Method and System for Genotyping Samples in a Normalized Allelic Space
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.
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
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.
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.
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® 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.
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.
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.
These and other features of the present teachings are set forth herein.DESCRIPTION
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.
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.
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).
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.
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).
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.
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.
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.
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.
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.
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.
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.
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).
Referring now to
γαiβj(Aij/δi+δiBij)−1 Equation 1
Aij and Bij are the measured allele signals for SNP assay i and sample j
γ is a parameter to compensate for variability in the overall run
αi is a parameter to compensate for variability in the SNP assay i
βj is a parameter to compensate for variability in the sample j
δi is a parameter to compensate for allele imbalance for a SNP assay i and sample j
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 α, β, γ and δ 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.
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.
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 χ2 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.
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 α and β parameters uniquely. For example, it can be seen that the model is insensitive to multiplying the α's by a factor and the β's by its reciprocal. Accordingly, the added constraints to prevent the degenerate condition are described below with respect to Equation 4.
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.
First, we temporarily disregard the allele imbalance in Equation 1 by removing δi. This provides the following relationship in (1) indicated in Equation 5 below. By substituting the Vij 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 α, β and γ a separate solution can be derived for an allele-balancing factor, δ.
(4) g+ai+bi+uij=0 Equation 5
- g=log γ
- ai=log αi
- bj=log βj
- uij=log Vij
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 Bij and the corresponding values in normalized allelic space of aij and b u is defined by the relationships in Equation 6.
bij=γαiβjδiBij Equation 6
- aij is a allele signal response mapped into the allelic space for allele Aij
- bij is a allele signal response mapped into the allelic space for allele Bij
Systematic variation in raw allele signal A and B is compensated through Equation 6 generating normalized allele signals aij and bij 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.
As a point of comparison,
In light of the distribution illustrated in
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.
Likewise, the prior probability distribution illustrated in
a is a normalized allele A in the allelic space
b is a normalized allele B in the allelic space
Fo is a model parameter
Sb2 is a measure of the dimension of the ellipse along the axis of allele b in allelic space
Sa2 is a measure of the dimension of the ellipse along the axis of allele a in allelic space
ao is an offset for the center of the ellipse along the axis of allele a in allelic space
bo is an offset for the center of the ellipse along the axis of allele b in allelic space
Equation 8 provides a more specific set of equations for the prior probability distributions provided that ao and bo are the expected genotype coordinates (a,b) for homozygous allele AA, heterozygous allele AB and homozygous allele BB with corresponding coordinates (1,0), (½, ½) and (0,1) in the unit based normalized allelic space.
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.
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.
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.
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.
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.
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).
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”).
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.
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.
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), (½, ½) 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), (½, ½) 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;
- 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), (½, ½) 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.