U.S. patent application number 09/391811 was filed with the patent office on 2002-04-11 for automated analysis of real-time nucleic acid amplification.
Invention is credited to WITTWER, CARL T..
Application Number | 20020042051 09/391811 |
Document ID | / |
Family ID | 26829286 |
Filed Date | 2002-04-11 |
United States Patent
Application |
20020042051 |
Kind Code |
A1 |
WITTWER, CARL T. |
April 11, 2002 |
AUTOMATED ANALYSIS OF REAL-TIME NUCLEIC ACID AMPLIFICATION
Abstract
A method is described for analyzing a sample for the presence of
a nucleic acid wherein the sample is amplified, illustratively
using PCR, in the presence of a fluorescent probe capable of
detecting the presence of the nucleic acid sample. A baseline
region is determined by comparing the fluorescence at various
amplification cycles, and the fluorescence at a selected
amplification cycle is compared to the baseline region to determine
whether the fluorescence measurement falls outside of that baseline
region, indicating the presence of the nucleic acid.
Inventors: |
WITTWER, CARL T.; (SALT LAKE
CITY, UT) |
Correspondence
Address: |
BARNES & THORNBURG
11 SOUTH MERIDIAN
INDIANAPOLIS
IN
46204
US
|
Family ID: |
26829286 |
Appl. No.: |
09/391811 |
Filed: |
September 8, 1999 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60131256 |
Apr 27, 1999 |
|
|
|
Current U.S.
Class: |
435/6.18 ;
435/6.1; 435/91.1; 435/91.2; 536/23.1; 536/24.3 |
Current CPC
Class: |
C12Q 2561/101 20130101;
C12Q 2545/114 20130101; C12Q 1/686 20130101; C12Q 1/686 20130101;
G01N 21/6428 20130101 |
Class at
Publication: |
435/6 ; 435/91.1;
435/91.2; 536/23.1; 536/24.3 |
International
Class: |
C12Q 001/68; C07H
021/02; C07H 021/04; C12P 019/34 |
Claims
1. A method for determining the presence of a nucleic acid
comprising the steps of providing a fluorescent entity capable of
indicating the presence of the nucleic acid and capable of
providing a signal related to the quantity of the nucleic acid,
amplifying the nucleic acid through a plurality of amplification
cycles in the presence of the fluorescent entity, measuring the
fluorescence of the fluorescent entity during each of the plurality
of amplification cycles, analyzing the measured fluorescence to
identify amplification cycles for use in establishing a baseline
fluorescence region, and ascertaining whether the fluorescence
measurement during any of the plurality of amplification cycles is
outside the baseline fluorescence region.
2. The method of claim 1 wherein the cycles used in establishing
the baseline fluorescence region are identified by calculating
slopes of a fluorescence verses amplification cycle plot at the
plurality of amplification cycles.
3. The method of claim 2 wherein the slopes are calculated by
linear regression of each local neighborhood.
4. The method of claim 2 wherein the cycles used in establishing
the baseline fluorescence region comprise an interval of cycles
that includes the amplification cycle with the slope having an
absolute value closest to zero
5. The method of claim 4 wherein the amplification cycle with the
slope having the absolute value closest to zero comprises a central
cycle of the interval of cycles used to establish the baseline
fluorescence region.
6. The method of claim 4 wherein the baseline fluorescence is
centered on a line passing through the measured fluorescence of the
amplification cycle with the slope having the absolute value
closest to zero, the line further comprising a slope equal to the
slope having the absolute value closest to zero, and the baseline
fluorescence region including an area on at least one side of the
line defined by a variance measure of the fluorescence values.
7. The method of claim 6 wherein the variance measure is calculated
from the amplification cycles used in establishing the baseline
fluorescence.
8. The method of claim 1 wherein the fluorescent entity comprises a
FRET oligonucleotide pair.
9. The method of claim 1 further comprising the steps of generating
a well-behaved amplification curve, determining a cutoff cycle,
calculating the slope of the fluorescence verses cycle plot for
each of the of amplification cycles prior to the cutoff cycle, and
choosing the fluorescence measurement of the amplification cycle
with the slope having an absolute value closest to zero.
10. The method of claim 9 wherein the cutoff cycle is selected from
the group consisting of a maximum second derivative, a maximum
first derivative, and a minimum second derivative of a fluorescence
verses cycle curve.
11. The method of claim 1 further comprising the steps of
generating a well-behaved amplification curve, determining the
cycle having the maximum fluorescence, and determining whether the
maximum fluorescence is outside the baseline fluorescence
region.
12. The method of claim 1 further comprising the steps of
generating an amplification curve which is not well behaved, and
determining if the fluorescence of a last cycle tested is outside
the baseline fluorescence region.
13. A method for determining the presence of a nucleic acid
comprising the steps of providing a fluorescent entity capable of
indicating the presence of the nucleic acid and capable of
providing a signal related to the quantity of the nucleic acid,
initially amplifying the nucleic acid through a set number of
amplification cycles in the presence of the fluorescent entity,
measuring the fluorescence of the fluorescent entity during each of
the amplification cycles, analyzing the measured fluorescence to
identify amplification cycles for use in establishing a baseline
fluorescence region, ascertaining whether a positive result is
indicated by determining whether the fluorescence measurement
during any of the of amplification cycles is outside the baseline
fluorescence region, and continuing amplification through
additional amplification cycles and repeating the measuring,
determining, and ascertaining steps after each additional
amplification cycle until either the positive result is obtained or
a maximum cycle number is reached.
14. The method of claim 13 further comprising the steps of
performing additional amplification cycles after the positive
result is obtained, and analyzing the nucleic acid for additional
information.
15. The method of claim 13 wherein the nucleic acid is further
analyzed to determine the presence of a particular allele.
16. The method of claim 13 wherein the measured fluorescence is
further analyzed to determine initial concentration.
17. An automated method for determining the presence of a nucleic
acid comprising the steps of placing a sample into a container
containing a fluorescent entity capable of indicating the presence
of the nucleic acid and capable of providing a signal related to
the quantity of the nucleic acid, placing the container into a
device for amplifying the nucleic acid through a plurality of
amplification cycles in the presence of the fluorescent entity,
measuring the fluorescence of the fluorescent entity during each of
the plurality of amplification cycles, determining a baseline
fluorescence region by analyzing the fluorescence at various
amplification cycles, and outputting a positive result if the
fluorescence measurement during any of the plurality of
amplification cycles is outside the baseline fluorescence region.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims priority under 35 U.S.C. .sctn.119
(e) to U.S. Provisional Application No. 60/131,256, filed Apr. 27,
1999, which is expressly incorporated by reference herein.
FIELD OF THE INVENTION
[0002] The present invention relates to a method of analyzing a
sample for the presence of a nucleic acid. More particularly, the
present invention is directed to an automated method for detecting
and reporting the presence of a predetermined nucleic acid in a
sample using polymerase chain reaction and a fluorescent detecting
entity.
BACKGROUND AND SUMMARY OF THE INVENTION
[0003] Amplification of DNA by polymerase chain reaction (PCR) is a
technique fundamental to molecular biology. Nucleic acid analysis
by PCR requires sample preparation, amplification, and product
analysis. Although these steps are usually performed sequentially,
amplification and analysis can occur simultaneously. DNA dyes or
fluorescent probes can be added to the PCR mixture before
amplification and used to analyze PCR products during
amplification. Sample analysis occurs concurrently with
amplification in the same tube within the same instrument. This
combined approach decreases sample handling, saves time, and
greatly reduces the risk of product contamination for subsequent
reactions, as there is no need to remove the samples from their
closed containers for further analysis. The concept of combining
amplification with product analysis has become known as "real time"
PCR. See, for example, WO/9746707A2, WO/9746712A2, WO/9746714A1,
all published Dec. 11, 1997, incorporated herein by reference.
[0004] Monitoring fluorescence each cycle of PCR initially involved
the use of ethidium bromide. Higuchi R, G Dollinger, P S Walsh and
R. Griffith, Simultaneous amplification and detection of specific
DNA sequences, Bio/Technology 10:413-417, 1992; Higuchi R, C
Fockler G Dollinger and R Watson, Kinetic PCR analysis: real time
monitoring of DNA amplification reactions, Bio/Technology
11:1026-1030, 1993. In that system fluorescence is measured once
per cycle as a relative measure of product concentration. Ethidium
bromide detects double stranded DNA; if template is present
fluorescence intensity increases with temperature cycling.
Furthermore, the cycle number where an increase in fluorescence is
first detected increases inversely proportionally to the log of the
initial template concentration. Other fluorescent systems have been
developed that are capable of providing additional data concerning
the nucleic acid concentration and sequence.
[0005] While PCR is an invaluable molecular biology tool, the
practical implementation of real time PCR techniques has lagged
behind the conceptual promise. Currently available instrumentation
does not actually analyze data during PCR; it simply acquires the
data for later analysis. After PCR has been completed, multiple
manual steps are necessary to analyze the acquired data, and human
judgment is typically required to provide the analysis result. What
is needed is a system for automating data acquisition and analysis
so that no user intervention is required for reporting the
analytical results. Thus, when the temperature cycling in a
polymerase chain reaction amplification is complete, the system
software is automatically triggered and the results, for example,
the presence or absence of a given pathogen, is immediately
displayed on screen. Algorithms for detection, quantification, and
genotyping are needed. Moreover, initiation of the analysis
algorithm can be implemented prior to completion of temperature
cycling. Data processing can occur during amplification and
concomitant analysis results can be used to modify temperature
cycling and to acquire additional data during the latter stages of
the amplification procedure to optimize amplification protocol and
data quality.
[0006] A major problem in automating PCR data analysis is
identification of baseline fluorescence. Background fluorescence
varies from reaction to reaction. Moreover, baseline drift, wherein
fluorescence increases or decreases without relation to
amplification of nucleic acids in the sample, is a common
occurrence. Prior attempts to automate amplification data analysis
involved setting the baseline fluorescence as that measured at one
or more predetermined early cycle numbers. This technique accounts
for the variation in background fluorescence, but it does not
compensate for baseline drift. Without compensation for baseline
drift, automated amplification data analysis can easily provide
both false negative and false positive results.
[0007] Thus, one aspect of the present invention is directed to a
method of determining the presence of a nucleic acid in a sample by
using a fluorescent entity capable of detecting the nucleic acid
and amplifying the nucleic acid in the presence of the fluorescent
entity. A baseline fluorescence region is determined by analyzing
the fluorescence measurements of a number of amplification cycles,
and the fluorescence measurements during specific amplification
cycles are compared to the baseline fluorescence region to
determine the presence or absence of the nucleic acid. In a
preferred embodiment, the baseline fluorescence region is
determined by calculating the slope of a fluorescence intensity
verses amplification cycle plot at each of the amplification cycles
and choosing the fluorescence measurement of the amplification
cycle with the slope having an absolute value closest to zero.
Preferably, the baseline fluorescence region is generated as the
square root of the mean square error.
[0008] In another embodiment, the baseline fluorescence region is
determined and the fluorescence values are compared thereto after
each amplification cycle. Thus, the presence of the nucleic acid
sequence can be determined more quickly in samples containing
higher copy number. Furthermore, the remaining cycles may be used
to acquire other information concerning the nucleic acid sample,
such as initial copy number and allelic data.
[0009] In an additional embodiment, the process is automated so
that a user can prepare a biological sample and simply place it in
a thermal cycler having a sensor for reporting fluorescence values
as a function of cycle number and a processor programmed with an
algorithm capable of processing the values and reporting a positive
or negative result.
[0010] Additional features of the present invention will become
apparent to those skilled in the art upon consideration of the
following detailed description of preferred embodiments
exemplifying the best mode of carrying out the invention as
presently perceived.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 is a comparison of three fluorescence monitoring
schemes, (A) dsDNA dye, (B) exonuclease probe, and (C)
hybridization probe, for PCR amplification, wherein each scheme is
illustrated (I) before amplification and (II) after amplification,
and fluorescence values are shown (III) once during each cycle of
PCR and (IV) continuously during PCR.
[0012] FIG. 2 is a graph illustrating logistic growth.
[0013] FIG. 3 shows a comparison of various
cycle-verses-fluorescence curve types.
[0014] FIG. 4 illustrates a sliding window analysis for determining
the slope of the fluorescence-verses-cycle number graph at each
cycle.
[0015] FIG. 5 shows typical fluorescence verses amplification cycle
graphs for (A) a negative sample and (B) a positive sample.
[0016] FIG. 6 also shows typical amplification graphs wherein (A)
shows fluorescence verses amplification cycle, (B) is the first
derivative of fluorescence verses amplification cycle, and (C) is
the second derivative of fluorescence verses amplification
cycle.
[0017] FIGS. 7-11 show the results for various samples wherein open
white circles represent the fluorescence measurement at each cycle,
open black circles represent the first derivatives, closed black
circles represent second derivatives, large black circles connected
by lines represent the points contributing to the baseline
calculation, and the horizontal lines illustrate the baseline
region. FIGS. 7 and 8 illustrate positive results, while FIGS. 9-11
illustrate negative results.
DETAILED DESCRIPTION OF THE INVENTION
[0018] In describing and claiming the invention, the following
terminology will be used in accordance with the definitions set
forth below.
[0019] As used herein, "nucleic acid," "DNA," and similar terms
also include nucleic acid analogs, i.e. analogs having other than a
phosphodiester backbone. For example, the so-called "peptide
nucleic acids," which are known in the art and have peptide bonds
instead of phosphodiester bonds in the backbone, are considered
within the scope of the present invention.
[0020] As used herein, "fluorescence resonance energy transfer
pair" or "FRET pair" refers to a pair of fluorophores comprising a
donor fluorophore and acceptor fluorophore, wherein the donor
fluorophore is capable of transferring resonance energy to the
acceptor fluorophore. In other words the emission spectrum of the
donor fluorophore overlaps the absorption spectrum of the acceptor
fluorophore. In preferred fluorescence resonance energy transfer
pairs, the absorption spectrum of the donor fluorophore does not
substantially overlap the absorption spectrum of the acceptor
fluorophore.
[0021] As used herein, "FRET oligonucleotide pair" refers to a pair
of oligonucleotides, each labeled with a member of a fluorescent
resonance energy transfer pair, wherein hybridization to
complementary target nucleic acid sequences brings the fluorescent
entities into a fluorescence resonance energy transfer
relationship.
[0022] The present invention is directed to a method of analyzing a
sample for the presence of a nucleic acid wherein the sample is
amplified, preferably using PCR, in the presence of a fluorescent
probe capable of detecting the presence of the nucleic acid sample.
A baseline region is determined by comparing the fluorescence at
various amplification cycles, and the fluorescence at each of
various amplification cycles is compared to the baseline region to
determine whether the fluorescence measurements fall outside of
that baseline region.
[0023] Many different probes have recently become available for
monitoring PCR. Although not sequence specific, double stranded DNA
(dsDNA) specific dyes can be used in any amplification without the
need for probe synthesis. Such dyes include ethidium bromide and
SYBR.TM. Green I. With dsDNA dyes, product specificity can be
increased by analysis of melting curves or by acquiring
fluorescence at a high temperature where nonspecific products have
melted. Ririe K M, Rasmussen R P and C T Wittwer, Product
differentiation by analysis of DNA melting curves during the
polymerase chain reaction, Anal. Biochem. 245-154-160, 1997;
Morrison T B, J&J Weis and C T Wittwer, Quantification of low
copy transcripts by continuous SYBR Green I monitoring during
amplification,BioTechniques 24:954-962, 1998.
[0024] Oligonucleotide probes can also be covalently labeled with
fluorescent molecules. Hairpin primers (Sunrise.TM. primers),
hairpin probes (Molecular Beacons.TM.) and exonuclease probes
(TaqMan.TM.) are dual-labeled oligonucleotides that can be
monitored during PCR. These probes depend on fluorescence quenching
of a fluorophore by a quencher on the same oligonucleotide.
Fluorescence increases when hybridization or exonuclease hydrolysis
occurs.
[0025] A preferred design employs two oligonucleotides, each
labeled with a fluorescent probe. Hybridization of these
oligonucleotides to a target nucleic acid brings the two
fluorescent probes close together to allow resonance energy
transfer to occur. Wittwer C T, M G Herrmann, A A Moss and R P
Rasmussen, Continuous fluorescence monitoring of rapid cycle DNA
amplification,BioTechniques 22:130-138, 1997. These hybridization
probes require only a single fluorescent label per probe and are
easier to design and synthesize than dual labeled probes.
Acceptable fluorophore pairs for use as fluorescent resonance
energy transfer pairs are well known to those skilled in the art
and include, but are not limited to, fluorescein/rhodamine,
phycoerythrin/Cy7, fluorescein/Cy5, fluorescein/Cy5.5,
fluorescein/LC Red 640, and fluorescein/LC Red 705.
[0026] SYBR.TM. Green I, exonuclease probe and hybridization probe
designs are shown in FIG. 1. For each design, schematics both
before (I) and after (II) amplification are shown, as well as cycle
verses fluorescence amplification plots of positive and negative
controls (III), and temperature verses fluorescence plots from
continuous monitoring (IV). SYBR Green I fluorescence increases as
more dsDNA is made (FIG. 1A). Because the dye is not sequence
specific, a negative control also increases in fluorescence during
later cycles as primer dimers are formed. In FIG. 1B, dual-labeled
fluorescein/rhodarnine probes are cleaved during polymerase
extension by 5'-exonuclease activity, separating the fluorophores
and increasing the fluorescein emission. The signal generated is
cumulative and the fluorescence continues to increase even after
the amount of product has reached a plateau. FIG. 1C shows use of a
FRET oligonucleotide pair wherein two probes hybridize next to each
other, one labeled 3' with fluorescein and the other labeled 5'
with Cy5. As product accumulates during PCR, fluorescence energy
transfer to Cy5 increases. The fluorescence of hybridization probes
decreases at high cycle number because of probe/product
competition.
[0027] Standard instruments for PCR complete 30 cycles in about two
to four hours. A preferred system is a rapid thermal cycling device
using capillary tubes and hot air temperature control. See, for
example, U.S. Pat. No. 5,455,175, herein incorporated by reference.
Because of the low heat capacity of air and the thin walls and high
surface area of capillary tubes, small volume samples could be
cycled quickly. The total amplification time for 30 cycles is
reduced to 15 minutes with excellent results.
[0028] The use of capillaries with forced air heating allows
precise control of sample temperature at a speed not possible with
other designs. For example, sample temperature verses time plots in
capillaries show sharp spikes at denaturation and annealing
temperatures, whereas several seconds are required for all of the
sample to reach equilibrium in conical plastic tubes. Wittwer, C T,
G B Reed and K M Ririe, Rapid cycle DNA amplification, in K Mullis,
F Ferre, and R Gibbs (Eds.), The polymerase chain reaction,
Springer-Verlag, Deerfield Beach, Fla. pp. 174-181, 1994; Wittwer,
C T, B C Marshall, G B Reed, and J L Cherry, Rapid cycle
allele-specific amplification: studies with the cystic fibrosis
delta F508 locus, Clin. Chem., 39:804-809, 1993. Rapid temperature
cycling with minimal annealing and denaturation times improves
quantitative PCR and increases the discrimination of allele
specific amplification. Weis, J H, S S Tan, B K Martin, and C T
Wittwer, Detection of rare mRNA species via quantitative RT-PCR,
Trends in Genetics, 8:263-4, 1992; Tan S T and J H Weis,
Development of a sensitive reverse transcriptase PCR assay,
RT-RPCR, utilizing rapid cycle times, PCR Meth. and Appl.
2:137-143, 1992. Rapid cycling for cycle sequencing reduces
sequencing artifacts and minimizes "shadow banding" in dinucleotide
repeat amplifications. Swerdlow H, K Dew-Jager and R F Gesteland,
Rapid cycle sequencing in an air thermal cycler, BioTechniques
15:512-519, 1993; Odelberg S J and R White, A method for accurate
amplification of polymorphic CA-repeat sequences, PCR Meth. Appl.
3:7-12, 1993. For long PCR, yield is improved when the sample is
exposed as little as possible to high denaturation temperatures.
Gustafson C E, R A Alm and T J Trust, Effect of heat denaturation
of target DNA on the PCR amplification. Gene 23:241-244, 1993. The
RapidCycler.TM., developed by Idaho Technology, is an example of a
rapid thermal cycling device. The LightCycler.TM. is a rapid
temperature cycler with a fluorimeter, wherein light emitting
diodes are used for excitation and photodiodes are used for
detection.
[0029] The present invention is directed to methods for automating
detection nucleic acids with real time PCR. While these algorithms
may be applied to any amplification system, it is preferred to
integrate these algorithms into the LightCycler.TM. platform. These
analysis routines are triggered by the completion of rapid thermal
cycling for "hands off" amplification, analysis, and final results
presentation in a total of less than 15 min. The analysis routines
take from <1 second for detection and quantification to <10
seconds for genotyping. Lab View (National Instruments, Austin,
Tex.), a graphical programming language, is preferred for
LightCycler.TM. instrument control. The LightCycler.TM. is a
PC-based instrument.
[0030] Perhaps the most basic analysis of real time PCR data is a
judgement of whether a targeted nucleic acid is present. If the
nucleic acid is present, further quantification and genotyping may
take place. In many cases, a yes/no judgement is all that is
needed. For example, one may want to determine whether E. coli
0157:H7 is in a sample of hamburger, whether anthrax is on a swab
from a soldier; or whether hepatitis C is in a unit of blood. Real
time PCR can improve yes/no detection over end point PCR assays
because fluorescence is acquired at each cycle.
[0031] Inspection of cycle verses fluorescence data from positive
and negative real time PCR runs (see FIG. 1BIII and 1CIII) suggests
that discrimination is simple. The positive samples increase with
cycle number while the negative samples remain at baseline. A
trained observer expects positive samples to follow an S-shape
curve, beginning with a baseline, followed by an exponential
segment, and finishing with a plateau. The expected curve is
similar to the logistic model for population growth, where the rate
of growth is proportional to both the population size y and to the
difference L-y, where L is the maximum population that can be
supported. For small y, growth is exponential, but as y nears L the
growth rate approaches zero. An example of logistic growth is shown
in FIG. 2.
[0032] Although intuitively simple, accurately discriminating
between positive and negative samples is not easy in practice. The
simplest approach is to set a horizontal fluorescence threshold as
a discriminator between positive and negative samples. This works
best with a stable baseline (between and within samples) and a
known fluorescence intensity that correlates with "positive."
Although this method will work on obvious samples (e.g. FIG. 1BIII
and 1CIII), a more robust algorithm is desired that will work under
a wider variety of conditions. For example, the baseline may drift
and the fluorescence intensity may vary greatly between different
samples and probe techniques. Thus, the present invention is
directed to a method that will: (1) automatically identify the
baseline, (2) use the baseline variance to establish a confidence
region, and (3) call each sample positive or negative based on the
relationship of the confidence region to the fluorescence data.
[0033] FIG. 3 displays various types of amplification curves, all
of which have been observed in LightCycler.TM. runs. FIGS. 3A and B
show curves from samples that are negative with no template
present. The fluorescence scales in FIGS. 3A and B are magnified
(compared to FIGS. 3C-F) to demonstrate the baseline drift and to
provide algorithms capable of being independent of the fluorescence
intensity. There is always some baseline drift during cycling. This
drift usually is greatest at the beginning of cycling but later
levels off, and may be either downward (FIG. 3A) or upward (FIG.
3B). This baseline drift of negative reactions must be
distinguished from positive reactions of either low copy numbers
(FIG. 3C) or high copy numbers (FIG. 3D) of starting template. The
method needs to work with various probe designs, including
exonuclease (FIG. 3E) and hybridization (FIG. 3F) probes.
[0034] Automatic identification of the background is surprisingly
difficult. In prior art methods, the baseline is determined as a
function of measured fluorescence at a fixed range of cycles near
the beginning of amplification. However, selection of a fixed range
of cycles is not adequate because both downward drift (FIG. 3A) and
high copy (FIG. 3D) amplifications may be incorrectly called.
[0035] In the present invention, the background is identified by
analyzing the fluorescent measurements over a wide range of
amplification cycles. Preferably, the background is identified by
selecting the sliding window (FIG. 4) with the shallowest slope.
That is, calculate the slope at each cycle by linear regression of
the local neighborhood (for example, a 7 point sliding window). The
window with the slope of lowest absolute value (least difference
from zero) defines the background region. Once the background
region has been identified, the variation of these background
points about their regression line (the square root of the mean
square error) is multiplied by a constant to determine a confidence
band. This confidence band will have a slope near zero and is
extrapolated across all cycles. If the fluorescence of the last
cycle is within the confidence band it is negative, if it is
outside the band it is positive. FIG. 5 demonstrates both
cases.
[0036] This algorithm should work well in most cases. However, with
the high copy fluorescence curve type (FIG. 3D), the shallowest
slope might be found at early cycles (resulting in a correct
positive call) or at late cycles (resulting in an incorrect
negative call). This exception may be handled by analyzing the
curve shape. In a well-behaved amplification, the expected
amplification curve shape is ordered by cycle number as
follows:
[0037] 1. Minimum fluorescence
[0038] 2. Maximum second derivative (F")
[0039] 3. Maximum first derivative (F')
[0040] 4. Minimum second derivative (F')
[0041] 5. Maximum fluorescence
[0042] This gives the characteristic S-curve shape we expect during
PCR (FIG. 6A). The maximum slope (first derivative) is obtained
from the sliding window analysis already performed for background
identification. Preferably, the second derivatives are calculated
by a 3-point sliding window linear regression of the first
derivatives. If the curve shape is well behaved (that is, if
looking at a graph of FIG. 6, and reading from lowest to highest
cycle number, the features occur in the order listed above), then
the background is only selected from sliding windows centered at
cycle numbers less than the second derivative maximum. This solves
the potential analysis problem with FIG. 3D. In other preferred
embodiments, cycle numbers less than the first derivative maximum
or cycle numbers less than the second derivative minimum may be
used. It will be further understood that any cycle number between
the second derivative maximum and the second derivative minimum is
a suitable cutoff cycle for use with this technique and is within
the scope of this invention.
[0043] Another method is to compare the cycle with the greatest
fluorescence (which is not necessarily the last cycle) to the
confidence band. This is especially suited for hybridization probes
that may decrease in fluorescence with extensive cycling, such as
seen in FIG. 3F. The cycle with the greatest fluorescence only
should be used when the curve shape is well behaved, in order to
prevent false positive calls with downward drifts, such as shown in
FIG. 3A.
[0044] The variables to optimize for automatic detection are: 1)
the window size for the first derivative estimate, 2) the window
size for the second derivative estimate, and 3) the confidence band
factor. A reasonable value for the first derivative window size is
7, although 3, 5, 9, and 11 are also quite useful. For the second
derivative the preferred window size is 3, but 5, and 7 have also
proven to be useful values. A preferred confidence band factor is
20. As the first derivative window size increases the variance
estimate is more accurate, but the edge cycles (beginning and
ending) are lost.
[0045] This algorithm is best understood by referring to the
fluorescence verses cycle test result plot shown in FIGS. 7-11. The
input data consist of one fluorescence value for each cycle of
amplification, shown as the closed white circles. Let this equal
array Yi, where i is the cycle number and N is the total number of
cycles. The detection criteria are:
[0046] A=the number of fluorescence values used to determine the
first derivatives. It is convenient to use odd numbers, so that the
first derivatives correspond to integer cycle numbers. As discussed
above, reasonable values include 3, 5, 7, 9, and 11. Preferably, 7
is used as the first derivative window size.
[0047] B=the number of first derivative values used to determine
the second derivatives. Again, it is convenient to use odd numbers,
so that the second derivative values also correspond to integer
cycle numbers. Reasonable values include 3, 5, and 7, with 3 being
the preferred value.
[0048] C=the confidence band factor. This factor determines the
confidence band by multiplying it by a variance measure, preferably
the square root of the mean square error.
[0049] The first step is to calculate the first and second
derivatives. Although there are many ways to accomplish this, a
preferred method is to determine the first derivatives as the slope
of a linear regression line through A points, and assigning the
value to the central cycle number. Some cycles on either edge
cannot be assigned first derivatives, but first derivatives can be
provided for cycles (A+1)/2 through N-(A-1)/2. Similarly, the
second derivatives are calculated as the slope of the first
derivative points and assigned to cycles (A+1)/2+(B-1)/2 through
[N-(A-1)/2]-(B-1)/2. Calculation of the first and second
derivatives provide arrays Y'i and Y"i, with some edge values
missing. In FIG. 7, the first and second derivatives are displayed
as open black circles and closed black circles, respectively.
[0050] The next step is to determine whether the fluorescence curve
has a well-behaved shape. As discussed above, the well-behaved
shape occurs when the cycles with minimum fluorescence, maximum
second derivative, maximum first derivative, minimum second
derivative, and maximum fluorescence occur in that order, from low
to high cycle number.
[0051] The baseline is then determined. If the fluorescence curve
does not have the expected shape, the cycle whose first derivative
is closest to zero is used. If the fluorescence curve has a
well-behaved shape, the cycle whose first derivative is closest to
zero chosen from among all cycles prior to the cycle with the
maximum second derivative (again, any cycle between the maximum
second derivative and the minimum second derivative may also be
used as the cutoff cycle number). The baseline is drawn through the
fluorescence value of the chosen cycle with a slope of its first
derivative. In FIG. 7, the A points contributing to the first
derivative calculation for the baseline are displayed as large
black dots connected by a line.
[0052] The next step is to determine the test point cycle, that is,
the cycle used to compare against the baseline for determining a
positive or negative result. It the curve is not well-behaved, the
test point is the last cycle. If the fluorescence curve is
well-behaved, the test point is the cycle with fluorescence
farthest from the baseline. The test point fluorescence of a
negative sample can be predicted as the intersection of the
baseline with the test point cycle.
[0053] Next, a confidence interval can be determined about the
predicted negative test point. Preferably, this is done by finding
the square root of the mean square error about the baseline of A
points used to determine the baseline. This is multiplied by C. The
product is added to the predicted negative test point to get the
upper fluorescence limit of the confidence interval and is
subtracted from the predicted negative test point to get the lower
limit of the confidence interval. These limits are shown on FIG. 7
as two solid horizontal lines.
[0054] The final step is to declare the sample positive or
negative. If the test point fluorescence is outside of the
confidence interval, the sample is positive. If it is within the
interval, the sample is negative. FIGS. 7 and 8 are samples which
are positive, while FIGS. 9-11 are negative samples.
[0055] Although the invention has been described in detail with
reference to preferred embodiments, variations and modifications
exist within the scope and spirit of the invention as described and
defined in the following claims.
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