U.S. patent application number 15/926535 was filed with the patent office on 2018-07-26 for method and system for genotyping samples in a normalized allelic space.
The applicant listed for this patent is APPLIED BIOSYSTEMS, LLC. Invention is credited to David Holden, Mark Pratt.
Application Number | 20180211000 15/926535 |
Document ID | / |
Family ID | 36596379 |
Filed Date | 2018-07-26 |
United States Patent
Application |
20180211000 |
Kind Code |
A1 |
Pratt; Mark ; et
al. |
July 26, 2018 |
Method and System for Genotyping Samples in a Normalized Allelic
Space
Abstract
Aspects of the present invention describe an apparatus and
method for generating genotype calls for a sample. The genotyping
initially models allelic signal response into an allelic model
having one or more model parameters for an identified one or more
sources of systematic variation. The model and parameters are then
used to transform the allelic signals to a normalized allelic space
that serves to compensate for the one or more sources of systematic
variation. By compensating for the systematic variation in this
manner, the genotype for the sample is readily determined based
upon its relationship to the representation of the allelic signals
in normalized allelic space and in accordance with the allelic
model.
Inventors: |
Pratt; Mark; (San Mateo,
CA) ; Holden; David; (Burlingame, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
APPLIED BIOSYSTEMS, LLC |
Carlsbad |
CA |
US |
|
|
Family ID: |
36596379 |
Appl. No.: |
15/926535 |
Filed: |
March 20, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13602676 |
Sep 4, 2012 |
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15926535 |
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12551438 |
Aug 31, 2009 |
8359166 |
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13602676 |
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11259162 |
Oct 25, 2005 |
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12551438 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G16B 25/00 20190201 |
International
Class: |
G06F 19/20 20060101
G06F019/20 |
Claims
1. A method for generating genotype calls using an allele signal
detection system that comprises a fluorescent probe having at least
one of an associated discrete marker and a reporter dye responsive
to an allele to be detected, the method comprising: generating, by
a processor, an allelic model having one or more parameters source
of systematic variation; detecting, by the allele signal detection
system, an allelic signal response from a plurality of biological
samples; determining, by the processor, a Cartesian distance from a
sample to an expected one or more genotype coordinates in a
normalized allelic space, the normalized allelic space being
compensated for systemic variation based on a plurality of data
points stored within a memory coupled to the processor, the data
points being gathered from at least one of a plurality of runs and
a plurality of samples; displaying, by the allele signal detection
system, a genotype call for the sample based on the shortest
measured Cartesian distance between the sample and one of the
expected one or more genotype coordinates.
2. The method of claim 1, wherein the expected one or more genotype
coordinates is selected from a set of genotype coordinates
including: a homozygous allele A, a heterozygous allele AB and a
homozygous allele B having corresponding coordinates (1, 0), (1/2,
1/2) and (0, 1) respectively.
3. The method of claim 1, wherein the systematic variation
comprises at least one of variability arising from different
samples, and variability arising from different run.
4. The method of claim 1, wherein the allele signal detection
system records a measured fluorescent intensity to determine an
allelic composition of the sample.
5. The method of claim 1, wherein the parameter associated with
each source of systematic variation is modified, by the processor,
to minimize overall variation in the allelic signals and a model of
the alleles in a training population.
6. The computer implemented method of claim 5, wherein the model of
the alleles in the training population arc assigned a unit
probability, by the processor, of occurrence in the allele space of
homozygous and heterozygous alleles.
7. A non-transitory machine-readable storage device comprising
instructions executable by a programmable processor within an
allele signal detection system, the instructions operable to cause
the programmable processor to cause the allele signal detection
system to: detect an allelic signal response from a sample using a
fluorescent probe having at least one of an associated discrete
marker and a reporter dye responsive to an allele to be detected;
generate an allelic model using the allelic signal response, by the
processor, the model having one or more parameters of systematic
variation; determine a genotype for the sample based upon its
relationship to the representation of the allelic signal in a
normalized allelic space and in accordance with the allelic model,
the normalized allelic space being configured to compensate for
systemic variation based on a plurality of data points gathered
from at least one of a plurality of runs and a plurality of
samples; display the genotype for the sample based on the shortest
measured Cartesian distance between the sample and one of the
expected one or more genotype coordinates within the normalized
allelic space.
8. The non-transitory machine-readable storage device of claim 7,
wherein the systematic variation comprises at least variability
arising from different samples, and variability arising from
different runs.
9. The non-transitory machine-readable storage device of claim 7,
wherein the expected one or more genotype coordinates is selected
from a set of genotype coordinates including: a homozygous allele
A, a heterozygous allele AB and a homozygous allele B having
corresponding coordinates (1, 0), (1/2, 1/2) and (0, 1)
respectively.
10. The non-transitory machine-readable storage device of claim 7,
wherein the instructions further comprises instructions when
executed that cause the processor to cause the allele signal system
to, create a fixed prior probability distribution of normalized
allele signals from a statistically significant training set of
genotype data by fitting, by the processor, a normalized training
set of genotype data to probability distributions that reflect a
set of allowed genotypes in the normalized allelic space; and
display the genotype call for the sample, the call determined upon
a greatest prior probability as reflected by the fitted probability
distribution and applied to the sample normalized in the normalized
allelic space.
11. The non-transitory machine-readable storage device of claim 10,
wherein the probability distributions are based upon elliptical
Gaussian probability distributions.
12. A system for generating genotype calls for a sample, comprising
an allele signal detection system configured to detect an allelic
signal response, the detection system comprising a fluorescent
probe having at least one of an associated discrete marker and a
reporter dye responsive to an allele to be detected; a computer
processor operable to: model the allelic signal response, by a
processor, into an allelic model having one or more parameters
sources of systematic variation; transform the allelic signals
through the one or more parameters of the allelic model to a
normalized allelic space, by the processor, the normalized allelic
space configured to compensate for systemic variation based on a
plurality of data points gathered from at least one of a plurality
of runs and a plurality of samples; determine a genotype for the
sample, by the processor, according to a clustering of the
normalized allelic data signals in the normalized allelic space;
measure a relative angular offset of values for the normalized
allelic data signals, by the processor, in the normalized allelic
space; and call, by the processor, a genotype for the sample based
upon its proximity to the different angular offsets of values and
their corresponding genotype classifications; and a display
operable to display the genotype call for the sample.
13. The system of claim 12, wherein the expected one or more
genotype coordinates is selected from a set of genotype coordinates
including: a homozygous allele A, a heterozygous allele AB and a
homozygous allele B having corresponding coordinates (1, 0), (1/2,
1/2) and (0, 1) respectively.
14. The system of claim 12, wherein determining the genotype for
the sample further comprises, presenting the cluster of allelic
data signals in a diagram along with a confidence factor for the
sample and genotype classification.
15. The system of claim 12, wherein the allele signal detection
system records a measured fluorescent intensity to determine an
allelic composition of the sample.
16. The system of claim 12, wherein the normalized allelic space is
further configured to transform a relative measure of an allelic
signal response into a unit-less scalar measure.
17. The system of claim 12, wherein the systematic variation
comprises at least one of variability arising from different
samples, and variability arising from different runs.
18. The system of claim 17, wherein the systematic variation
further comprises variability arising from signal response
imbalance from pairs of complementary alleles.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to U.S. Provisional
Application No. 60/622,279, filed Oct. 25, 2004 assigned to the
assignee of the present invention and titled "Self Calibration and
Joint Modeling of High Throughput Genotype Data", and to U.S.
patent application Ser. No. 11/259,162, both of which is
incorporated herein by reference.
INTRODUCTION
[0002] Genotyping analysis can be hampered by noise and other
perturbations affecting signal response. Oftentimes, conventional
approaches to determine genotype calls inadequately address
resolving these factors thus increasing the uncertainty and
subjectivity of the analysis. In certain instances, conventional
genotyping routines may discard data that does not conform to an
identifiable signal cluster despite the overall effort to keep this
information.
[0003] Removal of data from a sample set in this manner may
actually prevent identification of critical data points and reduce
the overall efficiency of the genotyping analysis. Further,
including noisy allele signal response may reduce genotype call
accuracy as it can skew or throw off certain conventional
genotyping approaches.
[0004] Improved computational processing of genetic samples and
their associated signal responses is of growing importance. This is
especially true in the context of high throughput platforms such as
SNPlex.RTM. by Applied Biosystems Corporation that are capable of
performing genotyping on smaller reaction volumes and larger
multiplexed assays. For such systems, it is desirable to maintain
the ability to operate at high speeds while producing accurate
results even with data that is conventionally difficult to
evaluate.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] The skilled artisan will understand that the drawings,
described below, are for illustration purposes only. The drawings
are not intended to limit the scope of the present teachings in any
way.
[0006] FIG. 1 is a schematic illustration of a system for
performing genotyping on genetic samples in accordance with some
implementations of the present invention;
[0007] FIG. 2 is a schematic flowchart of the operations used to
call genotypes using various aspects of the present invention as
well as those available through clustering;
[0008] FIG. 3 is a flowchart diagram depicting the operations
associated with normalizing the allelic signal response and
transforming the signals into an normalized allelic space in
accordance with some implementations of the present invention;
[0009] FIG. 4A is a schematic representation that illustrates the
expected genotype values and basis for some of the constraints used
by some implementations of the present invention;
[0010] FIG. 4B illustrates the more random appearing distribution
of allelic signals before normalization and processing performed in
accordance with some aspects of the present invention;
[0011] FIG. 4C illustrates the effect of normalization on allelic
signal data from FIG. 4B;
[0012] FIG. 4D illustrates the distribution of a large number of
normalized training genotypes used to develop the prior probability
distributions for the three expected genotypes.
[0013] FIG. 5A presents the operations of using a Cartesian
coordinate system in the normalized allelic space to call the
genotype for a given sample;
[0014] FIG. 5B provides an alternative approach to calling
genotypes using a fixed prior probability distribution in
accordance with implementations of the present
[0015] FIG. 5C is a flowchart diagram of the operations for
generating the fixed prior probability distribution used in calling
the genotypes
[0016] FIG. 6 depicts a schematic system and methods for calling
genotypes in accordance with implementations of the present
invention.
SUMMARY
[0017] Aspects of the present invention describe all apparatus and
method for generating genotype calls for one or more samples. The
genotyping approach transforms and corrects for systematic
variation in an allelic signal response with an allelic model
represented with one or more model parameters. The parameters in
the model are associated with noise and other sources of systematic
variation. The model and parameters may then be used to transform
the allelic signals into a representation of normalized allelic
space that serves to compensate for the one or more sources of the
noise or systematic variation. In various implementations,
systematic variation may arise from instrument artifacts, chemistry
artifacts, process artifacts, operational artifacts, temperature
artifacts, humidity artifacts, volume artifacts and assay
artifacts. Compensating for these variations in this manner, makes
it possible to determine the genotype for the sample based upon its
relationship to the representation of the allelic signals in
normalized allelic space and in accordance with the allelic
model.
[0018] These and other features of the present teachings are set
forth herein.
DESCRIPTION
[0019] FIG. 1 is a schematic illustration of a system configured
for genotypic analysis of samples in accordance with some
implementations of the present invention. System 100 includes
biological/genetic samples 102, assays 104, sample processing
systems 106, allele signal detection and acquisition system 108
(hereinafter allelic signal detection system 108), allele signal
response database 110, normalized allelic space transform and
genotype analysis system 112 (hereinafter normalized allelic space
transform system 112), genotype database derived from normalized
allelic space 114 and output systems and interface for genotyping
analysis 116.
[0020] In general, system 100 may be used in genetic and biological
research to classify genetic sequence variations in samples 102
that may include insertions, deletions, restriction fragment length
polymorphisms ("RFLPSs"), short tandem repeat polymorphisms
("STRPs") and single nucleotide polymorphisms ("SNPs"). Many of the
examples and descriptions contained herein below directly relate to
this latter SNP type of genetic sequence variation. Detailed
analysis SNP is useful in studying the relationship between
nucleotide variations and diseases or other conditions. However,
SNPs are but one of many different types of nucleotide variations
and it is contemplated that application of these concepts with
respect to SNPs can also be applied to many other sources of
genetic sequence variations described hereinabove and known to
those skilled in the art.
[0021] Often, a large amount of data may be generated and analyzed
when performing a genetic analysis or experiments. For example,
this may be accomplished in sample processing systems 106 in part
by placing samples in multiple wells and then evaluating with
assays 104. In an exemplary application of the present invention,
96 wells of genetic samples may be evaluated with 48 assays 104
sensitive to 48 different SNPs on the genetic samples 102. This
results in a total of 4608 different tests to be performed for each
tray of samples and a corresponding set of results. Assays 104 can
be multiplexed with multiple assays for each sample or singleplexed
whereby a single assay can be evaluated individually with each
sample.
[0022] Allele signal detection system 106 assays the various
samples and produces corresponding allele signal response. These
signals may be diagrammed using a scatter plot or other
diagrammatic representation. In one implementation, allele signal
detection system 106 assays utilize a pair of fluorescent probes
having an associated discrete marker or reporter dye responsive to
each of the different alleles to be detected. During readout of the
sample, allele signal detection system 106 records and associates
the fluorescent intensities measured for each sample to determine
its particular allelic composition. Generally, the results of such
an assay are used to determine if a selected sample tested is
homozygous for a first allele (e.g., A/A), homozygous for a second
allele (e.g., B/B) or heterozygous for a combination of alleles
(e.g., A/B).
[0023] In one aspect, homozygous portions of the sample tend to
exhibit an increased degree of fluorescence in one or another
marker type with the amount of observed fluorescence from the
opposing marker type significantly diminished or completely absent.
Conversely, portions of the sample identified as heterozygous for
both alleles (e.g., A/B) typically present a more uniform degree of
fluorescence from both markers thus indicating a contribution from
two different alleles A and B. A commercial implementation of these
operations is performed in Applied Biosystems SNPlex system and
Taqman platforms and further employs Applied Biosystems' 3730,
3730x1 and 3100 Prism Genetic Analyzers, Prism 7700 and 7900HT
sequence detection systems and Biotrove OpenArray systems to
monitor and record the aforementioned amplified fluorescence
signals.
[0024] In one aspect, the raw data of the resulting allelic signal
response is stored in allele signal response database 110. This
information may also be represented visually as values in a scatter
or cluster plot. Conventional genotyping systems typically
represent the allelic signal response data from allele signal
response database 110 in such representations to aid in
visualization of clusters of signals representing the different
genotypes. In some cases, these clusters tend to form three
distinct groupings of signal data interpreted as representing a
propensity that is homozygous for a first allele (e.g., A/A),
homozygous for a second allele (e.g., BIB) or heterozygous for a
combination of alleles (e.g., A/B).
[0025] In other situations, data may tend to aggregate in greater
or fewer than three different clusters. In such instances, it may
become difficult to call the allele unambiguously. U.S. patent
application Ser. No. 10/611,414 by Holden et al. entitled "A System
and Method for SNP Genotype Clustering" (hereinafter Holden)
incorporated by reference herein provides at least one approach for
clustering analysis and calling genotypes when the distribution of
allele signals do not readily and distinctly translate to the
different alleles. In Holden, the clusters are discriminated using
a relative angular measure of the allele signal response and
clusters they form.
[0026] Normalized allelic space transform and genotype analysis
system 112 (hereinafter normalized allelic space transform system
112) further improves calling an allele by recognizing and
compensating for systematic variation that may be present in system
100 and genetic samples 102. For example, this may be introduced
from consistent sources of variation inherent to each sample,
variation from run to run (i.e., variation in the run), imbalance
between the signal response from pairs of complementary alleles
(i.e., allelic imbalance) and many other factors that may arise
during genotype analysis.
[0027] By recognizing and compensating for this variation, the
alleles can be called with greater accuracy and in a manner that
can be more readily automated for high throughput analytical
genotyping systems. In at least one implementation of the present
invention, signal response detected from the alleles are
transformed from a relative measure of the allelic signal response
into a unit-less scalar measure of the various alleles (i.e.,
homozygous A/B and heterozygous). Through this transformation, the
representation of alleles in a normalized allelic space provides a
more consistent and more accurate representation of the alleles
being measured in a given sample.
[0028] Processing performed by normalized allelic space transform
112 also tends to preserve more data and increase the sample sets
stored in genotype database derived from normalized allelic space
114. Computer based analytical operations can be performed with
fewer exceptions or the need to eliminate data that otherwise would
appear as outlying data points or noise. Output systems and
interface for genotyping analysis 116 can therefore provide more
automated genotyping based on rules rather than requiring visual
inspection or subjective viewing of the datasets. For example, a
representation of genotypes in the normalized allelic space 114 can
be more readily analyzed using a computer and require less
visualization and subjective judgment from a user or operator of
the analytic equipment used in genotyping.
[0029] FIG. 2 is a schematic flowchart of the operations used to
call genotypes using both aspects of the present invention as well
as those available through clustering. The analytical framework for
genotyping operations generally works in three stages: a genotype
preprocessing 200, a genotype classification 202 and genotype
presentation 204 as illustrated in FIG. 2. It is contemplated that
the preprocessing transformations of the allelic signals in
accordance with aspects of the present invention provides a
superior approach to genotype analysis though conventional
clustering and other approaches as suggested by Holden should also
be considered. Consequently, the operations outlined in FIG. 2 as
indicated below include clustering as part of the analytical
framework as an option even though genotype calling may be
performed with sufficient accuracy without these additional
operations or steps in most cases.
[0030] In genotype preprocessing 200, allelic signal intensity
information is gathered for a combination of experimental samples
and corresponding assays as represented by allele A 206 A and
allele B 206 B sample matrices. For example, each of 48 assays are
applied to 96 samples each tested for two alleles for a total of
9216 measurements contained in both allele A 206 A and allele B 206
B matrices of intensity data points. As previously recognized,
these intensity values generally include several sources of
systematic variation thus causing the cluster or scatter plots to
not exhibit the expected genotype distributions of homozygous A/A,
B/B or heterozygous A/B alleles.
[0031] In one implementation, it is observed that sources of
systematic variation can be attributed to a number of factors
including variability in the different samples, variability from
one run to another run over time and an imbalance in the signal
response from one allele over a complementary allele. As will be
described in further detail later herein, implementations of the
present invention transform the allelic signals to a normalized
allelic space through a model and model parameters that compensate
for these identified systematic variations (208). Essentially, this
step of the operation not only compensates for these systematic
variations but also serves to preserve more data.
[0032] Once transformed into the normalized allelic space,
implementations of the present invention can then call the genotype
for a target sample according to its relationships with expected
distributions in normalized allelic space (210). Several approaches
can be used to compare the measurements associated with the target
experimental sample and the other samples in normalized allelic
space. For example, a proximity approach identifies a minimum
distance between the target experimental sample and an expected
genotype using Cartesian coordinates in the normalized allelic
space. An alternative implementation performs additional genotype
preprocessing 200 to create a fixed prior probability distribution
of alleles normalized in a normalized allelic space. In this
operation, training data derived from many different assays,
samples and runs are combined together for analysis using a common
model and several parameters. It is presumed that each of these
data sets are normalized as previously described by identifying an
appropriate set of parameters to compensate for the one or more
sources of systematic variation. These normalized values are
associated with an error function that further refines the
distribution presented in the normalized allelic space. Instead of
a Cartesian measurement to an expected genotype coordinate, this
alternate implementation determines a maximum probability genotype
for the target sample as it relates to the error function and
neighboring data samples used as training data. Further details on
this operation are provided later herein.
[0033] In either of the above or other implementations described
above or similarly contemplated, genotype classification (212) can
also employ conventional clustering as described in Holden. In
particular, the call for the genotype of the target sample is
performed according to a clustering of the allelic signal response
as described in Holden. For example, this may involve measuring a
relative angular offset of values for various allelic signals
identified for a set of samples and assays. Genotype calls for the
target sample in normalized allelic space (210) or based upon
clustering of allelic data signals are then presented along with a
confidence factor for each call and classification (214).
[0034] Referring now to FIG. 3, a flowchart diagram depicts the
operations associated with normalizing the allelic signal response
and transforming the signals into a normalized allelic space in
accordance with some implementations of the present invention.
Implementations of the present invention initially model the
allelic signal response with one or more model parameters for each
source of systematic variation (302). A basic assumption or
constraint for the model is that the normalized signal of any pair
of alleles whether homozygous A/A, B/B or heterozygous A/B should
sum to unity. Schematically, parameters are incorporated into the
model that provide sufficient flexibility to account for a
multiplicative variability as contributed by each run, sample and
each allele within a SNP assay. Accordingly, one implementation of
this model appears below in Equation 1.
.gamma..alpha..sub.i.beta..sub.j(A.sub.ij/.delta..sub.i+.delta..sub.iB.s-
ub.ij)-1 Equation 1
Where:
[0035] A.sub.ij and B.sub.ij are the measured allele signals for
SNP assay i and sample j
[0036] .gamma. is a parameter to compensate for variability in the
overall run
[0037] .alpha..sub.i is a parameter to compensate for variability
in the SNP assay i
[0038] .beta..sub.j is a parameter to compensate for variability in
the sample j
[0039] .delta..sub.i is a parameter to compensate for allele
imbalance for a SNP assay i and sample j
[0040] Provided this model in Equation 1 or other useful models,
aspects of the present invention identify model parameters that
reduce overall variation between the allelic signal response and
their representation in the normalized allelic space (304).
Essentially, this operation identifies values for the parameters
.alpha., .beta., .gamma. and .delta. that represent the systematic
variation of our measured allelic signal response. One example
technique used to identify these parameters minimizes an
appropriately selected error function. In Equation 2 provided
below, a Chi-square error function is selected to identify the
parameters that reduce this overall variation however, it is
contemplated that many other error functions could be selected and
solved to identify these parameter values.
.chi. 2 = i = 1 N j = 1 M [ .gamma..alpha. i .beta. j ( A ij /
.delta. i + .delta. i B ij ) - 1 .sigma. ij ] 2 Where : .chi. 2 a
Chi - square statistic .sigma. ij is an estimation of the error
associated with measuring the allelic signal response for a SNP
assay i and sample j N is the maximum number of SNP assays M is the
maximum number of samples Equation 2 ##EQU00001##
[0041] The Chi-square in Equation 2 is a robust statistic often
used to process data of uneven quality. Chi-square statistics also
behave appropriately as an error function as the values generated
are non-negative and its minima usually indicate optimal parameters
and describe goodness-of-fit. In this application, the Chi-square
statistic operates by comparing the actual, or observed, signal
values for each allele compared to the expected signal values if
there were no relationship at all between of the set of allele
signals in a run made with several samples and SNP assays. The
Chi-square statistic in Equation 2 is useful because it tends to
discount or reduce weight of data points that may have large error.
Likewise, data with smaller error, which should be emphasized, are
weighted more heavily.
[0042] Minimizing the Chi-square statistic for the allele signals
from Equation 2 above can be accomplished by requiring that the
first partial derivatives of the Chi-square statistic each be set
to zero. This is a requirement to determine an extrema of the
Chi-squared statistic. It should be understood that it is typically
sufficient to require an extrema of .chi..sup.2 as error functions
generally do not have maxima. Accordingly, a set of partial first
derivatives as found in Equation 3 below can be used to solve for
the parameters used in Equation 1 and Equation 2 above without
requiring additional constraints on the negativity of second
derivatives However, in the case of non-linear equations, some care
must be taken to insure that the minimum identified is a global
minimum and not merely local minimum.
.differential. .chi. 2 .differential. .gamma. = 0 .differential.
.chi. 2 .differential. .alpha. i = 0 .differential. .chi. 2
.differential. .delta. i = 0 .differential. .chi. 2 .differential.
.beta. j = 0 Where : .differential. .chi. 2 .differential. .gamma.
is partial derivative of Chi - square with respect to .gamma. , the
overall run compensation factor .differential. .chi. 2
.differential. .alpha. i is partial derivative of Chi - square with
respect to .alpha. i , the SNP assay compensation factor
.differential. .chi. 2 .differential. .delta. i is partial
derivative of Chi - square with respect to .delta. i , the allele
balance compensation factor .differential. .chi. 2 .differential.
.beta. j is partial derivative of Chi - square with respect to
.beta. j , the sample compensation factor Equation 3
##EQU00002##
[0043] In some cases, the set of equations in Equation 3 may be
degenerate and require additional constraints. In its degenerate
form, Equation 3 would not be able to specify the .alpha. and
.beta. parameters uniquely. For example, it can be seen that the
model is insensitive to multiplying the .alpha.'s by a factor and
the .beta.'s by its reciprocal. Accordingly, the added constraints
to prevent the degenerate condition are described below with
respect to Equation 4.
Equation 4 i = 1 N .alpha. i = 1 ( 1 ) j = 1 M .beta. j = 1 Where :
i = 1 N .alpha. i is a repeated product of correction factors for
SNP assays having a geometric mean of 1. j = 1 M .beta. j is a
repeated product of correction factors for the samples having a
geometric mean of 1. ( 2 ) ##EQU00003##
[0044] To expedite identifying a solution, the non-linear model and
constraints provided in Equations 1-4 are recast into separate
operations that can be solved quickly with linear algebra. This
approach also eliminates concerns of solving these equations and
finding local minima rather than the global minima for the
function. It also allows the approximate solution to Equation 1 to
be found optimally without otherwise expending a computationally
significant time to find the solution. It is satisfactory to recast
this model into separate steps that can be solved with linear
algebra.
[0045] First, we temporarily disregard the allele imbalance in
Equation 1 by removing .delta..sub.i. This provides the following
relationship in (1) indicated in Equation 5 below. By substituting
the V.sub.ij according to the relationship (2) Equation 5, and
applying the logarithm to both sides of the equation we have the
relationship (3) from Equation 5 below and the linear equation in
(4) readily solved in accordance with methods known to those
skilled in the art. As a last step subsequent to the solution of
(4) and .alpha., .beta. and .gamma. a separate solution can be
derived for an allele-balancing factor, .delta..
(1) .gamma..alpha..sub.i.beta..sub.j(A.sub.ij+B.sub.ij)=1
(2) V.sub.ij=A.sub.ij+B.sub.ij
(3) log(.gamma..alpha..sub.i.beta..sub.jV.sub.ij)=0
(4) g+a.sub.i+b.sub.i+u.sub.ij=0 Equation 5 [0046] Where: [0047]
g=log .gamma. [0048] a.sub.i=log .alpha..sub.i [0049] b.sub.j=log
.beta..sub.j [0050] u.sub.ij=log V.sub.ij
[0051] Once determined, the parameters are then applied to the
measured allele signals to transform our allele pairs into a
normalized allelic space rather than the allelic signal space
originally measured. This resulting normalized allelic space may be
universally used as it is largely free of systematic instrument and
chemistry artifacts and can be used across runs as well as samples,
and alleles within a SNP assays. The conversion between the signal
response between alleles A and B.sub.ij and the corresponding
values in normalized allelic space of a.sub.ij and b u is defined
by the relationships in Equation 6.
a.sub.ij=.gamma..alpha..sub.i.beta..sub.jA.sub.ij/.delta..sub.i
b.sub.ij=.gamma..alpha..sub.i.beta..sub.j.delta..sub.iB.sub.ij
Equation 6 [0052] Where: [0053] a.sub.ij is a allele signal
response mapped into the allelic space for allele A.sub.ij [0054]
b.sub.ij is a allele signal response mapped into the allelic space
for allele B.sub.ij
[0055] Systematic variation in raw allele signal A and B is
compensated through Equation 6 generating normalized allele signals
a.sub.ij and b.sub.ij in the normalized allelic space. The
genotyping is then determined for the sample based upon the
relationship to the representation of the allelic signals in this
normalized allelic space and in accordance with the model (306).
Details on this determination is provided in further detail later
herein.
[0056] In FIG. 4A, a schematic representation illustrates the
expected genotype values and basis for some of the constraints used
by some implementations of the present invention. In particular,
three different possible alleles are mapped in a unit space at
expected genotype values along Cartesian coordinates (1, 0), (1/2,
1/2) and (0, 1). Each of the genotype value coordinates corresponds
to homozygous AA alleles, heterozygous AB alleles and homozygous BB
alleles with an expectation that sum of each genotype pair is unity
or one.
[0057] As a point of comparison, FIG. 4B illustrates the more
random appearing distribution of approximately eighty-thousand
pairs of allelic signals before normalization and processing
performed in accordance with some aspects of the present invention.
Namely, the scatter plot of allele signal intensity points in FIG.
4B do not appear to form three distinct representation of the
expected genotypes from FIG. 4A but instead provide ambiguous
information about the relative existence of one allele over
another.
[0058] In contrast, FIG. 4C illustrates a rather distinct grouping
of the three expected genotypes in a unit space as illustrated in
FIG. 4A. The points in FIG. 4C fall into the expected genotype
values as set forth in FIG. 4A and encompassed by the model and
parameters used to normalize the values from FIG. 4B as provided in
Equation 1 through Equation 6 provided hereinabove. Normalization
not only removes ambiguity of the values presented in the
conventional scatter plot but also serves to preserve data
otherwise considered outlying and noisy by normal clustering and
other analytical genotyping tools.
[0059] FIG. 4D provides yet another distinct grouping of the three
expected genotypes in accordance with other aspects of the present
invention. These contours are frequency determinations of a
training set that are subsequently used to fit prior probability
distributions. In particular, the genotypes and parameters fitted
to an elliptical Gaussian distribution provide even more
differentiation between the alleles.
[0060] In light of the distribution illustrated in FIG. 4C, calling
a genotype can readily be determined immediately and without the
need for clustering. FIG. 5A presents the operations of using a
Cartesian coordinate system in the normalized allelic space to call
the genotype for a given sample. This is sometimes referred to as a
proximity genotyping approach. Using the normalized allelic space
representation, implementations of the present invention measure a
Cartesian coordinate distance from an allelic signal response
represented in the normalized allelic space to each of the expected
one or more genotype coordinates (502). For example, the expected
genotype coordinates for homozygous alleles AA, heterozygous
alleles AB and homozygous alleles BB corresponds to coordinates
(1,0), (1/4, 1/4) and (0,1) for the unit based normalized allelic
space.
[0061] Next, various implementations of the present invention call
a genotype for the sample that represents the shortest Cartesian
distance between the sample represented in normalized allelic space
and the expected one or more genotype coordinates for each allele
(504). As previously described, clustering can also be used as an
additional indicia for genotyping but may not be required given the
relatively straightforward ability to call the genotype in the
normalized allelic space.
[0062] Likewise, the prior probability distribution illustrated in
FIG. 4D also facilitates calling a genotype immediately and without
the need for clustering. FIG. 5B provides an alternative approach
to calling genotypes using a fixed prior probability distribution
in accordance with implementations of the present invention.
Initially, this approach identifies a probability of each
experimental genotype according to the prior probability model
distributions (506). Normalized allelic values for each
experimental genotype are used in the equations that describe the
prior probability distribution. For example, the normalized allelic
values are entered into a set of elliptical Gaussian equations.
Details on determining the fixed prior probability distribution are
described herein below in FIG. 5C. Next, the genotype for the
experimental sample is called based upon the greatest prior
probability result (506). In practice, calling the genotype for the
experimental sample is based upon a greatest prior probability and
reflected by the probability distribution as applied to the sample
normalized in normalized allelic space. The highest resulting
probability indicates the most likely genotype for the experimental
sample.
[0063] FIG. 5C is a flowchart diagram of the operations for
generating the fixed prior probability distribution used in calling
the genotypes. Initially, a large set of training data genotypes
510 A and 510 B are used to establish the prior probability
distribution. Essentially, the frequency of occurrence of these
normalized signals in the training set is what establishes the
expected distribution in normalized allelic space subsequent
genotype samples. As before, the systematic variation is
compensated for by normalizing and transforming the allelic signal
response of the various training genotypes into scalar values in
normalized allelic space (512). Various implementations of the
present invention fit the normalized set of genotype training data
to one or more probability distributions that reflects the set of
alleles (610). In some implementations, the distribution can be
modeled using three elliptical Gaussian distributions as described
by the general form set formed in Equation 7 below.
F(a,b)=Fe.sup.-(a-a.sup.o.sup.).sup.2.sup./s.sup.o.sup.2.sup.-(b-b.sup.o-
.sup.).sup.2.sup./s.sup.b.sup.2 Equation 7
Where:
[0064] a is a normalized allele A in the allelic space
[0065] b is a normalized allele B in the allelic space
[0066] F.sub.o is a model parameter
[0067] S.sub.b.sup.2 is a measure of the dimension of the ellipse
along the axis of allele b in allelic space
[0068] S.sub.a.sup.2 is a measure of the dimension of the ellipse
along the axis of allele a in allelic space
[0069] a.sub.o is an offset for the center of the ellipse along the
axis of allele a in allelic space
[0070] b.sub.o is an offset for the center of the ellipse along the
axis of allele b in allelic space
[0071] Equation 8 provides a more specific set of equations for the
prior probability distributions provided that a.sub.o and b.sub.o
are the expected genotype coordinates (a,b) for homozygous allele
AA, heterozygous allele AB and homozygous allele BB with
corresponding coordinates (1,0), (1/2, 1/2) and (0,1) in the unit
based normalized allelic space.
Homozygous.sub.aa(a,b)=Fe.sup.-(a-1).sup.2.sup./s.sup.a.sup.2.sup.-(b-0)-
.sup.2.sup./s.sup.b.sup.2
Heterozygous.sub.ab(a,b)=Fe.sup.-(a-1/2).sup.2.sup./s.sup.a.sup.2.sup.-(-
b-1/2).sup.2.sup./s.sup.b.sup.2
Homozygous.sub.bb(a,b)=Fe.sup.-(a-0).sup.2.sup./s.sup.a.sup.2.sup.-(b-1)-
.sup.2.sup./s.sup.b.sup.2 Equation 8
[0072] FIG. 6 depicts a schematic system 112 and methods for
calling genotypes in accordance with implementations of the present
invention. System 112 includes a memory 602 to hold executing
programs typically random access memory (RAM) or read-only memory
(ROM) such as Flash, a display interface 604, a spectral detector
interface 606, a secondary storage 608, a network communication
port 610, and a processor 612, operatively coupled together over an
interconnect 614.
[0073] Display interface 604 allows presentation of information
related to genotyping in normalized allelic space and with
clustering of signals. Spectral detector interface 606 contains
circuitry to control operation of a spectral detector including
duplex transmission of data in real-time or in a batch operation.
Secondary storage 608 can contain experimental results and programs
for long-term storage including allelic signal response data,
normalized allelic space transformation data, normalized and raw
genotype training data, target samples and other data useful in
genotyping in accordance with aspects of the present invention.
Network communication port 601 transmits and receives results and
data over a network to other computer systems and databases.
Processor 612 executes the routines and modules contained in memory
602.
[0074] In the illustration, memory 602 includes allelic
normalization component 616, fixed prior probability distribution
component 618, cluster genotyping component 620, normalized allelic
space genotyping component 622 and a run-time system 628 for
managing computing resources used in conjunction with one or more
of the above components.
[0075] Allelic normalization component 616 contains routines to
transform allelic signals in a signal domain to scalar values in
the normalized allelic space described previously. Essentially,
this component uses a model and corresponding model parameters to
compensate for systematic variation in the one or more allelic
signals detected.
[0076] Fixed prior probability distribution component 618 gathers
many data points from various runs, samples and SNP assays to
create a probability distribution and basis for genotyping new
samples. As previously described, the prior probability
distribution in normalized allelic space can be further modeled
using a Gaussian elliptical representation for each of the
homozygous alleles (both AA and BB) as well as the heterozygous
allele.
[0077] Run-time system 628 manages system resources used when
processing one or more of the previously mentioned modules. For
example, run-time system 628 can be a general-purpose operating
system, an embedded operating system or a real-time operating
system or controller.
[0078] System 112 can be preprogrammed, in ROM, for example, using
field-programmable gate array (FPGA) technology or it can be
programmed (and reprogrammed) by loading a program from another
source (for example, from a floppy disk, an ordinary disk drive, a
CD-ROM, or another computer). In addition, system 112 can be
implemented using customized application specific integrated
circuits (ASICs).
[0079] Having thus described various implementations and
embodiments of the present invention, it should be noted by those
skilled in the art that the disclosures are exemplary only and that
various other alternatives, adaptations and modifications may be
made within the scope of the present invention. For example, it is
mentioned that aspects of the present invention are useful for
genotyping as it relates to SNPs and SNP assays. However, it is
also contemplated that the teachings performed in accordance with
implementations of the present invention can also be performed to
facilitate genotyping of insertions, deletions, restriction
fragment length polymorphisms ("RFLPSs"), short tandem repeat
polymorphisms ("STRPs") as well as single nucleotide polymorphisms
("SNPs").
[0080] Embodiments of the invention can be implemented in digital
electronic circuitry, or in computer hardware, firmware, software,
or in combinations of thereof. Apparatus of the invention can be
implemented in a computer program product tangibly embodied in a
machine-readable storage device for execution by a programmable
processor; and method steps of the invention can be performed by a
programmable processor executing a program of instructions to
perform functions of the invention by operating on input data and
generating output. The invention can be implemented advantageously
in one or more computer programs that are executable on a
programmable system including at least one programmable processor
coupled to receive data and instructions from, and to transmit data
and instructions to, a data storage system, at least one input
device, and at least one output device. Each computer program can
be implemented in a high-level procedural or object-oriented
programming language, or in assembly or machine language if
desired; and in any case, the language can be a compiled or
interpreted language. Suitable processors include, by way of
example, both general and special purpose microprocessors.
Generally, a processor will receive instructions and data from a
read-only memory and/or a random access memory. Generally, a
computer will include one or more mass storage devices for storing
data files; such devices include magnetic disks, such as internal
hard disks and removable disks; magneto-optical disks; and optical
disks. Storage devices suitable for tangibly embodying computer
program instructions and data include all forms of non-volatile
memory, including by way of example semiconductor memory devices,
such as EPROM, EEPROM, and flash memory devices; magnetic disks
such as internal hard disks and removable disks; magneto-optical
disks; and CD-ROM disks. Any of the foregoing can be supplemented
by, or incorporated in, ASICs.
[0081] Thus, the invention is not limited to the specific
embodiments described and illustrated above. Instead, the invention
is construed according to the claims that follow and the full-scope
of their equivalents thereof.
* * * * *