction of a second
rotamer at the same variable position. If the worst interaction of
the first rotamer is still better than the best interaction of the
second rotamer, then the second rotamer cannot possibly be in the
optimal conformation of the sequence. The original DEE theorem is
shown in Equation 18: E .function. ( ia ) + j .times. [ min .times.
.times. over .times. .times. t .times. { E .function. ( ia , jt ) }
] > E .function. ( ib ) + j .times. [ max .times. .times. over
.times. .times. t .times. { E .function. ( ib , jt ) } ] Equation
.times. .times. 18 ##EQU6##
[0134] In Equation 18, rotamer ia is being compared to rotamer ib.
The left side of the inequality is the best possible interaction
energy (E.sub.total) of ia with the rest of the protein; that is,
"min over t" means find the rotamer t on position j that has the
best interaction with rotamer ia. Similarly, the right side of the
inequality is the worst possible (max) interaction energy of
rotamer ib with the rest of the protein. If this inequality is
true, then rotamer ia is Dead-Ending and can be Eliminated. The
speed of DEE comes from the fact that the theorem only requires
sums over the sequence length to test and eliminate rotamers.
[0135] In a preferred embodiment, a variation of DEE is performed.
Goldstein DEE, based on Goldstein, (1994) (supra), hereby expressly
incorporated by reference, is a variation of the DEE computation,
as shown in Equation 19: E(ia)-E(ib)+.SIGMA.[min over t{E(ia,
jt)-E(ib, jt)}]>0 Equation 19
[0136] In essence, the Goldstein Equation 19 says that a first
rotamer a of a particular position i (rotamer ia) will not
contribute to a local energy minimum if the energy of conformation
with ia can always be lowered by just changing the rotamer at that
position to ib, keeping the other residues equal. If this
inequality is true, then rotamer ia is Dead-Ending and can be
Eliminated.
[0137] Thus, in a preferred embodiment, a first DEE computation is
done where rotamers at a single variable position are compared,
("singles" DEE) to eliminate rotamers at a single position. This
analysis is repeated for every variable position, to eliminate as
many single rotamers as possible. In addition, every time a rotamer
is eliminated from consideration through DEE, the minimum and
maximum calculations of Equation 18 or 19 change, depending on
which DEE variation is used, thus conceivably allowing the
elimination of further rotamers. Accordingly, the singles DEE
computation can be repeated until no more rotamers can be
eliminated; that is, when the inequality is not longer true such
that all of them could conceivably be found on the global
optimum.
[0138] In a preferred embodiment, "doubles" DEE is additionally
done. In doubles DEE, pairs of rotamers are evaluated; that is, a
first rotamer at a first position and a second rotamer at a second
position are compared to a third rotamer at the first position and
a fourth rotamer at the second position, either using original or
Goldstein DEE. Pairs are then flagged as nonallowable, although
single rotamers cannot be eliminated, only the pair. Again, as for
singles DEE, every time a rotamer pair is flagged as nonallowable,
the minimum calculations of Equation 18 or 19 change (depending on
which DEE variation is used) thus conceivably allowing the flagging
of further rotamer pairs. Accordingly, the doubles DEE computation
can be repeated until no more rotamer pairs can be flagged; that
is, where the energy of rotamer pairs overlap such that all of them
could conceivably be found on the global optimum.
[0139] In addition, in a preferred embodiment, rotamer pairs are
initially prescreened to eliminate rotamer pairs prior to DEE. This
is done by doing relatively computationally inexpensive
calculations to eliminate certain pairs up front. This may be done
in several ways, as is outlined below.
[0140] In a preferred embodiment, the rotamer pair with the lowest
interaction energy with the rest of the system is found. Inspection
of the energy distributions in sample matrices has revealed that an
i.sub.uj.sub.v pair that dead-end eliminates a particular
i.sub.rj.sub.s pair can also eliminate other i.sub.rj.sub.s pairs.
In fact, there are often a few i.sub.uj.sub.v pairs, which we call
"magic bullets," that eliminate a significant number of
i.sub.rj.sub.s pairs. We have found that one of the most potent
magic bullets is the pair for which maximum interaction energy,
t.sub.max([i.sub.uj.sub.v])k.sub.t, is least. This pair is referred
to as [i.sub.uj.sub.v].sub.mb. If this rotamer pair is used in the
first round of doubles DEE, it tends to eliminate pairs faster.
[0141] Our first speed enhancement is to evaluate the first-order
doubles calculation for only the matrix elements in the row
corresponding to the [i.sub.uj.sub.v].sub.mb pair. The discovery of
[i.sub.uj.sub.v].sub.mb is an n.sup.2 calculation (n=the number of
rotamers per position), and the application of Equation 19 to the
single row of the matrix corresponding to this rotamer pair is
another n.sup.2 calculation, so the calculation time is small in
comparison to a full first-order doubles calculation. In practice,
this calculation produces a large number of dead-ending pairs,
often enough to proceed to the next iteration of singles
elimination without any further searching of the doubles
matrix.
[0142] The magic bullet first-order calculation will also discover
all dead-ending pairs that would be discovered by the Equation 18
or 19, thereby making it unnecessary. This stems from the fact that
.epsilon..sub.max([i.sub.uj.sub.v].sub.mb) must be less than or
equal to any .epsilon..sub.max([i.sub.uj.sub.v]) that would
successfully eliminate a pair by he Equation 18 or 19.
[0143] Since the minima and maxima of any given pair has been
precalculated as outlined herein, a second speed-enhancement
precalculation may be done. By comparing extrema, pairs that will
not dead end can be identified and thus skipped, reducing the time
of the DEE calculation. Thus, pairs that satisfy either one of the
following criteria are skipped:
.epsilon..sub.min([i.sub.rj.sub.s])<.epsilon..sub.min([i.sub.uj.sub.v]-
) Equation 20
.epsilon..sub.max([i.sub.rj.sub.s])<.epsilon..sub.max([i.sub.uj.sub.v]-
) Equation 21
[0144] Because the matrix containing these calculations is
symmetrical, half of its elements will satisfy the first inequality
Equation 20, and half of those remaining will satisfy the other
inequality Equation 21. These three quarters of the matrix need not
be subjected to the evaluation of Equation 18 or 19, resulting in a
theoretical speed enhancement of a factor of four.
[0145] The last DEE speed enhancement refines the search of the
remaining quarter of the matrix. This is done by constructing a
metric from the precomputed extrema to detect those matrix elements
likely to result in a dead-ending pair.
[0146] A metric was found through analysis of matrices from
different sample optimizations. We searched for combinations of the
extrema that predicted the likelihood that a matrix element would
produce a dead-ending pair. Interval sizes (see FIG. 12) for each
pair were computed from differences of the extrema. The size of the
overlap of the i.sub.rj.sub.s and i.sub.uj.sub.v intervals were
also computed, as well as the difference between the minima and the
difference between the maxima. Combinations of these quantities, as
well as the lone extrema, were tested for their ability to predict
the occurrence of dead-ending pairs. Because some of the maxima
were very large, the quantities were also compared
logarithmically.
[0147] Most of the combinations were able to predict dead-ending
matrix elements to varying degrees. The best metrics were the
fractional interval overlap with respect to each pair, referred to
herein as q.sub.rs and q.sub.uv. q rs = .times. interval .times.
.times. overlap interval .function. ( [ i r .times. j s ] ) =
.times. max .function. ( [ i u .times. j v ] ) - min .function. ( [
i r .times. j s ] ) max .function. ( [ i r .times. j s ] ) - min
.function. ( [ i r .times. j s ] ) Equation .times. .times. 22 q uv
= interval .times. .times. overlap interval .function. ( i u
.times. j v ) = max .function. ( [ i u .times. j v ] ) - min
.function. ( [ i r .times. j s ] ) max .function. ( [ i u .times. j
v ] ) - min .function. ( [ i u .times. j v ] ) Equation .times.
.times. 23 ##EQU7##
[0148] These values are calculated using the minima and maxima
equations 24, 25, 26 and 27 (see FIG. 14): max .function. ( [ i r
.times. j s ] ) = .function. ( [ i r .times. j s ] ) + k .noteq. i
.noteq. j .times. max l .times. .function. ( [ i r .times. j s ] ,
k ) Equation .times. .times. 24 min .function. ( [ i r .times. j s
] ) = .function. ( [ i r .times. j s ] ) + k .noteq. i .noteq. j
.times. min t .times. .function. ( [ i r .times. j s ] , k l )
Equation .times. .times. 25 max .function. ( [ i u .times. j v ] )
= .function. ( [ i u .times. j v ] ) + k .noteq. i .noteq. j
.times. max t .times. .function. ( [ i u .times. j v ] , k t )
Equation .times. .times. 26 min .function. ( [ i u .times. j v ] )
= .function. ( [ i u .times. j v ] ) + k .noteq. i .noteq. j
.times. min t .times. .function. ( [ i u .times. j v ] , k l )
Equation .times. .times. 27 ##EQU8##
[0149] These metrics were selected because they yield ratios of the
occurrence of dead-ending matrix elements to the total occurrence
of elements that are higher than any of the other metrics tested.
For example, there are very few matrix elements (-2%) for which
q.sub.rs>0.98, yet these elements produce 30-40% of all of the
dead-ending pairs.
[0150] Accordingly, the first-order doubles criterion is applied
only to those doubles for which q.sub.rs>0.98 and
q.sub.uv>0.99. The sample data analyses predict that by using
these two metrics, as many as half of the dead-ending elements may
be found by evaluating only two to five percent of the reduced
matrix.
[0151] Generally, as is more fully described below, single and
double DEE, using either or both of original DEE and Goldstein DEE,
is run until no further elimination is possible. Usually,
convergence is not complete, and further elimination must occur to
achieve convergence. This is generally done using "super residue"
DEE.
[0152] In a preferred embodiment, additional DEE computation is
done by the creation of "super residues" or "unification", as is
generally described in Desmet, Nature 356:539-542 (1992); Desmet,
et al., The Protein Folding Problem and Tertiary Structure
Prediction, Ch. 10:1-49 (1994); Goldstein, et al., supra. A super
residue is a combination of two or more variable residue positions
which is then treated as a single residue position. The super
residue is then evaluated in singles DEE, and doubles DEE, with
either other residue positions or super residues. The disadvantage
of super residues is that there are many more rotameric states
which must be evaluated; that is, if a first variable residue
position has 5 possible rotamers, and a second variable residue
position has 4 possible rotamers, there are 20 possible super
residue rotamers which must be evaluated. However, these super
residues may be eliminated similar to singles, rather than being
flagged like pairs.
[0153] The selection of which positions to combine into super
residues may be done in a variety of ways. In general, random
selection of positions for super residues results in inefficient
elimination, but it can be done, although this is not preferred. In
a preferred embodiment, the first evaluation is the selection of
positions for a super residue is the number of rotamers at the
position. If the position has too many rotamers, it is never
unified into a super residue, as the computation becomes too
unwieldy. Thus, only positions with fewer than about 100,000
rotamers are chosen, with less than about 50,000 being preferred
and less than about 10,000 being especially preferred.
[0154] In a preferred embodiment, the evaluation of whether to form
a super residue is done as follows. All possible rotamer pairs are
ranked using Equation 28, and the rotamer pair with the highest
number is chosen for unification: fraction .times. .times. of
.times. .times. flagged .times. .times. pairs _ .times. .times. log
( number .times. .times. of .times. .times. super .times. .times.
rotamers .times. .times. resulting .times. .times. from .times.
.times. the .times. .times. potential .times. .times. unification )
Equation .times. .times. 28 ##EQU9##
[0155] Equation 28 is looking for the pair of positions that has
the highest fraction or percentage of flagged pairs but the fewest
number of super rotamers. That is, the pair that gives the highest
value for Equation 28 is preferably chosen. Thus, if the pair of
positions that has the highest number of flagged pairs but also a
very large number of super rotamers (that is, the number of
rotamers at position i times the number of rotamers at position j),
this pair may not be chosen (although it could) over a lower
percentage of flagged pairs but fewer super rotamers.
[0156] In an alternate preferred embodiment, positions are chosen
for super residues that have the highest average energy; that is,
for positions i and j, the average energy of all rotamers for i and
all rotamers for j is calculated, and the pair with the highest
average energy is chosen as a super residue.
[0157] Super residues are made one at a time, preferably. After a
super residue is chosen, the singles and doubles DEE computations
are repeated where the super residue is treated as if it were a
regular residue. As for singles and doubles DEE, the elimination of
rotamers in the super residue DEE will alter the minimum energy
calculations of DEE. Thus, repeating singles and/or doubles DEE can
result in further elimination of rotamers.
[0158] FIG. 3 is a detailed illustration of the processing
operations associated with a ranking module 34 of the invention.
The calculation and storage of the singles and doubles energies 70
is the first step, although these may be recalculated every time.
Step 72 is the optional application of a cutoff, where singles or
doubles energies that are too high are eliminated prior to further
processing. Either or both of original singles DEE 74 or Goldstein
singles DEE 76 may be done, with the elimination of original
singles DEE 74 being generally preferred. Once the singles DEE is
run, original doubles (78) and/or Goldstein doubles (80) DEE is
run. Super residue DEE is then generally run, either original (82)
or Goldstein (84) super residue DEE. This preferably results in
convergence at a global optimum sequence. As is depicted in FIG. 3,
after any step any or all of the previous steps can be rerun, in
any order.
[0159] The addition of super residue DEE to the computational
processing, with repetition of the previous DEE steps, generally
results in convergence at the global optimum. Convergence to the
global optimum is guaranteed if no cutoff applications are made,
although generally a global optimum is achieved even with these
steps. In a preferred embodiment, DEE is run until the global
optimum sequence is found. That is, the set of optimized protein
sequences contains a single member, the global optimum.
[0160] In a preferred embodiment, the various DEE steps are run
until a managable number of sequences is found, i.e. no further
processing is required. These sequences represent a set of
optimized protein sequences, and they can be evaluated as is more
fully described below. Generally, for computational purposes, a
manageable number of sequences depends on the length of the
sequence, but generally ranges from about 1 to about 10.sup.15
possible rotamer sequences.
[0161] Alternatively, DEE is run to a point, resulting in a set of
optimized sequences (in this context, a set of remainder sequences)
and then further compututational processing of a different type may
be run. For example, in one embodiment, direct calculation of
sequence energy as outlined above is done on the remainder possible
sequences. Alternatively, a Monte Carlo search can be run.
[0162] In a preferred embodiment, the computation processing need
not comprise a DEE computational step. In this embodiment, a Monte
Carlo search is undertaken, as is known in the art. See Metropolis
et al., J. Chem. Phys. 21:1087 (1953), hereby incorporated by
reference. In this embodiment, a random sequence comprising random
rotamers is chosen as a start point. In one embodiment, the
variable residue positions are classified as core, boundary or
surface residues and the set of available residues at each position
is thus defined. Then a random sequence is generated, and a random
rotamer for each amino acid is chosen. This serves as the starting
sequence of the Monte Carlo search. A Monte Carlo search then makes
a random jump at one position, either to a different rotamer of the
same amino acid or a rotamer of a different amino acid, and then a
new sequence energy (E.sub.total sequence) is calculated, and if
the new sequence energy meets the Boltzmann criteria for
acceptance, it is used as the starting point for another jump. If
the Boltzmann test fails, another random jump is attempted from the
previous sequence. In this way, sequences with lower and lower
energies are found, to generate a set of low energy sequences.
[0163] If computational processing results in a single global
optimum sequence, it is frequently preferred to generate additional
sequences in the energy neighborhood of the global solution, which
may be ranked. These additional sequences are also optimized
protein sequences. The generation of additional optimized sequences
is generally preferred so as to evaluate the differences between
the theoretical and actual energies of a sequence. Generally, in a
preferred embodiment, the set of sequences is at least about 75%
homologous to each other, with at least about 80% homologous being
preferred, at least about 85% homologous being particularly
preferred, and at least about 90% being especially preferred. In
some cases, homology as high as 95% to 98% is desirable. Homology
in this context means sequence similarity or identity, with
identity being preferred. Identical in this context means identical
amino acids at corresponding positions in the two sequences which
are being compared. Homology in this context includes amino acids
which are identical and those which are similar (functionally
equivalent). This homology will be determined using standard
techniques known in the art, such as the Best Fit sequence program
described by Devereux, et al., Nucl. Acid Res., 12:387-395 (1984),
or the BLASTX program (Altschul, et al., J. Mol. Biol., 215:403-410
(1990)) preferably using the default settings for either. The
alignment may include the introduction of gaps in the sequences to
be aligned. In addition, for sequences which contain either more or
fewer amino acids than an optimum sequence, it is understood that
the percentage of homology will be determined based on the number
of homologous amino acids in relation to the total number of amino
acids. Thus, for example, homology of sequences shorter than an
optimum will be determined using the number of amino acids in the
shorter sequence.
[0164] Once optimized protein sequences are identified, the
processing of FIG. 2 optionally proceeds to step 56 which entails
searching the protein sequences. This processing may be implemented
with the search module 36. The search module 36 is a set of
computer code that executes a search strategy. For example, the
search module 36 may be written to execute a Monte Carlo search as
described above. Starting with the global solution, random
positions are changed to other rotamers allowed at the particular
position, both rotamers from the same amino acid and rotamers from
different amino acids. A new sequence energy (E.sub.total sequence)
is calculated, and if the new sequence energy meets the Boltzmann
criteria for acceptance, it is used as the starting point for
another jump. See Metropolis et al., 1953, supra, hereby
incorporated by reference. If the Boltzmann test fails, another
random jump is attempted from the previous sequence. A list of the
sequences and their energies is maintained during the search. After
a predetermined number of jumps, the best scoring sequences may be
output as a rank-ordered list. Preferably, at least about 10.sup.6
jumps are made, with at least about 10.sup.7 jumps being preferred
and at least about 10.sup.8 jumps being particularly preferred.
[0165] Preferably, at least about 100 to 1000 sequences are saved,
with at least about 10,000 sequences being preferred and at least
about 100,000 to 1,000,000 sequences being especially preferred.
During the search, the temperature is preferably set to 1000 K.
[0166] Once the Monte Carlo search is over, all of the saved
sequences are quenched by changing the temperature to 0 K, and
fixing the amino acid identity at each position. Preferably, every
possible rotamer jump for that particular amino acid at every
position is then tried.
[0167] The computational processing results in a set of optimized
protein sequences. These optimized protein sequences are generally,
but not always, significantly different from the wild-type sequence
from which the backbone was taken. That is, each optimized protein
sequence preferably comprises at least about 5-10% variant amino
acids from the starting or wild-type sequence, with at least about
15-20% changes being preferred and at least about 30% changes being
particularly preferred.
[0168] These sequences can be used in a number of ways. In a
preferred embodiment, one, some or all of the optimized protein
sequences are constructed into designed proteins, as show with step
58 of FIG. 2. Thereafter, the protein sequences can be tested, as
shown with step 60 of the FIG. 2. Generally, this can be done in
one of two ways.
[0169] In a preferred embodiment, the designed proteins are
chemically synthesized as is known in the art. This is particularly
useful when the designed proteins are short, preferably less than
150 amino acids in length, with less than 100 amino acids being
preferred, and less than 50 amino acids being particularly
preferred, although as is known in the art, longer proteins can be
made chemically or enzymatically.
[0170] In a preferred embodiment, particularly for longer proteins
or proteins for which large samples are desired, the optimized
sequence is used to create a nucleic acid such as DNA which encodes
the optimized sequence and which can then be cloned into a host
cell and expressed. Thus, nucleic acids, and particularly DNA, can
be made which encodes each optimized protein sequence. This is done
using well known procedures. The choice of codons, suitable
expression vectors and suitable host cells will vary depending on a
number of factors, and can be easily optimized as needed.
[0171] Once made, the designed proteins are experimentally
evaluated and tested for structure, function and stability, as
required. This will be done as is known in the art, and will depend
in part on the original protein from which the protein backbone
structure was taken. Preferably, the designed proteins are more
stable than the known protein that was used as the starting point,
although in some cases, if some constaints are placed on the
methods, the designed protein may be less stable. Thus, for
example, it is possible to fix certain residues for altered
biological activity and find the most stable sequence, but it may
still be less stable than the wild type protein. Stable in this
context means that the new protein retains either biological
activity or conformation past the point at which the parent
molecule did. Stability includes, but is not limited to, thermal
stability, i.e. an increase in the temperature at which reversible
or irreversible denaturing starts to occur; proteolytic stability,
i.e. a decrease in the amount of protein which is irreversibly
cleaved in the presence of a particular protease (including
autolysis); stability to alterations in pH or oxidative conditions;
chelator stability; stability to metal ions; stability to solvents
such as organic solvents, surfactants, formulation chemicals;
etc.
[0172] In a preferred embodiment, the modelled proteins are at
least about 5% more stable than the original protein, with at least
about 10% being preferred and at least about 20-50% being
especially preferred.
[0173] The results of the testing operations may be computationally
assessed, as shown with step 62 of FIG. 2. An assessment module 38
may be used in this operation. That is, computer code may be
prepared to analyze the test data with respect to any number of
metrices.
[0174] At this processing juncture, if the protein is selected (the
yes branch at block 64) then the protein is utilized (step 66), as
discussed below. If a protein is not selected, the accumulated
information may be used to alter the ranking module 34, and/or step
56 is repeated and more sequences are searched.
[0175] In a preferred embodiment, the experimental results are used
for design feedback and design optimization.
[0176] Once made, the proteins of the invention find use in a wide
variety of applications, as will be appreciated by those in the
art, ranging from industrial to pharmacological uses, depending on
the protein. Thus, for example, proteins and enzymes exhibiting
increased thermal stability may be used in industrial processes
that are frequently run at elevated temperatures, for example
carbohydrate processing (including saccharification and
liquifaction of starch to produce high fructose corn syrup and
other sweetners), protein processing (for example the use of
proteases in laundry detergents, food processing, feed stock
processing, baking, etc.), etc. Similarly, the methods of the
present invention allow the generation of useful pharmaceutical
proteins, such as analogs of known proteinaceous drugs which are
more thermostable, less proteolytically sensitive, or contain other
desirable changes.
[0177] The following examples serve to more fully describe the
manner of using the above-described invention, as well as to set
forth the best modes contemplated for carrying out various aspects
of the invention. It is understood that these examples in no way
serve to limit the true scope of this invention, but rather are
presented for illustrative purposes. All references cited herein
are explicitly incorporated by reference in their entirety.
EXAMPLES
Example 1
Protein Design Using van der Waals and Atomic Solvation Scoring
Functions with DEE
[0178] A cyclical design strategy was developed that couples
theory, computation and experimental testing in order to address
the problems of specificity and learning (FIG. 4). Our protein
design automation (PDA) cycle is comprised of four components: a
design paradigm, a simulation module, experimental testing and data
analysis. The design paradigm is based on the concept of inverse
folding (Pabo, Nature 301:200 (1983); Bowie, et al., Science
253:164-170 (1991)) and consists of the use of a fixed backbone
onto which a sequence of side-chain rotamers can be placed, where
rotamers are the allowed conformations of amino acid side chains
(Ponder, et al., (1987) (supra)). Specific tertiary interactions
based on the three dimensional juxtaposition of atoms are used to
determine the sequences that will potentially best adopt the target
fold. Given a backbone geometry and the possible rotamers allowed
for each residue position as input, the simulation must generate as
output a rank ordered list of solutions based on a cost function
that explicitly considers the atom positions in the various
rotamers. The principle obstacle is that a fixed backbone comprised
of n residues and m possible rotamers per residue (all rotamers of
all allowed amino acids) results in m.sup.n possible arrangements
of the system, an immense number for even small design problems.
For example, to consider 50 rotamers at 15 positions results in
over 10.sup.25 sequences, which at an evaluation rate of 10.sup.9
sequences per second (far beyond current capabilities) would take
10.sup.9 years to exhaustively search for the global minimum. The
synthesis and characterization of a subset of amino acid sequences
presented by the simulation module generates experimental data for
the analysis module. The analysis section discovers correlations
between calculable properties of the simulated structures and the
experimental observables. The goal of the analysis is to suggest
quantitative modifications to the simulation and in some cases to
the guiding design paradigm. In other words, the cost function used
in the simulation module describes a theoretical potential energy
surface whose horizontal axis comprises all possible solutions to
the problem at hand. This potential energy surface is not
guaranteed to match the actual potential energy surface which is
determined from the experimental data. In this light, the goal of
the analysis becomes the correction of the simulation cost function
in order to create better agreement between the theoretical and
actual potential energy surfaces. If such corrections can be found,
then the output of subsequent simulations will be amino acid
sequences that better achieve the target properties. This design
cycle is generally applicable to any protein system and, by
removing the subjective human component, allows a largely unbiased
approach to protein design, i.e. protein design automation.
[0179] The PDA side-chain selection algorithm requires as input a
backbone structure defining the desired fold. The task of designing
a sequence that takes this fold can be viewed as finding an optimal
arrangement of amino acid side chains relative to the given
backbone. It is not sufficient to consider only the identity of an
amino acid when evaluating sequences. In order to correctly account
for the geometric specificity of side-chain placement, all possible
conformations of each side chain must also be examined. Statistical
surveys of the protein structure database (Ponder, et al., supra)
have defined a discrete set of allowed conformations, called
rotamers, for each amino acid side chain. We use a rotamer library
based on the Ponder and Richards library to define allowed
conformations for the side chains in PDA.
[0180] Using a rotamer description of side chains, an optimal
sequence for a backbone can be found by screening all possible
sequences of rotamers, where each backbone position can be occupied
by each amino acid in all its possible rotameric states. The
discrete nature of rotamer sets allows a simple calculation of the
number of rotamer sequences to be tested. A backbone of length n
with m possible rotamers per position will have m.sup.n possible
rotamer sequences. The size of the search space grows exponentially
with sequence length which for typical values of n and m render
intractable an exhaustive search. This combinatorial "explosion" is
the primary obstacle to be overcome in the simulation phase of
PDA.
[0181] Simulation algorithm: An extension of the Dead End
Elimination (DEE) theorem was developed (Desmet, et al.,
(1992((supra); Desmet, et al., (1994) (supra); Goldstein, (1994)
(supra) to solve the combinatorial search problem. The DEE theorem
is the basis for a very fast discrete search algorithm that was
designed to pack protein side chains on a fixed backbone with a
known sequence. Side chains are described by rotamers and an
atomistic forcefield is used to score rotamer arrangements. The DEE
theorem guarantees that if the algorithm converges, the global
optimum packing is found. The DEE method is readily extended to our
inverse folding design paradigm by releasing the constraint that a
position is limited to the rotamers of a single amino acid. This
extension of DEE greatly increases the number of rotamers at each
position and requires a significantly modified implementation to
ensure convergence, described more fully herein. The guarantee that
only the global optimum will be found is still valid, and in our
extension means that the globally optimal sequence is found in its
optimal conformation.
[0182] DEE was implemented with a novel addition to the
improvements suggested by Goldstein (Goldstein, (1994) (supra)). As
has been noted, exhaustive application of the R=1 rotamer
elimination and R=0 rotamer-pair flagging equations and limited
application of the R=1 rotamer-pair flagging equation routinely
fails to find the global solution. This problem can be overcome by
unifying residues into "super residues" (Desmet, et al.,
(1992((supra); Desmet, et al., (1994) (supra); Goldstein, (1994)
(supra). However, unification can cause an unmanageable increase in
the number of super rotamers per super residue position and can
lead to intractably slow performance since the computation time for
applying the R=1 rotamer-pair flagging equation increases as the
fourth power of the number of rotamers. These problems are of
particular importance for protein design applications given the
requirement for large numbers of rotamers per residue position. In
order to limit memory size and to increase performance, we
developed a heuristic that governs which residues (or super
residues) get unified and the number of rotamer (or super rotamer)
pairs that are included in the R=1 rotamer-pair flagging equation.
A program called PDA_DEE was written that takes a list of rotamer
energies from PDA_SETUP and outputs the global minimum sequence in
its optimal conformation with its energy.
[0183] Scoring functions: The rotamer library used was similar to
that used by Desmet and coworkers (Desmet, et al., (1992) (supra)).
.chi..sub.1 and .chi..sub.2 angle values of rotamers for all amino
acids except Met, Arg and Lys were expanded plus and minus one
standard deviation about the mean value from the Ponder and
Richards library (supra) in order to minimize possible errors that
might arise from the discreteness of the library. C.sub.3 and
c.sub.4 angles that were undetermined from the database statistics
were assigned values of 0.degree. and 180.degree. for Gin and
60.degree., -60.degree. and 180.degree. for Met, Lys and Arg. The
number of rotamers per amino acid is: Gly, 1; Ala, 1; Val, 9; Ser,
9; Cys, 9; Thr, 9; Leu, 36; Ile, 45; Phe, 36; Tyr, 36; Trp, 54;
His, 54; Asp, 27; Asn, 54; Glu, 69; Gin, 90; Met, 21; Lys, 57; Arg,
55. The cyclic amino acid Pro was not included in the library.
Further, all rotamers in the library contained explicit hydrogen
atoms. Rotamers were built with bond lengths and angles from the
Dreiding forcefield (Mayo, et al., J. Phys. Chem. 94:8897
(1990)).
[0184] The initial scoring function for sequence arrangements used
in the search was an atomic van der Waals potential. The van der
Waals potential reflects excluded volume and steric packing
interactions which are important determinants of the specific three
dimensional arrangement of protein side chains. A Lennard-Jones
12-6 potential with radii and well depth parameters from the
Dreiding forcefield was used for van der Waals interactions.
Non-bonded interactions for atoms connected by one or two bonds
were not considered. van der Waals radii for atoms connected by
three bonds were scaled by 0.5. Rotamer/rotamer pair energies and
rotamer/template energies were calculated in a manner consistent
with the published DEE algorithm (Desmet, et al., (1992) (supra)).
The template consisted of the protein backbone and the side chains
of residue positions not to be optimized. No intra-side-chain
potentials were calculated. This scheme scored the packing geometry
and eliminated bias from rotamer internal energies. Prior to DEE,
all rotamers with template interaction energies greater than 25
kcal/mol were eliminated. Also, any rotamer whose interaction was
greater than 25 kcal/mol with all other rotamers at another residue
position was eliminated. A program called PDA_SETUP was written
that takes as input backbone coordinates, including side chains for
positions not optimized, a rotamer library, a list of positions to
be optimized and a list of the amino acids to be considered at each
position. PDA_SETUP outputs a list of rotamer/template and
rotamer/rotamer energies.
[0185] The pairwise solvation potential was implemented in two
components to remain consistent with the DEE methodology:
rotamer/template and rotamer/rotamer burial. For the
rotamer/template buried area, the reference state was defined as
the rotamer in question at residue i with the backbone atoms only
of residues i-1, i and i+1. The area of the side chain was
calculated with the backbone atoms excluding solvent but not
counted in the area. The folded state was defined as the area of
the rotamer in question at residue i, but now in the context of the
entire template structure including non-optimized side chains. The
rotamer/template buried area is the difference between the
reference and the folded states. The rotamer/rotamer reference area
is simply the sum of the areas of the isolated rotamers. The folded
state is the area of the two rotamers placed in their relative
positions on the protein scaffold but with no template atoms
present. The Richards definition of solvent accessible surface area
(Lee & Richards, 1971, supra) was used, with a probe radius of
1.4 .ANG. and Drieding van der Waals radii. Carbon and sulfur, and
all attached hydrogens, were considered nonpolar. Nitrogen and
oxygen, and all attached hydrogens, were considered polar. Surface
areas were calculated with the Connolly algorithm using a dot
density of 10 .ANG.-2 (Connolly, (1983) (supra)). In more recent
implementations of PDA_SETUP, the MSEED algorithm of Scheraga has
been used in conjunction with the Connolly algorithm to speed up
the calculation (Perrot, et al., J. Comput. Chem. 13:1-11
(1992)).
[0186] Monte Carlo search: Following DEE optimization, a rank
ordered list of sequences was generated by a Monte Carlo search in
the neighborhood of the DEE solution. This list of sequences was
necessary because of possible differences between the theoretical
and actual potential surfaces. The Monte Carlo search starts at the
global minimum sequence found by DEE. A residue was picked randomly
and changed to a random rotamer selected from those allowed at that
site. A new sequence energy was calculated and, if it met the
Boltzman criteria for acceptance, the new sequence was used as the
starting point for another jump. If the Boltzman test failed, then
another random jump was attempted from the previous sequence. A
list of the best sequences found and their energies was maintained
throughout the search. Typically 106 jumps were made, 100 sequences
saved and the temperature was set to 1000 K. After the search was
over, all of the saved sequences were quenched by changing the
temperature to 0 K, fixing the amino acid identity and trying every
possible rotamer jump at every position. The search was implemented
in a program called PDA_MONTE whose input was a global optimum
solution from PDA_DEE and a list of rotamer energies from
PDA_SETUP. The output was a list of the best sequences rank ordered
by their score. PDA_SETUP, PDA_DEE and PDA_MONTE were implemented
in the CERIUS2 software development environment (Biosym/Molecular
Simulations, San Diego, Calif.).
[0187] PDA_SETUP, PDA_DEE, and PDA_MONTE were implemented in the
CERIUS2 software development environment (Biosym/Molecular
Simulations, San Diego, Calif.).
[0188] Model system and experimental testing: The homodimeric
coiled coil of a helices was selected as the initial design target.
Coiled coils are readily synthesized by solid phase techniques and
their helical secondary structure and dimeric tertiary organization
ease characterization. Their sequences display a seven residue
periodic HP pattern called a heptad repeat,
(a.cndot.b.cndot.c.cndot.d.cndot.e.cndot.f.cndot.g) (Cohen &
Parry, Proteins Struc. Func. Genet. 7:1-15 (1990)). The a and d
positions are usually hydrophobic and buried at the dimer interface
while the other positions are usually polar and solvent exposed
(FIG. 5). The backbone needed for input to the simulation module
was taken from the crystal structure of GCN4-p1 (O'Shea, et al.,
Science 254:539 (1991)). The 16 hydrophobic a and d positions were
optimized in the crystallographically determined fixed field of the
rest of the protein. Homodimer sequence symmetry was enforced, only
rotamers from hydrophobic amino acids (A, V, L, I, M, F, Y and W)
were considered and the asparagine at an a position, Asn 16, was
not optimized.
[0189] Homodimeric coiled coils were modeled on the backbone
coordinates of GCN4-p1, PDB ascension code 2ZTA (Bernstein, et al.,
J. Mol. Biol. 112:535 (1977); O'Shea, et al., supra). Atoms of all
side chains not optimized were left in their crystallographically
determined positions. The program BIOGRAF (Biosym/Molecular
Simulations, San Diego, Calif.) was used to generate explicit
hydrogens on the structure which was then conjugate gradient
minimized for 50 steps using the Dreiding forcefield. The HP
pattern was enforced by only allowing hydrophobic amino acids into
the rotamer groups for the optimized a and d positions. The
hydrophobic group consisted of Ala, Val, Leu, Ile, Met, Phe, Tyr
and Trp for a total of 238 rotamers per position. Homodimer
symmetry was enforced by penalizing by 100 kcal/mol rotamer pairs
that violate sequence symmetry. Different rotamers of the same
amino acid were allowed at symmetry related positions. The
asparagine that occupies the a position at residue 16 was left in
the template and not optimized. A 10.sup.6 step Monte Carlo search
run at a temperature of 1000 K generated the list of candidate
sequences rank ordered by their score. To test reproducibility, the
search was repeated three times with different random number seeds
and all trials provided essentially identical results. The Monte
Carlo searches took about 90 minutes. All calculations in this work
were performed on a Silicon Graphics 200 MHz R4400 processor.
[0190] Optimizing the 16 a and d positions each with 238 possible
hydrophobic rotamers results in 238.sup.16 or 10.sup.38 rotamer
sequences. The DEE algorithm finds the global optimum in three
minutes, including rotamer energy calculation time. The DEE
solution matches the naturally occurring GCN4-p1 sequence of a and
d residues for all of the 16 positions. A one million step Monte
Carlo search run at a temperature of 1000 K generated the list of
sequences rank ordered by their score. To test reproducibility, the
search was repeated three times with different random number seeds
and all trials provided essentially identical results. The second
best sequence is a Val 30 to Ala mutation and lies three kcal/mol
above the ground state sequence. Within the top 15 sequences up to
six mutations from the ground state sequence are tolerated,
indicating that a variety of packing arrangements are available
even for a small coiled coil. Eight sequences with a range of
stabilities were selected for experimental testing, including six
from the top 15 and two more about 15 kcal/mol higher in energy,
the 56th and 70th in the list (Table 1). TABLE-US-00001 TABLE 1
Name Sequence Rank Energy PDA-3H.sup.b
RMKQLEDKVEELLSKNYHLENEVARLKKLVGER (SEQ ID NO:23) 1 -118.1 PDA-3A
RMKQLEDKVEELLSKNYHLENEVARLKKLAGER (SEQ ID NO:24) 2 -115.3 PDA-3G
RMKQLEDKVEELLSKNYHLENEMARLKKLVGER (SEQ ID NO:25) 5 -112.8 PDA-3B
RLKQMEDKVEELLSKNYHLENEVARLKKLVGER (SEQ ID NO:26) 6 -112.6 PDA-3D
RLKQMEDKVEELLSKNYHLENEVARLKKLAGER (SEQ ID NO:27) 13 -109.7 PDA-3C
RMKQWEDKAEELLSKNYHLENEVARLKKLVGER (SEQ ID NO:28) 14 -109.6 PDA-3F
RMKQFEDKVEELLSKNYHLENEVARLKKLVGER (SEQ ID NO:29) 56 -103.9 PDA-3E
RMKQLEDKVEELLSKNYHAENEVARLKKLVGER (SEQ ID NO:30) 70 -103.1
[0191] Thirty-three residue peptides were synthesized on an Applied
Biosystems Model 433A peptide synthesizer using Fmoc chemistry,
HBTU activation and a modified Rink amide resin from Novabiochem.
Standard 0.1 mmol coupling cycles were used and amino termini were
acetylated. Peptides were cleaved from the resin by treating
approximately 200 mg of resin with 2 mL trifluoroacetic acid (TFA)
and 100 .mu.L water, 100 .mu.L thioanisole, 50 .mu.L ethanedithiol
and 150 mg phenol as scavengers. The peptides were isolated and
purified by precipitation and repeated washing with cold methyl
tert-butyl ether followed by reverse phase HPLC on a Vydac C8
column (25 cm by 22 mm) with a linear acetonitrile-water gradient
containing 0.1% TFA. Peptides were then lyophilized and stored at
-20.degree. C. until use. Plasma desorption mass spectrometry found
all molecular weights to be within one unit of the expected
masses.
[0192] Circular dichroism CD spectra were measured on an Aviv 62DS
spectrometer at pH 7.0 in 50 mM phosphate, 150 mM NaCl and 40 .mu.M
peptide. A 1 mm pathlength cell was used and the temperature was
controlled by a thermoelectric unit. Thermal melts were performed
in the same buffer using two degree temperature increments with an
averaging time of 10 s and an equilibration time of 90 s. T.sub.m
values were derived from the ellipticity at 222 nm
([.theta.].sub.222) by evaluating the minimum of the
d[.theta.].sub.222/dT.sup.1 versus T plot (Cantor & Schimmel,
Biophysical Chemistry. New York: W. H. Freemant and Company, 1980).
The T.sub.m's were reproducible to within one degree. Peptide
concentrations were determined from the tyrosine absorbance at 275
nm (Huyghues-Despointes, et al., supra).
[0193] Size exclusion chromatography: Size exclusion chromatography
was performed with a Synchropak GPC 100 column (25 cm by 4.6 mm) at
pH 7.0 in 50 mM phosphate and 150 mM NaCl at 0.degree. C. GCN4-p1
and p-LI (Harbury, et al., Science 262:1401 (1993)) were used as
size standards. 10 .mu.l injections of 1 mM peptide solution were
chromatographed at 0.20 ml/min and monitored at 275 nm. Peptide
concentrations were approximately 60 .mu.M as estimated from peak
heights. Samples were run in triplicate.
[0194] The designed a and d sequences were synthesized as above
using the GCN4-p1 sequence for the b.cndot.c and e.cndot.f.cndot.g
positions. Standard solid phase techniques were used and following
HPLC purification, the identities of the peptides were confirmed by
mass spectrometry. Circular dichroism spectroscopy (CD) was used to
assay the secondary structure and thermal stability of the designed
peptides. The CD spectra of all the peptides at 1.degree. C. and a
concentration of 40 mM exhibit minima at 208 and 222 nm and a
maximum at 195 nm, which are diagnostic for a helices (data not
shown). The ellipticity values at 222 nm indicate that all of the
peptides are >85% helical (approximately -28000 deg
cm.sup.2/dmol), with the exception of PDA-3C which is 75% helical
at 40 mM but increases to 90% helical at 170 mM (Table 2).
TABLE-US-00002 TABLE 2 CD data and calculated structural properties
of the PDA peptides. E.sub.MC E.sub.CQ E.sub.CG E.sub.vdW
-[.theta.].sub.222 (deg T.sub.m (kcal/ .DELTA.A.sub.np
.DELTA.A.sub.p Vol Rot (kcal/ (kcal/ (kcal/ Name cm.sup.2/dmol)
(.degree. C.) mol) (.ANG..sup.2) (.ANG..sup.2) (.ANG..sup.3) bonds
mol) mol) mol) Npb Pb PDA-3H 33000 57 -118.1 2967 2341 1830 28 -234
-308 409 207 128 PDA-3A 30300 48 -115.3 2910 2361 1725 26 -232 -312
400 203 128 PDA-3B 28200 47 -112.6 2977 2372 1830 28 -242 -306 379
210 127 PDA-3G 30700 47 -112.8 3003 2383 1878 32 -240 -309 439 212
128 PDA-3F 28800 39 -103.9 3000 2336 1872 28 -188 -302 420 212 128
PDA-3D 27800 39 -109.7 2920 2392 1725 26 -240 -310 370 206 127
PDA-3C 24100 26 -109.6 2878 2400 1843 26 -149 -304 398 215 129
PDA-3E 27500 24 -103.1 2882 2361 1674 24 -179 -309 411 203 127
*E.sub.MC is the Monte Carlo energy; .DELTA.A.sub.np and
.DELTA.A.sub.p are the changes in solvent accessible non-polar and
polar surface areas upon folding, respectively; E.sub.CQ is the
electrostatic energy using equilibrated charges; E.sub.CG is the
electrostatic energy using Gasteiger charges; E.sub.vdW is the van
der Waals energy; Vol is the side chain van der Waals volume; Rot
bonds is the number of side chain rotatable bonds (excluding methyl
rotors); Npb and Pb are the number of buried non-polar and polar
atoms, respectively.
[0195] The melting temperatures (T.sub.m's) show a broad range of
values (data not shown), with 6 of the 8 peptides melting at
greater than physiological temperature. Also, the T.sub.m's were
not correlated to the number of sequence differences from GCN4-p1.
Single amino acid changes resulted in some of the most and least
stable peptides, demonstrating the importance of specificity in
sequence selection.
[0196] Size exclusion chromatography confirmed the dimeric nature
of these designed peptides. Using coiled coil peptides of known
oligomerization state as standards, the PDA peptides migrated as
dimers. This result is consistent with the appearance of 8-branched
residues at a positions and leucines at d positions, which have
been shown previously to favor dimerization over other possible
oligomerization states (Harbury, et al., supra).
[0197] The characterization of the PDA peptides demonstrates the
successful design of several stable dimeric helical coiled coils.
The sequences were automatically generated in the context of the
design paradigm by the simulation module using well-defined inputs
that explicitly consider the HP patterning and steric specificity
of protein structure. Two dimensional nuclear magnetic resonance
experiments aimed at probing the specificity of the tertiary
packing are the focus of further studies on these peptides. Initial
experiments show significant protection of amide protons from
chemical exchange and chemical shift dispersion comparable to
GCN4-p1 (unpublished results) (Oas, et al., Biochemistry 29:2891
(1990)); Goodman & Kim, Biochem. 30:11615 (1991)).
[0198] Data analysis and design feedback A detailed analysis of the
correspondence between the theoretical and experimental potential
surfaces, and hence an estimate of the accuracy of the simulation
cost function, was enabled by the collection of experimental data.
Using thermal stability as a measure of design performance, melting
temperatures of the PDA peptides were plotted against the sequence
scores found in the Monte Carlo search (FIG. 6). The modest
correlation, 0.67, in the plot shows that while an exclusively van
der Waals scoring function can screen for stable sequences, it does
not accurately predict relative stabilities. In order to address
this issue, correlations between calculated structural properties
and T.sub.m's were systematically examined using quantitative
structure activity relationships (QSAR), which is a statistical
technique commonly used in structure based drug design (Hopfinger,
J. Med. Chem. 28:1133 (1985)).
[0199] Table 2 lists various molecular properties of the PDA
peptides in addition to the van der Waals based Monte Carlo scores
and the experimentally determined T.sub.m's. A wide range of
properties was examined, including molecular mechanics components,
such as electrostatic energies, and geometric measures, such as
volume. The goal of QSAR is the generation of equations that
closely approximate the experimental quantity, in this case
T.sub.m, as a function of the calculated properties. Such equations
suggest which properties can be used in an improved cost function.
The PDA analysis module employs genetic function approximation
(GFA) (Rogers & Hopfinger, J. Chem. Inf. Comput. Scie. 34:854
(1994)), a novel method to optimize QSAR equations that selects
which properties are to be included and the relative weightings of
the properties using a genetic algorithm. GFA accomplishes an
efficient search of the space of possible equations and robustly
generates a list of equations ranked by their correlation to the
data.
[0200] Equations are scored by lack of fit (LOF), a weighted least
square error measure that resists overfitting by penalizing
equations with more terms (Rogers & Hopfinger, supra). GFA
optimizes both the length and the composition of the equations and,
by generating a set of QSAR equations, clarifies combinations of
properties that fit well and properties that recur in many
equations. All of the top five equations that correct the
simulation energy (E.sub.MC) contain burial of nonpolar surface
area, .DELTA.A.sub.np (Table 3). TABLE-US-00003 TABLE 3 Top five
QSAR equations generated by GFA with LOF, correlation coefficient
and cross validation scores. QSAR equation LOF r.sup.2 CV r.sup.2
-1.44*E.sub.MC + 0.14*.DELTA.A.sub.np - 0.73*Npb 16.23 .98 .78
-1.78*E.sub.MC + 0.20*.DELTA.A.sub.np - 2.43*Rot 23.13 .97 .75
-1.59*E.sub.MC + 0.17*.DELTA.A.sub.np - 0.05*Vol 24.57 .97 .36
-1.54*E.sub.MC + 0.11*.DELTA.A.sub.np 25.45 .91 .80 -1.60*E.sub.MC
+ 0.09*.DELTA.A.sub.np - 0.12*.DELTA.A.sub.p 33.88 .96 .90
.DELTA.A.sub.np and .DELTA.A.sub.p are nonpolar and polar surface
buried upon folding, respectively. Vol is side chain volume, Npb is
the number of buried nonpolar atoms and Rot is the number of buried
rotatable bonds.
[0201] The presence of .DELTA.A.sub.np in all of the top equations,
in addition to the low LOF of the QSAR containing only E.sub.MC and
.DELTA.A.sub.np, strongly implicates nonpolar surface burial as a
critical property for predicting peptide stability. This conclusion
is not surprising given the role of the hydrophobic effect in
protein energetics (Dill, Biochem. 29:7133 (1990)).
[0202] Properties were calculated using BIOGRAF and the Dreiding
forcefield. Solvent accessible surface areas were calculated with
the Connolly algorithm (Connolly, (1983) (supra)) using a probe
radius of 1.4 .ANG. and a dot density of 10 .ANG.-2. Volumes were
calculated as the sum of the van der Waals volumes of the side
chains that were optimized. The number of buried polar and nonpolar
heavy atoms were defined as atoms, with their attached hydrogens,
that expose less than 5 .ANG..sup.2 in the surface area
calculation. Electrostatic energies were calculated using a
dielectric of one and no cutoff was set for calculation of
non-bonded energies. Charge equilibration charges (Rappe &
Goddard ill, J. Phys. Chem. 95:3358 (1991) and Gasteiger (Gasteiger
& Marsili, Tetrahedron 36:3219 (1980) charges were used to
generate electrostatic energies. Charge equilibration charges were
manually adjusted to provide neutral backbones and neutral side
chains in order to prevent spurious monopole effects. The selection
of properties was limited by the requirement that properties could
not be highly correlated. Correlated properties cannot be
differentiated by QSAR techniques and only create redundancy in the
derived relations.
[0203] Genetic function approximation (GFA) was performed in the
CERIUS2 simulation package version 1.6 (Biosym/Molecular
Simulations, San Diego, Calif.). An initial population of 300
equations was generated consisting of random combinations of three
properties. Only linear terms were used and initial coefficients
were determined by least squares regression for each set of
properties. Redundant equations were eliminated and 10000
generations of random crossover mutations were performed. If a
child had a better score than the worst equation in the population,
the child replaced the worst equation. Also, mutation operators
that add or remove terms had a 50% probability of being applied
each generation, but these mutations were only accepted if the
score was improved. No equation with greater than three terms was
allowed. Equations were scored during evolution using the lack of
fit (LOF) parameter, a scaled least square error (LSE) measure that
penalizes equations with more terms and hence resists overfitting.
LOF is defined as: LOF = LSE ( 1 - 2 .times. C M ) 2 ' ##EQU10##
where c is the number of terms in the equation and M is the number
of data points. Five different randomized runs were done and the
final equation populations were pooled. Only equations containing
the simulation energy, E.sub.MC, were considered which resulted in
108 equations ranked by their LOF.
[0204] To assess the predictive power of these QSAR equations, as
well as their robustness, cross validation analysis was carried
out. Each peptide was sequentially removed from the data set and
the coefficients of the equation in question were refit. This new
equation was then used to predict the withheld data point. When all
of the data points had been predicted in this manner, their
correlation to the measured T.sub.m's was computed (Table 3). Only
the E.sub.MC/.DELTA.A.sub.np QSAR and the
E.sub.MC/.DELTA.A.sub.np/.DELTA.A.sub.p QSAR performed well in
cross validation. The E.sub.MC/.DELTA.A.sub.np equation could not
be expected to fit the data as smoothly as QSAR's with three terms
and hence had a lower cross validated r.sup.2. However, all other
two term QSAR's had LOF scores greater than 48 and cross validation
correlations less than 0.55 (data not shown). The QSAR analysis
independently predicted with no subjective bias that consideration
of nonpolar and polar surface area burial is necessary to improve
the simulation. This result is consistent with previous studies on
atomic solvation potentials (Eisenberg, et al., (1986) (supra);
Wesson, et al., Protein Sci. 1:227 (1992)). Further, simpler
structural measures, such as number of buried atoms, that reflect
underlying principles such as hydrophobic solvation (Chan, et al.,
Science 267:1463 (1995)) were not deemed as significant by the QSAR
analysis. These results justify the cost of calculating actual
surface areas, though in some studies simpler potentials have been
shown to perform well (van Gunsteren, et al. J. Mol. Biol. 227:389
(1992)).
[0205] .DELTA.a.sub.np and .DELTA.A.sub.p were introduced into the
simulation module to correct the cost function. Contributions to
surface burial from rotamer/template and rotamer/rotamer contacts
were calculated and used in the interaction potential.
Independently counting buried surface from different rotamer pairs,
which is necessary in DEE, leads to overestimation of burial
because the radii of solvent accessible surfaces are much larger
than the van der Waals contact radii and hence can overlap greatly
in a close packed protein core. To account for this discrepancy,
the areas used in the QSAR were recalculated using the pairwise
area method and a new E.sub.MC/.DELTA.A.sub.np/.DELTA.A.sub.p QSAR
equation was generated. The ratios of the E.sub.MC coefficient to
the .DELTA.A.sub.np and .DELTA.A.sub.p coefficients are scale
factors that are used in the simulation module to convert buried
surface area into energy, i.e. atomic solvation parameters. Thermal
stabilities are predicted well by this cost function (FIG. 6B). In
addition, the improved cost function still predicts the naturally
occurring GCN4-p1 sequence as the ground state. The surface area to
energy scale factors, 16 cal/mol/.ANG..sup.2 favoring nonpolar area
burial and 86 cal/mol/.ANG..sup.2 opposing polar area burial, are
similar in sign, scale and relative magnitude to solvation
potential parameters derived from small molecule transfer data
(Wesson & Eisenberg, supra).
[0206] .lamda. repressor mutants: To demonstrate the generality of
the cost function, other proteins were examined using the
simulation module. A library of core mutants of the DNA binding
protein .lamda. repressor has been extensively characterized by
Sauer and coworkers (Lim & Sauer, J. Mol. Biol. 219:359
(1991)). Template coordinates were taken from PDB file 1LMB (Beamer
& Pabo, J. Mol. Biol. 227:177 (1992)). The subunit designated
chain 4 in the PDB file was removed from the context of the rest of
the structure (accompanying subunit and DNA) and using BIOGRAF
explicit hydrogens were added. The hydrophobic residues with side
chains within 5 .ANG. of the three mutation sites (V36 M40 V47) are
Y22, L31, A37, M42, L50, F51, L64, L65, I68 and L69. All of these
residues are greater than 80% buried except for M42 which is 65%
buried and L64 which is 45% buried. A37 only has one possible
rotamer and hence was not optimized. The other nine residues in the
5 .ANG. sphere were allowed to take any rotamer conformation of
their amino acid ("floated"). The mutation sites were allowed any
rotamer of the amino acid sequence in question. Depending on the
mutant sequence, 5.times.10.sup.16 to 7.times.10.sup.18
conformations were possible. Rotamer energy and DEE calculation
times were 2 to 4 minutes. The combined activity score is that of
Hellinga and Richards (Hellinga, et al., (1994) (supra)).
Seventy-eight of the 125 possible combinations were generated.
Also, this dataset has been used to test several computational
schemes and can serve as a basis for comparing different
forcefields (Lee & Levitt, Nature 352:448 (1991); van Gunsteren
& Mark, supra; Hellinga, et al., (1994) (supra)). The
simulation module, using the cost function found by QSAR, was used
to find the optimal conformation and energy for each mutant
sequence. All hydrophobic residues within 5 .ANG. of the three
mutation sites were also left free to be relaxed by the algorithm.
This 5 .ANG. sphere contained 12 residues, a significantly larger
problem than previous efforts (Lee & Levitt, supra; Hellinga,
(1994) (supra)), that were rapidly optimized by the DEE component
of the simulation module. The rank correlation of the predicted
energy to the combined activity score proposed by Hellinga and
Richards is shown in FIG. 7. The wildtype has the lowest energy of
the 125 possible sequences and the correlation is essentially
equivalent to previously published results which demonstrates that
the QSAR corrected cost function is not specific for coiled coils
and can model other proteins adequately.
Example 2
Automated Design of the Surface Positions of Protein Helices
[0207] GCN4-p1, a homodimeric coiled coil, was again selected as
the model system because it can be readily synthesized by solid
phase techniques and its helical secondary structure and dimeric
tertiary organization ease characterization. The sequences of
homodimeric coiled coils display a seven residue periodic
hydrophobic and polar pattern called a heptad repeat,
(a.cndot.b.cndot.c.cndot.d.cndot.e.cndot.f.cndot.g) (Cohen &
Parry, supra). The a and d positions are buried at the dimer
interface and are usually hydrophobic, whereas the b, c, e, f, and
g positions are solvent exposed and usually polar (FIG. 5).
Examination of the crystal structure of GCN4-p1 (O'Shea, et al.,
supra) shows that the b, c, and f side chains extend into solvent
and expose at least 55% of their surface area. In contrast, the e
and g residues bury from 50 to 90% of their surface area by packing
against the a and d residues of the opposing helix. We selected the
12 b, c, and f residue positions for surface sequence design:
positions 3, 4, 7, 10, 11, 14, 17, 18, 21, 24, 25, and 28 using the
numbering from PDB entry 2zta (Bernstein, et al., J. Mol. Biol.
112:535 (1977)). The remainder of the protein structure, including
all other side chains and the backbone, was used as the template
for sequence selection calculations. The symmetry of the dimer and
lack of interactions of surface residues between the subunits
allowed independent design of each subunit, thereby significantly
reducing the size of the sequence optimization problem.
[0208] All possible sequences of hydrophilic amino acids (D, E, N,
Q, K, R, S, T, A, and H) for the 12 surface positions were screened
by our design algorithm. The torsional flexibility of the amino
acid side chains was accounted for by considering a discrete set of
all allowed conformers of each side chain, called rotamers (Ponder,
et al., (1987((supra); Dunbrack, et al., Struc. Biol. Vol.
1(5):334-340 (1994)). Optimizing the 12 b, c, and f positions each
with 10 possible amino acids results in 1012 possible sequences
which corresponds to .about.10.sup.28 rotamer sequences when using
the Dunbrack and Karplus backbone-dependent rotamer library. The
immense search problem presented by rotamer sequence optimization
is overcome by application of the Dead-End Elimination (DEE)
theorem (Desmet, et al., (1992((supra); Desmet, et al., (1994)
(supra); Goldstein, (1994) (supra)). Our implementation of the DEE
theorem extends its utility to sequence design and rapidly finds
the globally optimal sequence in its optimal conformation.
[0209] We examined three potential-energy functions for their
effectiveness in scoring surface sequences. Each candidate scoring
function was used to design the b, c, and f positions of the model
coiled coil and the resulting peptide was synthesized and
characterized to assess design performance. A hydrogen-bond
potential was used to check if predicted hydrogen bonds can
contribute to designed protein stability, as expected from studies
of hydrogen bonding in proteins and peptides (Stickle, et al.,
supra; Huyghues-Despointes, et al., supra). Optimizing sequences
for hydrogen bonding, however, often buries polar protons that are
not involved in hydrogen bonds. This uncompensated loss of
potential hydrogen-bond donors to water prompted examination of a
second scoring scheme consisting of a hydrogen-bond potential in
conjunction with a penalty for burial of polar protons (Eisenberg,
(1986) (supra)). We tested a third scoring scheme which augments
the hydrogen bond potential with the empirically derived helix
propensities of Baldwin and coworkers (Chakrabartty, et al.,
supra). Although the physical basis of helix propensities is
unclear, they can have a significant effect on protein stability
and can potentially be used to improve protein designs (O'Neil
& DeGrado, 1990; Zhang, et al., Biochem. 30:2012 (1991);
Blaber, etaaL, Science 260:1637 (1993); O'shea, et al., 1993;
Villegas, et al., Folding and Design 1:29 (1996)). A van der Waals
potential was used in all cases to account for packing interactions
and excluded volume.
[0210] Several other sequences for the b, c and f positions were
also synthesized and characterized to help discern the relative
importance of the hydrogen-bonding and helix-propensity potentials.
The sequence designed with the hydrogen-bond potential was randomly
scrambled, thereby disrupting the designed interactions but not
changing the helix propensity of the sequence. Also, the sequence
with the maximum possible helix propensity, all positions set to
alanine, was made. Finally, to serve as undesigned controls, the
naturally occurring GCN4-p1 sequence and a sequence randomly
selected from the hydrophilic amino acid set were synthesized and
studied.
[0211] Sequence design: Scoring functions and DEE: The protein
structure was modeled on the backbone coordinates of GCN4-p1, PDB
record 2zta (Bernstein, et al., supra; O'Shea, et al., supra).
Atoms of all side chains not optimized were left in their
crystallographically determined positions. The program BIOGRAF
(Molecular Simulations Incorporated, San Diego, Calif.) was used to
generate explicit hydrogens on the structure which was then
conjugate gradient minimized for 50 steps using the DREIDING
forcefield (Mayo, et al., 1990, supra). The symmetry of the dimer
and lack of interactions of surface residues between the subunits
allowed independent design of each subunit. All computations were
done using the first monomer to appear in 2zta (chain A). A
backbone-dependent rotamer library was used (Dunbrack, et al.
(1993) (supra)). C.sub.3 angles that were undetermined from the
database statistics were assigned the following values: Arg,
-60.degree., 60.degree., and 180.degree.; Gln, -120.degree.,
-60.degree., 0.degree., 60.degree., 120.degree., and 180.degree.;
Glu, 0.degree., 60.degree., and 120.degree.; Lys, -60.degree.,
60.degree., and 180.degree.. c.sub.4 angles that were undetermined
from the database statistics were assigned the following values:
Arg, -120.degree., -60.degree., 60.degree., 120.degree., and
180.degree.; Lys, -60.degree., 60.degree., and 180.degree..
Rotamers with combinations of c.sub.3 and c.sub.4 that resulted in
sequential g.sup.+/g.sup.- or g.sup.-/g.sup.+ angles were
eliminated. Uncharged His rotamers were used. A Lennard-Jones 12-6
potential with van der Waals radii scaled by 0.9 (Dahiyat, et al.,
First fully automatic design of a protein achieved by Caltech
scientists, new press release (1997) was used for van der Waals
interactions. The hydrogen bond potential consisted of a
distance-dependent term and an angle-dependent term, as depicted in
Equation 9, above. This hydrogen bond potential is based on the
potential used in DREIDING, with more restrictive angle-dependent
terms to limit the occurrence of unfavorable hydrogen bond
geometries. The angle term varies depending on the hybridization
state of the donor and acceptor, as shown in Equations 10 to 13,
above.
[0212] In Equations 10-13, .theta. is the donor-hydrogen-acceptor
angle, .phi. is the hydrogen-acceptor-base angle (the base is the
atom attached to the acceptor, for example the carbonyl carbon is
the base for a carbonyl oxygen acceptor), and .phi. is the angle
between the normals of the planes defined by the six atoms attached
to the sp.sup.2 centers (the supplement of .phi. is used when .phi.
is less than 90.degree.). The hydrogen-bond function is only
evaluated when 2.6 .ANG.<R<3.2 .ANG., .phi.>90.degree.,
f-109.5.degree.<90.degree. for the sp.sup.3 donor--sp.sup.3
acceptor case, and, .phi.>90.degree. for the sp.sup.3
donor--sp.sup.2 acceptor case; no switching functions were used.
Template donors and acceptors that were involved in
template-template hydrogen bonds were not included in the donor and
acceptor lists. For the purpose of exclusion, a template-template
hydrogen bond was considered to exist when 2.5
.ANG..gtoreq.R.gtoreq.3.3 .ANG. and .theta.>135.degree.. A
penalty of 2 kcal/mol for polar hydrogen burial, when used, was
only applied to buried polar hydrogens not involved in hydrogen
bonds, where a hydrogen bond was considered to exist when E.sub.HB
was less than -2 kcal/mol. This penalty was not applied to template
hydrogens. The hydrogen-bond potential was also supplemented with a
weak coulombic term that included a distance-dependent dielectric
constant of 40R, where R is the interatomic distance. Partial
atomic charges were only applied to polar functional groups. A net
formal charge of +1 was used for Arg and Lys and a net formal
charge of -1 was used for Asp and Glu. Energies associated with
.alpha.-helical propensities were calculated using equation 14,
above. In Equation 14, E.sub..alpha. is the energy of
.alpha.-helical propensity, .DELTA.G.degree..sub.aa is the standard
free energy of helix propagation of the amino acid, and
.DELTA.G.degree..sub.ala is the standard free energy of helix
propagation of alanine used as a standard, and N.sub.ss is the
propensity scale factor which was set to 3.0. This potential was
selected in order to scale the propensity energies to a similar
range as the other terms in the scoring function. The DEE
optimization followed the methods of our previous work (Dahiyat, et
al., (1996) (supra)). Calculations were performed on either a 12
processor, R10000-based Silicon Graphics Power Challenge or a 512
node Intel Delta.
[0213] Peptide synthesis and purification and CD analysis was as in
Example 1. NMR samples were prepared in 90/10H.sub.2O/D.sub.2O and
50 mM sodium phosphate buffer at pH 7.0. Spectra were acquired on a
Varian Unityplus 600 MHz spectrometer at 25.degree. C. 32
transients were acquired with 1.5 seconds of solvent presaturation
used for water suppression. Samples were .about.1 mM. Size
exclusion chromatography was performed with a PolyLC hydroxyethyl A
column (20 cm.times.9 mm) at pH 7.0 in 50 mM phosphate and 150 mM
NaCl at 0.degree. C. GCN4-p1 and p-LI (Harbury, et al., supra) were
used as size standards for dimer and tetramer, respectively. 5
.mu.l injections of -1 mM peptide solution were chromatographed at
0.50 ml/min and monitored at 214 nm. Samples were run in
triplicate.
[0214] The surface sequences of all of the peptides examined in
this study are shown in Table 4. TABLE-US-00004 TABLE 4 Sequences
and properties of the synthesized peptides Surface Sequence
.SIGMA..DELTA.G.degree. N Peptide Design method bcf bcf bcf bcf
T.sub.m (.degree. C.) (kcal/mol) GCN4-p1 none KQD EES YHN ARK (SEQ
ID NO:31) 57 3.831 2 6A HB EKD RER RRE RRE (SEQ ID NO:32) 71 2.193
2 6B HB + PB EKQ KER ERE ERQ (SEQ ID NO:33) 72 2.868 2 6C HB + HP
ARA AAA RRR ARA (SEQ ID NO:34) 69 -2.041 2 6D scrambled HB REE RRR
EDR KRE (SEQ ID NO:35) 71 2.193 2 6E random polar NTR AKS ANH NTQ
(SEQ ID NO:36) 15 4.954 2 6F poly(Ala) AAA AAA AAA AAA (SEQ ID
NO:37) 73 -3.096 4 For clarity only the designed surface residues
are shown and they are grouped by position (b, c, and f). The
sequence numbers of the designed positions are: 3, 4, 7, 10, 11,
14, 17, 18, 21, 24, 25, and 28. Melting temperatures (T.sub.m's)
were determined by circular dichroism and oligomerization states
(N) were determined by size exclusion chromatography.
.SIGMA..DELTA.G.degree. is the sum of the standard free energy of
helix propagation of the 12 b, c, and f positions # (Chakrabartty,
et al., 1994). Abbreviations for design methods are: hydrogen bonds
(HB), polar hydrogen burial penalty (PB), and helix propensity
(HP).
[0215] Sequence 6A (SEQ ID NO:32), designed with a hydrogen-bond
potential, has a preponderance of Arg and Glu residues that are
predicted to form numerous hydrogen bonds to each other. These long
chain amino acids are favored because they can extend across turns
of the helix to interact with each other and with the backbone.
When the optimal geometry of the scrambled 6A (SEQ ID NO:32)
sequence, 6D (SEQ ID NO:35), was found with DEE, far fewer hydrogen
bonding interactions were present and its score was much worse than
6A's (SEQ ID NO:32). 6B (SEQ ID NO:33), designed with a polar
hydrogen burial penalty in addition to a hydrogen-bond potential,
is still dominated by long residues such as Lys, Glu and Gin but
has fewer Arg. Because Arg has more polar hydrogens than the other
amino acids, it more often buries nonhydrogen-bonded protons and
therefore is disfavored when using this potential function. 6C (SEQ
ID NO:34) was designed with a hydrogen-bond potential and helix
propensity in the scoring function and consists entirely of Ala and
Arg residues, the amino acids with the highest helix propensities
(Chakrabartty, et al., supra). The Arg residues form hydrogen bonds
with Glu residues at nearby e and g positions. The random
hydrophilic sequence, 6E (SEQ ID NO:36), possesses no hydrogen
bonds and scores very poorly with all of the potential functions
used.
[0216] The secondary structures and thermal stabilities of the
peptides were assessed by circular dichroism (CD) spectroscopy. The
CD spectra of the peptides at 1.degree. C. and 40 .mu.M are
characteristic of a helices, with minima at 208 and 222 nm, except
for the random surface sequence peptide 6E (SEQ ID NO:36). 6E (SEQ
ID NO:36) has a spectrum suggestive of a mixture of a helix and
random coil with a [.theta.].sub.222 of -12000 deg cm.sup.2/dmol,
while all the other peptides are greater than 90% helical with
[.theta.].sub.222 of less than -30000 deg cm.sup.2/dmol. The
melting temperatures (T.sub.m's) of the designed peptides are
12-16.degree. C. higher than the T.sub.m of GCN4-p1 (SEQ ID NO:
31), with the exception of 6E (SEQ ID NO: 36) which has a T.sub.m
of 15.degree. C. CD spectra taken before and after melts were
identical indicating reversible thermal denaturation. The redesign
of surface positions of this coiled coil produces structures that
are much more stable than wildtype GCN4-p1 (SEQ ID NO:31), while a
random hydrophilic sequence largely disrupts the peptide's
stability.
[0217] ize exclusion chromatography (SEC) showed that all the
peptides were dimers except for 6F, the all Ala surface sequence,
which migrated as a tetramer. These data show that surface redesign
did not change the tertiary structure of these peptides, in
contrast to some core redesigns (Harbury, et al., supra). In
addition, nuclear magnetic resonance (NMR) spectra of the peptides
at .about.1 mM showed chemical shift dispersion similar to GCN4-p1
(SEQ ID NO:31) (data not shown).
[0218] Peptide 6A (SEQ ID NO:32), designed with a hydrogen-bond
potential, melts at 71.degree. C. versus 57.degree. C. for GCN4-p1
(SEQ ID NO: 31), demonstrating that rational design of surface
residues can produce structures that are markedly more stable than
naturally occurring coiled coils. This gain in stability is
probably not due to improved hydrogen bonding since 6D (SEQ ID NO:
35), which has the same surface amino acid composition as 6A (SEQ
ID NO: 32) but a scrambled sequence and no predicted hydrogen
bonds, also melts at 71.degree. C. Further, 6B (SEQ ID NO:33) was
designed with a different scoring function and has a different
sequence and set of predicted hydrogen bonds but a very similar
T.sub.m of 72.degree. C.
[0219] An alternative explanation for the increased stability of
these sequences relative to GCN4-p1 (SEQ ID NO:31) is their higher
helix propensity. The long polar residues selected by the hydrogen
bond potential, Lys, Glu, Arg and Gln, are also among the best
helix formers (Chakrabartty, et al., supra). Since the effect of
helix propensity is not as dependent on sequence position as that
of hydrogen bonding, especially far from the helix ends, little
effect would be expected from scrambling the sequence of 6A (SEQ ID
NO: 32). A rough measure of the helix propensity of the surface
sequences, the sum of the standard free energies of helix
propagation (.SIGMA..DELTA.G.degree.) (Chakrabartty, et al.,
supra), corresponds to the peptides' thermal stabilities (Table 4).
Though .SIGMA..DELTA.G.degree. matches the trend in peptide
stability, it is not quantitatively correlated to the increased
stability of these coiled coils.
[0220] Peptide 6C (SEQ ID NO: 34) was designed with helix
propensity as part of the scoring function and it has a
.SIGMA..DELTA.G.degree. of -2.041 kcal/mol. Though 6C (SEQ ID
NO:34) is more stable than GCN4-p1 (SEQ ID No:31), its T.sub.m of
69.degree. C. is slightly lower than 6A (SEQ ID NO: 32) and 6B (SEQ
ID NO:33), in spite of 6C's (SEQ ID NO:34) higher helix propensity.
Similarly, 6F has the highest helix propensity possible with an all
Ala sequence and a .SIGMA..DELTA.G.degree. of -3.096 kcal/mol, but
its T.sub.m of 73.degree. C. is only marginally higher than that of
6A (SEQ ID NO:32) or 6B (SEQ ID NO: 33). 6F also migrates as a
tetramer during SEC, not a dimer, likely because its poly(Ala)
surface exposes a large hydrophobic patch that could mediate
association. Though the results for 6C (SEQ ID NO:34) and 6F (SEQ
ID NO:37) support the conclusion that helix propensity is important
for surface design, they point out possible limitations in using
propensity exclusively. Increasing propensity does not necessarily
confer the greatest stability on a structure, perhaps because other
factors are being effected unfavorably. Also, as is evident from 6F
(SEQ ID NO: 37), changes in the tertiary structure of the protein
can occur.
[0221] The characterization of these peptides clearly shows that
surface residues have a dramatic impact on the stability of
.alpha.-helical coiled coils. The wide range of stabilities
displayed by the different surface designs is notable, with greater
than a 50.degree. C. spread between the random hydrophilic sequence
(T.sub.m 15.degree. C.) and the designed sequences (T.sub.m
69-72.degree. C.). This result is consistent with studies on other
proteins that demonstrated the importance of solvent exposed
residues (O'Neil & DeGrado, 1990; Zhang, et al., 1991; Minor,
et al., (1994) (supra); Smith, et al., Science 270:980-982 (1995)).
Further, these designs have significantly higher T.sub.m's than the
wildtype GCN4-p1 sequence, demonstrating that surface residues can
be used to improve stability in protein design (O'shea, et al.,
supra). Though helix propensity appears to be more important than
hydrogen bonding in stabilizing the designed coiled coils, hydrogen
bonding could be important in the design and stabilization of other
types of secondary structure.
Example 3
Design of a Protein Containing Core, Surface and Boundary Residues
Using van der Waals, H-Bonding, Secondary Structure and Solvation
Scoring Functions
[0222] In this example, core, boundary and surface residue work was
combined. In selecting a motif to test the integration of our
design methodologies, we sought a protein fold that would be small
enough to be both computationally and experimentally tractable, yet
large enough to form an independently folded structure in the
absence of disulfide bonds or metal binding sites. We chose the
.beta..beta..alpha. motif typified by the zinc finger DNA binding
module (Pavletich, et al. (1991) (supra)). Though it consists of
less than 30 residues, this motif contains sheet, helix, and turn
structures. Further, recent work by Imperiali and coworkers who
designed a 23 residue peptide, containing an unusual amino acid
(D-proline) and a non-natural amino acid
(3-(1,10-phenanthrol-2-yl)-L-alanine), that takes this structure
has demonstrated the ability of this fold to form in the absence of
metal ions (Struthers, et al., 1996a). The Brookhaven Protein Data
Bank (PDB) (Bernstein, et al., 1977) was examined for high
resolution structures of the .beta..beta..alpha. motif, and the
second zinc finger module of the DNA binding protein Zif268 (PDB
code 1 zaa) was selected as our design template (Pavletich, et al.
(1991) (supra)). The backbone of the second module aligns very
closely with the other two zinc fingers in Zif268 and with zinc
fingers in other proteins and is therefore representative of this
fold class. 28 residues were taken from the crystal structure
starting at lysine 33 in the numbering of PDB entry 1 zaa which
corresponds to our position 1. The first 12 residues comprise the a
sheet with a tight turn at the 6.sup.th and 7.sup.th positions. Two
residues connect the sheet to the helix, which extends through
position 26 and is capped by the last two residues.
[0223] In order to assign the residue positions in the template
structure into core, surface or boundary classes, the extent of
side-chain burial in Zif268 and the direction of the
C.alpha.-C.beta. vectors were examined. The small size of this
motif limits to one (position 5) the number of residues that can be
assigned unambiguously to the core while six residues (positions 3,
12, 18, 21, 22, and 25) were classified as boundary. Three of these
residues are from the sheet (positions 3, 5, and 12) and four are
from the helix (positions 18, 21, 22, and 25). One of the zinc
binding residues of Zif268 is in the core and two are in the
boundary, but the fourth, position 8, has a C.alpha.-C.beta. vector
directed away from the protein's geometric center and is therefore
classified as a surface position. The other surface positions
considered by the design algorithm are 4, 9, and 11 from the sheet,
15, 16, 17, 19, 20, and 23 from the helix and 14, 27, and 28 which
cap the helix ends. The remaining exposed positions, which either
were in turns, had irregular backbone dihedrals or were partially
buried, were not included in the sequence selection for this
initial study. As in our previous studies, the amino acids
considered at the core positions during sequence selection were A,
V, L, I, F, Y, and W; the amino acids considered at the surface
positions were A, S, T, H, D, N, E, Q, K, and R; and the combined
core and surface amino acid sets (16 amino acids) were considered
at the boundary positions.
[0224] In total, 20 out of 28 positions of the template were
optimized during sequence selection. The algorithm first selects
Gly for all positions with 0 angles greater than 0.degree. in order
to minimize backbone strain (residues 9 and 27). The 18 remaining
residues were split into two sets and optimized separately to speed
the calculation. One set contained the 1 core, the 6 boundary
positions and position 8 which resulted in 1.2.times.10.sup.9
possible amino acid sequences corresponding to 4.3.times.1 019
rotamer sequences. The other set contained the remaining 10 surface
residues which had 1010 possible amino acid sequences and
4.1.times.10.sup.23 rotamer sequences. The two groups do not
interact strongly with each other making their sequence
optimizations mutually independent, though there are strong
interactions within each group. Each optimization was carried out
with the non-optimized positions in the template set to the
crystallographic coordinates.
[0225] The optimal sequences found from the two calculations were
combined and are shown in FIG. 8 (SEQ ID NOS:1 and 2) aligned with
the sequence from the second zinc finger of Zif268 (SEQ ID NO:1).
Even though all of the hydrophilic amino acids were considered at
each of the boundary positions, only nonpolar amino acids were
selected. The calculated seven core and boundary positions form a
well-packed buried cluster. The Phe side chains selected by the
algorithm at the zinc binding His positions, 21 and 25, are 80%
buried and the Ala at 5 is 100% buried while the Lys at 8 is
greater than 60% exposed to solvent. The other boundary positions
demonstrate the strong steric constraints on buried residues by
packing similar side chains in an arrangement similar to Zif268.
The calculated optimal configuration buried .about.830 .ANG..sup.2
of nonpolar surface area, with Phe 12 (96% buried) and Leu 18 (88%
buried) anchoring the cluster. On the helix surface, the algorithm
positions Asn 14 as a helix N-cap with a hydrogen bond between its
side-chain carbonyl oxygen and the backbone amide proton of residue
16. The six charged residues on the helix form three pairs of
hydrogen bonds, though in our coiled coil designs helical surface
hydrogen bonds appeared to be less important than the overall helix
propensity of the sequence. Positions 4 and 11 on the exposed sheet
surface were selected to be Thr, one of the best .beta.-sheet
forming residues (Kim & Berg, 1993; Minor, et al., (1994)
(supra); Smith, et al., (1995) (supra)).
[0226] Combining the 20 designed positions with the Zif268 (SEQ ID
NO:1) amino acids at the remaining 8 sites results in a peptide
with overall 39% ( 11/28) homology to Zif268, which reduces to 15%
( 3/20) homology when only the designed positions are considered. A
BLAST (Altschul, et al., 1990) search of the non-redundant protein
sequence database of the National Center for Biotechnology
Information finds weak homology, less than 40%, to several zinc
finger proteins and fragments of other unrelated proteins. None of
the alignments had significance values less than 0.26. By
objectively selecting 20 out of 28 residues on the Zif268 (SEQ ID
NO:1) template, a peptide with little homology to known proteins
and no zinc binding site was designed.
[0227] Experimental characterization: The far UV circular dichroism
(CD) spectrum of the designed molecule, pda8d, shows a maximum at
195 nm and minima at 218 nm and 208 nm, which is indicative of a
folded structure. The thermal melt is weakly cooperative, with an
inflection point at 39.degree. C., and is completely reversible.
The broad melt is consistent with a low enthalpy of folding which
is expected for a motif with a small hydrophobic core. This
behavior contrasts the uncooperative transitions observed for other
short peptides (Weiss & Keutmann, 1990; Scholtz, et al., PNAS
USA 88:2854 (1991); Struthers, et al., J. Am. Chem. Soc. 118:3073
(1996b)).
[0228] Sedimentation equilibrium studies at 100 .mu.M and both
7.degree. C. and 25.degree. C. give a molecular mass of 3490, in
good agreement with the calculated mass of 3362, indicating the
peptide is monomeric. At concentrations greater than 500 .mu.M,
however, the data do not fit well to an ideal single species model.
When the data were fit to a monomer-dimer-tetramer model,
dissociation constants of 0.5-1.5 mM for monomer-to-dimer and
greater than 4 mM for dimer-to-tetramer were found, though the
interaction was too weak to accurately measure these values.
Diffusion coefficient measurements using the water-sLED pulse
sequence (Altieri, et al., 1995) agreed with the sedimentation
results: at 100 .mu.M pda8d has a diffusion coefficient close to
that of a monomeric zinc finger control, while at 1.5 mM the
diffusion coefficient is similar to that of protein G.beta.1, a 56
residue protein. The CD spectrum of pda8d is concentration
independent from 10 .mu.M to 2.6 mM. NMR COSY spectra taken at 2.1
mM and 100 .mu.M were almost identical with 5 of the H.alpha.-HN
crosspeaks shifted no more than 0.1 ppm and the rest of the
crosspeaks remaining unchanged. These data indicate that pda8d
undergoes a weak association at high concentration, but this
association has essentially no effect on the peptide's
structure.
[0229] The NMR chemical shifts of pda8d are well dispersed,
suggesting that the protein is folded and well-ordered. The
H.alpha.-HN fingerprint region of the TOCSY spectrum is
well-resolved with no overlapping resonances (Figure (9A) and all
of the Ha and HN resonances have been assigned. NMR data were
collected on a Varian Unityplus 600 MHz spectrometer equipped with
a Nalorac inverse probe with a self-shielded z-gradient. NMR
samples were prepared in 90/10H.sub.2O/D.sub.2O or 99.9% D.sub.2O
with 50 mM sodium phosphate at pH 5.0. Sample pH was adjusted using
a glass electrode with no correction for the effect of D.sub.2O on
measured pH. All spectra for assignments were collected at
7.degree. C. Sample concentration was approximately 2 mM. NMR
assignments were based on standard homonuclear methods using
DQF-COSY, NOESY and TOCSY spectra (Wuthrich, NMR of Proteins and
Nucleic Acids (John Wiley & Sons, New York, 1986). NOESY and
TOCSY spectra were acquired with 2K points in F2 and 512 increments
in F1 and DQF-COSY spectra were acquired with 4K points in F2 and
1024 increments in F1. All spectra were acquired with a spectral
width of 7500 Hz and 32 transients. NOESY spectra were recorded
with mixing times of 100 and 200 ms and TOCSY spectra were recorded
with an isotropic mixing time of 80 ms. In TOCSY and DQF-COSY
spectra water suppression was achieved by presaturation during a
relaxation delay of 1.5 and 2.0 s, respectively. Water suppression
in the NOESY spectra was accomplished with the WATERGATE pulse
sequence (Piotto, et al., 1992). Chemical shifts were referenced to
the HOD resonance. Spectra were zero-filled in both F2 and F1 and
apodized with a shifted gaussian in F2 and a cosine bell in F1
(NOESY and TOCSY) or a 30.degree. shifted sine bell in F2 and a
shifted gaussian in F1 (DQF-COSY).
[0230] Water-sLED experiments (Altieri, et al., 1995) were run at
25.degree. C. at 1.5 mM, 400 .mu.M and 100 .mu.M in 99.9% D.sub.2O
with 50 mM sodium phosphate at pH 5.0. Axial gradient field
strength was varied from 3.26 to 53.1 G/cm and a diffusion time of
50 ms was used. Spectra were processed with 2 Hz line broadening
and integrals of the aromatic and high field aliphatic protons were
calculated and fit to an equation relating resonance amplitude to
gradient strength in order to extract diffusion coefficients
(Altieri, et al., 1995). Diffusion coefficients were
1.48.times.10.sup.-7, 1.62.times.10.sup.-7 and 1.73.times.10.sup.-7
cm.sup.2/s at 1.5 mM, 400 .mu.M and 100 .mu.M, respectively. The
diffusion coefficient for the zinc finger monomer control was
1.72.times.10.sup.-7 cm.sup.2/s and for protein G b1 was
1.49.times.10.sup.-7 cm.sup.2/s.
[0231] All unambiguous sequential and medium-range NOEs are shown
in FIG. 9A. H.alpha.-HN and/or HN-HN NOEs were found for all pairs
of residues except R6-17 and K16-E17, both of which have degenerate
HN chemical shifts, and P2-Y3 which have degenerate Ha chemical
shifts. An NOE is present, however, from a P2H.delta. to the Y3 HN
analogous to sequential HN-HN connections. Also, strong K1 H.alpha.
to P2H.delta. NOEs are present and allowed completion of the
resonance assignments.
[0232] The structure of pda8d was determined using 354 NOE
restraints (12.6 restraints per residue) that were non-redundant
with covalent structure. An ensemble of 32 structures (data not
shown) was obtained using X-PLOR (Brunger, 1992) with standard
protocols for hybrid distance geometry-simulated annealing. The
structures in the ensemble had good covalent geometry and no NOE
restraint violations greater than 0.3 .ANG.. As shown in Table 5,
the backbone was well defined with a root-mean-square (rms)
deviation from the mean of 0.55 .ANG. when the disordered termini
(residues 1, 2, 27, and 28) were excluded. The rms deviation for
the backbone (3-26) plus the buried side chains (residues 3, 5, 7,
12, 18, 21, 22, and 25) was 1.05 .ANG.. TABLE-US-00005 TABLE 5 NMR
structure determination of pda8d: distance restraints, structural
statistics, atomic root-mean-square (rms) deviations, and
comparison to the design target. <SA> are the 32 simulated
annealing structures, SA is the average structure and SD is the
standard deviation. The design target is the backbone of Zif268.
Distance restraints Intraresidue 148 Sequential 94 Short range
(|i-j| = 2-5 residues) 78 Long range (|i-j| > 5 residues) 34
Total 354 Structural statistics <SA> .+-. SD Rms deviation
from distance restraints (.ANG.) 0.049 .+-. .004 Rms deviation from
idealized geometry (.ANG.) Bonds (.ANG.) 0.0051 .+-. 0.0004 Angles
(degrees) 0.76 .+-. 0.04 Impropers (degrees) 0.56 .+-. 0.04 Atomic
rms deviations (.ANG.)* <SA> vs. SA .+-. SD Backbone 0.55
.+-. 0.03 Backbone + nonpolar side chains 1.05 .+-. 0.06 Heavy
atoms 1.25 .+-. 0.04 Atomic rms deviations between pda8d and the
design target (.ANG.)* SA vs. target Backbone 1.04 Heavy atoms 2.15
*Atomic rms deviations are for residues 3 to 26, inclusive. The
termini, residues 1, 2, 27, and 28, were highly disordered and had
very few non-sequential or non-intraresidue contacts.
[0233] The NMR solution structure of pda8d shows that it folds into
a bba motif with well-defined secondary structure elements and
tertiary organization which match the design target. A direct
comparison of the design template, the backbone of the second zinc
finger of Zif268, to the pda8d solution structure highlights their
similarity (data not shown). Alignment of the pda8d backbone to the
design target is excellent, with an atomic rms deviation of 1.04
.ANG. (Table 5). Pda8d and the design target correspond throughout
their entire structures, including the turns connecting the
secondary structure elements.
[0234] In conclusion, the experimental characterization of pda8d
shows that it is folded and well-ordered with a weakly cooperative
thermal transition, and that its structure is an excellent match to
the design target. To our knowledge, pda8d is the shortest sequence
of naturally occurring amino acids that folds to a unique structure
without metal binding, oligomerization or disulfide bond formation
(McKnight, et al., Nature Struc. Biol. 4:180 (1996)). The
successful design of pda8d supports the use of objective,
quantitative sequence selection algorithms for protein design. This
robustness suggests that the program can be used to design
sequences for de novo backbones.
Example 4
Protein Design Using a Scaled van der Waals Scoring Function in the
Core Region
[0235] An ideal model system to study core packing is the .beta.1
immunoglobulin-binding domain of streptococcal protein G (G.beta.1)
(Gronenborn, et al., Science 253:657 (1991); Alexander, et al.,
Biochem. 31: 3597 (1992); Barchi, et al., Protein Sci. 3:15 (1994);
Gallagher, et al., 1994; Kuszewski, et al., 1994; Orban, et al.,
1995). Its small size, 56 residues, renders computations and
experiments tractable. Perhaps most critical for a core packing
study, G.beta.1 contains no disulfide bonds and does not require a
cofactor or metal ion to fold. Further, G.beta.1 contains sheet,
helix and turn structures and is without the repetitive side-chain
packing patterns found in coiled coils or some helical bundles.
This lack of periodicity reduces the bias from a particular
secondary or tertiary structure and necessitates the use of an
objective side-chain selection program to examine packing
effects.
[0236] Sequence positions that constitute the core were chosen by
examining the side-chain solvent accessible surface area of
G.beta.1. Any side chain exposing less than 10% of its surface was
considered buried. Eleven residues meet this criteria, with seven
from the .beta. sheet (positions 3, 5, 7, 20, 43, 52 and 54), three
from the helix (positions 26, 30, and 34) and one in an irregular
secondary structure (position 39). These positions form a
contiguous core. The remainder of the protein structure, including
all other side chains and the backbone, was used as the template
for sequence selection calculations at the eleven core
positions.
[0237] All possible core sequences consisting of alanine, valine,
leucine, isoleucine, phenylalanine, tyrosine or tryptophan (A, V,
L, I, F, Y or W) were considered. Our rotamer library was similar
to that used by Desmet and coworkers (Desmet, et al., (1992)
(supra)). Optimizing the sequence of the core of G.beta.1 (SEQ ID
NO:38) with 217 possible hydrophobic rotamers at all 11 positions
results in 217.sup.11, or 5.times.10.sup.25, rotamer sequences. Our
scoring function consisted of two components: a van der Waals
energy term and an atomic solvation term favoring burial of
hydrophobic surface area. The van der Waals radii of all atoms in
the simulation were scaled by a factor .alpha. (Eqn. 3) to change
the importance of packing effects. Radii were not scaled for the
buried surface area calculations. By predicting core sequences with
various radii scalings and then experimentally characterizing the
resulting proteins, a rigorous study of the importance of packing
effects on protein design is possible.
[0238] The protein structure was modeled on the backbone
coordinates of G.beta.1, PDB record 1 pga (Bernstein, et al.,
supra; Gallagher, et al., 1994). Atoms of all side chains not
optimized were left in their crystallographically determined
positions. The program BIOGRAF (Molecular Simulations Incorporated,
San Diego, Calif.) was used to generate explicit hydrogens on the
structure which was then conjugate gradient minimized for 50 steps
using the Dreiding forcefield (Mayo, et al., 1990, supra). The
rotamer library, DEE optimization and Monte Carlo search was as
outlined above. A Lennard-Jones 12-6 potential was used for van der
Waals interactions, with atomic radii scaled for the various cases
as discussed herein. The Richards definition of solvent-accessible
surface area (Lee & Richards, supra) was used and areas were
calculated with the Connolly algorithm (Connolly, (1983) (supra)).
An atomic solvation parameter, derived from our previous work, of
23 cal/mol/.ANG..sup.2 was used to favor hydrophobic burial and to
penalize solvent exposure. To calculate side-chain nonpolar
exposure in our optimization framework, we first consider the total
hydrophobic area exposed by a rotamer in isolation. This exposure
is decreased by the area buried in rotamer/template contacts, and
the sum of the areas buried in pairwise rotamer/rotamer
contacts.
[0239] Global optimum sequences for various values of the radius
scaling factor .alpha. were found using the Dead-End Elimination
theorem (Table 6) (SEQ ID NOS:38-49). Optimal sequences, and their
corresponding proteins, are named by the radius scale factor used
in their design. For example, the sequence designed with a radius
scale factor of .alpha.=0.90 is called .alpha.90 (SEQ ID NO:43).
TABLE-US-00006 TABLE 6 G.beta.1 sequence (SEQ ID .alpha. vol TYR
LEU LEU ALA ALA PHE ALA VAL TRP PHE VAL NO: 38) 3 5 7 20 26 30 34
39 43 52 54 0.70 1.28 TRP TYR ILE ILE PHE TRP LEU ILE PHE LEU ILE
(SEQ ID NO: 39) 0.75 1.23 PHE ILE PHE ILE VAL TRP VAL LEU | | ILE
(SEQ ID NO: 40) 0.80 1.13 PHE | ILE | | | ILE ILE | TRP ILE (SEQ ID
NO: 41) 0.85 1.15 PHE | ILE | | | LEU ILE | TRP PHE (SEQ ID NO: 42)
0.90 1.01 PHE | ILE | | | | ILE | | | (SEQ ID NO: 43) 0.95 1.01 PHE
| ILE | | | | ILE | | | (SEQ ID NO: 44) 1.0 0.99 PHE | VAL | | | |
ILE | | | (SEQ ID NO: 45) 1.05 0.93 PHE | ALA | | | | | | | | (SEQ
ID NO: 46) 1.075 0.83 ALA ALA ILE | | ILE | | | ILE ILE (SEQ ID NO:
47) 1.10 0.77 ALA | ALA | | ALA | | | ILE ILE (SEQ ID NO: 48) 1.15
0.68 ALA ALA ALA | | ALA | | | LEU | (SEQ ID NO: 49)
[0240] In Table 6, the G.beta.1 sequence (SEQ ID NO:38) and
position numbers are shown at the top. vol is the fracton of core
side-chain volume relative to the G.beta.1 sequence (SEQ ID NO:38).
A vertical bar indicates identity with the G.beta.1 sequence (SEQ
ID NO:38).
[0241] .alpha.100 was designed with .alpha.=1.0 and hence serves as
a baseline for full incorporation of steric effects.
[0242] The .alpha.100 sequence (SEQ ID NO:45) is very similar to
the core sequence of (G.beta.1 (SEQ ID NO:38) (Table 6) even though
no information about the naturally occurring sequence was used in
the side-chain selection algorithm. Variation of a from 0.90 to
1.05 caused little change in the optimal sequence, demonstrating
the algorithm's robustness to minor parameter perturbations.
Further, the packing arrangements predicted with .alpha.=0.90-1.05
closely match G.beta.1 with average .chi. angle differences of only
4.degree. from the crystal structure. The high identity and
conformational similarity to G.beta.1 imply that, when packing
constraints are used, backbone conformation strongly determines a
single family of well packed core designs. Nevertheless, the
constraints on core packing were being modulated by .alpha. as
demonstrated by Monte Carlo searches for other low energy
sequences. Several alternate sequences and packing arrangements are
in the twenty best sequences found by the Monte Carlo procedure
when .alpha.=0.90. These alternate sequences score much worse when
.alpha.=0.95, and when .alpha.=1.0 or 1.05 only strictly
conservative packing geometries have low energies. Therefore,
.alpha.=1.05 and .alpha.=0.90 define the high and low ends,
respectively, of a range where packing specificity dominates
sequence design.
[0243] For .alpha.<0.90, the role of packing is reduced enough
to let the hydrophobic surface potential begin to dominate, thereby
increasing the size of the residues selected for the core (Table
6). A significant change in the optimal sequence appears between
.alpha.=0.90 and 0.85 with both .alpha.85 and .alpha.80 containing
three additional mutations relative to .alpha.90. Also, .alpha.85
and .alpha.80 have a 15% increase in total side-chain volume
relative to G.beta.1. As a drops below 0.80 an additional 10%
increase in side-chain volume and numerous mutations occur, showing
that packing constraints have been overwhelmed by the drive to bury
nonpolar surface. Though the jumps in volume and shifts in packing
arrangement appear to occur suddenly for the optimal sequences,
examination of the suboptimal low energy sequences by Monte Carlo
sampling demonstrates that the changes are not abrupt. For example,
the .alpha.85 optimal sequence is the 11.sup.th best sequence when
.alpha.=0.90, and similarly, the .alpha.90 optimal sequence is the
9.sup.th best sequence when .alpha.=0.85.
[0244] For .alpha.>1.05 atomic van der Waals repulsions are so
severe that most amino acids cannot find any allowed packing
arrangements, resulting in the selection of alanine for many
positions. This stringency is likely an artifact of the large
atomic radii and does not reflect increased packing specificity
accurately. Rather, .alpha.=1.05 is the upper limit for the usable
range of van der Waals scales within our modeling framework.
[0245] Experimental characterization of core designs. Variation of
the van der Waals scale factor a results in four regimes of packing
specificity: regime 1 where 0.9.ltoreq..alpha..ltoreq.1.05 and
packing constraints dominate the sequence selection; regime 2 where
0.8.ltoreq..alpha.<0.9 and the hydrophobic solvation potential
begins to compete with packing forces; regime 3 where
.alpha.<0.8 and hydrophobic solvation dominates the design; and,
regime 4 where .alpha.>1.05 and van der Waals repulsions appear
to be too severe to allow meaningful sequence selection. Sequences
that are optimal designs were selected from each of the regimes for
synthesis and characterization. They are .alpha.90 from regime 1,
.alpha.85 from regime 2, .alpha.70 from regime 3 and .alpha.107
from regime 4. For each of these sequences, the calculated amino
acid identities of the eleven core positions are shown in Table 6;
the remainder of the protein sequence matches G.beta.1. The goal
was to study the relation between the degree of packing specificity
used in the core design and the extent of native-like character in
the resulting proteins.
[0246] Peptide synthesis and purification. With the exception of
the eleven core positions designed by the sequence selection
algorithm, the sequences synthesized match Protein Data Bank entry
1 pga. Peptides were synthesized using standard Fmoc chemistry, and
were purified by reverse-phase HPLC. Matrix assisted laser
desorption mass spectrometry found all molecular weights to be
within one unit of the expected masses.
[0247] CD and fluorescence spectroscopy and size exclusion
chromatography. The solution conditions for all experiments were 50
mM sodium phosphate buffer at pH 5.5 and 25.degree. C. unless
noted. Circular dichroism spectra were acquired on an Aviv 62DS
spectrometer equipped with a thermoelectric unit. Peptide
concentration was approximately 20 .mu.M. Thermal melts were
monitored at 218 nm using 20 increments with an equilibration time
of 120 s. T.sub.m's were defined as the maxima of the derivative of
the melting curve. Reversibility for each of the proteins was
confirmed by comparing room temperature CD spectra from before and
after heating. Guanidinium chloride denaturation measurements
followed published methods (Pace, Methods. Enzymol. 131:266
(1986)). Protein concentrations were determined by UV
spectrophotometry. Fluorescence experiments were performed on a
Hitachi F-4500 in a 1 cm pathlength cell. Both peptide and ANS
concentrations were 50 .mu.M. The excitation wavelength was 370 nm
and emission was monitored from 400 to 600 nm.
[0248] Size exclusion chromatography was performed with a PolyLC
hydroxyethyl A column at pH 5.5 in 50 mM sodium phosphate at
0.degree. C. Ribonuclease A, carbonic anhydrase and G.beta.1 were
used as molecular weight standards. Peptide concentrations during
the separation were .about.15 .mu.M as estimated from peak heights
monitored at 275 nm.
[0249] Nuclear magnetic resonance spectroscopy. Samples were
prepared in 90/10H.sub.2O/D.sub.2O and 50 mM sodium phosphate
buffer at pH 5.5. Spectra were acquired on a Varian Unityplus 600
MHz spectrometer at 25.degree. C. Samples were approximately 1 mM,
except for .alpha.70 which had limited solubility (100 .mu.M). For
hydrogen exchange studies, an NMR sample was prepared, the pH was
adjusted to 5.5 and a spectrum was acquired to serve as an
unexchanged reference. This sample was lyophilized, reconstituted
in D.sub.2O and repetitive acquisition of spectra was begun
immediately at a rate of 75 s per spectrum. Data acquisition
continued for .about.20 hours, then the sample was heated to
99.degree. C. for three minutes to fully exchange all protons.
After cooling to 25.degree. C., a final spectrum was acquired to
serve as the fully exchanged reference. The areas of all
exchangeable amide peaks were normalized by a set of non-exchanging
aliphatic peaks. pH values, uncorrected for isotope effects, were
measured for all the samples after data acquisition and the time
axis was normalized to correct for minor differences in pH (Rohl,
et al., Biochem. 31:1263 (1992)).
[0250] .alpha.90 and .alpha.85 have ellipticities and spectra very
similar to G.beta.1 (not shown), suggesting that their secondary
structure content is comparable to that of Gb1 (FIG. 10).
Conversely, .alpha.70 has much weaker ellipticity and a perturbed
spectrum, implying a loss of secondary structure relative to
G.beta.1. .alpha.107 has a spectrum characteristic of a random
coil. Thermal melts monitored by CD are shown in FIG. 10B.
.alpha.85 and .alpha.90 both have cooperative transitions with
melting temperatures (T.sub.m's) of 83.degree. C. and 92.degree.
C., respectively. .alpha.107 shows no thermal transition, behavior
expected from a fully unfolded polypeptide, and .alpha.70 has a
broad, shallow transition, centered at -40.degree. C.,
characteristic of partially folded structures. Relative to
G.beta.1, which has a T.sub.m of 87.degree. C. (Alexander, et al.,
supra), .alpha.85 is slightly less thermostable and .alpha.90 is
more stable. Chemical denaturation measurements of the free energy
of unfolding (.DELTA.G.sub.u) at 25.degree. C. match the trend in
T.sub.m's.
[0251] .alpha.90 has a larger AG, than that reported for G.beta.1
(Alexander, et at., supra) while .alpha.85 is slightly less stable.
It was not possible to measure .DELTA.G.sub.u for .alpha.70 or
.alpha.107 because they lack discernible transitions.
[0252] The extent of chemical shift dispersion in the proton NMR
spectrum of each protein was assessed to gauge each protein's
degree of native-like character (data not shown). .alpha.90
possesses a highly dispersed spectrum, the hallmark of a
well-ordered native protein. .alpha.85 has diminished chemical
shift dispersion and peaks that are somewhat broadened relative to
.alpha.90, suggesting a moderately mobile structure that
nevertheless maintains a distinct fold. .alpha.70's NMR spectrum
has almost no dispersion. The broad peaks are indicative of a
collapsed but disordered and fluctuating structure. .alpha.107 has
a spectrum with sharp lines and no dispersion, which is indicative
of an unfolded protein.
[0253] Amide hydrogen exchange kinetics are consistent with the
conclusions reached from examination of the proton NMR spectra.
Measuring the average number of unexchanged amide protons as a
function of time for each of the designed proteins results as
follows (data not shown): .alpha.90 protects .about.13 protons for
over 20 hours of exchange at pH 5.5 and 25.degree. C. The .alpha.90
exchange curve is indistinguishable from G.beta.1's (not shown).
.alpha.85 also maintains a well-protected set of amide protons, a
distinctive feature of ordered native-like proteins. The number of
protected protons, however, is only about half that of .alpha.90.
The difference is likely due to higher flexibility in some parts of
the .alpha.85 structure. In contrast, .alpha.70 and .alpha.107 were
fully exchanged within the three minute dead time of the
experiment, indicating highly dynamic structures.
[0254] Near UV CD spectra and the extent of 8-anilino-1-naphthalene
sulfonic acid (ANS) binding were used to assess the structural
ordering of the proteins. The near UV CD spectra of .alpha.85 and
.alpha.90 have strong peaks as expected for proteins with aromatic
residues fixed in a unique tertiary structure while .alpha.70 and
.alpha.107 have featureless spectra indicative of proteins with
mobile aromatic residues, such as non-native collapsed states or
unfolded proteins. .alpha.70 also binds ANS well, as indicated by a
three-fold intensity increase and blue shift of the ANS emission
spectrum. This strong binding suggests that .alpha.70 possesses a
loosely packed or partially exposured cluster of hydrophobic
residues accessible to ANS. ANS binds .alpha.85 weakly, with only a
25% increase in emission intensity, similar to the association seen
for some native proteins (Semisotnov, et al., Biopolymers 31:119
(1991)). .alpha.90 and .alpha.107 cause no change in ANS
fluorescence. All of the proteins migrated as monomers during size
exclusion chromatography.
[0255] In summary, .alpha.90 is a well-packed native-like protein
by all criteria, and it is more stable than the naturally occurring
G.beta.1 sequence, possibly because of increased hydrophobic
surface burial. .alpha.85 is also a stable, ordered protein, albeit
with greater motional flexibility than .alpha.90, as evidenced by
its NMR spectrum and hydrogen exchange behavior. .alpha.70 has all
the features of a disordered collapsed globule: a non-cooperative
thermal transition, no NMR spectral dispersion or amide proton
protection, reduced secondary structure content and strong ANS
binding. .alpha.107 is a completely unfolded chain, likely due to
its lack of large hydrophobic residues to hold the core together.
The clear trend is a loss of protein ordering as a decreases below
0.90.
[0256] The different packing regimes for protein design can be
evaluated in light of the experimental data. In regime 1, with
0.9.ltoreq..alpha..ltoreq.1.05, the design is dominated by packing
specificity resulting in well-ordered proteins. In regime 2, with
0.8.ltoreq..alpha.<0.9, packing forces are weakened enough to
let the hydrophobic force drive larger residues into the core which
produces a stable well-packed protein with somewhat increased
structural motion. In regime 3, .alpha.<0.8, packing forces are
reduced to such an extent that the hydrophobic force dominates,
resulting in a fluctuating, partially folded structure with no
stable core packing. In regime 4, .alpha.>1.05, the steric
forces used to implement packing specificity are scaled too high to
allow reasonable sequence selection and hence produce an unfolded
protein. These results indicate that effective protein design
requires a consideration of packing effects. Within the context of
a protein design algorithm, we have quantitatively defined the
range of packing forces necessary for successful designs. Also, we
have demonstrated that reduced specificity can be used to design
protein cores with alternative packings.
[0257] To take advantage of the benefits of reduced packing
constraints, protein cores should be designed with the smallest a
that still results in structurally ordered proteins. The optimal
protein sequence from regime 2, .alpha.85, is stable and well
packed, suggesting 0.8.ltoreq..alpha.<0.9 as a good range. NMR
spectra and hydrogen exchange kinetics, however, clearly show that
.alpha.85 is not as structurally ordered as .alpha.90. The packing
arrangements predicted by our program for W43 in .alpha.85 and
.alpha.90 present a possible explanation. For .alpha.90, W43 is
predicted to pack in the core with the same conformation as in the
crystal structure of G.beta.1. In .alpha.85, the larger side chains
at positions 34 and 54, leucine and phenylalanine respectively,
compared to alanine and valine in .alpha.90, force W43 to expose 91
.ANG..sup.2 of nonpolar surface compared to 19 .ANG..sup.2 in
.alpha.90. The hydrophobic driving force this exposure represents
seems likely to stabilize alternate conformations that bury W43 and
thereby could contribute to .alpha.85's conformational flexibility
(Dill, 1985; Onuchic, et al., 1996). In contrast to the other core
positions, a residue at position 43 can be mostly exposed or mostly
buried depending on its side-chain conformation. We designate
positions with this characteristic as boundary positions, which
pose a difficult problem for protein design because of their
potential to either strongly interact with the protein's core or
with solvent.
[0258] A scoring function that penalizes the exposure of
hydrophobic surface area might assist in the design of boundary
residues. Dill and coworkers used an exposure penalty to improve
protein designs in a theoretical study (Sun, et al., Protein Eng.
8(12)1205-1213 (1995)).
[0259] A nonpolar exposure penalty would favor packing arrangements
that either bury large side chains in the core or replace the
exposed amino acid with a smaller or more polar one. We implemented
a side-chain nonpolar exposure penalty in our optimization
framework and used a penalizing solvation parameter with the same
magnitude as the hydrophobic burial parameter.
[0260] The results of adding a hydrophobic surface exposure penalty
to our scoring function are shown in Table 7. TABLE-US-00007 TABLE
7 .alpha. = 0.85 (SEQ ID # A.sub.np TYR LEU LEU ALA ALA PHE ALA VAL
TRP PHE VAL NO: 38) 3 5 7 20 26 30 34 39 43 52 54 1 109 PHE | ILE |
| | LEU ILE | TRP PHE (SEQ ID NO: 50) 2 109 | | ILE | | | LEU ILE |
TRP PHE (SEQ ID NO: 51) 3 104 PHE | ILE | | | LEU ILE | | PHE (SEQ
ID NO: 52) 4 104 | | ILE | | | LEU ILE | | PHE (SEQ ID NO: 53) 5
108 PHE | ILE | | | LEU | | TRP PHE (SEQ ID NO: 54) 6 62 PHE | ILE
| | | LEU ILE VAL TRP PHE (SEQ ID NO: 55) 7 103 PHE | ILE | | | LEU
ILE | TYR PHE (SEQ ID NO: 56) 8 109 PHE | VAL | | | LEU ILE | TRP
PHE (SEQ ID NO: 57) 9 30 PHE | ILE | | | | ILE | | | (SEQ ID NO:
58) 10 38 PHE | ILE | | | | ILE | TRP | (SEQ ID NO: 59) 11 108 | |
ILE | | | LEU | | TRP PHE (SEQ ID NO: 60) 12 62 | | ILE | | | LEU
ILE VAL TRP PHE (SEQ ID NO: 61) 13 109 PHE | ILE | | TYR LEU ILE |
TRP PHE (SEQ ID NO: 62) 14 103 | | ILE | | | LEU ILE | TYR PHE (SEQ
ID NO: 63) 15 109 | | VAL | | | LEU ILE | TRP PHE (SEQ ID NO:
64)
[0261] Table 7 depicts the 15 best sequences (SEQ ID NOS:50-64) for
the core positions of G.beta.1 (SEQ ID NO:38) using .alpha.=0.85
without an exposure penalty. A.sub.np is the exposed nonpolar
surface area in .ANG..sup.2.
[0262] When .alpha.=0.85 the nonpolar exposure penalty dramatically
alters the ordering of low energy sequences. The .alpha.85
sequence, the former ground state, drops to 7.sup.th and the rest
of the 15 best sequences expose far less hydrophobic area because
they bury W43 in a conformation similar to .alpha.90 (model not
shown). The exceptions are the 8.sup.th and 14.sup.th sequences
(SEQ ID NOS: 57 and 63, respectively), which reduce the size of the
exposed boundary residue by replacing W43 with an isoleucine, and
the 13.sup.th best sequence which replaces W43 with a valine. The
new ground state sequence is very similar to .alpha.90, with a
single valine to isoleucine mutation, and should share .alpha.90's
stability and structural order. In contrast, when .alpha.=0.90, the
optimal sequence does not change and the next 14 best sequences,
found by Monte Carlo sampling, change very little. This minor
effect is not surprising, since steric forces still dominate for
.alpha.=0.90 and most of these sequences expose very little surface
area. Burying W43 restricts sequence selection in the core
somewhat, but the reduced packing forces for .alpha.=0.85 still
produce more sequence variety than .alpha.=0.90. The exposure
penalty complements the use of reduced packing specificity by
limiting the gross overpacking and solvent exposure that occurs
when the core's boundary is disrupted. Adding this constraint
should allow lower packing forces to be used in protein design,
resulting in a broader range of high-scoring sequences and reduced
bias from fixed backbone and discrete rotamers.
[0263] To examine the effect of substituting a smaller residue at a
boundary position, we synthesized and characterized the 13.sup.th
best sequence of the .alpha.=0.85 optimization with exposure
penalty (Table 8). TABLE-US-00008 TABLE 8 .alpha. = 0.85 exposure
penalty (SEQ ID # A.sub.np TYR LEU LEU ALA ALA PHE ALA VAL TRP PHE
VAL NO: 38) 3 5 7 20 26 30 34 39 43 52 54 1 30 PHE | ILE | | | |
ILE | | ILE (SEQ ID NO: 65) 2 29 PHE | ILE | | | ILE ILE | | | (SEQ
ID NO: 66) 3 29 PHE ILE PHE | | | | ILE | | | (SEQ ID NO: 67) 4 30
| | ILE | | | | ILE | | ILE (SEQ ID NO: 68) 5 29 | | ILE | | | ILE
ILE | | | (SEQ ID NO: 69) 6 29 | ILE PHE | | | | ILE | | | (SEQ ID
NO: 70) 7 109 PHE | ILE | | | LEU ILE | TRP PHE (SEQ ID NO: 71) 8
52 PHE | ILE | | | LEU ILE ILE | PHE (SEQ ID NO: 72) 9 29 | | ILE |
| | | ILE | | | (SEQ ID NO: 73) 10 29 PHE | ILE | | | | ILE | | |
(SEQ ID NO: 74) 11 109 | | ILE | | | LEU ILE | TRP PHE (SEQ ID NO:
75) 12 38 PHE | ILE | | | | ILE | TRP ILE (SEQ ID) NO: 76) 13 62
PHE | ILE | | | LEU ILE VAL TRP PHE (SEQ ID NO: 77) 14 52 | | ILE |
| | LEU ILE ILE | PHE (SEQ ID NO: 78) 15 30 PHE | ILE | | | | ILE |
TYR ILE (SEQ ID NO: 79)
[0264] Table 8 depicts the 15 best sequences (SEQ ID NOS: 65-79) of
the core positions of G.beta.1 (SEQ ID NO:38) using .alpha.=0.85
with an exposure penalty. A.sub.np is the exposed nonpolar surface
area in .ANG..sup.2.
[0265] This sequence, .alpha.85W43V, replaces W43 with a valine but
is otherwise identical to .alpha.85. Though the 8.sup.th and
14.sup.th sequences (SEQ ID NOS:72 and 78, respectively) also have
a smaller side chain at position 43, additional changes in their
sequences relative to .alpha.85 would complicate interpretation of
the effect of the boundary position change. Also, .alpha.85W43V has
a significantly different packing arrangement compared to G.beta.1,
with 7 out of 11 positions altered, but only an 8% increase in
side-chain volume. Hence, .alpha.85W43V is a test of the tolerance
of this fold to a different, but nearly volume conserving, core.
The far UV CD spectrum of .alpha.85W43V is very similar to that of
G.beta.1 with an ellipticity at 218 nm of -14000 deg cm.sup.2/dmol.
While the secondary structure content of .alpha.85W43V is
native-like, its T.sub.m is 65.degree. C., nearly 20.degree. C.
lower than .alpha.85. In contrast to .alpha.85W43V's decreased
stability, its NMR spectrum has greater chemical shift dispersion
than .alpha.85 (data not shown). The amide hydrogen exchange
kinetics show a well protected set of about four protons after 20
hours (data not shown). This faster exchange relative to .alpha.85
is explained by .alpha.85W43V's significantly lower stability (Mayo
& Baldwin, 1993). .alpha.85W43V appears to have improved
structural specificity at the expense of stability, a phenomenon
observed previously in coiled coils (Harbury, et al., 1993). By
using an exposure penalty, the design algorithm produced a protein
with greater native-like character.
[0266] We have quantitatively defined the role of packing
specificity in protein design and have provided practical bounds
for the role of steric forces in our protein design program. This
study differs from previous work because of the use of an
objective, quantitative program to vary packing forces during
design, which allows us to readily apply our conclusions to
different protein systems. Further, by using the minimum effective
level of steric forces, we were able to design a wider variety of
packing arrangements that were compatible with the given fold.
Finally, we have identified a difficulty in the design of side
chains that lie at the boundary between the core and the surface of
a protein, and we have implemented a nonpolar surface exposure
penalty in our sequence design scoring function that addresses this
problem.
Example 5
Design of a Full Protein
[0267] The entire amino acid sequence of a protein motif has been
computed. As in Example 4, the second zinc finger module of the DNA
binding protein Zif268 was selected as the design template. In
order to assign the residue positions in the template structure
into core, surface or boundary classes, the orientation of the
C.alpha.-C.beta. vectors was assessed relative to a solvent
accessible surface computed using only the template C.alpha. atoms.
A solvent accessible surface for only the C.alpha. atoms of the
target fold was generated using the Connolly algorithm with a probe
radius of 8.0 .ANG., a dot density of 10 .ANG..sup.2, and a
C.alpha. radius of 1.95 .ANG.. A residue was classified as a core
position if the distance from its C.alpha., along its
C.alpha.-C.beta. vector, to the solvent accessible surface was
greater than 5 .ANG., and if the distance from its C.beta. to the
nearest surface point was greater than 2.0 .ANG.. The remaining
residues were classified as surface positions if the sum of the
distances from their C.alpha., along their C.alpha.-C.beta. vector,
to the solvent accessible surface plus the distance from their
C.beta. to the nearest surface point was less than 2.7 .ANG.. All
remaining residues were classified as boundary positions. The
classifications for Zif268 were used as computed except that
positions 1, 17 and 23 were converted from the boundary to the
surface class to account for end effects from the proximity of
chain termini to these residues in the teriary structure and
inaccuracies in the assignment.
[0268] The small size of this motif limits to one (position 5) the
number of residues that can be assigned unambiguously to the core
while seven residues (positions 3, 7, 12, 18, 21, 22, and 25) were
classified as boundary and the remaining 20 residues were assigned
to the surface. Interestingly, while three of the zinc binding
positions of Zif268 are in the boundary or core, one residue,
position 8, has a C.alpha.-C.beta. vector directed away from the
protein's geometric center and is classified as a surface position.
As in our previous studies, the amino acids considered at the core
positions during sequence selection were A, V, L, I, F, Y, and W;
the amino acids considered at the surface positions were A, S, T,
H, D, N, E, Q, K, and R; and the combined core and surface amino
acid sets (16 amino acids) were considered at the boundary
positions. Two of the residue positions (9 and 27) have .phi.
angles greater than 0.degree. and are set to Gly by the sequence
selection algorithm to minimize backbone strain.
[0269] The total number of amino acid sequences that must be
considered by the design algorithm is the product of the number of
possible amino acid types at each residue position. The
.beta..beta..alpha. motif residue classification described above
results in a virtual combinatorial library of 1.9.times.10.sup.27
possible amino acid sequences (one core position with 7 possible
amino acids, 7 boundary positions with 16 possible amino acids, 18
surface positions with 10 possible amino acids and 2 positions with
0 angles greater than 0.degree. each with 1 possible amino acid). A
corresponding peptide library consisting of only a single molecule
for each 28 residue sequence would have a mass of 11.6 metric tons.
In order to accurately model the geometric specificity of
side-chain placement, we explicitly consider the torsional
flexibility of amino acid side chains in our sequence scoring by
representing each amino acid with a discrete set of allowed
conformations, called rotamers. As above, a backbone dependent
rotatmer library was used (Dunbrack and Karplus, supra), with
adjustments in the .chi..sub.1 and .chi..sub.2 angles of
hydrophobic residues. As a result, the design algorithm must
consider all rotamers for each possible amino acid at each residue
position. The total size of the search space for the
.beta..beta..alpha. motif is therefore 1.1.times.10.sup.62 possible
rotamer sequences. The rotamer optimization problem for the
.beta..beta..alpha. motif required 90 CPU hours to find the optimal
sequence.
[0270] The optimal sequence, shown in FIG. 11, is called Full
Sequence Design-1 (FSD-1) (SEQ ID NO:3). Even though all of the
hydrophilic amino acids were considered at each of the boundary
positions, the algorithm selected only nonpolar amino acids. The
eight core and boundary positions are predicted to form a
well-packed buried cluster. The Phe side chains selected by the
algorithm at the zinc binding His positions of Zif268, positions 21
and 25, are over 80% buried and the Ala at position 5 is 100%
buried while the Lys at position 8 is greater than 60% exposed to
solvent. The other boundary positions demonstrate the strong steric
constraints on buried residues by packing similar side chains in an
arrangement similar to that of Zif268. The calculated optimal
configuration for core and boundary residues buries .about.1150
.ANG..sup.2 of nonpolar surface area. On the helix surface, the
program positions Asn 14 as a helix N-cap with a hydrogen bond
between its side-chain carbonyl oxygen and the backbone amide
proton of residue 16. The eight charged residues on the helix form
three pairs of hydrogen bonds, though in our coiled coil designs
helical surface hydrogen bonds appeared to be less important than
the overall helix propensity of the sequence (Dahiyat, et al.,
Science (1997)). Positions 4 and 11 on the exposed sheet surface
were selected to be Thr, one of the best i-sheet forming residues
(Kim, et al. 1993).
[0271] FIG. 11 shows the alignment of the sequences for FSD-1 (SEQ
ID NO:3) and Zif268 (SEQ ID NO:1). Only 6 of the 28 residues (21%)
are identical and only 11 (39%) are similar. Four of the identities
are in the buried cluster, which is consistent with the expectation
that buried residues are more conserved than solvent exposed
residues for a given motif (Bowie, et al., Science 247:1306-1310
(1990)). A BLAST (Altschul, et al., supra) search of the FSD-1
sequence (SEQ ID NO:3) against the non-redundant protein sequence
database of the National Center for Biotechnology Information did
not find any zinc finger protein sequences. Further, the BLAST
search found only low identity matches of weak statistical
significance to fragments of various unrelated proteins. The
highest identity matches were 10 residues (36%) with p values
ranging from 0.63-1.0. Random 28 residue sequences that consist of
amino acids allowed in the .beta..beta..alpha. position
classification described above produced similar BLAST search
results, with 10 or 11 residue identities (36-39%) and p values
ranging from 0.35-1.0, further suggesting that the matches found
for FSD-1 are statistically insignificant. The very low identity to
any known protein sequence demonstrates the novelty of the FSD-1
sequence (SEQ ID NO:3) and underscores that no sequence information
from any protein motif was used in our sequence scoring
function.
[0272] In order to examine the robustness of the computed sequence,
the sequence of FSD-1 (SEQ ID NO:3) was used as the starting point
of a Monte Carlo simulated annealing run. The Monte Carlo search
finds high scoring, suboptimal sequences in the neighborhood of the
optimal solution (Dahiyat, et al., (1996) (supra)). The energy
spread from the ground-state solution to the 1000.sup.th most
stable sequence is about 5 kcal/mol indicating that the density of
states is high. The amino acids comprising the core of the
molecule, with the exception of position 7, are essentially
invariant (FIG. 11). Almost all of the sequence variation occurs at
surface positions, and typically involves conservative changes. Asn
14, which is predicted to form a helix N-cap, is among the most
conserved surface positions. The strong sequence conservation
observed for critical areas of the molecule suggests that if a
representative sequence folds into the design target structure,
then perhaps thousands of sequences whose variations do not disrupt
the critical interactions may be equally competent. Even if
billions of sequences would successfully achieve the target fold,
they would represent only a vanishingly small proportion of the
1027 possible sequences.
[0273] Experimental validation. FSD-1 was synthesized in order to
characterize its structure and assess the performance of the design
algorithm. The far UV circular dichroism (CD) spectrum of FSD-1
shows minima at 220 nm and 207 nm, which is indicative of a folded
structure (data not shown). The thermal melt is weakly cooperative,
with an inflection point at 39.degree. C., and is completely
reversible (data not shown). The broad melt is consistent with a
low enthalpy of folding which is expected for a motif with a small
hydrophobic core. This behavior contrasts the uncooperative thermal
unfolding transitions observed for other folded short peptides
(Scholtz, et al., 1991). FSD-1 is highly soluble (greater than 3
mM) and equilibrium sedimentation studies at 100 .mu.M, 500 .mu.M
and 1 mM show the protein to be monomeric. The sedimentation data
fit well to a single species, monomer model with a molecular mass
of 3630 at 1 mM, in good agreement with the calculated monomer mass
of 3488. Also, far UV CD spectra showed no concentration dependence
from 50 .mu.M to 2 mM, and nuclear magnetic resonance (NMR) COSY
spectra taken at 100 .mu.M and 2 mM were essentially identical.
[0274] The solution structure of FSD-1 was solved using homonuclear
2D .sup.1H NMR spectroscopy (Piantini, et al., 1982). NMR spectra
were well dispersed indicating an ordered protein structure and
easing resonance assignments. Proton chemical shift assignments
were determined with standard homonuclear methods (Wuthrich, 1986).
Unambiguous sequential and short-range NOEs indicate helical
secondary structure from residues 15 to 26 in agreement with the
design target.
[0275] The structure of FSD-1 was determined using 284 experimental
restraints (10.1 restraints per residue) that were non-redundant
with covalent structure including 274 NOE distance restraints and
10 hydrogen bond restraints involving slowly exchanging amide
protons. Structure calculations were performed using X-PLOR
(Brunger, 1992) with standard protocols for hybrid distance
geometry-simulated annealing (Nilges, et al., FEBS Lett. 229:317
(1988)). An ensemble of 41 structures converged with good covalent
geometry and no distance restraint violations greater than 0.3
.ANG. (Table 9). TABLE-US-00009 TABLE 9 NMR structure
determination: distance restraints, structural statistics and
atomic root-mean-square (rms) deviations. <SA> are the 41
simulated annealing structures, SA is the average structure before
energy minimization, (SA).sub.r is the restrained energy minimized
average structure, and SD is the standard deviation. Distance
restraints Intraresidue 97 Sequential 83 Short range (|i-j| = 2-5
59 residues) Long range (|i-j| > 5 35 residues) Hydrogen bond 10
Total 284 Structural statistics <SA> .+-. SD (SA).sub.r Rms
deviation from 0.043 .+-. 0.003 0.038 distance restraints (.ANG.)
Rms deviation from idealized geometry Bonds (.ANG.) 0.0041 .+-.
0.0002 0.0037 Angles (degrees) 0.67 .+-. 0.02 0.65 Impropers 0.53
.+-. 0.05 0.51 (degrees) Atomic rms deviations (.ANG.)* <SA>
vs. <SA> vs. SA .+-. SD (SA).sub.r .+-. SD Backbone 0.54 .+-.
0.15 0.69 .+-. 0.16 Backbone + 0.99 .+-. 0.17 1.16 .+-. 0.18
nonpolar side chains.dagger. Heavy atoms 1.43 .+-. 0.20 1.90 .+-.
0.29 *Atomic rms deviations are for residues 3 to 26, inclusive.
Residues 1, 2, 27 and 28 were disordered (.phi., .psi. angular
order parameters (34) < 0.78) and had only sequential and |i-j|
= 2 NOEs. .dagger.Nonpolar side chains are from residues 3, 5, 7,
12, 18, 21, 22, and 25 which consitute the core of the protein.
[0276] The backbone of FSD-1 is well defined with a
root-mean-square (rms) deviation from the mean of 0.54 .ANG.
(residues 3-26). Considering the buried side chains (residues 3, 5,
7, 12, 18, 21, 22, and 25) in addition to the backbone gives an rms
deviation of 0.99 .ANG., indicating that the core of the molecule
is well ordered. The stereochemical quality of the ensemble of
structures was examined using PROCHECK (Laskowski, et al., J. Appl.
Crystallogr. 26:283 (1993)). Not including the disordered termini
and the glycine residues, 87% of the residues fall in the most
favored region and the remainder in the allowed region of .phi.,
.psi., space. Modest heterogeneity is present in the first strand
(residues 3-6) which has an average backbone angular order
parameter (Hyberts, et al., 1992) of <S>=0.96.+-.0.04
compared to the second strand (residues 9-12) with an
<S>=0.98.+-.0.02 and the helix (residues 15-26) with an
<S>=0.99.+-.0.01. Overall, FSD-1 is notably well ordered and,
to our knowledge, is the shortest sequence consisting entirely of
naturally occurring amino acids that folds to a unique structure
without metal binding, oligomerization or disulfide bond formation
(McKnight, et al., 1997).
[0277] The packing pattern of the hydrophobic core of the NMR
structure ensemble of FSD-1 (Tyr 3, Ile 7, Phe 12, Leu 18, Phe 21,
Ile 22, and Phe 25) is similar to the computed packing arrangement.
Five of the seven residues have .chi..sub.1 angles in the same
gauche.sup.+, gauche.sup.- or trans category as the design target,
and three residues match both .chi..sub.1 and .chi..sub.2 angles.
The two residues that do not match their computed .chi..sub.1
angles are Ile 7 and Phe 25, which is consistent with their
location at the less constrained, open end of the molecule. Ala 5
is not involved in its expected extensive packing interactions and
instead exposes about 45% of its surface area because of the
displacement of the strand 1 backbone relative to the design
template. Conversely, Lys 8 behaves as predicted by the algorithm
with its solvent exposure (60%) and .chi..sub.1 and .chi..sub.2
angles matching the computed structure. Most of the solvent exposed
residues are disordered which precludes examination of the
predicted surface residue hydrogen bonds. Asn 14, however, forms a
helix N-cap from its sidechain carbonyl oxygen as predicted, but to
the amide of Glu 17, not Lys 16 as expected from the design. This
hydrogen bond is present in 95% of the structure ensemble and has a
donor-acceptor distance of 2.6 .+-.0.06 .ANG.. In general, the side
chains of FSD-1 correspond well with the design program
predictions.
[0278] A comparison of the average restrained minimized structure
of FSD-1 and the design target was done (data not shown). The
overall backbone rms deviation of FSD-1 from the design target is
1.98 .ANG. for residues 3-26 and only 0.98 .ANG. for residues 8-26
(Table 10). TABLE-US-00010 TABLE 10 Comparison of the FSD-1
experimentally determined structure and the design target
structure. The FSD-1 structure is the restrained energy minimized
average from the NMR structure determination. The design target
structure is the second DNA binding module of the zinc finger
Zif268 (9). Atomic rms deviations (.ANG.) Backbone, residues 3-26
1.98 Backbone, residues 8-26 0.98 Super-secondary structure
parameters* FSD-1 Design Target h(.ANG.) 9.9 8.9 .theta.(degrees)
14.2 16.5 .OMEGA.(degrees) 13.1 13.5 *h, .theta., .OMEGA. are
calculated as previously described (36, 37). h is the distance
between the centroid of the helix C.alpha. coordinates (residues
15-26) and the least-square plane fit to the C.alpha. coordinates
of the sheet (residues 3-12. .theta. is the angle of inclination of
the principal moment of the helix C.alpha. atoms with the plane of
the sheet. .OMEGA. is the angle between the projection of the
principal moment of the helix onto the sheet and the projection of
the # average least-square fit line to the strand C.alpha.
coordinates (residues 3-6 and 9-12) onto the sheet.
[0279] The largest difference between FSD-1 and the target
structure occurs from residues 4-7, with a displacement of 3.0-3.5
.ANG. of the backbone atom positions of strand 1. The agreement for
strand 2, the strand to helix turn, and the helix is remarkable,
with the differences nearly within the accuracy of the structure
determination. For this region of the structure, the rms difference
of .phi.,.psi. angles between FSD-1 and the design target is only
14.+-.90. In order to quantitatively assess the similarity of FSD-1
to the global fold of the target, we calculated their
supersecondary structure parameters (Table 9) (Janin & Chothia,
J. Mol. Biol. 143:95 (1980); Su & Mayo, Protein Sci. in press,
1997), which describe the relative orientations of secondary
structure units in proteins. The values of 8, the inclination of
the helix relative to the sheet, and 0, the dihedral angle between
the helix axis and the strand axes, are nearly identical. The
height of the helix above the sheet, h, is only 1 .ANG. greater in
FSD-1. A study of protein core design as a function of helix height
for G.beta.1 variants demonstrated that up to 1.5 .ANG. variation
in helix height has little effect on sequence selection (Su &
Mayo, supra, 1997). The comparison of secondary structure parameter
values and backbone coordinates highlights the excellent agreement
between the experimentally determined structure of FSD-1 and the
design target, and demonstrates the success of our algorithm at
computing a sequence for this .beta..beta..alpha. motif.
[0280] The quality of the match between FSD-1 and the design target
demonstrates the ability of our program to design a sequence for a
fold that contains the three major secondary structure elements of
proteins: sheet, helix, and turn. Since the .beta..beta..alpha.
fold is different from those used to develop the sequence selection
methodology, the design of FSD-1 represents a successful transfer
of our program to a new motif.
Example 6
Calculation of Solvent Accessible Surface Area Scaling Factors
[0281] In contrast to the previous work, backbone atoms are
included in the calculation of surface areas. Thus, the calculation
of the scaling factors proceeds as follows.
[0282] The program BIOGRAF (Molecular Simulations Incorporated, San
Diego, Calif.) was used to generate explicit hydrogens on the
structures which were then conjugate gradient minimized for 50
steps using the DREIDING force field. Surface areas were calculated
using the Connolly algorithm with a dot density of 10 .ANG.-2,
using a probe radius of zero and an add-on radius of 1.4 .ANG. and
atomic radii from the DREIDING force-field. Atoms that contribute
to the hydrophobic surface area are carbon, sulfur and hydrogen
atoms attached to carbon and sulfur.
[0283] For each side-chain rotamer rat residue position i with a
local tri-peptide backbone t3, we calculated
A.sup.0.sub.i.sub.r.sub.t3 the exposed area of the rotamer and its
backbone in the presence of the local tri-peptide backbone, and
A.sub.i.sub.r.sub.t the exposed area of the rotamer and its
backbone in the presence of the entire template t which includes
the protein backbone and any side-chains not involved in the
calculation (FIG. 13). The difference between
A.sup.0.sub.i.sub.r.sub.t3, and A.sub.i.sub.r.sub.t is the total
area buried by the template for a rotamer r at residue position i.
For each pair of residue positions i and j and rotamers r and s on
i and j, respectively, A.sub.i.sub.r.sub.j.sub.s.sub.t the exposed
area of the rotamer pair in the presence of the entire template, is
calculated. The difference between A.sub.i.sub.r.sub.j.sub.s.sub.t
and the sum of A.sub.i.sub.r.sub.t and A.sub.j.sub.s.sub.t is the
area buried between residues i and j, excluding that area by the
template. The pairwise approximation to the total buried surface
area is: Equation .times. .times. 29 .times. : ##EQU11## A buried
pairwise = i .times. ( A i r .times. t3 0 - A i r .times. t ) + f
.times. i < j .times. ( A i r .times. t + A j s .times. t - A i
r .times. j s .times. t ) ##EQU11.2##
[0284] As shown in FIG. 13, the second sum in Equation 29
over-counts the buried area. We have therefore multiplied the
second sum by a scale factor f whose value is to be determined
empirically. Expected values of f are discussed below.
[0285] Noting that the buried and exposed areas should add to the
total area, .SIGMA..sub.i A.sup.0.sub.i.sub.r.sub.t3, the
solvent-exposed surface area is: Equation .times. .times. 30
.times. : ##EQU12## A exposed pairwise = i .times. A i r .times. t
- f .times. i < j .times. ( A i r .times. t + A j s .times. t -
A i r .times. j s .times. t ) ##EQU12.2##
[0286] The first sum of Equation 30 represents the total exposed
area of each rotamer in the context of the protein template
ignoring interactions with other rotamers. The second sum of
Equation 30 subtracts the buried areas between rotamers and is
scaled by the same parameter f as in Equation 29.
[0287] Some insight into the expected value of f can be gained from
consideration of a close-packed face centered cubic lattice of
spheres or radius r. When the radii are increased from r to R, the
surface area on one sphere buried by a neighboring sphere is
2.pi.R(R-r). We take r to be a carbon radius (1.95 .ANG.), and R is
1.4 .ANG. larger. Then, using: f = true .times. .times. buried
.times. .times. area pairwise .times. .times. buried .times.
.times. area ##EQU13## and noting that each sphere has 12
neighbors, results in: f = 4 .times. .pi. .times. .times. R 2 12
.times. x2 .times. .times. .pi. .times. .times. R .function. ( R -
r ) ##EQU14##
[0288] This yields f=0.40. A close-packed face centered cubic
lattice has a packing fraction of 74%. Protein interiors have a
similar packing fraction, although because many atoms are
covalently bonded the close packing is exaggerated. Therefore this
value of f should be a lower bound for real protein cores. For
non-core residues, where the packing fraction is lower, a somewhat
larger value of f is expected.
[0289] We classified residues from ten proteins ranging in size
from 54 to 289 residues into core or non-core as follows. We
classified resides as core or non-core using an algorithm that
considered the direction of each side-chain's C.alpha.-C.beta.
vector relative to the surface computed using only the template
C.alpha. atoms with a carbon radius of 1.95 .ANG., a probe radius
of 8 .ANG. and no add-on radius. A residue was classified as a core
position if both the distance from its C.alpha. atom (along its
C.alpha.-C.beta. vector) to the surface was greater than 5.0 .ANG.
and the distance from its C.beta. atom to the nearest point on the
surface was greater than 2.0 .ANG.. The advantage of such an
algorithm is that a knowledge of the amino acid type actually
present at each residue position is not necessary. The proteins
were as shown in Table I, showing selected proteins, total number
of residues and the number of residues in the core and non-core of
each protein (Gly and pro were not considered). TABLE-US-00011
Brookhaven Identifier Total Size Core Size Non-Core Size 1enh 54 10
40 1pga 56 10 40 1ubi 76 16 50 1mol 94 19 61 1kpt 105 27 60 4azu-A
128 39 71 1gpr 158 39 89 1gcs 174 53 98 1edt 266 95 133 1pbn 289 96
143
[0290] The classification into core and non-core was made because
core residues interact more strongly with one another than do
non-core residues. This leads to greater over-counting of the
buried surface area for core residues.
[0291] Considering the core and non-core cases separately, the
value of f which most closely reproduced the true Lee and Richards
surface areas was calculated for the ten proteins. The pairwise
approximation very closely matches the true buried surface area
(data not shown). It also performs very well for the exposed
hydrophobic surface area of non-core residues (data not shown). The
calculation of the exposed surface area of the entire core of a
protein involves the difference of two large and nearly equal areas
and is less accurate; as will be shown, however, when there is a
mixture of core and non-core residues, a high accuracy can still be
achieved. These calculations indicate that for core residues f is
0.42 and for non-core residues f is 0.79.
[0292] To test whether the classification of residues into core and
non-core was sufficient, we examined subsets of interacting
residues in the core and non-core positions, and compared the true
buried area of each subset with that calculated (using the above
values of f). For both subsets of the core and the non-core, the
correlation remained high (R.sup.2=1.00) indicating that no further
classification is necessary (data not shown). (Subsets were
generated as follows: given a seed residue, a subset of size two
was generated by adding the closest residue: the next closest
residue was added for a subset of size three, and this was repeated
up to the size of the protein. Additional subsets were generated by
selecting different seed residues.) It remains to apply this
approach to calculating the buried or exposed surface areas of an
arbitrary selection of interacting core and non-core residues in a
protein. When a core residue and a non-core residue interact, we
replace Equation 29 with: Equation .times. .times. 31 .times. :
##EQU15## A buried pairwise = i .times. ( A i r .times. t3 0 - A i
r .times. t ) + i < j .times. ( f i .times. A i r .times. t + f
j .times. A j f .times. t - f ij .times. A i r .times. j f .times.
t ) ##EQU15.2## and Equation 30 with Equation 32: A exposed
pairwise = i .times. A i r .times. t - i < j .times. ( f i
.times. A i r .times. t + f j .times. A j f .times. t - f ij
.times. A i r .times. j f .times. t ) ##EQU16## where f.sub.i and
f.sub.j are the values of f appropriate for residues i and j,
respectively, and f.sub.{ij} takes on an intermediate value. Using
subsets from the whole of 1 pga, the optimal value of f.sub.ij was
found to be 0.74. This value was then shown to be appropriate for
other test proteins (data not shown).
Example 7
The Use of Supersecondary Structure Parameters to Incorporate
Backbone Flexibility
[0293] This example is concerned primarily with coupling backbone
flexibility and the selection of amino acids for protein cores and
an assessment of the tolerance of our side-chain selection
algorithm to perturbations in protein backbone geometry. An ideal
model system for these purposes is the .beta.1
immunoglobulin-binding domain of streptococcal protein G (G.beta.1)
(Gronenborn et al., Science 253:657-661(1991 "A novel, highly
stable fold of the immunoglobulin binding domain of streptococcal
protein G"). Its small size, 56 residues, renders computations more
tractable and simplifies production of the protein by either
synthetic or recombinant methods. A solution structure (Gronenborn
et al., id) and several crystal structures (Gallagher et al.,
Biochemistry 33:4721-4729 (1994), "Two crystal structures of the
.beta.1 immunoglobulin-binding domain of streptococcal protein G
and comparison with NMR") are available to provide backbone
templates for the side-chain selection algorithm. In addition, the
energetics and structural dynamics of G.beta.1 have been
extensively characterized (Alexander et al. Biochemistry
31:3597-3603, (1992) "Thermodynamic analysis of the folding of the
streptococcal protein G IgG-binding domains .beta.1 and
.beta.2--Why small proteins tend to have high denaturation
temperatures"); Barchi et al., Protein Sci 3:15-21 (1994)
"Investigation of the backbone dynamics of the IgG-binding domain
of spreptococcal protein G by heteronuclear two-dimensional
.sup.1H-.sup.15N nuclear magnetic resonance spectroscopy");
Kuszewski et al., Protein Sci 3:1945-1952 (1994) "Fast folding of a
prototypic polypeptide--The immunoglobulin binding domain of
streptococcal protein G"); Orban et al., Biochemistry
34:15291-15300 (1995) "Assessment of stability differences in the
protein G.beta.1 and .beta.2 domains from hydrogen deuterium
exchange--Comparison with calorimetric data"). G.beta.1 contains no
disulfide bonds and does not require a cofactor or metal ion to
fold, but relies upon the burial of its hydrophobic core for
stability. Further, G.beta.1 contains sheet, helix and turn
structures and is without the repetitive side-chain packing
patterns found in coiled coils and some helical bundles. This lack
of periodicity reduces the bias from a particular secondary or
tertiary structure and necessitates the use of an objective
algorithm for side-chain selection. Perhaps most important for this
study, the G.beta.1 backbone can be classified as an .alpha./.beta.
fold, a class for which extensive super-secondary structure
analysis has been performed (Chothia et al., 1977 (id); Janin &
Chothia, 1980 (id); Cohen et al., 1982 (id); Chou et al., 1985
(id)).
[0294] Sequence positions that constitute the core were chosen by
examining the side-chain solvent accessible surface area of
G.beta.1. We selected the ten most buried positions which includes
residues 3, 5, 7, 20, 26, 30, 34, 39, 52 and 54. The remainder of
the protein structure, including all other side chains and the
backbone, was used as the template for sequence selection
calculations at the ten core positions.
Backbone Perturbation, Scoring Functions and DEE
[0295] The initial G.beta.1 structure was taken from PDB entry 1
pga (Bernstein et al., J. Mol. Biol. 112:535-542 (1977) "The
Protein Data Bank: A computer-based archival file for
macromolecular structures"); Gallagher et al., 1994 (id). The
program BIOGRAF (Molecular Simulations Incorporated, San Diego,
Calif.) was used to generate explicit hydrogens on the structure
which was then conjugate gradient minimized for 50 steps using the
DREIDING forcefield (Mayo et al., 1990 (id)). The coordinate
positions of atoms not involved in core sequence selection or
backbone perturbations were kept fixed. Concerted backbone
movements were performed by repositioning the .alpha.-helix
(residues 23 through 36) to reflect the desired change in the
indicated super-secondary structure parameter value. The coordinate
positions of atoms belonging to residues 23, 24, 25, 27, 28, 29,
31, 32, 33, 35 and 36 were kept fixed after repositioning the
helix. The distorted peptide bonds that result from backbone
perturbations were left unchanged. The .DELTA.h, .DELTA..OMEGA. and
.DELTA..sigma.-series perturbations were carried out by translating
the helix along the sheet axis, rotating the helix about the sheet
axis and rotating the helix about the vector parallel to the helix
axis that passes through the helix center, respectively (see FIG.
14). The .DELTA..theta.-series perturbations were carried out by
rotating the helix about the vector resulting from the cross
product of the sheet axis and the vector parallel to the helix axis
that passes through the helix center. A Lennard-Jones 12-6
potential was used for van der Waals interactions with atomic radii
scaled by either 1.0 or 0.9 as indicated (Dahiyat & Mayo,
submitted). The Richards definition of solvent-accessible surface
area (Lee & Richards, 1971, supra) was used and areas were
calculated with the Connolly algorithm (Connolly, 1983, supra). An
atomic solvation parameter of 23.2 cal/mol/.ANG..sup.2 was used to
favor hydrophobic burial (Dahiyat & Mayo, 1996, supra). The
rotamer library and DEE optimization followed the methods of our
previous work (Dahiyat & Mayo, 1996, supra). Calculations were
performed on either a 12 processor, R10000-based Silicon Graphics
Power Challenge or a 512 node Intel Delta.
Mutagenesis and Protein Purification
[0296] A synthetic G.beta.1 gene (Minor & Kim, 1994) was cloned
into pET11a (Novagen) and used as the template for inverse PCR
mutagenesis (Hemsley et al., 1989). 5' phosphorylated oligos
(Genosys) were used without further purification. Mutant sequences
were confirmed by DNA sequencing. The expression and purification
of the mutant proteins followed published procedures (Minor &
Kim, 1994). Incomplete N-terminal processing resulted in a mixture
of 56 and 57 residue proteins which were separated by HPLC (Minor
& Kim, 1994, supra). The 57 residue proteins were used in all
cases except for mutants .DELTA.h.sub.0.9[-1.50 .ANG.] and
.DELTA.h.sub.0.9[+1.50 .ANG.], where the 56 residue proteins were
used. Molecular weights were confirmed by mass spectrometry.
CD and NMR
[0297] CD spectra were measured on an Aviv 62DS spectrometer at pH
6.0, 50 mM sodium phosphate buffer, 25.degree. C. and 50 .mu.M
protein. A 1 mm pathlength cell was used and the temperature was
controlled by a thermoelectric unit. Thermal melts were performed
in the same buffer using two degree temperature increments with an
averaging time of 10 s and an equilibration time of 90 s. T.sub.m
values were derived from the ellipticity at 218 nm ([0]218) by
evaluating the maximum of a d[.theta.].sub.218/dT versus T plot.
The T.sub.m's were reproducible to within two degrees. Protein
concentrations were determined by UV spectrophotometry. NMR samples
were prepared in 90/10H.sub.2O/D.sub.2O and 50 mM phosphate buffer
at pH 6.0. Spectra were acquired on a Varian Unity Plus 600 MHz
spectrometer at 25.degree. C. 1024 transients were acquired with
1.5 seconds of solvent presaturation used for water suppression.
Samples were approximately 0.5 mM.
Results
[0298] Four sets of perturbed backbones were generated by varying
G.beta.1's super-secondary structure parameter values (FIG. 14).
All possible core sequences consisting of alanine, valine, leucine,
isoleucine, phenylalanine, tyrosine and tryptophan (A, V, L, I, F,
Y and W) were considered for each perturbed backbone. The rotamer
library was as described above (see Dahiyat & Mayo, 1996,
supra). Optimizing the sequences of the cores of G.beta.1 and its
structural homologues with 217 possible hydrophobic rotamers
considered at each of the ten core positions results in 217.sup.10
(.about.10.sup.23) rotamer sequences. Our scoring function
consisted of two components: a van der Waals energy term and an
atomic salvation term favoring burial of hydrophobic surface area.
The van der Waals radii of the atoms in the simulation were scaled
by either 1.0 or 0.9 in order to reduce the effects of using
discrete rotamers (see Mayo et al., 1990, supra, and Example 6).
Global optimum sequences for each of the backbone variants were
found using the Dead-End Elimination (DEE) theorem (Desmet et al.,
1992, supra; Desmet et al., 1994, supra; Goldstein, 1994, supra).
Optimal sequences, and their corresponding proteins, are named by
the backbone perturbation type, the size of the perturbation and
the radius scale factor used in their design. For example, the
sequence designed using a template whose helix was translated by
+1.50 .ANG. along the sheet axis and a radius scale factor of 0.9
is called .DELTA.h.sub.0.9[+1.50 .ANG.]. Backbone perturbations
that result in the same calculated core sequence are named by the
perturbation with the greatest magnitude. For example,
.DELTA.h.sub.0.9 backbone perturbations of +1.25 and +1.50 .ANG.
result in the same sequence which is called .DELTA.h.sub.0.9[+1.50
.ANG.]. The calculated core sequences corresponding to various
backbone perturbations are listed in Tables 1-5, below.
TABLE-US-00012 TABLE 11 DEE determined optimal sequences for the
core positions of G.beta.1 as a function of .DELTA.h.sub.0.9.sup.a-
G.beta.1 sequence (SEQ ID NO: 38) .DELTA.h.sub.0.9 Tm (.ANG.) vol
TYR LEU LEU ALA ALA PHE ALA VAL PHE VAL (.degree. C.) NMR 3 5 7 20
26 30 34 39 52 54 -1.50 1.04 PHE ILE VAL VAL | | | ILE | |(SEQ ID
NO: 80) 69 + -1.25 1.04 PHE ILE VAL VAL | | | ILE | |(SEQ ID NO:
80) 69 + -1.00 0.99 PHE | VAL | | | | ILE | |(SEQ ID NO: 81) 89 +
-0.75 0.99 PHE | VAL | | | | ILE | |(SEQ ID NO: 81) 89 + -0.50 0.99
PHE | VAL | | | | ILE | |(SEQ ID NO: 81) 89 + -0.25 0.99 PHE | VAL
| | | | ILE | |(SEQ ID NO: 81) 89 + 0.00 1.01 PHE | ILE | | | | ILE
| |(SEQ ID NO: 82) 91 + -0.25 1.05 PHE | ILE | | | | ILE TRP |(SEQ
ID NO: 83) 89 + +0.50 1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO:
83) 89 + +0.75 1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO: 83) 89 +
+1.00 1.13 PHE | ILE | | | ILE ILE TRP |(SEQ ID NO: 84) 85 + +1.25
1.20 PHE | ILE | LEU | ILE ILE TRP |(SEQ ID NO: 85) 53 - +1.50 1.20
PHE | ILE | LEU | ILE ILE TRP |(SEQ ID NO: 85) 53 - .sup.aThe
G.beta.1 wild-type sequence (SEQ ID NO: 38) and position numbers
are shown at the top of the Table. A vertical bar indicates
identity with the G.beta.1 sequence (SEQ ID NO: 38). .DELTA.h is
the change in the super-secondary structure parameter, h; vol is
the fraction of core side-chain volume relative to the G.beta.1
sequence (SEQ ID NO: 38); T.sub.m is the melting temperature
measured by circular dichroism; NMR is a qualitative indication of
the degree of chemical shift dispersion in the 1D .sup.1H NMR
spectra. The T.sub.m'S for .DELTA.h.sub.0.9[-1.50 .ANG.] and
.DELTA.h.sub.0.9[+1.50 .ANG.] were determined for 56 residue
proteins (compared to 57 residue proteins for G.beta.1 and all
other mutants) which overstates the melting temperature by about
2.degree. C., the melting temperature difference between the 56 and
57 residue versions of G.beta.1.
[0299] TABLE-US-00013 TABLE 12 DEE determined optimal sequences for
the core positions of G.beta.1 as a function of
.DELTA.h.sub.1.0.sup.a- G.beta.1 sequence (SEQ ID NO: 38)
.DELTA.h.sub.1.0 Tm (.ANG.) vol TYR LEU LEU ALA ALA PHE ALA VAL PHE
VAL (.degree. C.) NMR 3 5 7 20 26 30 34 39 52 54 -1.50 0.52 ALA ALA
ALA | | ALA | LEU ALA ALA (SEQ ID NO: 86) ND ND -1.25 0.62 PHE ALA
ALA | | ALA | LEU ALA ALA (SEQ ID NO: 87) ND ND -1.00 0.62 PHE ALA
ALA | | ALA | LEU ALA ALA (SEQ ID NO: 87) ND ND -0.75 0.91 PHE ALA
VAL | | | | ILE | |(SEQ ID NO: 88) ND ND -0.50 0.99 PHE | VAL | | |
| ILE | |((SEQ ID NO: 89) 89 + -0.25 0.99 PHE | VAL | | | | ILE |
|(SEQ ID NO: 89) 89 + 0.00 1.01 PHE | ILE | | | | ILE | |(SEQ ID
NO: 90) 91 + +0.25 1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO: 91)
89 + +0.50 1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO: 91) 89 +
+0.75 1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO: 91) 89 + +1.00
1.05 PHE | ILE | | | | ILE TRP |(SEQ ID NO: 91) 89 + +1.25 1.05 PHE
| ILE | | | | ILE TRP |(SEQ ID NO: 91) 89 + +1.50 1.11 PHE | ILE |
| LEU ILE ILE TRP |(SEQ ID NO: 92) 73 + .sup.aThe G.beta.1
wild-type sequence (SEQ ID NO: 38) and position numbers are shown
at the top of the Table. A vertical bar indicates identity with the
G.beta.1 sequence (SEQ ID NO: 38). .DELTA.h is the change in the
super-secondary structure parameter, h; vol is the fraction of core
side-chain volume relative to the G.beta.1 sequence (SEQ ID NO:
38); T.sub.m is the melting temperature measured by circular
dichroism; NMR is a qualitative indication of the degree of
chemical shift dispersion in the 1D .sup.1H NMR spectra; ND
indicates a property that was not determined.
[0300] TABLE-US-00014 TABLE 13 DEE determined optimal sequences for
the core positions of G.beta.1 as a function of
.DELTA..OMEGA..sub.0.9.sup.a- G.beta.1 sequence (SEQ ID NO: 38)
.DELTA..OMEGA.(.degree.) vol TYR LEU LEU ALA ALA PHE ALA VAL PHE
VAL Tm (.degree. C.) NMR 3 5 7 20 26 30 34 39 52 54 -10.0 1.00 VAL
| VAL VAL | | | ILE | |(SEQ ID NO: 93) ND ND -7.5 0.99 PHE | VAL |
| | | ILE | |(SEQ ID NO: 89) 89 + -5.0 0.99 PHE | VAL | | | | ILE |
|(SEQ ID NO: 89) 89 + -2.5 0.99 PHE | VAL | | | | ILE | |(SEQ ID
NO: 89) 89 + 0.0 1.01 PHE | ILE | | | | ILE | |(SEQ ID NO: 90) 91 +
+2.5 1.01 PHE | ILE | | | | ILE | |(SEQ ID NO: 90) 91 + +5.0 1.06
PHE | ILE VAL | | | ILE | |(SEQ ID NO: 94) ND ND +7.5 1.06 PHE |
ILE VAL | | | ILE | |(SEQ ID NO: 94) ND ND +10.0 1.06 PHE | ILE VAL
| | | ILE | |(SEQ ID NO: 94) ND ND .sup.aThe G.beta.1 wild-type
sequence (SEQ ID NO: 38) and position numbers are shown at the top
of the Table. A vertical bar indicates identity with the G.beta.1
sequence (SEQ ID NO: 38). .DELTA..OMEGA. is the change in the
super-secondary structure parameter, .OMEGA.; vol is the fraction
of core side-chain volume relative to the G.beta.1 sequence (SEQ ID
NO: 38); T.sub.m is the melting temperature measured by circular
dichroism; NMR is a qualitative indication of the degree of
chemical shift dispersion in the 1D .sup.1H NMR spectra; ND
indicates a property that was not determined.
[0301] TABLE-US-00015 TABLE 14 DEE determined optimal sequences for
the core positions of G.beta.1 as a function of
.DELTA..theta..sub.0.9.sup.a- G.beta.1 sequence (SEQ ID NO: 38) Tm
.DELTA..theta._(.degree.) vol TYR LEU LEU ALA ALA PHE ALA VAL PHE
VAL (.degree. C.) NMR 3 5 7 20 26 30 34 39 52 54 -10.0 0.98 PHE |
ALA | | | | LEU TRP |(SEQ ID NO: 95) ND ND -7.5 1.00 PHE | LEU | |
| | LEU TRP ALA (SEQ ID NO: 96) ND ND -5.0 1.03 PHE | VAL | | | |
ILE TRP |(SEQ ID NO: 97) ND.sup.+ ND.sup.+ -2.5 1.03 PHE | VAL | |
| | ILE TRP |(SEQ ID NO: 97) ND.sup.+ ND.sup.+ 0.0 1.01 PHE | ILE |
| | | ILE | |(SEQ ID NO: 90) 91 + +2.5 1.01 PHE | ILE | | | | ILE |
|(SEQ ID NO: 90) 91 + +5.0 1.01 PHE | ILE | | | | ILE | |(SEQ ID
NO: 90) 91 + +7.5 1.08 PHE | ILE VAL | TRP | ILE LEU |(SEQ ID NO:
98) ND ND +10.0 1.08 PHE | ILE VAL | TRP | ILE LEU |(SEQ ID NO: 98)
ND ND .sup.aThe G.beta.1 wild-type sequence (SEQ ID NO: 38) and
position numbers are shown at the top of the Table. A vertical bar
indicates identity with the G.beta.1 sequence (SEQ ID NO: 38).
.DELTA..theta. is the change in the super-secondary structure
parameter, .theta.; vol is the fraction of core side-chain volume
relative to the G.beta.1 sequence (SEQ ID NO: 38); T.sub.m is the
melting temperature measured by circular dichroism; NMR is a
qualitative indication of the degree of chemical shift dispersion
in the 1D .sup.1H NMR spectra; ND indicates a property that was not
determined; ND.sup.+ indicates a property that was not determined,
but that is expected to be "positive" based on sequence similarity
to other DEE solutions (see .DELTA.h.sub.0.9[+0.75 .ANG.]).
[0302] TABLE-US-00016 TABLE 15 DEE determined optimal sequences for
the core positions of G.beta.1 as a function of
.DELTA..sigma..sub.0.9.sup.a G.beta.1 sequence (SEQ ID NO: 38)
.DELTA..sigma._(.degree.) vol TYR LEU LEU ALA ALA PHE ALA VAL PHE
VAL Tm (.degree. C.) NMR 3 5 7 20 26 30 34 39 52 54 -10.0 1.01 PHE
| ILE | | | | ILE | |(SEQ ID NO: 90) 91 + -7.5 1.01 PHE | ILE | | |
| ILE | |(SEQ ID NO: 90) 91 + -5.0 1.01 PHE | ILE | | | | ILE |
|(SEQ ID NO: 90) 91 + -2.5 1.01 PHE | ILE | | | | ILE | |(SEQ ID
NO: 90) 91 + 0.0 1.01 PHE | ILE | | | | ILE | |(SEQ ID NO: 90) 91 +
+2.5 0.99 PHE | VAL | | | | ILE | |(SEQ ID NO: 89) 89 + +5.0 1.03
PHE | VAL | | | | ILE TRP |(SEQ ID NO: 97) ND.sup.+ ND.sup.+ +7.5
1.04 PHE | VAL | | TYR | ILE TRP |(SEQ ID NO: 99) ND ND +10.0 1.04
PHE | VAL | | TYR | ILE TRP |(SEQ ID NO: 99) ND ND .sup.aThe
G.beta.1 wild-type sequence (SEQ ID NO: 38) and position numbers
are shown at the top of the Table. A vertical bar indicates
identity with the G.beta.1 sequence (SEQ ID NO: 38). .DELTA..sigma.
is the change in the super-secondary structure parameter, .sigma.;
vol is the fraction of core side-chain volume relative to the
G.beta.1 sequence (SEQ ID NO: 38); T.sub.m is the melting
temperature measured by circular dichroism; NMR is a qualitative
indication of the degree of chemical shift dispersion in the 1D
.sup.1H NMR spectra; ND indicates a property that was not
determined; ND.sup.+ indicates a property that was not determined,
but that is expected to be "positive" based on sequence similarity
to other DEE solutions (see .DELTA.h.sub.0.9[+0.75 .ANG.]).
[0303] The optimal sequence for the ten core positions of G.beta.1
(SEQ ID NO:38) that is calculated using the native backbone (i.e.,
no perturbation) contains three conservative mutations relative to
the wild-type sequence (Table 11). Y3F and V39I are likely the
result of the hydrophobic surface area burial term in the scoring
function. L7I reflects a bias in the rotamer library used for these
calculations. The crystal structure of G.beta.1 has the leucine at
position 7 with a nearly eclipsed .chi..sub.2 of 111.degree.. This
strained .chi..sub.2 is unlikely to be an artifact of the structure
determination since it is present in two crystal forms and a
solution structure (Gronenborn et al., 1991; Gallagher et al.,
1994). Our rotamer library does not contain eclipsed rotamers and
no staggered leucine rotamers pack well at this position. Instead,
the side-chain selection algorithm chose an isoleucine rotamer that
conserves the .chi..sub.1 dihedral and is able to pack well. We
expect the removal of the strained leucine rotamer to stabilize the
protein, a prediction that is tested in the experimental section of
this work. The sequences that result from varying individual
super-secondary structure parameter values show two notable trends.
Small variations in the parameter values tend to have little or no
effect on the calculated sequences. For example, varying
.DELTA.h.sub.0.9 from -0.25 to -1.00 .ANG. (Table 11) and
.DELTA.h.sub.1.0 from +0.25 to +1.25 .ANG. (Table 2) has no effect
on the calculated sequences which demonstrates the side-chain
selection algorithm's tolerance to small variations in the initial
backbone geometry. Large variations in the parameter values tend to
result in greater sequence diversity. For example,
.DELTA.h.sub.1.0[+1.50 .ANG.] contains six out of ten possible
mutations relative to G.beta.1 (Table 12). The apparently anomalous
result that occurs for .DELTA.h.sub.0.9 at -1.25 and -1.50 .ANG.,
an increase in core volume, is explained by the observation that
translating the helix towards the sheet plane results in creating a
pocket of space in the vicinity of position 20 that ultimately
leads to the observed A20V mutation.
[0304] Experimental validation of the designed cores focused on
seven of the Ah-series mutants which contain between three and six
sequence changes relative to G.beta.1. The designed sequences
resulting from .DELTA..OMEGA., .DELTA..theta. and .DELTA..sigma.
perturbations are, however, in many cases identical to various
Ah-series sequences. Typical far UV circular dichroism (CD) spectra
are shown in FIG. 15. .DELTA.h.sub.0.9[-1.00 .ANG.],
.DELTA.h.sub.0.9[0.00 .ANG.], .DELTA.h.sub.0.9[+0.75 .ANG.] and
.DELTA.h.sub.0.9[+1.00 .ANG.] have CD spectra that are
indistinguishable from that of G.beta.1 while
.DELTA.h.sub.0.9[+1.50 .ANG.], .DELTA.h.sub.1.0[+1.50 .ANG.] and
.DELTA.h.sub.0.9[-1.50 .ANG.] have CD spectra similar to that of
G.beta.1 suggesting that all of the mutants have a secondary
structure content similar to the wild-type protein. Thermal melts
monitored by CD are shown in FIG. 16. All of the mutants have
cooperative transitions with melting temperatures (T.sub.m's)
ranging from 53.degree. C. for .DELTA.h.sub.0.9[+1.50 .ANG.] to
91.degree. C. for .DELTA.h.sub.0.9[0.00 .ANG.] (Table 11). The
T.sub.m for G.beta.1 is 85.degree. C. The measured T.sub.m's for
.DELTA.h.sub.0.9[-1.50 .ANG.] and .DELTA.h.sub.0.9[+1.50 .ANG.] are
for 56 residue proteins compared to 57 residue proteins in all
other cases (see Methods and materials) which results in T.sub.m's
that are estimated to be about 2.degree. C. higher than what would
be expected for the corresponding 57 residue proteins based on the
T.sub.m difference between the 56 and 57 residue versions of
G.beta.1. The removal of the strained leucine at position seven
(L71) along with the increased hydrophobic burial generated by the
Y3F and V39I mutations in .DELTA.h.sub.0.9[0.00 .ANG.] result in a
protein that is measurable more stable than wild-type G.beta.1. The
extent of chemical shift dispersion in the 1 D .sup.1H NMR spectrum
of each mutant was assessed to gauge each protein's degree of
native-like character (FIG. 5). All of the mutants, except
.DELTA.h.sub.0.9[+1.50 .ANG.], have NMR spectra with chemical shift
dispersion similar to that of G.beta.1 suggesting that the proteins
form well-ordered structures. .DELTA.h.sub.0.9[+1.50 .ANG.] has a
spectrum with broad peaks and no dispersion, which is indicative of
a collapsed but disordered and fluctuating structure or
non-specific association. All seven mutant proteins retain their
ability to bind IgG as measured by binding to an IgG-Sepharose
affinity column. The stability and native-like character of
.DELTA.h.sub.0.9[-1.50 .ANG.] and .DELTA.h.sub.1.0[+1.50 .ANG.]
indicate that the sequence selection algorithm is sufficiently
robust to tolerate Ah perturbations that are as large as 15% of
G.beta.1's native height super-secondary structure parameter value
of 10 .ANG..
[0305] Although structures have not yet been determined for the six
mutants that show good chemical shift dispersion in their NMR
spectra, the magnitude of the backbone perturbations used to
calculate these sequences are similar to the backbone perturbations
observed for core mutations in other proteins (Baldwin et al.,
1993; Lim et al., 1994). Elucidation of the structures of several
of the mutants should contribute to our general understanding of
the deformation modes available to protein backbones of the
.alpha./.beta. class and should help define ranges of
super-secondary structure parameter value perturbations that will
be useful in future sequence calculations.
Sequence CWU 1
1
99 1 28 PRT Mouse 1 Lys Pro Phe Gln Cys Arg Ile Cys Met Arg Asn Phe
Ser Arg Ser Asp 1 5 10 15 His Leu Thr Thr His Ile Arg Thr His Thr
Gly Glu 20 25 2 28 PRT Artificial Sequence Description of
Artificial Sequence Synthetic 2 Lys Pro Tyr Thr Ala Arg Ile Lys Gly
Arg Thr Phe Ser Asn Glu Lys 1 5 10 15 Glu Leu Arg Asp Phe Leu Glu
Thr Phe Thr Gly Arg 20 25 3 28 PRT Artificial Sequence Description
of Artificial Sequence Synthetic 3 Gln Gln Tyr Thr Ala Lys Ile Lys
Gly Arg Thr Phe Arg Asn Glu Lys 1 5 10 15 Glu Leu Arg Asp Phe Ile
Glu Lys Phe Lys Gly Arg 20 25 4 28 PRT Artificial Sequence
Description of Artificial Sequence Synthetic 4 Glu Gln Tyr Thr Ala
Lys Ile Lys Gly His Thr Phe Arg Asn Glu Lys 1 5 10 15 Glu Leu Arg
Asp Phe Ile Glu Arg Phe Lys Gly Arg 20 25 5 28 PRT Artificial
Sequence Description of Artificial Sequence Synthetic 5 Gln Gln Tyr
Thr Ala Lys Ile Arg Gly Thr Thr Phe Arg Asn Glu Lys 1 5 10 15 Glu
Leu Arg Asp Phe Ile Glu Lys Phe Lys Gly Arg 20 25 6 28 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 6
Gln Gln Tyr Thr Ala Lys Phe Lys Gly Arg Thr Phe Arg Asn Glu Lys 1 5
10 15 Glu Leu Arg Asp Phe Ile Glu Lys Phe Glu Gly Arg 20 25 7 28
PRT Artificial Sequence Description of Artificial Sequence
Synthetic 7 Gln Gln Tyr Thr Ala Lys Ile Lys Gly Arg Ile Phe Arg Asn
Glu Lys 1 5 10 15 Glu Leu Arg Asp Phe Ile Glu Arg Phe Glu Gly Arg
20 25 8 28 PRT Artificial Sequence Description of Artificial
Sequence Synthetic 8 Glu Gln Tyr Thr Ala Lys Ile Lys Gly Lys Thr
Phe Arg Asn Lys Arg 1 5 10 15 Glu Leu Arg Asp Phe Ile Glu Lys Phe
Lys Gly Arg 20 25 9 28 PRT Artificial Sequence Description of
Artificial Sequence Synthetic 9 Glu Gln Tyr Thr Ala Lys Tyr Lys Gly
Arg Thr Phe Arg Asn Lys Arg 1 5 10 15 Glu Leu Arg Asp Phe Ile Glu
Lys Phe Lys Gly Arg 20 25 10 28 PRT Artificial Sequence Description
of Artificial Sequence Synthetic 10 Glu Gln Tyr Thr Ala Lys Ile Lys
Gly Gln Thr Phe Arg Asn Glu Lys 1 5 10 15 Glu Leu Arg Asp Phe Ile
Glu Lys Phe Lys Gly Arg 20 25 11 28 PRT Artificial Sequence
Description of Artificial Sequence Synthetic 11 Gln Arg Tyr Thr Ala
Lys Ile Lys Gly Arg Thr Phe Arg Asn Glu Lys 1 5 10 15 Glu Leu Arg
Asp Phe Ile Glu Arg Phe Lys Gly Arg 20 25 12 28 PRT Artificial
Sequence Description of Artificial Sequence Synthetic 12 Gln Glu
Tyr Thr Ala Lys Ile Lys Gly Arg Thr Phe Arg Asn Glu Lys 1 5 10 15
Glu Leu Arg Asp Phe Ile Glu Arg Phe Lys Gly Arg 20 25 13 27 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 13
Gln Tyr Thr Ala Lys Ile Lys Gly Arg Thr Phe Arg Asn Lys Arg Glu 1 5
10 15 Leu Arg Asp Phe Ile Glu His Phe Lys Gly Arg 20 25 14 28 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 14
Thr Gln Tyr Thr Ala Lys Ile Lys Gly Arg Thr Phe Arg Asn Lys Glu 1 5
10 15 Glu Leu Lys Lys Phe Ile Glu Lys Phe Lys Gly Arg 20 25 15 28
PRT Artificial Sequence Description of Artificial Sequence
Synthetic 15 Gln Glu Tyr Thr Ala Lys Ile Lys Gly Arg Thr Phe Arg
Asn Lys Arg 1 5 10 15 Glu Leu Arg Asp Phe Ile Glu Lys Phe Lys Gly
Arg 20 25 16 28 PRT Artificial Sequence Description of Artificial
Sequence Synthetic 16 Glu Gln Tyr Thr Ala Lys Ile Lys Gly Arg Thr
Phe Arg Asn Glu Lys 1 5 10 15 Glu Ile Arg Asp Phe Ile Glu Lys Phe
Thr Gly Arg 20 25 17 28 PRT Artificial Sequence Description of
Artificial Sequence Synthetic 17 Glu Gln Tyr Thr Ala Lys Ile Lys
Gly Lys Thr Phe Arg Asn Glu Arg 1 5 10 15 Glu Leu Arg Asp Phe Ile
Glu Lys Phe Lys Gly Arg 20 25 18 28 PRT Artificial Sequence
Description of Artificial Sequence Synthetic 18 Gln Gln Tyr Thr Ala
Lys Ile Lys Gly Lys Thr Phe Arg Asn Lys Asp 1 5 10 15 Glu Leu Lys
Lys Phe Ile Glu Lys Phe Lys Gly Arg 20 25 19 28 PRT Artificial
Sequence Description of Artificial Sequence Synthetic 19 Gln Gln
Tyr Thr Ala Lys Ile Lys Gly Lys Thr Phe Arg Asn Lys Arg 1 5 10 15
Glu Leu Gln Asp Phe Ile Glu Lys Phe Lys Gly Arg 20 25 20 28 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 20
Glu Gln Tyr Thr Ala Lys Val Lys Gly Glu Thr Phe Glu Asn Glu Lys 1 5
10 15 Arg Leu Arg Asp Phe Ile Glu Lys Phe Lys Gly Arg 20 25 21 28
PRT Artificial Sequence Description of Artificial Sequence
Synthetic 21 Glu Gln Tyr Thr Ala Lys Ile Lys Gly Lys Thr Phe Arg
Asn Glu Lys 1 5 10 15 Glu Leu Lys Arg Phe Ile Glu Lys Phe Lys Gly
Arg 20 25 22 28 PRT Artificial Sequence Description of Artificial
Sequence Synthetic 22 Glu Gln Tyr Thr Ala Lys Phe Lys Gly Lys Thr
Phe Arg Asn Lys Glu 1 5 10 15 Glu Leu Lys Lys Phe Ile Glu Lys Phe
Lys Gly Arg 20 25 23 33 PRT yeast 23 Arg Met Lys Gln Leu Glu Asp
Lys Val Glu Glu Leu Leu Ser Lys Asn 1 5 10 15 Tyr His Leu Glu Asn
Glu Val Ala Arg Leu Lys Lys Leu Val Gly Glu 20 25 30 Arg 24 33 PRT
yeast 24 Arg Met Lys Gln Leu Glu Asp Lys Val Glu Glu Leu Leu Ser
Lys Asn 1 5 10 15 Tyr His Leu Glu Asn Glu Val Ala Arg Leu Lys Lys
Leu Ala Gly Glu 20 25 30 Arg 25 33 PRT yeast 25 Arg Met Lys Gln Leu
Glu Asp Lys Val Glu Glu Leu Leu Ser Lys Asn 1 5 10 15 Tyr His Leu
Glu Asn Glu Met Ala Arg Leu Lys Lys Leu Val Gly Glu 20 25 30 Arg 26
33 PRT yeast 26 Arg Leu Lys Gln Met Glu Asp Lys Val Glu Glu Leu Leu
Ser Lys Asn 1 5 10 15 Tyr His Leu Glu Asn Glu Val Ala Arg Leu Lys
Lys Leu Val Gly Glu 20 25 30 Arg 27 33 PRT yeast 27 Arg Leu Lys Gln
Met Glu Asp Lys Val Glu Glu Leu Leu Ser Lys Asn 1 5 10 15 Tyr His
Leu Glu Asn Glu Val Ala Arg Leu Lys Lys Leu Ala Gly Glu 20 25 30
Arg 28 33 PRT yeast 28 Arg Met Lys Gln Trp Glu Asp Lys Ala Glu Glu
Leu Leu Ser Lys Asn 1 5 10 15 Tyr His Leu Glu Asn Glu Val Ala Arg
Leu Lys Lys Leu Val Gly Glu 20 25 30 Arg 29 33 PRT yeast 29 Arg Met
Lys Gln Phe Glu Asp Lys Val Glu Glu Leu Leu Ser Lys Asn 1 5 10 15
Tyr His Leu Glu Asn Glu Val Ala Arg Leu Lys Lys Leu Val Gly Glu 20
25 30 Arg 30 33 PRT yeast 30 Arg Met Lys Gln Leu Glu Asp Lys Val
Glu Glu Leu Leu Ser Lys Asn 1 5 10 15 Tyr His Ala Glu Asn Glu Val
Ala Arg Leu Lys Lys Leu Val Gly Glu 20 25 30 Arg 31 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 31
Lys Gln Asp Glu Glu Ser Tyr His Asn Ala Arg Lys 1 5 10 32 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 32
Glu Lys Asp Arg Glu Arg Arg Arg Glu Arg Arg Glu 1 5 10 33 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 33
Glu Lys Gln Lys Glu Arg Glu Arg Glu Glu Arg Gln 1 5 10 34 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 34
Ala Arg Ala Ala Ala Ala Arg Arg Arg Ala Arg Ala 1 5 10 35 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 35
Arg Glu Glu Arg Arg Arg Glu Asp Arg Lys Arg Glu 1 5 10 36 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 36
Asn Thr Arg Ala Lys Ser Ala Asn His Asn Thr Gln 1 5 10 37 12 PRT
Artificial Sequence Description of Artificial Sequence Synthetic 37
Ala Ala Ala Ala Ala Ala Ala Ala Ala Ala Ala Ala 1 5 10 38 56 PRT
Streptococcus sp. 38 Met Thr Tyr Lys Leu Ile Leu Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Val
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Val Thr Glu 50 55 39 56 PRT Streptococcus sp. 39 Met Thr Trp Lys
Tyr Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ile Val Asp Ala Ala Thr Phe Glu Lys Val Trp Lys Gln 20 25 30
Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Phe Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Leu Thr Ile Thr Glu 50 55 40 56 PRT Streptococcus
sp. 40 Met Thr Phe Lys Ile Ile Phe Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ile Val Asp Ala Ala Thr Val Glu Lys Val
Trp Lys Gln 20 25 30 Tyr Val Asn Asp Asn Gly Leu Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr Ile Thr Glu 50 55
41 56 PRT Streptococcus sp. 41 Met Thr Phe Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ile Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Trp Thr Ile Thr Glu 50 55 42 56 PRT Streptococcus sp. 42 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55 43 56 PRT
Streptococcus sp. 43 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Val Thr Glu 50 55 44 56 PRT Streptococcus sp. 44 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 45 56 PRT Streptococcus
sp. 45 Met Thr Phe Lys Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55
46 56 PRT Streptococcus sp. 46 Met Thr Phe Lys Leu Ile Ala Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Val Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Val Thr Glu 50 55 47 56 PRT Streptococcus sp. 47 Met Thr
Ala Lys Ala Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Ile Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Val Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Ile Thr Ile Thr Glu 50 55 48 56 PRT
Streptococcus sp. 48 Met Thr Ala Lys Leu Ile Ala Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Ala Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Val
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Ile Thr
Ile Thr Glu 50 55 49 56 PRT Streptococcus sp. 49 Met Thr Ala Lys
Ala Ile Ala Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Ala Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Val Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Leu Thr Val Thr Glu 50 55 50 56 PRT Streptococcus
sp. 50 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55
51 56 PRT Streptococcus sp. 51 Met Thr Tyr Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Trp Thr Phe Thr Glu 50 55 52 56 PRT Streptococcus sp. 52 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Phe Thr Phe Thr Glu 50 55 53 56 PRT
Streptococcus sp. 53 Met Thr Tyr Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Phe Thr Glu 50 55 54 56 PRT Streptococcus sp. 54 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Leu Asn Asp Asn Gly Val Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55 55 56 PRT Streptococcus
sp. 55 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Val
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55
56 56 PRT Streptococcus sp. 56 Met Thr Phe Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Tyr Thr Phe Thr Glu 50 55 57 56 PRT Streptococcus sp.
57 Met Thr Phe Lys Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu Thr
1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe
Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr
Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55 58
56 PRT Streptococcus sp. 58 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys
Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala
Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly
Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe
Thr Val Thr Glu 50 55 59 56 PRT Streptococcus sp. 59 Met Thr Phe
Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr
Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25
30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala
35 40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55 60 56 PRT
Streptococcus sp. 60 Met Thr Tyr Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Val
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr
Phe Thr Glu 50 55 61 56 PRT Streptococcus sp. 61 Met Thr Tyr Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Val Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55 62 56 PRT Streptococcus
sp. 62 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Tyr Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55
63 56 PRT Streptococcus sp. 63 Met Thr Tyr Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Tyr Thr Phe Thr Glu 50 55 64 56 PRT Streptococcus sp. 64 Met Thr
Tyr Lys Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Tyr Thr Phe Thr Glu 50 55 65 56 PRT
Streptococcus sp. 65 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Ile Thr Glu 50 55 66 56 PRT Streptococcus sp. 66 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Ile Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 67 56 PRT Streptococcus
sp. 67 Met Thr Phe Lys Ile Ile Phe Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55
68 56 PRT Streptococcus sp. 68 Met Thr Tyr Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Ile Thr Glu 50 55 69 56 PRT Streptococcus sp. 69 Met Thr
Tyr Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ile Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 70 56 PRT
Streptococcus sp. 70 Met Thr Tyr Lys Ile Ile Phe Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Val Thr Glu 50 55 71 56 PRT Streptococcus sp. 71 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55 72 56 PRT Streptococcus
sp. 72 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Ile
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr Phe Thr Glu 50 55
73 56 PRT Streptococcus sp. 73 Met Thr Tyr Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Val Asp Gly Glu Ile Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Val Thr Glu 50 55 74 56 PRT Streptococcus sp. 74 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 75 56 PRT
Streptococcus sp. 75 Met Thr Tyr Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr
Phe Thr Glu 50 55 76 56 PRT Streptococcus sp. 76 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Ile Thr Glu 50 55 77 56 PRT Streptococcus
sp. 77 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn Gly Ile Asp Gly Glu Val
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Phe Thr Glu 50 55
78 56 PRT Streptococcus sp. 78 Met Thr Tyr Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Leu Asn Asp Asn
Gly Ile Asp Gly Glu Ile Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Phe Thr Glu 50 55 79 56 PRT Streptococcus sp. 79 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Tyr Thr Ile Thr Glu 50 55 80 56 PRT
Streptococcus sp. 80 Met Thr Phe Lys Ile Ile Val Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Val Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Val Thr Glu 50 55 81 56 PRT Streptococcus sp. 81 Met Thr Phe Lys
Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 82 56 PRT Streptococcus
sp. 82 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55
83 56 PRT Streptococcus sp. 83 Met Thr Phe Lys Leu Ile Ile Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Trp Thr Val Thr Glu 50 55 84 56 PRT Streptococcus sp. 84 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ile Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55 85 56 PRT
Streptococcus sp. 85 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Leu Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ile Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr
Val Thr Glu 50 55 86 56 PRT Streptococcus sp. 86 Met Thr Ala Lys
Ala Ile Ala Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Ala Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Leu Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Ala Thr Ala Thr Glu 50 55 87 56 PRT Streptococcus
sp. 87 Met Thr Phe Lys Ala Ile Ala Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Ala Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Leu Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Ala Thr Ala Thr Glu 50 55
88 56 PRT Streptococcus sp. 88 Met Thr Phe Lys Ala Ile Val Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Val Thr Glu 50 55 89 56 PRT Streptococcus sp. 89 Met Thr
Phe Lys Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 90 56 PRT
Streptococcus sp. 90 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Phe Thr
Val Thr Glu 50 55 91 56 PRT Streptococcus sp. 91 Met Thr Phe Lys
Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55 92 56 PRT Streptococcus
sp. 92 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp
Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55
93 56 PRT Streptococcus sp. 93 Met Thr Val Lys Leu Ile Val Asn Gly
Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Val Val Asp Ala
Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn
Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr
Phe Thr Val Thr Glu 50 55 94 56 PRT Streptococcus sp. 94 Met Thr
Phe Lys Leu Ile Ile Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15
Thr Thr Glu Val Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Phe Thr Val Thr Glu 50 55 95 56 PRT
Streptococcus sp. 95 Met Thr Phe Lys Leu Ile Ala Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr
Ala Glu Lys Val Phe Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Leu
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Trp Thr
Val Thr Glu 50 55 96 56 PRT Streptococcus sp. 96 Met Thr Phe Lys
Leu Ile Leu Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Phe Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Leu Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Ala Thr Glu 50 55 97 56 PRT Streptococcus
sp. 97 Met Thr Phe Lys Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu
Thr 1 5 10 15 Thr Thr Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val
Phe Lys Gln 20
25 30 Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp
Ala 35 40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55 98 56 PRT
Streptococcus sp. 98 Met Thr Phe Lys Leu Ile Ile Asn Gly Lys Thr
Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr Glu Val Val Asp Ala Ala Thr
Ala Glu Lys Val Trp Lys Gln 20 25 30 Tyr Ala Asn Asp Asn Gly Ile
Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35 40 45 Thr Lys Thr Leu Thr
Val Thr Glu 50 55 99 56 PRT Streptococcus sp. 99 Met Thr Phe Lys
Leu Ile Val Asn Gly Lys Thr Leu Lys Gly Glu Thr 1 5 10 15 Thr Thr
Glu Ala Val Asp Ala Ala Thr Ala Glu Lys Val Tyr Lys Gln 20 25 30
Tyr Ala Asn Asp Asn Gly Ile Asp Gly Glu Trp Thr Tyr Asp Asp Ala 35
40 45 Thr Lys Thr Trp Thr Val Thr Glu 50 55
* * * * *