Methods and systems for decomposing and quantifying DNA mixtures from multiple contributors of known or unknown genotypes

Abstract

Provided are methods and systems for quantifying and deconvoluting nucleic acid mixture samples that include nucleic acids with one or more contributors to known or unknown genomes. The methods and systems provided herein implement a process for determining the abundance and confidence intervals of genetically distinct contributors in chimeric samples using Bayesian probabilistic modeling techniques, thereby improving specificity, accuracy, and sensitivity, and greatly expanding the scope of applications over conventional methods.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims under 35 U.S.C. §119(e) U.S. Provisional Patent Application No. 62 / 522,605, filed on June 20, 2017, entitled Methods for Accurately Enumerating DNA Mixtures from Contributors of Unknown Genotypes, the entire contents of which are incorporated herein by reference. Background Art

[0003] Sequencing data from mixtures of nucleic acids (e.g., DNA or RNA) from closely related genomes are often found in research as well as clinical settings, and quantification of the mixed contributors has been challenging when the original genomes are unknown. For example, in the context of microbiology and metagenomics, researchers and clinicians may need to quantify closely related bacterial strains of the same species in environmental samples. In a forensic setting, law enforcement officers may need to quantify and identify human individuals from a blood sample containing DNA from multiple individuals. In a biomedical research setting, scientists may need to determine the purity or extended extent of contamination in a cell or DNA sample.

[0004] Another application is next-generation sequencing (NGS)-coupled liquid biopsy. NGS-coupled liquid biopsy is an emerging diagnostic strategy with potential applications in a variety of clinical settings. In the context of organ or tissue transplantation, NGS-coupled liquid biopsy provides a non-invasive method for monitoring the health of the allogeneic transplant by quantifying the amount of allogeneic DNA in the recipient's blood. In some applications, the donor and recipient genomes are unknown or partially unknown.

[0005] The term chimera has been used in modern medicine to describe an individual that includes cell populations derived from different individuals. The chimera state can occur spontaneously through inheritance, but is more often artificially created via transplantation, blood transfusion, or sample contamination.

[0006] Chimerism leaves informative signals in different DNA types depending on the type of transplant. For bone marrow and hematopoietic stem cell transplants, blood genomic DNA (gDNA) collected after transplant will have different levels of chimerism depending on the engraftment status of the transplant. For solid organ transplants, chimeric signals can be seen in DNA without blood cells (cfDNA). Such signals can be extracted through non-invasive liquid biopsies, as opposed to the invasive tissue biopsy process that is the current standard of care for organ transplant monitoring.

[0007] Reproducible and accurate determination of the relative contribution of donor genomes to chimeric DNA samples will provide an informative tool for transplant monitoring, allowing researchers and clinicians to non-invasively and objectively measure changes in the dynamics between donor and recipient cells, reflecting the health of donor cells and organs. The present disclosure introduces novel and improved methods for quantifying the relative contribution of each genome to chimeric samples. Summary of the invention

[0008] Some embodiments proposed herein provide computer-implemented methods and systems for quantitatively and deconvoluting nucleic acid mixture samples, which nucleic acid mixture samples include nucleic acids of two or more contributors of unknown genotypes. One aspect of the present disclosure relates to a method for quantitatively analyzing nucleic acid scores in nucleic acid samples, which nucleic acid samples include nucleic acids (e.g., DNA or RNA) of two or more contributors with different genomes. In some embodiments, as described below, nucleic acid mixture samples include biological tissues, cells, peripheral blood, saliva, urine and other biological liquids. In some applications, nucleic acid samples only include nucleic acids of a single contributor, and embodiments described herein can determine that nucleic acids of a single contributor account for 100% of nucleic acids in the sample. Therefore, although the description hereinafter refers to nucleic acid samples as nucleic acid mixture samples in some embodiments, it should be understood that samples can include nucleic acids of a single contributor, and the score of the contributor is 100% or 1. Of course, the method can also be used to quantify samples of nucleic acids comprising two or more contributors.

[0009] Because the various methods and systems provided herein implement strategies and processes using probabilistic mixture models and Bayesian inference techniques, embodiments provide technical improvements over conventional methods in the quantification and deconvolution of nucleic acid (e.g., DNA or RNA) mixture samples. Some embodiments provide improved analytical sensitivity and specificity, providing more accurate deconvolution and quantification of nucleic acid mixture samples.

[0010] Some embodiments allow accurate quantification of nucleic acid mixture samples whose nucleic acid amounts are too low for conventional methods to accurately quantify. Some embodiments allow accurate quantification of 3-10ng of cell-free DNA (cfDNA) mixture samples, which cannot be accurately quantified by conventional methods. Some embodiments allow application to mixed samples with 3 or more contributors, which cannot be processed by conventional methods. Some embodiments allow application to mixtures with one or more unknown genomes, which cannot be processed by conventional methods. Some embodiments described herein refer to DNA samples, but it should be understood that these embodiments are also applicable to the analysis of RNA samples.

[0011] In some embodiments, the method is implemented on a computer system comprising one or more processors and system memory, the computer system being configured to deconvolute and quantify a nucleic acid mixture sample comprising nucleic acids from two or more contributors.

[0012] Some embodiments provide a method for quantifying the nucleic acid fraction of a contributor in a nucleic acid mixture sample including nucleic acids of a contributor and at least one other contributor. The method includes: (a) extracting nucleic acid molecules from the nucleic acid sample; (b) amplifying the extracted nucleic acid molecules; (c) sequencing the amplified nucleic acid molecules using a nucleic acid sequencer to generate nucleic acid sequence reads; (d) mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence by one or more processors; (e) using the mapped nucleic acid sequence reads and determining the allele counts of the nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci by one or more processors; and (f) using a probabilistic mixture model and quantifying one or more fractions of nucleic acids of one or more contributors in the nucleic acid sample by one or more processors, wherein using the probabilistic mixture model includes applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and wherein the probabilistic mixture model uses a probability distribution to model the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci, and the probability distribution takes into account errors in the nucleic acid sequence reads.

[0013] In some embodiments, the mapping of (d) comprises mapping using computer hashing or computer dynamic programming. In some embodiments, the quantification of (f) comprises quantification using a novel optimization method that combines multi-iteration grid search and Broyden-Fletcher-Goldfarb-Shanno (BFGS)-quasi-Newton method. In some embodiments, the quantification of (f) comprises quantification using iterative weighted linear regression. These features require computer execution and are rooted in computer technology.

[0014] In some embodiments, the method further comprises determining, using a probabilistic mixture model and by one or more processors, one or more genotypes of one or more contributors at one or more polymorphic loci.

[0015] In some embodiments, the method further comprises determining the risk of one contributor (recipient) rejecting a tissue or organ transplanted from another contributor (donor) using one or more fractions of nucleic acid from one or more contributors.

[0016] In some embodiments, one or more contributors includes two or more contributors.

[0017] In some embodiments, the nucleic acid molecule comprises a DNA molecule or an RNA molecule.

[0018] In some embodiments, a nucleic acid sample comprises nucleic acid from zero, one or more contaminant genomes, and a genome of interest.

[0019] In some embodiments, the one or more contributors comprise zero, one or more donors of a transplant, and a recipient of the transplant, and wherein the nucleic acid sample comprises a sample obtained from the recipient.

[0020] In some embodiments, the transplant comprises an allogeneic or xenogeneic transplant.

[0021] In some embodiments, the nucleic acid sample comprises a biological sample obtained from a recipient.

[0022] In some embodiments, the nucleic acid sample comprises a biological sample obtained from a cell culture.

[0023] In some embodiments, the extracted nucleic acid molecules comprise cell-free nucleic acid.

[0024] In some embodiments, the extracted nucleic acid molecules comprise cellular DNA.

[0025] In some embodiments, the one or more polymorphic loci comprise one or more biallelic polymorphic loci.

[0026] In some embodiments, the one or more alleles at one or more polymorphic loci comprise one or more single nucleotide polymorphism (SNP) alleles.

[0027] In some embodiments, a probabilistic mixture model uses a single locus likelihood function to model allele counts at a single polymorphic locus. The single locus likelihood function includes:

[0028] M(n 1i , n 2i |p 1i ,θ)

[0029] n 1i is the allele count of allele 1 at locus i, n 2i is the allele count of allele 2 at locus i, p 1i is the expected fraction of allele 1 at locus i, and θ comprises one or more model parameters.

[0030] In some embodiments, p 1i Modeled as a function of: (i) the genotype of the contributor at locus i, or g i =(g 11i , ..., gD1i ), which is a vector of the number of copies of allele 1 at locus i in contributors 1...D; (ii) the read count error caused by the sequencing operation in (c), or λ; and (iii) the nucleic acid fraction of the contributor in the nucleic acid sample, or β = (β1, ..., β D ), where D is the number of contributors. In some embodiments, the contributors include two or more contributors, and p 1i = p(g i ,λ,β)←[(1-λ)g i +λ(2-g i )] / 2·β, where · is the vector dot product operator.

[0031] In some embodiments, the contributor includes two contributors, and the p1′ value in Table 3 is used to obtain p 1i .

[0032] In some embodiments, zero, one or more genotypes of the contributor are unknown. In some embodiments, (f) comprises marginalizing over multiple possible combinations of genotypes to enumerate the probability parameter p 1i In some embodiments, the method further comprises determining a genotype configuration at each of the one or more polymorphic loci, the genotype configuration comprising two alleles for each of the one or more contributors. In some embodiments, the single locus likelihood function comprises a first binomial distribution. In some embodiments, the first binomial distribution is represented as follows:

[0033] n 1i ~BN(n i , p 1i )

[0034] n 1i is the allele count of the nucleic acid sequence read for allele 1 at locus i; and n i is the total read count at locus i, which is equal to the total genome copy number n". In some embodiments, (f) comprises maximizing a multi-locus likelihood function calculated from multiple single-locus likelihood functions.

[0035] In some embodiments, (f) includes: calculating multiple multi-locus likelihood values ​​using multiple potential score values ​​and a multi-locus likelihood function of the allele counts of the nucleic acid sequence reads determined in (e); identifying one or more potential score values ​​associated with the maximum multi-locus likelihood value; and quantifying one or more fractions of nucleic acid from one or more contributors in the nucleic acid sample as the identified potential score values.

[0036] In some embodiments, a multi-locus likelihood function comprises:

[0037] L(β, θ, λ, π; n1, n2)=Π i [∑g i M(n 1i , n 2i |p(g i ,λ,β),θ)·P(g i |π)]

[0038] L(β, θ, λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2; p(g i , λ, β) is based on the genotype g of the contributor at locus i i The expected fraction or probability of observing allele 1 at locus i; P(g i |π) is the observed genotype g at locus i given the population allele frequency (π). i The prior probability of i represents the summation over the multiple possible combinations of contributor genotypes.

[0039] In some embodiments, a multi-locus likelihood function comprises:

[0040] L(β, λ, π; n1, n2)=∏ i [∑g i BN(n 1i |n i ,·p(g i ,λ,β))·P(g i |π)]

[0041] In some embodiments, the contributors include two contributors, and the likelihood function includes:

[0042] L(β, λ, π; n1, n2)=П i ∑ g1ig2i BN(n 1i |n i , p 1i (g 1i , g 2i ,λ,β)·P(g 1i , g 2i |π)

[0043] L(β, λ, π; n1, n2) is the likelihood of observing the allele count vector n1 to n2 for alleles 1 and 2 given the parameters β and π; p 1i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p1′ in Table 3, indicating the probability of the genotypes of the two contributors (g 1i , g2i ) of allele 1 at locus i; and P(g 1i , g 2i |π) is the a priori joint probability of observing the two contributor genotypes given the population allele frequencies (π).

[0044] In some embodiments, a marginal distribution P(g 1i |π) and P(g 2i |π) to calculate the prior joint probability.

[0045] In some embodiments a genetic relationship between two contributors is used to calculate a priori joint probability.

[0046] In some embodiments, the probabilistic mixture model takes into account the nucleic acid molecule copy number errors caused by the extraction of nucleic acid molecules performed in (a), and the read count errors caused by the sequencing operation in (c). In some embodiments, the probabilistic mixture model uses a second binomial distribution to model the allele counts of the extracted nucleic acid molecules for alleles at one or more polymorphic loci. In some embodiments, the second binomial distribution is expressed as follows:

[0047] n 1i ″~BN(n i ″,p 1i )

[0048] n 1i ″ is the allele count of the extracted nucleic acid molecule of allele 1 at locus i; n i ″ is the total nucleic acid molecule count at locus i; and p iu is a probability parameter indicating the probability of allele 1 at locus i.

[0049] In some embodiments, the first binomial distribution is expressed as 1i ″ / n i " is the condition. In some embodiments, the first binomial distribution is reparameterized as follows:

[0050] n 1i ~BN(n i , n 1i ″ / n i ″)

[0051] n 1i is the allele count of the nucleic acid sequence reads of allele 1 at locus i; n i ″ is the total number of nucleic acid molecules at locus i, which is equal to the total genome copy number n″; n i is the total read count at locus i; and n1i ″ is the number of extracted nucleic acid molecules of allele 1 at locus i.

[0052] In some embodiments, the probability mixture model uses a first Beta distribution to approximate n 1i In some embodiments, the first Beta distribution has a mean and variance that match the mean and variance of the second binomial distribution. In some embodiments, locus i is modeled as a biallelic gene and the first Beta distribution is represented as follows:

[0053] n i1 ″ / n″~Beta((n″-1)p 1i , (n″-1)p 2i )

[0054] p 1i is a probability parameter indicating the probability of the first allele at locus i; and p 2i is a probability parameter indicating the probability of the second allele at locus i.

[0055] In some embodiments, (f) comprises combining a first binomial distribution that models sequencing read counts and a first beta distribution that models the number of extracted nucleic acid molecules to obtain a single locus likelihood function that follows a first beta-binomial distribution. In some embodiments, the first beta-binomial distribution has the following form: n 1i ~BB(n i , (n″-1)·p 1i , (n″-1)·p 2i ), or alternatively approximate: n 1i ~BB(n i , n″·p 1i , n″·p 2i ). In some embodiments, the multi-locus likelihood function comprises:

[0056] L(β,n″,λ,π;n1,n2)=Πi[∑g i BB(n 1i |n i , (n″-1)·p 1i , (n”-1)·p 2i )·P(g i |π)]

[0057] L(β, n″, λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2 at all loci, and p 1i = p(g i ,λ,β),p 2i =1-p 1i .

[0058] In some embodiments, a contributor comprises two contributors and a multi-locus likelihood function comprises:

[0059] L(β,n″,λ,π;n1,n2)=

[0060] ∏ i ∑ g1ig2i BB(n 1i , n 2i |n i , (n″-1)·p 1i (g 1i , g 2i ,λ,β),(n″-1)·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π).

[0061] L(β, n″, λ, π; n1, n2) is the likelihood of observing the allele count vector of the first alleles of all loci (n1) and the allele count vector of the second alleles of all loci (n2) given the parameters β, n″, λ, and π; p 1i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p1′ in Table 3, indicating the probability of the genotypes of the two contributors (g 1i , g 2i ) is the probability of allele 1 at locus i; p 2i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p2′ in Table 3, indicating the probability of 1i , g 2i ) of allele 2 at locus i; and P(g 1i , g 2i |n) is the first contributing genotype (g) of the first allele at locus i observed given the population allele frequency (π). 1i ) and the second contributor genotype of the first allele (g 2i ) is the prior joint probability of .

[0062] In some embodiments, (f) includes estimating the total extracted genome copy number n″ from a large number of extracted nucleic acid molecules. In some embodiments, the estimated total extracted genome copy number n″ is adjusted according to the fragment size of the extracted nucleic acid molecules.

[0063] In some embodiments, the probabilistic mixture model takes into account the error in the number of nucleic acid molecules caused by the amplification of nucleic acid molecules performed in (b), and the error in the read count caused by the sequencing operation in (c). In some embodiments, the amplification process of (b) is modeled as follows:

[0064] x t+1 =x t +y t+1

[0065] x t+1 is the number of nucleic acid copies of a given allele after cycle t+1 of amplification; x t is the number of nucleic acid copies of a given allele after cycle t of amplification; y t+1 is a new copy generated in cycle t+1, and it follows the binomial distribution y t+1 ~BN(x t , r t+1 ); and t+1 is the amplification rate at cycle t+1.

[0066] In some embodiments, a probabilistic mixture model uses a second Beta distribution to model the allele fractions of amplified nucleic acid molecules for alleles at one or more polymorphic loci.

[0067] In some embodiments, locus i is biallelic and the second Beta distribution is represented as follows:

[0068] n 1i ′ / (n 1i ′+n 2i ′)~Beta(n″·ρ i ·p 1i , n″·ρ i ·p 2i )

[0069] n 1i ' is the allele count of the amplified nucleic acid molecule of the first allele at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of the second allele at locus i; n" is the total nucleic acid molecule count at any locus; p i is a constant related to the average amplification rate r; p 1i is the probability of the first allele at locus i; and p 2i is the probability of the second allele at locus i. In some embodiments, p i is (1+r) / (1-r) / [1-(1+r) -t ], and r is the average amplification rate per cycle. In some embodiments, p i Approximately (1+r) / (1-r).

[0070] In some embodiments, (f) comprises combining the first binomial distribution and the second beta distribution to obtain n following a second beta-binomial distribution. 1i In some embodiments, the second beta-binomial distribution has the following form:

[0071] n 1i ~BB(n i , n″·ρ i ·p 1i , n″·ρ i ·p 2i )

[0072] n 1i is the allele count of the nucleic acid sequence read of the first allele at locus i; p 1i is a probability parameter indicating the probability of the first allele at locus i; and p 2i is a probability parameter indicating the probability of the second allele at locus i.

[0073] In some embodiments, (f) includes reparameterizing the second beta-binomial distribution by assuming that one or more polymorphic loci have the same amplification rate as: n 1i ~BB(n i , n″·(1+r) / (1-r)·p 1i , n″·(1+r) / (1-r)·p 2i ), where r is the amplification rate. In some embodiments, the multi-locus likelihood function comprises:

[0074] L(β,n″,r,λ,π;n1,n2)=Πi[∑g i BB(n 1i |n i , n″·(1+r) / (1-r)·p 1i , n″·(1+r) / (1-r)·p 2i )·P(g i |π)]

[0075] In some embodiments, a contributor comprises two contributors and a multi-locus likelihood function comprises:

[0076] L(β,n″,r,λ,π;n1,n2)=

[0077] Π i ∑ g1ig2i [BB(n 1i |n i , n″·(1+r) / (1-r)·p 1i (g1i , g 2i ,λ,β),n″·(1+r) / (1-r)·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)]

[0078] L(β, n″, r, λ, π; n1, n2) is the likelihood of observing the allele count vector of the first allele of all loci (n1) and the allele count vector of the second allele of all loci (n2) given the parameters β, n″, r, λ and π.

[0079] In some embodiments (f) comprises reparameterizing the second beta-binomial distribution by defining the relative amplification rate of each polymorphic locus as proportional to the total reads for the locus as:

[0080] n 1i ~BB(n i , c′·n i ·p 1i , c′·n i ·p 2i )

[0081] c′ is the parameter to be optimized; and n i is the total read sequence at locus i.

[0082] In some embodiments, a multi-locus likelihood function comprises:

[0083] L(β,n″,c′,λ,π;n1,n2)=Πi[∑g i BB(n 1i |n i , c′·n i ·p 1i , c′·n i ·p 2i )·P(g i |π)]

[0084] In some embodiments, the probabilistic mixture model takes into account the error in the number of nucleic acid molecules caused by the extraction of nucleic acid molecules performed in (a) and the amplification of nucleic acid molecules performed in (b), as well as the read count error caused by the sequencing operation in (c). In some embodiments, the probabilistic mixture model uses a third Beta distribution to model the allele fractions of the amplified nucleic acid molecules for alleles at one or more polymorphic loci, taking into account the sampling error caused by the extraction of nucleic acid molecules performed in (a) and the amplification of nucleic acid molecules performed in (b). In some embodiments, locus i is biallelic and the third Beta distribution has the following form:

[0085] n 1i / (n 1i ′+n 2i ′)~Beta(n″·(1+r i ) / 2·p 1i ,n″·(1+r i ) / 2·p 2i )

[0086] n 1i ' is the allele count of the amplified nucleic acid molecule of the first allele at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of the second allele at locus i; n" is the total nucleic acid molecule count; r i is the average amplification rate of locus i; p 1i is the probability of the first allele at locus i; and p 2i is the probability of the second allele at locus i. In some embodiments, (f) comprises combining the first binomial distribution and the third beta distribution to obtain n following the third beta-binomial distribution. 1i The single locus likelihood function of .

[0087] In some embodiments, the third beta-binomial distribution has the following form:

[0088] n 1i ~BB(n i ,n″·(1+r i ) / 2·p 1i ,n″·(1+r i ) / 2·p 2i )

[0089] r i is the amplification rate.

[0090] In some embodiments, a multi-locus likelihood function comprises:

[0091] L(β,n″,r,λ,π;n1,n2)=

[0092] Πi[Σg i BB(n 1i |n i , n″·(1+r) / 2·p 1i , n″·(1+r) / 2·p 2i )·P(g i |π)].

[0093] In some embodiments a contributor comprises two contributors, and wherein the multi-locus likelihood function comprises:

[0094] L(β,n″,r,λ,π;n1,n2)=Π i ∑ g1ig2i BB(n 1i |n i , n″·(1+r) / 2·p 1i (g 1i , g 2i ,λ,β),n″·(1+r) / 2·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)

[0095] L(n1,n2|β,n″,r,λ,π) is the observed allele count n1 of the first allele vector and the allele count n2 of the second allele vector given the parameters β,n″,r,λ and π.

[0096] In some embodiments, the method further comprises: (g) estimating one or more confidence intervals for one or more scores of nucleic acids of one or more contributors using a Hessian matrix of log-likelihood applying numerical differentiation.

[0097] In some embodiments, the mapping of (d) includes using computer hashing and computer dynamic programming by one or more processors to identify reads in the nucleic acid sequence reads that match any sequence of a plurality of unbiased target sequences, wherein the plurality of unbiased target sequences include subsequences of a reference sequence and sequences that differ from the subsequences by a single nucleotide. In some embodiments, the plurality of unbiased target sequences include five categories of sequences covering each polymorphic site in the plurality of polymorphic sites: (i) a reference target sequence that is a subsequence of the reference sequence, the reference target sequence having a reference allele having a reference nucleotide at the polymorphic site; (ii) alternative target sequences that each have an alternative allele having an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) mutated reference target sequences that include all possible sequences, each of which differs from the reference target sequence by only one nucleotide at a site that is a non-polymorphic site; (iv) mutated alternative target sequences that include all possible sequences, each of which differs from the alternative target sequence by only one nucleotide at a site that is a non-polymorphic site; and (v) unexpected allele target sequences, each of which has an unexpected allele that is different from the reference allele and the alternative allele, and each of which has a sequence that is different from the previous four categories of sequences.

[0098] In some embodiments, the method further includes estimating the sequencing error rate λ at the variant site based on the frequency of the unexpected allele target sequence observed in (v). In some embodiments, (e) includes using the identified reads and their matched unbiased target sequences to determine the allele counts of the nucleic acid sequence reads of the alleles at one or more polymorphic loci. In some embodiments, the multiple unbiased target sequences include sequences that are truncated to have the same length as the nucleic acid sequence reads. In some embodiments, the multiple unbiased target sequences include sequences stored in one or more hash tables, and the hash tables are used to identify the reads.

[0099] The disclosed embodiments also provide a computer program product including a non-transitory computer-readable medium having program instructions provided thereon for performing the recited operations and other computing operations described herein.

[0100] Some embodiments provide a system for quantifying the nucleic acid fraction of a contributor in a nucleic acid mixture sample, the nucleic acid mixture sample including the nucleic acid of the contributor and at least one other contributor. The system includes: a sequencer for receiving nucleic acid from a test sample and providing nucleic acid sequence information from the sample; a processor; and one or more computer-readable storage media having stored thereon instructions for execution on the processor to deconvolute and quantify the DNA mixture sample using the methods described herein.

[0101] Another aspect of the present disclosure provides a system for quantifying a nucleic acid sample, which contains nucleic acid from one or more contributors. The system includes: (a) a sequencer configured to (i) receive nucleic acid molecules extracted from the nucleic acid sample, (ii) amplify the extracted nucleic acid molecules, and (iii) sequence the amplified nucleic acid molecules under conditions that produce nucleic acid sequence reads; and (b) a computer including one or more processors configured to: map the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence; use the mapped nucleic acid sequence reads to determine the allele counts of the nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci; and use a probabilistic mixture model to quantify one or more fractions of nucleic acid from one or more contributors in the nucleic acid sample. Using a probabilistic mixture model includes applying a probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and the probabilistic mixture model uses a probability distribution to model the allele counts of the nucleic acid sequence reads at one or more polymorphic loci, which probability distribution takes into account errors in the nucleic acid sequence reads.

[0102] In some embodiments, the system includes a tool for extracting nucleic acid molecules from a nucleic acid sample. In some embodiments, the probability distribution includes the following first binomial distribution:

[0103] n 1i ~BN(n i , p 1i )

[0104] n 1i is the allele count of the nucleic acid sequence reads of allele 1 at locus i; n i is the total read count at locus i, which is equal to the total genome copy number n″; and p 1i is a probability parameter indicating the probability of allele 1 at locus i.

[0105] Another aspect of the present disclosure provides a computer program product, which includes a non-transitory machine-readable medium storing program code, which, when executed by one or more processors of a computer system, causes the computer system to implement a method for quantifying a nucleic acid sample containing nucleic acid of one or more contributors, the program code including: code for mapping nucleic acid sequence reads to one or more polymorphic loci on a reference sequence; code for determining allele counts of nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci using the mapped nucleic acid sequence reads; and code for quantifying one or more fractions of nucleic acid of one or more contributors in the nucleic acid sample using a probabilistic mixture model. Using the probabilistic mixture model includes applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and the probabilistic mixture model models the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci using a probability distribution that takes into account errors in the nucleic acid sequence reads.

[0106] Another aspect of the present disclosure provides a method for quantifying a nucleic acid sample containing nucleic acids of one or more contributors implemented at a computer system including one or more processors and a system memory. The method includes: (a) receiving a nucleic acid sequence read obtained from a nucleic acid sample by one or more processors; (b) mapping the nucleic acid sequence read to one or more polymorphic loci on a reference sequence by one or more processors using computer hashing and computer dynamic programming; (c) using the mapped nucleic acid sequence read and determining the allele counts of the nucleic acid sequence read of one or more alleles at one or more polymorphic loci by one or more processors; and (d) using a probabilistic mixture model and quantifying one or more scores of nucleic acids of one or more contributors in the nucleic acid sample and the confidence of the scores by one or more processors. Using a probabilistic mixture model includes applying a probabilistic mixture model to the allele counts of nucleic acid sequence reads. The probabilistic mixture model uses a probability distribution to model the allele counts of nucleic acid sequence reads at one or more polymorphic loci, which probability distribution takes into account errors in the mapped nucleic acid sequence reads. The quantitative approach uses (i) computer optimization methods combining multi-iteration grid search and BFGS-quasi-Newton method or iterative weighted linear regression, and (ii) numerical differentiation methods.

[0107] Although the examples herein relate to humans, and the language is primarily directed to humans, the concepts described herein are applicable to genomes from any plant or animal. These and other objects and features of the present disclosure will become more fully apparent from the following description and appended claims, or may be learned by the practice of the present disclosure as described below.

[0108] Incorporated herein by reference

[0109] All patents, patent applications, and other publications cited herein, including all sequences disclosed in such references, are expressly incorporated herein by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated for reference. All cited documents are, in relevant parts, fully incorporated herein by reference for the purposes indicated by the context of the references. However, the citation of any document should not be construed as an admission that it is prior art with respect to the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 A-1C shows an overview of the methods and statistical models designed for contributor DNA quantification.

[0112] Figure 2A A block diagram is shown illustrating a process for quantifying one or more fractions of nucleic acid (eg, DNA or RNA) of one or more contributors in a nucleic acid sample.

[0113] Figure 2B A block diagram illustrating the components of a probabilistic mixture model is shown.

[0114] Figure 2C Schematic illustration of sequencing errors that convert one allele to another and a true allele to an unexpected allele.

[0115] Figure 3 A block diagram illustrating a process for evaluating a nucleic acid sample for nucleic acid containing one or more contributors is shown.

[0116] Figure 4 A block diagram of a typical computer system that may be used as a computing device according to some embodiments is shown.

[0117] Figure 5 One embodiment of a decentralized system for generating a call or diagnosis from a test sample is shown.

[0118] Figure 6 Options for performing various operations of some embodiments at different locations are shown.

[0119] Figure 7 The respective performances of the disclosed and benchmark methods under different choices of the cfDNA length parameter are shown.

[0120] Figure 8 The analytical accuracy of some embodiments of another format is shown.

[0121] Fig. 9Shown are the coefficients of variation (CV) for 16 conditions used to determine the limit of quantitation (LOQ) for some embodiments. DETAILED DESCRIPTION

[0122] definition

[0123] Unless otherwise indicated, the practice of the methods and systems disclosed herein involves conventional techniques and apparatus commonly used in the fields of molecular biology, microbiology, protein purification, protein engineering, protein and DNA sequencing, and recombinant DNA within the skill of the art. Such techniques and apparatus are known to those skilled in the art and are described in many textbooks and reference works (see, e.g., Sambrook et al., "Molecular Cloning: A Laboratory Manual," 3rd ed. (Cold Spring Harbor,

[2001] ); and Ausubel et al., "Current Protocols in Molecular Biology"

[1987] ).

[0124] Numerical ranges include the numbers defining the ranges. Each maximum numerical limitation given throughout this specification is intended to include each lower numerical limitation, as if such lower numerical limitations were expressly written herein. Each minimum numerical limitation given throughout this specification will include each higher numerical limitation, as if such higher numerical limitations were expressly written herein. Each numerical range given throughout this specification will include each narrower numerical range that falls within such wider numerical range, as if such narrower numerical ranges were expressly written herein.

[0125] The headings provided herein are not intended to limit the disclosure.

[0126] Unless otherwise defined herein, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the art. Various scientific dictionaries including the terms included herein are well known and available to those skilled in the art. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the embodiments disclosed herein, some methods and materials are described.

[0127] The terms defined immediately below are more fully described by reference to the entire specification. It should be understood that the disclosure is not limited to the specific methods, protocols and reagents described, as these may vary, depending on the context used by one skilled in the art. As used herein, the singular terms "a", "an" and "the" include plural references unless the context clearly indicates otherwise.

[0128] Unless otherwise indicated, nucleic acids are written left to right in 5' to 3' orientation and amino acid sequences are written left to right in amino to carboxyl orientation, respectively.

[0129] The term "chimeric sample" is used herein to refer to a sample that is believed to contain DNA from two or more genomes. Chimeric analysis is used herein to refer to the biological and chemical treatment of a chimeric sample and / or the quantification of nucleic acids from two or more organisms in a chimeric sample. In some embodiments, the chimeric analysis also determines some or all of the sequence information of the genomes of the two or more organisms.

[0130] The term donor DNA (dDNA) refers to DNA molecules derived from cells of a transplant donor. In various embodiments, the dDNA is present in a sample obtained from a recipient who received a transplant tissue / organ from a donor.

[0131] Circulating cell-free DNA or simply cell-free DNA (cfDNA) are DNA fragments that are not confined within cells and circulate freely in the blood or other body fluids. As is known, cfDNA has different sources, in some cases from donor tissue DNA circulating in the recipient's blood, in some cases from tumor cells or cells affected by tumors, and in other cases from fetal DNA circulating in the mother's blood. Typically, cfDNA is fragmented and includes only a small portion of the genome, which may be different from the genome of the individual from whom the cfDNA was obtained.

[0132] The terms non-circulating genomic DNA (gDNA) or cellular DNA are used to refer to DNA molecules that are confined within a cell and typically include the entire genome.

[0133] The term "allele count" refers to the count or number of sequence reads of a particular allele. In some embodiments, it can be determined by mapping the reads to positions in a reference genome and counting the reads that include the allele sequence and are mapped to the reference genome.

[0134] The beta distribution is a family of continuous probability distributions defined on the interval [0, 1] that is parameterized by two positive shape parameters (e.g., denoted by α and β) that appear as exponentials of random variables and control the shape of the distribution. The beta distribution has been applied in various disciplines to model the behavior of random variables confined to intervals of finite length. In Bayesian inference, the beta distribution is the conjugate prior probability distribution of the Bernoulli, binomial, negative binomial, and geometric distributions. For example, the beta distribution can be used in Bayesian analysis to describe initial knowledge about the probability of success. If a random variable X follows a beta distribution, then the random variable X is written as X~beta(α, β).

[0135] The binomial distribution is a discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes / no question and each with its own Boolean outcome: a random variable containing a single bit of information: positive (with probability p) or negative (with probability q = 1-p). For a single trial, that is, n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is often used to model the number of successes of a sample of size n drawn with replacement from a population of size N. If a random variable X follows the parameters and p∈[0,1], then the random variable X is written as X~B(n,p).

[0136] The Poisson distribution, denoted herein as Pois(), is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed time and / or space interval if these events occur at a known average rate and are independent of the time since the last event. The Poisson distribution can also be used for multiple events in other specified intervals, such as distance, area, or volume. According to the Poisson distribution, the probability of observing k events in an interval is given by the following equation:

[0137]

[0138] where λ is the average number of events in the interval or the event rate, also known as the rate parameter e is 2.71828, Euler's number or the base of the natural logarithm, k takes the values ​​0, 1, 2, ... and k! is the factorial of k.

[0139] The gamma distribution is a two-parameter family of continuous probability distributions. There are three different parameter settings that are commonly used: shape parameter k and scale parameter θ; shape parameter α=k, and inverse scale parameter β=1 / θ, called the rate parameter; or shape parameter k and mean parameter μ=k / β. In each of these three forms, both parameters are positive real numbers. The gamma distribution is the maximum entropy probability distribution for a random variable X, for which E[X]=kθ=α / β is fixed and greater than zero, and E[ln(X)]=ψ(k)+In(θ)=ψ(α)-ln(β) is fixed (ψ is the digamma function).

[0140] Polymorphism and genetic polymorphism are used interchangeably herein and refer to the occurrence of two or more alleles at a genomic locus in the same population, each allele having a distinct frequency.

[0141] Polymorphic site and polymorphic site are used interchangeably herein to refer to the locus where two or more alleles are located on the genome. In some embodiments, it is used to refer to a single nucleotide variation of two alleles with different bases.

[0142] Allele frequency or gene frequency is the frequency of the allele of the gene (or variant of the gene) relative to other alleles of the gene, which can be expressed as a decimal or percentage.Allele frequency is usually associated with a specific genomic locus, because the gene is usually located at one or more loci.However, the allele frequency as used herein can also be associated with the fragment (size-based bin) based on size of DNA fragmentation.In this sense, the DNA fragmentation (such as cfDNA) comprising the allele is assigned to different fragments based on size.Relative to the frequency of other alleles, the frequency of the allele in the fragment based on size is the allele frequency.

[0143] The term "parameter" herein refers to a numerical value that characterizes an attribute of a system such as a physical feature, the value of which or other characteristics may affect a relevant condition such as a sample or DNA fragment. In some cases, the term "parameter" is used with reference to a variable that affects a mathematical relationship or model output, which may be an independent variable (i.e., an input to the model) or an intermediate variable based on one or more independent variables. Depending on the scope of the model, the output of one model may become the input to another model, thereby becoming a parameter of another model.

[0144] The term "plurality" refers to more than one element.

[0145] The term "paired-end reads" refers to reads from paired-end sequencing, which obtains one read from each end of a nucleic acid fragment. Paired-end sequencing can involve fragmenting a polynucleotide chain into short sequences called inserts. For shorter polynucleotides, such as cell-free DNA molecules, fragmentation is optional or unnecessary.

[0146] The terms "polynucleotide", "nucleic acid" and "nucleic acid molecule" are used interchangeably and refer to a covalently linked sequence of nucleotides (i.e., ribonucleotides for RNA and deoxyribonucleotides for DNA) in which the 3' position of the pentose of one nucleotide is linked to the 5' position of the pentose of another nucleotide via a phosphodiester group. Nucleotides include sequences of any form of nucleic acid, including but not limited to RNA and DNA molecules, such as cfDNA or cellular DNA molecules. The term "polynucleotide" includes but is not limited to single-stranded and double-stranded polynucleotides.

[0147] The term "test sample" herein refers to a sample generally derived from a biological fluid, cell, tissue, organ or organism, which contains nucleic acid or a mixture of nucleic acids. Such samples include, but are not limited to, sputum / oral fluid, amniotic fluid, blood, blood components or fine needle aspiration biopsy samples (e.g., surgical biopsy, fine needle aspiration biopsy, etc.), urine, peritoneal fluid, pleural fluid, etc. Although samples are generally taken from human subjects (e.g., patients), the assay can be used for samples of any mammal, including, but not limited to, dogs, cats, horses, goats, sheep, cattle, pigs, etc. The sample can be obtained directly from a biological source, or it can be pretreated to change the characteristics of the sample. For example, such pretreatment can include preparing plasma from blood, diluting viscous liquids, etc. Pretreatment methods can also include, but are not limited to, filtration, precipitation, dilution, distillation, mixing, centrifugation, freezing, freeze-drying, concentration, amplification, nucleic acid fragmentation, inactivation of interfering components, reagent addition, lysis, etc. If such pretreatment methods are applied to a sample, such pretreatment methods should generally result in the retention of the nucleic acid of interest in the test sample, sometimes at a concentration proportional to that in an untreated test sample (e.g., a sample that has not been subjected to any such pretreatment methods). With respect to the methods described herein, such "treated" or "processed" samples are still considered biological "test" samples.

[0148] The term "next generation sequencing (NGS)" herein refers to sequencing methods that allow for massively parallel sequencing of clonally amplified molecules and single nucleic acid molecules. Non-limiting examples of NGS include sequencing by synthesis using reversible dye terminators and sequencing by ligation.

[0149] The term "reading sequence" refers to a sequence obtained from a part of a nucleic acid sample. Generally, although not required, the reading sequence represents a short sequence of continuous base pairs in the sample. The reading sequence can be symbolically represented by the base pair sequence (represented by A, T, C or G) of the sample portion. It can be stored in a memory device and appropriately processed to determine whether it matches the reference sequence or meets other criteria. The reading sequence can be obtained directly from a sequencing device, or the reading sequence can be obtained indirectly from the stored sequence information related to the sample. In some cases, the reading sequence is a DNA sequence with sufficient length (e.g., at least about 25bp), which can be used to identify, for example, a larger sequence or region that can be compared and specifically assigned to a chromosome or genomic region or gene.

[0150] The term "genomic read" is used to refer to the read of any segment in the entire genome of an individual.

[0151] As used herein, the terms "aligned," "alignment," or "aligned" refer to the process of comparing a read or tag to a reference sequence and thereby determining whether the reference sequence contains the read sequence. If the reference sequence contains a read, the read can be mapped to the reference sequence, or in some embodiments, mapped to a specific position in the reference sequence. In some cases, the alignment simply indicates whether the read is a member of a specific reference sequence (i.e., whether the read exists or does not exist in the reference sequence). For example, an alignment of a read with a human chromosome 13 reference sequence will indicate whether the read exists in the reference sequence of chromosome 13. A tool that provides this information may be referred to as a set membership tester. In some cases, the alignment additionally indicates the position in the reference sequence to which the read or tag is mapped. For example, if the reference sequence is a full-length human genome sequence, the alignment may indicate that the read is present on chromosome 13, and may further indicate that the read is on a specific chain and / or site of chromosome 13.

[0152] The read sequence or label of the comparison is one or more sequences, which are identified as matching according to the order of their nucleic acid molecules and known sequences in the reference genome. Although usually realized by computer programs, the comparison can be performed manually because it is impossible to compare the read sequence within a reasonable period of time to realize the method disclosed herein. An example of a program from comparing sequences is the efficient local alignment (ELAND) computer program for nucleotide data distributed as a part of the Illumina genomics analysis pipeline. Alternatively, a bloom filter or similar set membership tester can be used to make the read sequence and the reference genome comparison. Referring to U.S. Patent Application No. 61 / 552,374 filed on October 27, 2011, which is incorporated herein by reference as a whole. The matching of the sequence read sequence in the comparison can be 100% sequence matching or less than 100% (non-perfect matching).

[0153] The term "mapping" as used herein refers to the use of alignment or membership assignment to specifically assign sequence reads to a larger sequence, such as a reference genome, a subsequence of the larger sequence.

[0154] As used herein, the term "reference genome" or "reference sequence" refers to any specific known genome sequence, whether partial or complete, of any organism or virus that can be used to reference an identified sequence from a subject. For example, reference genomes for human subjects as well as many other organisms can be found at the National Center for Biotechnology Information (ncbi.nlm.nih.gov). "Genome" refers to the complete genetic information of an organism or virus expressed as a nucleic acid sequence.

[0155] In various embodiments, the reference sequence is significantly larger than the read sequence to which it is aligned. For example, it can be at least about 100 times larger, or at least about 1000 times larger, or at least about 10,000 times larger, or at least about 10,000 times larger. 5 times, or at least about 10 6 times, or at least about 10 7 times.

[0156] In one example, the reference sequence is a sequence of a full-length human genome. Such sequences may be referred to as genome reference sequences. In another example, the reference sequence is limited to a specific human chromosome, such as chromosome 13. In some embodiments, the reference Y chromosome is a Y chromosome sequence from human genome version hg19. Such sequences may be referred to as chromosome reference sequences. Other examples of reference sequences include genomes of other species, and chromosomes, subchromosome regions (such as chains) of any species, etc.

[0157] In various embodiments, the reference sequence is a consensus sequence or other combination derived from multiple individuals. However, in certain applications, the reference sequence may be taken from a specific individual.

[0158] When used in the context of nucleic acids or nucleic acid mixtures, the term "derived" herein refers to the manner in which nucleic acids are obtained from the source from which they are derived. For example, in one embodiment, a mixture of nucleic acids derived from two different genomes refers to nucleic acids, such as cfDNA, which are naturally released by cells through naturally occurring processes (such as necrosis or apoptosis). In another embodiment, a mixture of nucleic acids derived from two different genomes refers to nucleic acids extracted from two different types of cells of a subject. For example, a nucleic acid mixture includes nucleic acids derived from donor cells and recipient cells obtained from an organ transplant subject. In some embodiments, a nucleic acid mixture comprises biological material from two or more contributor individuals. For example, a forensic sample comprising biological material from two or more individuals includes DNA from two or more individuals.

[0159] When used in the context of obtaining a specific quantitative value, the term "based on" herein means using another quantity as an input to calculate the specific quantitative value as an output.

[0160] The term "biological fluid" herein refers to a fluid obtained from a biological source, and includes, for example, blood, serum, plasma, sputum, lavage fluid, cerebrospinal fluid, urine, semen, sweat, tears, saliva, etc. As used herein, the terms "blood," "plasma," and "serum" expressly encompass fractions or processed portions thereof. Similarly, when a sample is obtained from a biopsy, swab, smear, etc., "sample" expressly encompasses processed fractions or portions obtained from the biopsy, swab, smear, etc.

[0161] As used herein, the term "corresponding to" sometimes refers to a nucleic acid sequence, such as a gene or chromosome, that is present in the genomes of different subjects and does not necessarily have the same sequence in all genomes, but is used to provide the identity of the sequence of interest (e.g., a gene or chromosome) rather than genetic information.

[0162] The term "contributor" herein refers to human contributors as well as non-human contributors, such as mammals, invertebrates, vertebrates, fungi, yeast, bacteria, and viruses. Although the examples herein involve humans, and the language is primarily directed to humans, the concepts disclosed herein are applicable to genomes from any plant or animal, and can be used in veterinary medicine, animal science, research laboratories, and the like.

[0163] As used herein, the term "sensitivity" refers to the probability that a test result is positive when the disease of interest is present. It can be calculated as the number of true positives divided by the sum of true positives and false negatives.

[0164] As used herein, the term "specificity" refers to the probability that a test result is negative when the disease of interest is not present. It can be calculated as the number of true negatives divided by the sum of true negatives and false positives.

[0165] As used herein, the term "primer" refers to an oligonucleotide that is separated as follows, and when placed under conditions (e.g., conditions including nucleotides, an inducing agent (such as a DNA polymerase) and a suitable temperature and pH) that induce the synthesis of an extension product, the oligonucleotide that is separated can serve as a synthesis starting point. For maximum amplification efficiency, the primer is preferably single-stranded, but can alternatively be double-stranded. If double-stranded, before being used to prepare an extension product, the primer is first treated to separate its chain. Preferably, the primer is an oligodeoxyribonucleotide. The primer must be long enough to initiate the synthesis of an extension product in the presence of an inducing agent. The exact length of the primer will depend on many factors, including temperature, primer source, use of the method, and parameters for primer design.

[0166] introduce

[0167] The present disclosure provides methods and systems for quantifying and deconvoluting nucleic acid mixture samples including nucleic acids of two or more unknown genotype contributors, thereby providing multiple advantages and technical improvements. For example, some embodiments apply probabilistic mixture modeling, Bayesian inference techniques, and numerical optimization methods to quantify the contributor DNA in the mixture without knowing the genotype of the contributor.

[0168] Sequencing data of a mixture of nucleic acids (eg, DNA or RNA) from closely related genomes are often found in research as well as clinical settings, and quantifying the mixed contributors has been challenging when the original genomes are unknown.

[0169] Conventional methods for chimerism analysis (applicable only for bone marrow and blood stem cell transplantation) utilize capillary electrophoresis (CE) fragment analysis or quantitative polymerase chain reaction (qPCR) analysis of short tandem repeats (STRs) or small insertions and deletions (Indels). These methods tend to have poor limitations of quantification, dynamic range, or reproducibility. They have a limited number of targets, complex workflows, and time-consuming and inaccurate manual input for analysis. Conventional methods tend to include these different metrics. CE methods have LOQs ranging from 1%-5% and suffer from low reproducibility. These limitations can be important in clinical use. For example, 99% of actual chimerism results will be reported as 100%. qPCR methods can achieve low LOQs of 0.1%, but require 66ng or more of chimeric DNA, regardless of the DNA required for pure benchmark samples. For solid organ transplantation, 66ng and 10ng are impossible for conventional cfDNA analysis. In addition, the dynamic range of qPCR-based chimerism is affected, and chimerism prediction is unreliable when minor contributors are greater than 30%.

[0170] Given the high input DNA requirements, CE and qPCR methods are only applicable to bone marrow or blood stem cell transplantation. Both methods cannot be used for solid organ transplantation monitoring because the amount of cfDNA from a typical blood draw is much less than 10 ng. In addition, even with the same amount, cfDNA is not as effective as gDNA as a PCR template.

[0171] In addition to the high input requirement for DNA, both CE and qPCR methods require pure pre-transplantation reference samples. They are also associated with complex assays and require manual intervention in selecting appropriate markers prior to quantification.

[0172] Besides these, our method systematically addresses two fundamental challenges in chimera quantification, which are not feasible with existing methods.

[0173] The first challenge is to quantify chimeric samples with more than two contributors, which corresponds to transplants using more than one donor. Multiple donor transplants are common in bone marrow and blood stem cell transplants. It also occurs in solid organ transplants, for example, a second kidney transplant after a previous kidney failure, or when a solid organ transplant occurs simultaneously with a transfusion from another donor.

[0174] The second challenge is to quantify chimeric samples when one of the contributors is unknown. This often occurs in clinical settings, such as 1) when the donor genome is not available; 2) in multiple donor cases, when the donor genome of the old organ is not available; or 3) when a solid organ transplant recipient also receives a blood transfusion from an unknown donor.

[0175] Although conventional methods cannot address these challenges, the methods disclosed herein can accurately quantify chimeric samples when an unknown donor is present. When there is only one donor, neither the donor genome nor the recipient genome is required to use the disclosed methods. In addition, the disclosed methods can work with any number of donors. Several empirical studies have validated the performance of the disclosed methods on 4 donors and achieved a LOQ of less than 0.35% at 10 ng total gDNA input.

[0176] In some embodiments, the disclosed methods achieve a LOQ of 0.1% to 0.2% with as little as 3 ng cfDNA input and achieve a wide dynamic range of 0.1% to 99.9%. Although knowing the benchmark can improve performance, some embodiments do not require knowing the benchmark genome. The disclosed methods can work with chimeric samples from any number of donors and have been experimentally validated with samples from 0-4 donors, which covers almost all clinically relevant cases of solid organ transplantation, bone marrow transplantation, and hematopoietic stem cell transplantation. In addition, the disclosed methods do not require any manual intervention in the selection of genetic markers, allowing digitization and automation of nucleic acid quantification.

[0177] Some embodiments provide methods and systems for quantifying contributor DNA from multi-marker targeted resequencing data of blood cfDNA or gDNA samples. Some embodiments provide methods and systems for quantifying contributor DNA from multi-marker targeted sequencing data of blood cfDNA or gDNA samples using novel probabilistic models and numerical optimization methods. Some embodiments provide methods and systems for quantifying contributor DNA of genetically related donors and recipients of unknown genotypes using a Bayesian model with a prior distribution encoding genetic relationships. By using genetic relationship information to provide prior information in a Bayesian framework, quantification of DNA mixtures can be improved compared to methods that do not use genetic relationship information.

[0178] Some embodiments provide methods and systems for estimating confidence intervals for DNA quantification by numerically computing Cramer-Rao bounds from the Hessian matrix of the estimate of the log-likelihood function.

[0179] Allelic bias in mapping of short sequencing reads confounds DNA quantification. In some embodiments, we reduce the impact of confounding through an unbiased mapping strategy of reads across variant sites.

[0180] Even if the genotype of the contributing genome is completely unknown, the embodiments described herein can accurately estimate the contributor DNA fraction.The allele fractions of marker loci after PCR amplification can be reliably modeled with a Beta distribution.

[0181] Using an unbiased reference DNA sequence database containing reference and alternate alleles, one can remove the read mapping bias to the reference allele and reliably estimate the allele counts and sequencing errors at variant sites.

[0182] Embodiments described herein can estimate confidence intervals for predicted contributor DNA fractions using a single sequencing run of a mixture DNA sample.

[0183] Formally, the Contributor DNA Quantification (CDQ) problem is as follows: given sequencing data of a DNA sample containing one or more contributors, determine the score of each contributor in the sample. When the genotype of the contributor genome is unknown, the CDQ problem is called blind contributor DNA quantification (blind CDQ); the opposite is called non-blind CDQ. Some descriptions of some embodiments refer to the two contributors as donors and recipients, but they do not limit the application of the method to the organ donation environment. In some descriptions of some embodiments below, a contributor is equivalent to a donor, and another contributor is equivalent to a recipient.

[0184] Blind CDQ is a more difficult problem than unblinded CDQ, but it is broadly applicable to all scenarios where only a single sequencing experiment can be performed on a mixture sample, while unblinded CDQ requires a prior sequencing experiment to determine the genotypes of contributors (e.g., organ donors and recipients).

[0185] The computational methods described in this paper address both blind CDQ and non-blind CDQ problems with single, two or more contributors.

[0186] Figure 1 A-1C shows an overview of the methods and statistical models designed for contributor DNA quantification. Figure 1 A shows the experimental pipeline for sequencing based allogeneic DNA detection. Figure 1 B shows the unbiased read mapping workflow for allele counting. Figure 1 C shows the stratified probabilistic mixture model of allele counts per marker locus.

[0187] Some embodiments employ Figure 1 The experimental pipeline shown in A. The general experimental pipeline has the following steps.

[0188] 1) Obtain a blood or other type of sample containing DNA from multiple genetic origins.

[0189] 2) Depending on the application, extract the appropriate type of DNA, such as cellular DNA (also called gDNA) or cell-free DNA (cfDNA).

[0190] 3) Targeting and enriching specific variant sites or polymorphic sites of the genome by methods such as PCR amplification or hybridization. Variant sites are pre-selected to be variable in different populations of humans (or another target organism). Alternatively, non-targeted (whole genome) sequencing can be performed and all variant sites will be covered.

[0191] 4) Sequence the DNA sample by NGS or other DNA sequencing methods (such as some of the techniques described below) to obtain sequencing reads.

[0192] The CDQ calculation methodology has three main components:

[0193] 1) Allele counting: A computer program based on hashing and dynamic programming for unbiased counting of sequencing reads for each allele from each target marker locus ( Figure 1 B), and

[0194] 2) Contributor DNA quantification: A novel combination of a hierarchical probabilistic model and a multi-iteration grid search strategy with the BFGS-quasi-Newton method, or in some embodiments, iterative weighted linear regression, is used to quantify the contributor DNA fraction ( Figure 1 C).

[0195] 3) Determine confidence intervals (uncertainly): Around the quantitative mixture fraction, the variance is determined based on the Hessian matrix of the log-likelihood function based on the information inequality.

[0196] The total number of these components for chimerism quantification is impossible to perform manually or in the mind of a human expert. They require computers and are computer-implemented techniques. These computational components enable the disclosed methods to achieve unparalleled quantitative sensitivity, dynamic range, and reproducibility. They also enable the disclosed methods to reliably quantify a variety of chimeric samples, including cfDNA or gDNA, 3-10 ng or more of input DNA, 0 to 4 or more donors, and genetically related or unrelated donors with known or unknown genomes.

[0197] Although some embodiments herein address only "relative quantification," meaning that these embodiments estimate the percentage or fraction of a DNA sample that originates from a contributor source, rather than the absolute amount (in terms of mass or copy number), if the total amount of input DNA has been measured or is known, additional steps can be taken to convert relative abundance to absolute abundance.

[0198] Overview of the process used to quantify the fraction of contributors in nucleic acid samples

[0199] Figure 2AA block diagram of a process 200 for quantifying one or more fractions of nucleic acid (e.g., DNA or RNA) of one or more contributors in a nucleic acid sample is shown. The method is implemented on a computer system including one or more processors and system memory, such as the system described below. In some embodiments and applications, the description herein refers to DNA, but those skilled in the art understand that other forms of nucleic acid can also be analyzed using the embodiments described herein. The various embodiments described herein can be used to analyze nucleic acid samples containing nucleic acids from one or more contributors. In some embodiments, a method and system for quantifying one or more fractions of nucleic acids of one or more contributors is provided. In some descriptions herein, nucleic acid samples are referred to as mixture samples because samples can include nucleic acids from more than two contributors. However, it should be understood that the use of the term "mixture" indicates that the sample contains the possibility of two or more contributor nucleic acids, and does not exclude the possibility that the sample only includes a single contributor nucleic acid. In the latter case, a number of 1 or a percentage of 100% (or a value within a margin of error) can be determined for a contributor.

[0200] In some embodiments, one or more contributors to the nucleic acid sample include a donor of a transplant and a recipient of a transplant. In some embodiments, the transplant includes an allogeneic or xenogeneic transplant. In some embodiments, the nucleic acid sample is a biological sample obtained from a recipient. In some embodiments, the nucleic acid sample includes cell-free nucleic acid. In some embodiments, the sample includes cellular DNA. In some embodiments, the nucleic acid sample includes nucleic acids from zero, one or more contaminant genomes, and one target genome. In some embodiments, the nucleic acid sample includes a biological sample obtained from a cell culture, which in some embodiments can be a mixture of multiple cell lines with different genetic origins.

[0201] Process 200 involves extracting nucleic acid molecules from a nucleic acid sample using techniques such as those described herein. See block 202.

[0202] Process 200 further includes amplification or enrichment of the extracted nucleic acid molecules. Referring to frame 204. Various amplification or enrichment techniques can be used, such as those described herein. In some embodiments, PCR is used to amplify the extracted nucleic acid molecules. In some embodiments, amplification is targeted at specific polymorphisms, and its amplification is also referred to as targeted enrichment. In other embodiments, whole genome amplification can be performed, and allele data of specific polymorphic sites can be obtained by sequencing.

[0203] Process 200 also involves sequencing the amplified or enriched nucleic acid molecules using a nucleic acid sequencer to generate nucleic acid sequence reads. See block 206. Various sequencing techniques and equipment are further described below, which can be applied in operation 206.

[0204] Process 200 further relates to mapping the nucleic acid sequence reads to one or more polymorphic loci on the reference sequence. In some embodiments, alignment techniques can be used to map the nucleic acid sequence reads to one or more polymorphic loci. In other embodiments, unbiased mapping techniques can be used to match the nucleic acid sequence reads to the polymorphic loci. Referring to frame 208. In some embodiments, the nucleic acid sequence reads are mapped to specific alleles at the polymorphic loci. Unbiased mapping techniques will be further described below. In some embodiments, one or more polymorphic loci (or polymorphic loci) include biallelic loci. In some embodiments, the alleles at one or more polymorphic loci include single nucleotide polymorphism (SNP) alleles.

[0205] In some embodiments, a unique molecular index (UMI) is attached to an extracted nucleic acid molecule, which is then amplified, sequenced, and mapped to a polymorphic locus or allele. The unique molecular index provides a mechanism to reduce errors that may occur during sample processing and analysis steps. For example, different reads that share the same unique molecular index (UMI) can be combined or overlapped to determine the sequence from which the read was derived, thereby effectively eliminating errors that occurred during amplification and sequencing.

[0206] Process 200 further involves determining allele counts of nucleic acid sequence reads of alleles at one or more polymorphic loci using the method of nucleic acid sequence reads. See block 210.

[0207] Process 200 also involves applying the probability mixture model to the allele counts of the nucleic acid sequence reads. The probability mixture model uses probability distribution to model the allele counts of the nucleic acid sequence reads at one or more polymorphic loci. The probability distribution takes into account the errors and noise in the nucleic acid sequence reads. The probability mixture model regards each allele count of the nucleic acid sequence reads as a random sample from the probability distribution.

[0208] In the equations below, the following symbols are used.

[0209] d: index of donors, d=1, 2..., D, where D is the total number of donors. D can be any natural number. In some embodiments, D is 5 or less. In some embodiments, D is 9 or less.

[0210] a: index of allele. In some embodiments, the allele comprises a biallelic SNP, and a=1 or 2.

[0211] i: index of the marker locus, i=1...I, where I is the total number of markers, for example 300.

[0212] g dai : The genotype of allele type a of contributor d of marker i. It takes values ​​of 0, 1 or 2, representing the number of copies of allele a of this locus in this contributor.

[0213] n ai , n ai ′,n ai ′: Read copies of the amplified DNA molecule and the pre-amplified DNA molecule of allele type a and marker locus i.

[0214] n i , n i ′, ni″: Total read sequence copies of the amplified nucleic acid molecule and the pre-amplified DNA molecule used to mark locus i.

[0215] r ai : The fraction of read counts for allele a and marker locus i.

[0216] p ai : The probability of seeing a read of allele type a at a given marker locus i.

[0217] Note that for g dai , n ai , n ai ′,n ai ″,n i , n i ′,n i ″,r ai , and p ai , when embodiments focus on a single locus, the subscript i is sometimes omitted.

[0218] β d : The fraction of nucleic acid from contributor d that contributes to the mixture sample.

[0219] λ: sequencing error rate.

[0220] Bold letters indicate vectors or matrices:

[0221] g=[g d1i ] i＝1...I，d＝1...D : Genotype matrix with reference allele counts among all contributors and all loci.

[0222] g i =[gd1i ] d＝1...D : genotype vector with all contributors and reference allele counts for a given locus i.

[0223] r=[r 1i ] i＝1...I : Allele fraction vector with the fraction of allele 1 reads for each locus.

[0224] n=[n i ] i＝1...I : A read count vector with the read counts for each locus.

[0225] p=[p 1i ] i＝1...I : A vector with the expected allele 1 fraction for each locus.

[0226] β=[β d ] d＝1...D. : Contributor score vector with the relative score of each contributor contributing to the nucleic acid sample.

[0227] In some embodiments, a probabilistic mixture model models allele counts at a single polymorphic locus using a single locus likelihood function, which can be expressed as:

[0228] M(n 1i , n 2i |p 1i ,θ), where n 1i is the allele count of allele 1 at locus i, n 2i is the allele count of allele 2 at locus i, p 1i is the expected fraction of allele 1 at locus i, and θ comprises one or more model parameters.

[0229] In some embodiments, p 1i Modeled as the following function p(g i , λ, β): (i) the genotype of the contributor at locus i, or g i =(g 11i , ..., g D1i ), which is the vector of the number of copies of allele 1 at locus i in contributors 1...D; (ii) the read count error caused by sequencing, or λ; and (iii) the nucleic acid fraction of the contributor in the nucleic acid sample, or β = (β1, ..., β D ), where D is the number of contributors.

[0230] In some embodiments, p 1i Calculated as p 1i = p(g i,λ,β)←[(1-λ)g i +λ(2-g i )] / 2·β, where · is the vector dot product operator.

[0231] In some embodiments, the contributors include two contributors, and p 1i is obtained using the p1 values ​​in Table 3 described below.

[0232] In some embodiments (method S), the single locus likelihood function is a probability distribution comprising a first binomial distribution. In some embodiments, the first binomial distribution comprises a quantity parameter indicating the total allele count at the locus and a probability parameter indicating the probability of the first allele at the locus. In some embodiments, the first binomial distribution is expressed as follows:

[0233] n 1i ~BN(n i , p 1i )

[0234] where n 1i is the allele count of the nucleic acid sequence reads of allele 1 at locus i; n i is the total read count at locus i; and p 1i is a probability parameter indicating the probability of allele 1 at locus i.

[0235] In some embodiments, the probability parameter p is a function of the nucleic acid fraction of the contributor or β. The probability parameter is also a function of the genotype g of one or more contributors. The probability parameter is also a function of the error caused by the sequencing operation of 206 or λ. In some embodiments, zero, one or more genotypes of the contributor are unknown. In some embodiments, the probabilistic mixture model includes such as Figure 2B The various probability distributions shown in .

[0236] return Figure 2A , process 200 involves quantifying one or more fractions of nucleic acid of one or more contributors in a nucleic acid sample using a probabilistic mixture model. See block 214. In some embodiments, quantification includes marginalizing over multiple possible combinations of genotypes to enumerate a probability parameter p. In some embodiments, quantification includes determining β, i.e., the nucleic acid fraction of the contributor, using a multi-locus likelihood function of allele counts of nucleic acid sequence reads determined in operation 210 conditioned on the parameters of the probabilistic mixture model.

[0237] In some embodiments, quantitatively include using a plurality of potential score values ​​and the multi-locus likelihood function of the allele count of the nucleic acid sequence reading to calculate a plurality of likelihood values.Quantitatively also relate to the potential score value associated with the likelihood value as the maximum in a plurality of likelihood values.In some embodiments, multiple likelihood values ​​are obtained for a plurality of parameters and values ​​thereof in a multidimensional grid.Quantitatively also relate to the nucleic acid score of the contributor in the nucleic acid sample with the potential score value with maximum likelihood identified to be quantitative.In some embodiments, the multi-locus likelihood function includes a plurality of marginal distributions for one or more polymorphic loci.

[0238] In some embodiments a multi-locus likelihood function for one or more contributors with known, unknown or partially known genotypes is calculated as follows:

[0239] L(β, θ, λ, π; n1, n2)=Π i [∑g i M(n 1i , n 2i |p(g i ,λ,β),θ)·P(g i |π)]

[0240] where L(β, θ, λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2; p(g i , λ, β) is based on the genotype g of the contributor at locus i i The expected fraction or probability of observing allele 1 at locus i; P(g i |π) is the observed genotype g at locus i given the population allele frequency (π). i The prior probability of i represents summing over multiple possible combinations of contributor genotypes subject to constraints on known genotypes of some or all contributors.

[0241] In some embodiments, a marginal distribution P(g 1i |π) and P(g 2i |π) to calculate the prior joint probability.

[0242] In some embodiments, all genotypes are known and a genotype vector g representing the known genotype combinations of the contributors is used. i Calculate the multi-locus likelihood function: L(β, θ, λ, π; n1, n2) = ∏ i [M(n 1i , n 2i |p(g i ,λ,β),θ)·P(g i|π)].

[0243] In some embodiments, the probabilistic mixture model takes into account errors in the number of nucleic acid molecule copies caused by the extraction of nucleic acid molecules performed in 202 and read count errors caused by the sequencing operation in 206.

[0244] In some embodiments, the probability mixture model uses a second binomial distribution to model the allele counts of the extracted nucleic acid molecules for alleles at one or more polymorphic loci. In some embodiments, the second binomial distribution is expressed as follows:

[0245] n 1i ″~BN(n i ″,p 1i )

[0246] where n 1i ″ is the allele count of the extracted nucleic acid molecule of allele 1 at locus i; n i ″ is the total nucleic acid molecule count at locus i, which is equal to the total genome copy number n″; and p 1i is a probability parameter indicating the probability of allele 1 at locus i.

[0247] In some embodiments, the first binomial distribution is expressed as 1i ″ / n i " is a condition. In some embodiments, the first binomial distribution is reparameterized as follows:

[0248] n 1i ~BN(n i , n 1i ″ / n i ″)

[0249] where n 1i is the allele count of the nucleic acid sequence reads for allele 1 at locus i.

[0250] In some embodiments, the probability mixture model uses a first Beta distribution to approximate n 1i In some embodiments, the first beta distribution has a mean and variance that match the mean and variance of the second binomial distribution.

[0251] In some embodiments, locus i is modeled as biallelic and a first Beta distribution is represented as follows:

[0252] n 1i ″ / n″~Beta((n″-1)p 1i , (n″-1)p 2i )

[0253] where p 1i is a probability parameter indicating the probability of the first allele at locus i; and p 2i is a probability parameter indicating the probability of the second allele at locus i.

[0254] In some embodiments, the process includes combining a first binomial distribution that models sequencing read counts and a first beta distribution that models the number of extracted nucleic acid molecules to obtain a single locus likelihood function that follows a first beta-binomial distribution.

[0255] In some embodiments, the first beta-binomial distribution has the following form:

[0256] n 1i ~BB(n i , (n″-1)·p 1i , (n″-1)·p 2i ),

[0257] Or alternative approximation:

[0258] n 1i ~BB(n i , n″·p 1i , n″·p 2i ).

[0259] In some embodiments, a multi-locus likelihood function can be expressed as:

[0260] L(β,n″,λ,π;n1,n2)=Π i [∑g i BB(n 1i |n i , (n″-1)·p 1i , (n”-1)·p 2i )·P(g i |π)]

[0261] where L(β, n″, λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2 at all loci, and p 1i = p(g i ,λ,β),p 2i =1-p 1i .

[0262] In some embodiments, a contributor comprises two contributors and the multi-locus likelihood function is expressed as:

[0263] L(β,n″,λ,π;n1,n2)=Π i ∑ g1ig2iBB(n 1i , n 2i |n i , (n″-1)·p 1i (g 1i , g 2i ,λ,β),(n″-1)·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)

[0264] where L(β, n″, λ, π; n1, n2) is the likelihood of observing the allele count vectors of the first alleles of all loci (n1) and the allele count vectors of the second alleles of all loci (n2) given the parameters β, n″, λ, and π; p 1i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p1′ in Table 3, indicating the probability of the genotypes of the two contributors (g 1i , g 2i ) is the probability of allele 1 at locus i; p 2i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p2′ in Table 3, indicating the probability of 1i , g 2i ) at locus i; and P(g 1i , g 2i |π) is the first contributing genotype (g) of the first allele at locus i observed given the population allele frequency (π). 1i ) and the second contributor genotype of the first allele (g 2i ) is the prior joint probability of .

[0265] In some embodiments, operation 214 includes estimating the total number of extracted genome copies n" from the plurality of extracted nucleic acid molecules. In some embodiments, the estimated total number of extracted genome copies n" is adjusted based on the fragment size of the extracted nucleic acid molecules, as further described below.

[0266] In some embodiments, the probabilistic mixture model takes into account errors in the number of nucleic acid molecules caused by amplifying nucleic acid molecules performed in 204, and errors in read counts caused by sequencing operations in 206. In some embodiments, the nucleic acid amplification process is modeled as follows:

[0267] x t+1 =x t +yt+1

[0268] where x t+1 is the number of nucleic acid copies of a given allele after cycle t+1 of amplification; x t is the number of nucleic acid copies of a given allele after cycle t of amplification; y t+1 is a new copy generated in cycle t+1, and it follows the binomial distribution y t+1 ~BN(x t , r t+1 ); and t+1 is the amplification rate at cycle t+1.

[0269] In some embodiments, the probabilistic mixture model uses a second Beta distribution to model the allele fractions of the amplified nucleic acid molecules for the alleles at one or more polymorphic loci. In some embodiments, locus i is modeled as a double allele, and the second Beta distribution is expressed as follows:

[0270] n 1i ′ / (n 1i ′+n 2i ′)~Beta(n″·ρ i ·p 1i , n″·ρ i ·p 2i )

[0271] where n 1i ' is the allele count of the amplified nucleic acid molecule of the first allele at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of the second allele at locus i; n" is the total nucleic acid molecule count at any locus; p i is the average amplification rate r over all amplification cycles i The related constant; p 1i is the probability of the first allele at locus i; and p 2i is the probability of the second allele at locus i. In some embodiments, p i is (1+r i ) / (1-r i ) / [1-(1+r i ) -t In some embodiments, i Approximately (1+r i ) / (1-r i ).

[0272] In some embodiments, operation 214 includes combining the first binomial distribution and the second beta distribution to obtain n following a second beta-binomial distribution. 1iIn some embodiments, the second beta-binomial distribution has the following form:

[0273] n 1i ~BB(n i , n″·ρ i ·p 1i , n″·ρ i ·p 2i ), where n 1i is the allele count of the nucleic acid sequence read of the first allele at locus i; p 1i is a probability parameter indicating the probability of the first allele at locus i; and p 2i is a probability parameter indicating the probability of the second allele at locus i.

[0274] In some embodiments, operation 214 includes reparameterizing the second Beta-binomial distribution by assuming that one or more polymorphic loci have the same amplification rate as:

[0275] n 1i ~BB(n i , n″·(1+r) / (1-r)·p 1i , n″·(1+r) / (1-r)·p 2i ), where r is the amplification rate.

[0276] In some embodiments, operation 214 includes quantifying one or more fractions of nucleic acid from one or more contributors in a nucleic acid sample using a multi-locus likelihood function obtained by applying a second beta-binomial distribution, the multi-locus likelihood function being as follows:

[0277] L(β,n″,r,λ,π;n1,n2)=∏ i [∑g i BB(n 1i |n i , n″·(1+r) / (1-r)·p 1i , n″·(1+r) / (1-r)·p 2i )·P(g i |π)]

[0278] In some embodiments, a contributor comprises two contributors and a multi-locus likelihood function comprises:

[0279] L(β,n″,r,λ,π;n1,n2)=Π i ∑ g1ig2i [BB(n 1i |n i , n″·(1+r) / (1-r)·p 1i (g1i , g 2i ,λ,β),n″·(1+r) / (1-r)·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)]

[0280] where L(β, n″, r, λ, π; n1, n2) is the likelihood of observing the allele count vector of the first allele of all loci (n1) and the allele count vector of the second allele of all loci (n2) given the parameters β, n″, r, λ and π.

[0281] In some embodiments, operation 214 comprises reparameterizing the second Beta-binomial distribution by defining the relative amplification rate of each polymorphic locus as proportional to the total reads for the locus as:

[0282] n 1i ~BB(n i , c′·n i ·p 1i , c′·n i ·p 2i ), where c′ is the parameter to be optimized.

[0283] In some embodiments, operation 214 includes quantifying one or more fractions of nucleic acid from one or more contributors in a nucleic acid sample using a multi-locus likelihood function obtained by applying a second beta-binomial distribution, the multi-locus likelihood function being as follows:

[0284] L(β,n″,c′,λ,π;n1,n2)=Πi[∑g i BB(n 1i |n i , c′·n i ·p 1i , c′·n i ·p 2i )·P(g i |π)]

[0285] In some embodiments, the probabilistic mixture model takes into account errors in the number of nucleic acid molecules caused by extracting nucleic acid molecules performed in 202 and amplifying nucleic acid molecules performed in 204, as well as errors in read counts caused by the sequencing operation in 206.

[0286] In some embodiments, a probabilistic mixture model uses a third Beta distribution to model the allele fractions of amplified nucleic acid molecules for alleles at one or more polymorphic loci, taking into account sampling errors caused by extracting nucleic acid molecules performed in 202 and amplifying nucleic acid molecules performed in 204. In some embodiments, locus i is modeled as bi-allelic and the third Beta distribution has the following form:

[0287] n 1i ′ / (n 1i ′+n 2i ′)~Beta(n″·(1+r i ) / 2·p 1i ,n″·(1+r i ) / 2·p 2i )

[0288] where n 1i ' is the allele count of the amplified nucleic acid molecule of the first allele at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of the second allele at locus i; n" is the total nucleic acid molecule count; r i is the average amplification rate of locus i; p 1i is the probability of the first allele at locus i; and p 2i is the probability of the second allele at locus i.

[0289] In some embodiments, operation 214 includes combining the first binomial distribution and the third beta distribution to obtain n following the third beta-binomial distribution. 1i In some embodiments, the third beta-binomial distribution has the following form:

[0290] n 1i ~BB(n i ,n″·(1+r i ) / 2·p 1i ,n″·(1+r i ) / 2·p 2i )

[0291] where r i is the amplification rate.

[0292] In some embodiments, a multi-locus likelihood function is:

[0293] L(β,n″,r,λ,π;n1,n2)=Πi[∑g i BB(n 1i |n i , n″·(1+r) / 2·p 1i, n″·(1+r) / 2·p 2i )·P(g i |π)],

[0294] where r is the amplification rate assumed to be equal for all loci.

[0295] In some embodiments, the contributors include two contributors and the multi-locus likelihood function is:

[0296] L(β,n″,r,λ,π;n1,n2)=∏ i ∑ g1ig2i BB(n 1i |n i , n″·(1+r) / 2·p 1i (g 1i , g 2i ,λ,β),n″·(1+r) / 2·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)

[0297] where L(n1,n2|β,n″,r,λ,π) is the observed allele count n1 of the first allele vector and the observed allele count n2 of the second allele vector given the parameters β,n″,r,λ and π.

[0298] In some embodiments, process 200 further comprises estimating one or more confidence intervals for one or more fractions of nucleic acids of one or more contributors using the Cramer-Rao inequality.

[0299] In some embodiments, the mapping operation of 208 includes identifying reads in the nucleic acid sequence reads that match any sequence of a plurality of unbiased target sequences, wherein the plurality of unbiased target sequences include subsequences of a reference sequence and sequences that differ from the subsequences by a single nucleotide.

[0300] In some embodiments, multiple unbiased target sequences include five categories of sequences covering each polymorphic site in multiple polymorphic sites: (i) a reference target sequence that is a subsequence of a reference sequence, the reference target sequence having a reference allele with a reference nucleotide at the polymorphic site; (ii) alternative target sequences that each have an alternative allele with an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) mutated reference target sequences that include all possible sequences, each of which differs from the reference target sequence by only one nucleotide at a site that is a non-polymorphic site; (iv) mutated alternative target sequences that include all possible sequences, each of which differs from the alternative target sequence by only one nucleotide at a site that is a non-polymorphic site; and (v) unexpected allele target sequences, each sequence having an unexpected allele that is different from the reference allele and the alternative allele, and each sequence having a sequence that is different from the previous four categories of sequences. In some embodiments, the five types of sequences have the same length and are located in the same region of the genome.

[0301] In some embodiments, operation 208 includes determining the allele count of the nucleic acid sequence read of the allele at one or more polymorphic loci using the identified read and the unbiased target sequence that matches it. In some embodiments, a plurality of unbiased target sequences include sequences that are truncated to have the same length as the nucleic acid sequence read. In some embodiments, a plurality of unbiased target sequences include sequences stored in one or more hash tables, and the hash tables are used to identify the read.

[0302] In some embodiments, process 200 further includes a process for determining whether a contributor of known genotypes is a true contributor to a mixture sample by comparing two versions of the maximized multi-locus likelihood values, wherein one version uses a genotyping matrix containing known genotypes of the contributors and the other version uses a genotyping matrix with unknown genotypes of the contributors.

[0303] In some embodiments, the process further includes determining one or more genotypes of one or more contributors at one or more polymorphic loci. In some embodiments, the process includes using one or more scores of the nucleic acid of one or more contributors to determine the risk of a contributor (recipient) excluding the tissue or organ transplanted from another contributor (donor). In many applications, risk is not or cannot be based only on the contributor score of estimation. On the contrary, the contributor score is used as an intermediate parameter or intermediate result for determining risk. In various embodiments, other parameters obtained from other methods are combined with the contributor score to determine risk. Such other methods include but are not limited to biopsy of tissue, serum creatinine measurement, HLA-DSA (donor specific antibody) analysis.

[0304] Figure 3 A block diagram illustrating a process 300 for evaluating a nucleic acid sample comprising nucleic acids of one or more contributors is shown. The process 300 begins by receiving nucleic acid sequence reads of one or more alleles at one or more polymorphic loci obtained from the nucleic acid sample. See block 302. In some embodiments, nucleic acid sequence reads are obtained by sequencing nucleic acids in the nucleic acid sample using various techniques described herein.

[0305] In some embodiments, a unique molecular index (UMI) is attached to an extracted nucleic acid molecule, which is then amplified, sequenced, and mapped to a polymorphic locus or allele. The unique molecular index provides a mechanism to reduce errors that may occur during sample processing and analysis steps. For example, different reads sharing the same unique molecular index (UMI) can be combined or overlapped to determine the sequence from which the read was derived, thereby effectively eliminating errors that occur during sample processing and sequencing. U.S. Patent Application Nos. 15 / 130,668, filed on April 16, 2016, and 15 / 863,737, filed on January 5, 2018, describe various methods and systems for sequencing nucleic acids using unique molecular indexes, and are incorporated herein by reference in their entirety for all purposes.

[0306] When UMIs are used in an assay, redundant DNA molecules generated by PCR amplification of template nucleotides are overlapped into a single read. For such experimental procedures, a preferred model for single-locus read counts is a first Beta-binomial distribution that combines a first binomial distribution that models sequencing read counts with a first Beta distribution that models the number of extracted nucleic acid molecules.

[0307] When UMIs are not used in an assay, the extraction, amplification, and sequencing of nucleic acids all contribute to the statistical variability of read counts. For such experimental procedures, the preferred model for single-locus read counts is a third Beta-binomial distribution that combines a first binomial distribution that models sequencing read counts, a third Beta distribution that models the allele fractions of amplified nucleic acid molecules, and a first Beta distribution that models the allele fractions in extracted nucleic acid molecules.

[0308] Process 300 further involves determining allele counts for one or more alleles at one or more polymorphic loci using the nucleic acid sequence reads.

[0309] Process 300 also involves applying a probabilistic mixture model to allele counts. The probabilistic model uses a probability distribution to model the allele counts of the alleles at one or more polymorphic loci. The probability distribution illustrates errors in the allele data. The errors include errors derived from nucleic acid extraction, sample handling, and sequencing operations.

[0310] In some embodiments, probability distribution comprises the first binomial distribution.In some embodiments, the first binomial distribution comprises the parameter of the total allele count indicated at the locus and the probability parameter of the probability of the first allele indicated at the locus.In some embodiments, probability parameter is the function of the nucleic acid score of one or more contributors in the nucleic acid sample.Probability parameter is also the function of the genotype or G of one or more contributors, and the error or 0 in the nucleic acid sequence reading data.In some embodiments, the error in the reading data comprises the error derived from nucleic acid extraction, sample handling and sequencing operation.

[0311] Process 300 also involves obtaining a likelihood value for the observed allele data given the model parameters and the potential nucleic acid score value. See block 308.

[0312] In some embodiments, process 300 involves using likelihood values ​​to quantify nucleic acid fractions of one or more contributors in a nucleic acid sample. See block 310 .

[0313] In some embodiments, process 300 further involves using the likelihood value to determine at least one genotype of at least one contributor. See block 312.

[0314] In some embodiments, the genotype of the contributor is unknown prior to process 300 .

[0315] In some embodiments, the probability mixture model uses a beta distribution to model the errors in the allele data. In some embodiments, the beta distribution is defined by a mean parameter and a concentration parameter. In some embodiments, the concentration parameter has a discrete prior representing different noise conditions. The concentration parameter changes on the locus.

[0316] In some embodiments, the quantification of operation 310 includes combining a first binomial distribution and a beta distribution to obtain a marginal distribution that follows a beta-binomial distribution.

[0317] In some embodiments, the quantification of 310 includes quantifying the nucleic acid fraction of one or more contributors in the nucleic acid sample using a multi-locus likelihood function of allele data. In some embodiments, quantification involves calculating multiple likelihood values ​​using a multi-locus likelihood function of multiple potential score values ​​and allele counts. Quantification also involves identifying a potential score vector associated with a maximum likelihood value, and quantifying the nucleic acid fraction of one or more contributors in the nucleic acid sample using the identified potential score vector.

[0318] In some embodiments, the multi-locus likelihood function depends on P(G|π), which is the prior probability of the genotype of one or more contributors given the population allele frequency (π). In some embodiments, virtual alleles with fixed prior probabilities representing mechanism leakage are considered to calculate prior probabilities.

[0319] In some embodiments, one or more contributors comprise two or more contributors.In some embodiments, process 300 comprises the operation of determining the total number of contributors in one or more contributors.In some embodiments, one or more genotypes of one or more contributors are unknown, and process 300 comprises the operation of determining the allele configuration at each locus of one or more polymorphic loci, and this allele configuration comprises the allele of each contributor in one or more contributors.In some embodiments, process 300 comprises the operation of determining the estimated probability of allele configuration.

[0320] In some embodiments, process 300 further includes obtaining a posterior probability that a particular contributor among one or more contributors has a particular genotype. In some embodiments, process 300 further includes calling out that the nucleic acid sample includes nucleic acid from a particular contributor based on the posterior probability. In some embodiments, obtaining a posterior probability that a particular contributor among one or more contributors has a particular genotype includes: (i) multiplying the prior probability of the genotype configuration by the likelihood of the genotype configuration; (ii) normalizing the product of (i) by the sum over the genotype space; and (iii) summing the genotype configurations that include the particular genotype to obtain the posterior probability.

[0321] In some embodiments, the specific genotype includes a multi-locus genotype, and the method further includes: summing the posterior probabilities that the contributor has the specific genotype at all loci across all contributors; and then determining that the specified multiple loci genotype occurs in any contributor based on the summed probability.

[0322] In some embodiments, the nucleic acid sample is a forensic sample and the data of the genotypes of the plurality of loci is obtained from a person of interest. The process further includes determining that the person of interest is a contributor to the nucleic acid sample.

[0323] In some embodiments, a probabilistic mixture model uses a second binomial distribution to model stuttering errors in allele data. In some embodiments, the second binomial distribution is expressed as follows:

[0324] s ik ~BN(n i(k+1) , r i )

[0325] where s ik is the Caton allele count at locus i of the Caton allele, which appears to be allele k but is actually caused by the Caton error of allele k+1; n i(k+1) is the raw allele count of allele k+1 at locus i; and r i is the jam rate at locus i.

[0326] In some embodiments, the jam rate r varies across loci and has a prior that represents different noise conditions that is shared across the loci.

[0327] In some embodiments, operation 310 includes quantifying the nucleic acid fraction of one or more contributors in a nucleic acid sample using a multi-locus likelihood function that includes the product of a likelihood of a non-catton allele count and a likelihood of a catton allele count.

[0328] In some embodiments applying a probabilistic mixture model includes adding a fixed number of molecules to the allele count assigned to allele k+1 when determining the number of molecules from which a jam may potentially originate.

[0329] In some embodiments, the probabilistic mixture model uses virtual out-of-sample alleles to model natural dropouts. In some embodiments, the prior of the virtual out-of-sample alleles is proportional to the number of unobserved alleles. In some embodiments, the number of unobserved alleles is estimated in the following manner: interpolate all integers between the shortest and longest observed integer-valued alleles, add any observed non-integer-valued alleles, and return the maximum and standard values ​​of the result values.

[0330] In some embodiments, application of a probabilistic mixture model involves trimming genotype configurations from data for quantitatively quantifying the nucleic acid fraction of one or more contributors in a nucleic acid sample. In some embodiments, trimming genotype configurations involves: by constructing a list of desired alleles and excluding loci that do not have enough contributors to explain all desired alleles, thereby limiting seemingly reasonable genotype configurations. In some embodiments, the list of desired alleles is essentially composed of the following alleles, which have allele counts that are higher than a threshold and are too high to be accepted due to the insertion of a Caton. In some embodiments, the threshold is the sum of the following: (i) maximum non-Caton allele counts, and (ii) a value multiplied by the potential Caton donor allele counts. In some embodiments, trimming genotype configurations involves removing genotype configurations that have a poor match between allele data and expected allele counts. In some embodiments, genotype configurations with a poor match have a root mean square error (RMSE) value greater than one or more thresholds.

[0331] In some embodiments, the alleles at one or more polymorphic loci comprise single nucleotide polymorphism (SNP) alleles and / or short tandem repeat (STR) alleles.

[0332] Method for unbiased mapping of reads to landmark sites

[0333] Conventional computational methods for mapping nucleic acid (e.g., DNA or RNA) sequencing reads to genomes can be biased by the reference genome used. Since there is only one allele (the reference allele) per variant site in the reference genome, mismatches between reads and reference are treated as sequencing errors in existing read mapping strategies. The problem is that when reads containing non-reference alleles are treated as containing sequencing errors, the alignment confidence (score) is reduced, and therefore, they are less likely to be retained as credibly mapped reads in subsequent filtering steps. This mapping bias can skew allele counts ( Figure 1 B), and subsequently impairs the estimate of the contributor DNA fraction.

[0334] To address the mapping bias issue and achieve optimal CDQ, some embodiments provide a novel workflow for mapping reads to variant sites. The new read mapping method can perform unbiased allele counting and estimate sequencing errors for variant and non-variant sites.

[0335] The read mapping workflow is as follows. The workflow first generates five types of sequences based on 1) the reference sequence and 2) the known alleles of the variant site (see Table 1). If more than one single mutation is allowed per sequence, more types of sequences will be generated. The five types of sequences are called ref, alt, ref.mut, alt.mut, and snp.mut. For example, for each biallelic SNP marker site covered by a target sequence of length L, there is one ref, one alt, [L-1]x3ref.mut, [L-1]x3 alt.mut, and 2 snp.mut sequences. All five types of sequences are then included in the "unbiased target sequence" database ( Figure 1 B). Then, depending on the length of the read from the sequencer, the unbiased target sequence is truncated into two versions. Let r be the read length. Version 1 of the truncated target sequence includes the r5' bases of all unbiased target sequences, and version 2 of the truncated target sequence includes the reverse complement of the r3' bases of all unbiased target sequences. The redundant sequences in the truncated target sequence are then removed. The unique sequences in the two truncated sequence databases are then recorded in two hash tables. Next, the sequence reads are counted using the hash tables. For the paired end sequencing strategy, the R1 reads and the R2 reads are counted using the first hash table and the second hash table, respectively. For non-paired end sequencing, all reads are counted using the first hash table. Finally, for each marker site, the counts are summarized into the five types defined above, depending on whether the truncated unbiased target sequence corresponds to the type in Table 1.

[0336] A similar strategy can be implemented when mapping is done using a sequence alignment tool instead of using a hash table. For each marker locus, ref and alt types of sequences are generated to form an unbiased sequence database. Each sequencing read is then aligned to this database with up to a predefined number of sequencing errors. The mapped reads are then classified based on Table 1. For SNP markers, only the bi-allelic scenario is presented here, but the approach is extended to multi-allelic loci.

[0337] Table 1. Definitions of the five types of target sequences generated from reference sequences around the variant sites.

[0338]

[0339]

[0340] The proposed read mapping workflow addresses the read mapping bias issue when tested with real data. In the workflow, the observed reference-to-substitution error and substitution-to-reference error ratios are identical. The sequencing error rates at non-variant sites on the reference DNA copy and at non-variant sites on the alternative DNA copy are also identical.

[0341] Relating contributor DNA fractions to allele fractions

[0342] Sequencing error-free scenario

[0343] We denote n1 as the number of Contributor 1 (e.g., organ recipient) cells that contribute DNA to the sample, and n2 as the number of Contributor 2 (e.g., organ donor) cells. Based on these cells, this embodiment defines the Contributor 2 score as β2=n2 / (n1+n2). For the two-contributor scenario, we refer to β2 as β. Depending on the genotypes of the two contributors at each specific locus, the two alleles have different scores (see Table 2 for details), and the general formula for calculating them is p i =[g 11 (1-β)+g 21 ·β] / 2 and p2=[g 12 (1-β)+g 22 ·β] / 2. Note that g 11 and g 12 is the contributor 1 (recipient) genotype, i.e., the copies of alleles 1 and 2 in the recipient genome; g 21 and g 22 is the contributor 2 (donor) genotype, i.e., copies of alleles 1 and 2 in the donor genome.

[0344] In matrix notation, the relationship for the multiple contributor case is usually implemented as p←g / 2·β, where p is the vector of expected allele 1 fractions for all loci, g is the matrix of genotypes for all loci in all contributors, and β = [β1, β2, ..., β D ] is a vector of nucleic acid scores of all contributors. This implementation is generally applicable to single contributor, dual contributor and multi-contributor scenarios.

[0345] Table 2: Parameters of the binomial model for the nine possible genotype combinations between contributor 1 and contributor 2 for a given variant site Expected allele 1 and allele 2 fractions p1 and p2

[0346] <![CDATA[g 11 ]]> <![CDATA[g 21 ]]> <![CDATA[p1]]> <![CDATA[p2]]> 0 0 0 1 0 1 β / 2 1-β / 2 0 2 β 1-β 1 0 (1-β) / 2 (1+β) / 2 1 1 1 / 2 1 / 2 1 2 (1+β) / 2 (1-β) / 2 2 0 1-β β 2 1 1-β / 2 β / 2 2 2 1 0

[0347] General scenarios with sorting errors

[0348] When there are two known alleles at a variant site, sequencing errors convert one allele to the other in addition to converting the two known alleles to the two remaining nucleotides at that locus. The result is that the allele fraction in the sequencing read will be different from the allele fraction in the NGS input sample.

[0349] Figure 2C Schematically illustrates sequencing errors that convert one allele to another and true alleles to unexpected alleles. Panel (A) shows nucleotide-dependent sequencing errors, and panel (B) shows uniform sequencing errors.

[0350] Let N1, N2 be the nucleotides of allele 1 and allele 2. Let p1′, p2′ be the probability of observing a read of allele 1 and allele 2, respectively, whether it is real or due to sequencing error; and p0′=1-p1′-p2′ is the probability of observing two unexpected alleles due to sequencing error. Let λ N1N2 is the mutation rate (probability) from N1 to N2, where N1 and N2 are unique for each SNP site, and

[0351] λ N1# : The probability of mutation from N1 to any of the non-N1 nucleotides within 3 nucleotides.

[0352] Figure 2C The transition diagram between the 4 nucleotides of the SNP site is shown. Based on this, the embodiment obtains the following equation for converting from the true allele fractions p1, p2 to the observed allele fractions p1', p2' and p0':

[0353] p1′=p1-p1·λ N1# +p2·λ N2N1

[0354] p2′=p2-p2λ N2# +p1·λ N1N2

[0355] p0′=p1·(λ N1# -λ N1N2 )+p2·(λ N2# -λ N2N1 ).

[0356] When embodiments assume a uniform sequencing error rate that is independent of nucleotide identity, embodiments have p1′=p1·(1-3·λ)+p2·λ

[0357] p2′=p2·(1-3·λ)+p i ·λ

[0358] p0′=2λ.

[0359] When implementation ignores unexpected alleles

[0360] p1′=(p1·(1-3·λ)+p2·λ) / (1-2λ)

[0361] p2′=(p2·(1-3·λ)+p1·λ) / (1-2λ),

[0362] use o (λ 2 ) approximate error, rewriting these as

[0363] p1′=p1·(1-λ)+p2·λ

[0364] p2′=p2·(1-λ)+p i ·λ

[0365] Or for locus i and replacing p with g and β:

[0366] p 1i ′←∑ d [(g d1i ·(1-λ)+g d2i ·λ]·β d ) / 2

[0367] P 2i ′←∑ d [(g d2i ·(1-λ)+g d1i ·λ]·β d ) / 2

[0368] It is called the error-adjusted genotype-weighted mixing coefficient.

[0369] Table 3 lists the formula that relates the score β of contributor 2 to the observed allele score p1′ in the two-contributor scenario.

[0370] Table 3: Expected probability of observed alleles 1 and 2 allowing for sequencing errors, conditional on each donor / recipient genotype combination in a two-contributor setting. Here, a uniform sequencing error rate λ is used for all nucleotide pairs N1 and N2 N1N2 =λ. Since the mutation rate λ is small, a first-order approximation is used.

[0371] <![CDATA[g 11 ]]> <![CDATA[g 21 ]]> <![CDATA[p1′]]> <![CDATA[p2′]]> 0 0 λ 1-λ 0 1 β / 2+λ-βλ 1-β / 2-λ+βλ 0 2 β+λ-2βλ 1-β-λ+2βλ 1 0 (1-β) / 2+βλ (1+β) / 2-βλ 1 1 1 / 2 1 / 2 1 2 (1+β) / 2-βλ (1-β) / 2+βλ 2 0 1-β-λ+2βλ β+λ-2βλ 2 1 1-β / 2-λ+βλ β / 2+λ-βλ 2 2 1-λ λ

[0372] In matrix format, the error-adjusted genotype of allele 1 taking into account sequencing error λ is implemented as: G←[(1-λ)g+λ(2-g)] / 2

[0373] For the general case with more than two contributors, the expected mixture fraction vector for allele 1 is calculated as: p←G·β, which is performed for nucleic acid mixtures with single, two or multiple contributors.

[0374] When λ=0, the implementation has a special case: p←g / 2·β

[0375] DNA extraction, PCR (amplification), and sequencing model overview

[0376] Three probability models are provided ( Figure 1 C) to simulate a general experimental pipeline ( Figure 1 A) consists of three main components: 1) DNA / RNA extraction; 2) DNA / RNA amplification (e.g., PCR) as a method to enrich the target DNA / RNA; 3) sequencing (e.g., NGS sequencing). These and other modeling components are then integrated together to implement the single-locus model and calculate the single-locus likelihood function M(n 1i , n 2i |p 1i , θ).

[0377] The following symbols are used in the mathematical models described in Table 4 and the rest of this section.

[0378] B(): Beta function

[0379] Beta(), BN(), Pois(), Gamma(): Beta, binomial, Poisson, and gamma distributions

[0380] NB() represents the negative binomial distribution, which is the discrete probability distribution of the number of successes in a series of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures, denoted r, occurs.

[0381] Table 4: Statistical models of the three main components in the general experimental pipeline ( Figure 1 ). The model for each component is conditioned on the previous components. The model is conditioned on each locus, with the locus index i omitted.

[0382]

[0383]

[0384] DNA Extraction Model: Model E

[0385] When cfDNA or cellular DNA is extracted from a blood sample, the DNA obtained is a small sample from a large DNA pool, and therefore, the implementation modeled the counts of the two alleles at each locus as two Poisson distributions. Therefore, the DNA copies of allele 1 (n1") at the locus conditioned on the total count n" follow a binomial distribution: n1"~BN(n",p1), with mean μ0=n"·p1, and variance δ0 2 =n”·p1·p2.

[0386] When gDNA is extracted from the sample, the resulting gDNA amount for each locus can again be variable due to extraction losses. Considering p1 as the number of allele 1 in the input sample, the amount of allele 1 in the extracted DNA can again be modeled by a binomial distribution: n1"~BN(n",p1).

[0387] PCR amplification model: Model P

[0388] We model the PCR amplification process as a random process in order to obtain the probability distribution of the allele 1 count in the PCR product. Let x t is the number of DNA copies of a given allele after cycle t of PCR amplification, let r t is the amplification rate of cycle t, and let y t is the new copy generated at cycle t. By assuming that each DNA strand has a probability r of being amplified and added to the DNA pool t , this embodiment has the following expansion model:

[0389] x t+1 =x t +y t+1 , where y t+1 ~BN(x t , r t+1 ) follows a binomial distribution, where x t and r t+1 as a parameter.

[0390] Based on this model, embodiments assume that the number of DNA copies of a locus in a PCR product approximately follows a gamma distribution. The reasons are as follows.

[0391] Step 1: Use the Yule process (continuous-time random process) to approximate the PCR (discrete-time random process).

[0392] PCR processx t+1 =x t +y t+1 , where y t+1 ~BN(x t , r t+1) is a discrete-time pure birth process: in a given time t cycle, each copy of the DNA is generated at a certain rate r t The continuous-time version of the pure birth process is known as the Yule-Furry process. For the continuous-time birth process, it is known that the final number of copies of a locus at a given time t follows a negative binomial distribution. When the total number of PCR cycles is not close to 1, embodiments can use the same distribution to approximate the discrete-time birth process.

[0393] Step 2: Use the gamma distribution (continuous distribution) to approximate the negative binomial distribution (discrete distribution).

[0394] The negative binomial random variable can be written as the sum of independent and identically distributed (iid) geometric random variables. It is known that the exponential distribution is a continuous form of the geometric distribution. Therefore, the sum of iid exponential random variables following the gamma distribution is a continuous form of the sum of binomial random variables that is the negative binomial.

[0395] The following embodiment estimates the parameters of the gamma distribution of allele counts in PCR products.

[0396] Based on the total variance law var(x t+1 )=var(E(x t+1 |x t )+E(var(x t+1 |x t )), the implementation method can recursively derive x t The mean and variance of are as follows:

[0397] μ t+1 =μ t ·(1+r t+1 )

[0398] 6 t+1 2 =μ t ·r t+1 ·(1-r t+1 )+δ t 2 ·(1+r t+1 ) 2

[0399] Among them, μ t =E(x t ), δ t 2 =var(x t ).

[0400] Assuming the average amplification rate per PCR cycle is r t+1 = r, then the implementation method has

[0401] μ t =μ0·(1+r) t

[0402] δ t 2 =μ0·(1+r) t ·[(1+r) t -1]·(1-r) / (i+r)+δ0 2 (1+r) 2t

[0403] Note that μ0 and δ0 2 are the mean and variance of the DNA allele counts in the PCR amplification input, and they can be calculated based on the DNA extraction model (Model E) described above. Alternatively, if the embodiment does not treat the cfDNA / cell DNA allele counts as random variables, the embodiment has μ0=n1″ or n2″, and δ0 2 =0.

[0404] The corresponding gamma distribution G(x) matches this mean and variance t |k,θ)=x k-1 e -x / θ / [θ k ·Γ(k)] has parameters:

[0405] θ=[(1+r) t -1]·(1-r) / (1+r)+δ0 2 / μ0·(1+r) t

[0406] k=μ0·(1+r) t / [[(1+r) t -1]·(1-r) / (1+r)+δ0 2 / μ0·(1+r) t ].

[0407] For a given locus with two alleles and two initial copies (n1', n2'), assuming the same amplification rate r1 = r2 = r for the two alleles at each locus, the two corresponding gamma distributions G(n1'|k1, θ1) and G(n2'|k2, θ2) have the following parameters:

[0408] θ1=[(1+r) t -1]·(1-r) / (1+r)+p2·(1+r) t

[0409] θ2=[(1+r) t -1]·(1-r) / (1+r)+P i (1+r)t

[0410] k1=n″p1 / [[1-(1+r) -t ]·(1-r) / (1+r)+p2]

[0411] k2=n″p2 / [[1-(1+r) -t ]·(1-r) / (1+r)+p i ].

[0412] When the embodiment adjusts the PCR model based on the DNA extraction model, stμ0=n1″ or n2″ and δ0 2 = 0, the implementation method has

[0413] θ1=[(1+r) t -1]·(1-r) / (1+r)

[0414] θ2=[(1+r) t -1]·(1-r) / (1+r)

[0415] k1=n1″·(1+r) / (1-r) / [1-(1+r) -t ]

[0416] k2=n2″·(1+r) / (1-r) / [1-(1+r) -t ].

[0417] Therefore, the allele copies n1′ and n2′ in the PCR products follow two gamma distributions with the same scale parameters θ1 and θ2, which depend only on the PCR process (number of cycles and amplification rate).

[0418] n1′ / (n1′+n2′)~Beta(n1″·ρ, n2″·ρ),

[0419] where ρ is a constant related to the amplification rate r, which depends only on the PCR process: ρ = (1 + r) / (1 - r) / [1 - (1 + r) -t ], or about ρ = (1 + r) / (1 - r) when the cycle number t is large. For a particular locus, it is written as n 1i ′ / (n 1i ′+n 2i ′)~Beta(n 1i ″·ρ i , n 2i ″·ρ i ) to capture locus-specific PCR amplification rates.

[0420] If the implementation ignores DNA sampling and assumes that all loci have the same total DNA copy number ni ″=n″, then n 1i ″=n″·p 1i And n 2i ″=n″·p 2i The allele fractions of the loci in the PCR products are as follows:

[0421] n 1i ′ / (n 1i ′+n 2i ′)~Beta(n″·ρ i ·p 1i , n″·ρ i ·p 2i ).

[0422] Note that without the gamma distribution approximation, the allele counts of the PCR products have n1′~NB(r1, p) and n2′~NB(r2, p), and the ratio n1′ / (n1′+n2′) does not have a closed form distribution. For the gamma distribution approximation, n1′~Gamma(n1″·ρ, θ) and n2′~Gamma(n2″·ρ, θ), and n1′ / (n1′+n2′) follows a Beta distribution.

[0423] Sequencing read count model: Model S

[0424] NGS sequencing is the process of sampling from a pool of DNA molecules provided to a sequencer and reading out the sequences of these molecules. The fraction of allele 1 at locus i in the PCR product is n 1i ′ / (n 1i ′+n 2i ′). This fraction determines the probability of allele 1 read appearing in the sequencing result. The total number of reads per locus n i As the condition, n 1i The distribution of the read count of allele 1 of the locus is then modeled as a binomial distribution n 1i ~BN(n i , n1′ / (n1′+n2′)).

[0425] Modeling genetic correlations between contributors as a prior distribution

[0426] If the contributor genotypes are fully known, they can be directly incorporated (using Table 2 or Table 3) as parameters of the component models described above. However, when the genotypes are unknown, embodiments exploit information about the genetic relationship between the donor and recipient in a two-contributor setting to achieve accurate mixture quantification. Genetic relationships are common in clinical applications such as organ transplantation. Here, we present embodiments for a two-contributor scenario, but this "genetic prior" approach can be generalized to any number of contributors.

[0427] We describe different types of donor-recipient relationships as different prior distributions over the space of possible genotype combinations of the donor (contributor 2) and the recipient (contributor 1). Assuming Hardy-Weinberg equilibrium, the genotype distribution of a given locus for a single individual is P(g = [0, 1, 2]) = [(1-π) 2 , 2π(1-π), π 2 ], where π is the population frequency of allele 1 and g is the number of copies of allele 1. Note that all genetic relationships are the result of father-child relationships. Based on the genetic relationships between parents and children for a given biallelic marker site (Table 5), embodiments can calculate the joint distribution of any genetic relationship between two or more contributors.

[0428] Table 5: Given the parental genotypes (father genotype g 父 and maternal genotype g 母 ), and the joint distribution between the parents assuming that the parents are not relatives.

[0429] g father g mother The probability of having children with genotypes [0, 1, 2] conditional on the genotypes of the parents P(g father, g mother) 0 0 [1，0，0] <![CDATA[(1-π) 4 ]]> 0 1 [1 / 2，1 / 2，0] <![CDATA[2π(1-π) 3 ]]> 0 2 [0，1，0] <![CDATA[π 2 (1-π) 2 ]]> 1 0 [1 / 2，1 / 2，0] <![CDATA[2π(1-π) 3 ]]> 1 1 [1 / 4，1 / 2，1 / 4] <![CDATA[4π 2 (1-π) 2 ]]> 1 2 [0，1 / 2，1 / 2] <![CDATA[2π 3 (1-π)]]> 2 0 [0，1，0] <![CDATA[π 2 (1-π) 2 ]]> 2 1 [0，1 / 2，1 / 2] <![CDATA[2π 3 (1-π)]]> 2 2 [0，0，1] <![CDATA[π 4 ]]>

[0430] The prior distributions for various types of genetic relationships between two contributors are provided further below.

[0431] Joint distribution between father and offspring genotypes

[0432] As an example, the joint distribution of father-child donor-recipient genotypes (GT) is calculated using the following formula:

[0433] P(recipient = my GT, donor = father GT) = ∑ 母亲 GT[P(my GT|father GT, mother GT)·P(father GT, mother GT)],

[0434] Among them, the values ​​of P(my GT|father GT, mother GT) and P(father GT, mother GT) are taken from the 3rd and 4th columns of Table 5 respectively.

[0435] Joint distribution between sibling genotypes

[0436] As an example, based on the conditional independence of the two sibling genotypes given the parental genomes, the following formula is used to calculate the joint distribution of my-sibling donor-recipient genotypes:

[0437] P(recipient = me GT, donor = sibling GT) = ∑ 母亲GT ∑ 父亲GT [P(I GT|Father GT, Mother GT)·P(Siblings GT|Father GT, Mother GT)·P(Father GT, Mother GT)],

[0438] Among them, the values ​​of P(my GT|father GT, mother GT), P(siblings GT|father GT, mother GT) and P(father GT, mother GT) are taken from the third, third and fourth columns of Table 5, respectively.

[0439] Joint distribution between uncle-nephew genotypes

[0440] As an example, the uncle / aunt-nephew / niece donor-recipient genotype joint distribution is calculated using the following formula:

[0441] P(recipient = me GT, donor = uncle GT)

[0442] =∑ 祖母GT ∑ 祖父GT ∑ 母亲GT ∑ 父亲GT [P(I GT | father GT, mother GT) · P(mother GT) · P(father GT | grandfather GT, grandmother GT) · P(uncle GT | grandfather, grandmother GT) · P(grandfather GT, grandmother GT)]

[0443] =∑ 母亲GT ∑ 父亲GT P(my GT|father GT, mother GT)·P(mother GT)·P(father GT, uncle GT),

[0444] Among them, the value of P(my GT|father GT, mother GT) is taken from the third column of Table 5, and the value of P(father GT, uncle GT) is the same as P(recipient = my GT, donor = sibling GT).

[0445] In matrix notation, parent / child prior matrices, sibling prior matrices, and single-genome prior vectors can be used

[0446] =[P(I GT, GT father)] 我，父亲 diag(1 / [P(father GT)] 父亲 )·[P(father GT, uncle GT)] 父亲，叔叔 To calculate

[0447] Joint distribution between cousin genotypes

[0448] Assuming that cousins ​​are genetically related by their fathers, who are brothers, and their mothers are genetically unrelated, then,

[0449] P(recipient = my GT, donor = cousin GT)

[0450] =∑ 姑母GT ∑ 叔叔GT ∑ 母亲 GT∑父亲 GT P(I GT|Father GT, Mother GT)·P(Mother GT)·P(Father GT, Uncle GT)·P(Aunt GT)·P(Cousin GT|Uncle GT, Aunt GT)

[0451] =∑ 姑母GT ∑ 叔叔GT P(I GT, uncle GT)·P(aunt GT)·P(cousin GT|uncle GT, aunt GT)

[0452] =∑ 叔叔GT P(I GT, uncle GT) · P(cousin GT, uncle GT) / P(uncle GT)

[0453] In matrix notation, this can be done using the uncle / niece prior matrix, the parent / child prior matrix, and the single genome prior vector

[0454] =[P(I GT, uncle GT)] 我，叔叔 ·diag(1 / [P(Uncle GT)] 叔叔 )·[P(cousin GT, uncle GT)] 叔叔，堂亲 To calculate

[0455] Note that P(cousin GT, uncle GT) is the same as the parent-child relationship.

[0456] Joint distribution between half-siblings genotypes

[0457] Assume that the half-siblings are linked by a single mother, and the two fathers are unrelated:

[0458] P(recipient = me GT, donor = half-sibling GT)

[0459] =∑ 父亲GT ∑ 母亲GT ∑ 继父GT P(I GT|Father GT, Mother GT) · P(Half-siblings GT|Stepfather GT, Mother GT) · P(Mother GT) · P(Father GT) · P(Stepfather GT)

[0460] =∑ 母亲GT P(I GT, mother GT) · P(half-sibling GT, mother GT) / P(mother GT)

[0461] In matrix notation, two parent-child prior matrices and a single genome prior vector can be used

[0462] =[P(I GT, mother GT)] 我，母亲 diag(1 / [P(mother GT] 母亲 )·[P(half-siblings GT, mother GT)] 半兄弟姐妹，母亲

[0463] Note that under Hardy-Weinberg equilibrium, half-sibling relationships follow the same distribution as uncle / aunt / nephew / niece relationships. Without Hardy-Weinberg equilibrium, this may not be true.

[0464] Summarize

[0465] Table 6 summarizes the results of the above derivation, and a specific example for a given population SNP allele frequency π=0.5 is provided in Table 7. Other relationships, such as grandparent-grandchild relationships or multi-contributor relationships, can be derived based on the same basic principles.

[0466] Table 6: Prior distribution of related or unrelated genomes P(g 11 , g 21 ). Assuming that all SNPs are from autosomes, all married couples are genetically unrelated and in Hardy-Weinberg equilibrium. 11 is the recipient genome, g 21 It is the donor genome.

[0467]

[0468] Table 7: Given a SNP population allele frequency π = 0.5, the prior distribution of related or unrelated genomes P (g 11 , g 21 ).

[0469]

[0470] The distributions of parent-child and sibling relationships are very different from unrelated relationships, while uncle / aunt-nephew / niece are almost unrelated. In the case where the donor genotype is unknown, embodiments can infer the genetic relationships by evaluating the likelihood function of the fitted model for each of the above genetic relationships. Alternatively, embodiments can allow for multiple free parameters in the genetic prior distribution (with the additional constraint that the marginal distributions should follow Hardy-Weinberg equilibrium) and estimate these parameters together with the estimate of the donor fraction.

[0471] Regulation of DNA copy number based on DNA length

[0472] For amplicon-based assays involving PCR DNA amplification, DNA length affects the effectiveness of DNA as a PCR template. In extreme cases, when DNA fragments are shorter than the expected amplicon length, their effectiveness as PCR templates is 0%. To correct for this effect, we use the following process to adjust the number of DNA copies using an average DNA length, which varies depending on the type of input DNA. Some embodiments adjust the number of effective input DNA molecules based on the average length of the input DNA template. In some embodiments, the number of effective input DNA molecules can be adjusted according to the following equation:

[0473] n″=w / w0·(LL a +1) / L,

[0474] where n″ is the number of effective input DNA molecules (haploid), w is the amount of input DNA, w0 (3.59x103 ng / copy) is the weight of a haploid human genome, L is the average length of the input DNA template, and L a is the average amplicon length (110 bp for our amplicon design).

[0475] DNA template efficiency is defined as e = (LL a +1) / L, which is defined as L>=L a Table 8 shows example DNA types and their efficiency as PCR templates.

[0476] Table 8. DNA types and their efficiency as PCR templates

[0477] DNA Type DNA length parameter (L) Template efficiency (e) Genomic DNA (gDNA) 100,000 0.9989 Cell-free DNA (cfDNA) 165 0.3394 Simulated cfDNA (mcfDNA) 160 0.3188

[0478] Integration of modeling components

[0479] The components of the probabilistic mixture model are integrated to provide a solution to the Contributor DNA Quantification (CDQ) problem. The population allele frequency π for each SNP locus can be obtained from public databases such as dbSNP. If the most informative SNP marker, i.e., the SNP with π=0.5, is selected in the experimental design, then π=0.5 can be set for all loci, and P(g 11 , g 21 ) as the prior distribution of genetic relationships as described in the previous section.

[0480] At a schematic level, Figure 2BA block diagram showing the various components of a probability mixture model 250 is shown. Some components are optional in some embodiments. The probability mixture model 250 includes a binomial distribution 258 for modeling allele counts of sequencing reads. In some embodiments, the probability mixture model also includes a component for modeling donor-recipient (or recipient) relationships using a genetic relationship prior distribution 252. In some embodiments, the probability mixture model also includes a binomial distribution 254 for modeling DNA extraction allele counts. In some embodiments, the probability mixture model 250 also includes a beta distribution 256 for modeling PCR product or amplification product allele scores. See box 256.

[0481] In some embodiments, the mixture model combines binomial distribution 208 with binomial distribution 254 to model DNA extraction errors and sequencing errors. In such embodiments, the mixture model uses Beta-binomial distribution 260 to model allele counts of sequencing reads while capturing the variability of allele counts due to DNA extraction.

[0482] In some embodiments, the probabilistic mixture model 250 combines the Beta distribution 256 and the Binomial distribution 258 and uses the Beta-binomial distribution 262 to model both errors in the PCR or amplification process and errors in the sequencing process.

[0483] In some embodiments, the probabilistic mixture model 250 combines the binomial distribution 254, the beta distribution 256, and the binomial distribution 258 to account for differences caused by the DNA extraction, amplification process, and sequencing process, respectively. In such embodiments, the probabilistic mixture model 200 first uses the beta distribution 264 to approximate the effects of the binomial distribution 254 and the beta distribution 256. Then, the probabilistic mixture model 250 uses the beta-binomial distribution 256 to combine the beta distribution 264 and the binomial distribution 258.

[0484] Sequencing model: Model S

[0485] The basic version of the full model ignores the DNA extraction model and the PCR model and only considers the sequencing model. For each locus, the sequencing read counts of the reference allele are given by a binomial distribution ( Figure 1 C)n 1i ~BN(n 1i , p 1i ) model, where the parameter p 1i (g 1i , g 2i , λ, β) is a function of the donor-recipient genotype combination at the locus (Tables 2 and 3). Assuming the genotype is unknown, for each locus,1i , g 2i |π) as the prior distribution (Table 6 and Table 7), this embodiment marginalizes the 9 possible genotype combinations. The complete likelihood function at all loci is the product of the marginal distributions of all loci:

[0486] L(β, λ, π; n1, n2)=Π i ∑ g1ig2i BN(n 1i |n i , p 1i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π), where L(β, λ, π; n1, n2) is the likelihood of observing the allele count vector n1 to n2 for alleles 1 and 2 given the parameters β and π; p 1i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p1′ in Table 3, indicating the probability of the genotypes of the two contributors (g 1i , g 2i ) is the probability of allele 1 at locus i; and P(g 1i , g 2i |π) is the a priori joint probability of observing the two contributor genotypes given the population allele frequencies (π).

[0487] Extending this to multiple contributors, the likelihood function can be expressed as:

[0488] L(β, λ, π; n1, n2)=Π i [∑g i BN(n 1i |n i ,·p(g i ,λ,β))·P(g i |π)]

[0489] Extract-Seq Composite Model: Model ES

[0490] More advanced model combines DNA extraction model and sequencing model.This embodiment ignores PCR step (that is, assuming that for each locus, the allele fraction in the PCR product is identical with the allele fraction in the DNA sample), and only DNA sampling and sequencing step are modeled.For each locus, there is a binomial distribution of allele counts in the input DNA sample.This captures the locus to locus variability of the allele fraction in the input DNA that is provided to NGS sequencing.

[0491] For the DNA extraction model, this embodiment has n 1i ″~BN(n″,p 1i ), and the sequencing model is n 1i |n 1i ″,n i ″~BN(n i , n 1i ″ / n i ″), where n i "=n" is the number of copies of the haploid genome corresponding to the input DNA. Unfortunately, n 1i There is no closed form formula for the marginal distribution of n. This implementation uses the Beta distribution Beta(a, b) to approximate n 1i ″ / n″ distribution, and by changing n 1i The mean and variance of ″ / n″ are similar to those obtained from the binomial model n 1i ″~BN(n″,p 1i ) to select the optimal Beta distribution by matching the mean and variance obtained:

[0492] p 1i =a / (a+b)

[0493] p 1i ·(1-p 1i ) / n″=ab / (a+b) 2 / (a+b+1).

[0494] Solving the equation gives the Beta distribution Beta((n″-1)p 1i , (n″-1)p 2i ) is the best approximation. Approximate to the DNA extraction model, then n 1i The marginal distribution of follows a beta-binomial distribution of the following form:

[0495] n 1i ~BB(n i , (n″-1)·p 1i , (n″-1)·p 2i ).

[0496] or in an alternative approximation:

[0497] n 1i ~BB(n i , n″·p 1i , n″·p 2i ).

[0498] Then the corresponding total likelihood function considering the genetic relationship prior is:

[0499] L(β,n″,λ,π;n1,n2)=∏i[∑gi BB(n 1i |n i , (n″-1)·p 1i , (n”-1)·p 2i )·P(g i |π)]

[0500] where L(β, n″, λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2 at all loci, and p 1i = p(g i ,λ,β),p 2i =1-p 1i .

[0501] Note that n″ and π=0.5 are both known parameters, and the final full likelihood function has only a single unknown parameter β, the donor DNA fraction.

[0502] The number of copies of the input DNA (haploid) n" can be derived from the input DNA mass. When the input DNA amount is 8ng, n" = 8ng / [3.59x10 -3 ng / copy]=2228.412.

[0503] PCR-Seq Composite Model: Model PS

[0504] Ignoring the DNA extraction model and assuming a known genotype combination for a given locus, the PCR model is: n 1i ′ / (n 1i ′+n 2i ′)~Beta(n″·ρ i ·p 1i , n″·ρ i ·p 2i ) and sequencing model n 1i ~BN(n i , n1′ / (n1′+n2′)) can be combined into the Beta-binomial distribution BB(n i , n″·ρ i ·p 1i , n″·ρ i ·p 2i ). Note that there are two basic locus-specific PCR amplification rates, p i If the embodiment assumes that all loci have the same intrinsic amplification rate, then the embodiment will have BB(n i , c.p 1i (g 11 , g 21 , β), c·p 2i (g 11 , g21 , β)).

[0505] Then, the full likelihood model over all loci is:

[0506] L(β,n″,c,λ,π;n1,n2)=∏i[∑g i BB(n 1i |n i , c.p 1i , c.p 2i )·P(g i |π)], where c and β are the two parameters to be estimated.

[0507] Alternatively, embodiments may define the relative amplification rate of each locus as proportional to the total reads per locus and reparameterize the beta-binomial as n 1i ~BB(n i , c′·n i ·p 1i , c′·n i ·p 2i ), where c′ is the parameter to be optimized; and n i is the total read sequence at locus i.

[0508] Then, the total likelihood model at all loci is: L(β, n″, c′, λ, π; n1, n2) = Πi[∑g i BB(n 1i |n i , c′·n i ·p 1i , c′·n i ·p 2i )·P(g i |π)], where c and β are the two parameters to be estimated.

[0509] Extract-PCR-Seq Multiplex Model: Model EPS

[0510] If an embodiment combines the DNA extraction and PCR models into one model and approximates them with a single beta distribution, all three components in the extraction-PCR-sequencing general experimental pipeline can be modeled together by the beta-binomial. Intuitively, although the expected value of the allele 1 fraction in the PCR product (n1′ / n′, see Table 4) is still p1, the uncertainty (variance) of n1′ / n′ comes from both the DNA extraction and PCR steps. In order to obtain a beta distribution beta(a, b) to model DNA extraction and PCR together, the embodiment calculates n based on the following law 1i The unconditional mean and variance of ′ / n′: E(n 1i ' / n')=E(E(n1i ′ / n i ′|n 1i ″ / n″) and var(n i1 ' / n') = var(E(n 1i ′ / n i ′|n 1i ″ / n″))+E(var(n 1i ′ / n i ′|n 1i ″ / n″)). This gives: E(n 1i ′ / n′)=p 1i , and var(n 1i ′ / n′)=p 1i p 2i / n″+P 1i p 2i / (n″·ρ i +1)-p1p2 / [n″·(n″·ρ i +1)], where ρ i =(1+r i ) / (1-r i )>1 is related to the amplification rate r i Since n″ is large, the implementation has the following approximate value var(n 1i ′ / n′)=p 1i P 2i / [n″·(1+r i ) / 2]. Then, the optimal Beta distribution for simulating DNA extraction and PCR is Beta([n″·(1+r i ) / 2-1]p 1i ,[n″·(1+r i ) / 2-1]p 2i ). Note that this is different from the Beta((n″-1)p 1i , (n″-1)p 2i ) distribution is very close, but the variance is now larger. i = 0.8 to 0.95 for a typical PCR reaction, embodiments have n″·(1+r i ) / 2=0.9·n″ to 0.975·n″.

[0511] The full multi-locus likelihood function for the cfDNA-PCR-Seq model is:

[0512] L(β,n″,r,λ,π;n1,n2)=Π i ∑ g1ig2i BB(n 1i |n i , n″·(1+r) / 2·p1i (g 1i , g 2i ,λ,β),n″·(1+r) / 2·p 2i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π).

[0513] Baseline method: NaiveLM or KGT.NaiveLM

[0514] Conventional methods for quantifying the DNA fraction of contributors use a basic linear regression formula, which does not use the same probability model or cost function described above. Instead, its cost function is expressed as:

[0515] E=[rp] T ·[rp], where r is the allele fraction vector, p=g / 2·β is the expected allele fraction vector, g is the genotype matrix, and β is the contributor DNA fraction vector. The method only works when all the benchmarks are known.

[0516] Methods for estimating contributor nucleic acid fractions and their confidence intervals

[0517] Numerical optimization for estimating contributor DNA fractions

[0518] The contributor DNA fraction β is estimated as the value that maximizes the total likelihood function L(n1, n2|β). As described above, although DNA is referred to in this and other examples, RNA and other nucleic acid molecules can be similarly processed and analyzed. Similarly, although the examples involve nucleic acid mixture samples, the sample may only include nucleic acid from a single contributor, in which case the contributor fraction will be estimated to be 1 or within an error margin from 1.

[0519] During the calculation of L(n1, n2|β), multiple small probability values ​​are multiplied. To avoid numerical underflow when multiplying small probabilities, this embodiment performs all summations and multiplications on a logarithmic scale. The summation of small probabilities on a logarithmic scale is performed as follows. 1) Obtain the maximum value of the logarithmic probability as x max ; 2) Subtract the maximum value from all log probabilities; 3) Raise the resulting value to a power and then sum; 4) Logarithmically transform the sum; 5) Add back the maximum log probability. log(exp(x1-x max )+exp(x2-x max )+...+exp(x n -x max ))+x max .

[0520] To ensure that the positive contributor score is between 0 and 1, a logit transformation β = 1 / (1 + e -η ).

[0521] As described below, a novel numerical optimization computer strategy is implemented that seamlessly integrates iterative grid search with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method.

[0522] Step 1: Grid initialization method generates an even grid in N-1 dimensional space, where N is the number of contributors. In applications with only two contributors, to ensure global optimization and avoid local optimality, the total likelihood function is initialized to β0 = 1 / (1+e -η 0), where η0 is -10, -9.9, -9.8, ..., -0.1, 0, which makes L(n1, n2|β0 = 1 / (1+e -η 0)). In applications with multiple contributors, β is transformed using a softmax and then initialized on a high-dimensional grid.

[0523] Step 2: Perform an exhaustive search on the grid to identify the mixture fraction that minimizes -log2(L).

[0524] Step 3: Initialize with the identified mixture fraction and then numerically optimize η using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method that minimizes -log2(L). Record the optimized mixture fraction as well as convergence.

[0525] Step 4: Compute the Hessian matrix of -log 2(L) using numerical differentiation of the identified mixture fraction.

[0526] Step 5: Determine the error and confidence interval around the calculated mixture fraction based on the inverse of the Hessian matrix. Also, determine whether the Hessian matrix is ​​positive semidefinite.

[0527] Step 6: If the BFGS optimization has not converged or the Hessian matrix is ​​not positive semidefinite, the process is configured for the next iteration of the optimization. Otherwise, the optimization is completed.

[0528] Step 7: When the next iteration of the optimization is to be performed, a finer N-1 dimensional grid is constructed that covers 2 dimensions around the previously determined η. N-1 The original grid corresponds to the estimated mixture fraction. The process then returns to step 2 for the next iteration of grid search and BFGS optimization.

[0529] A human expert cannot perform all of these steps manually or in their head. Instead, one or more computers are needed to perform these steps.

[0530] Iterative strategy for model S with known genotypes (KGT.IterLM)

[0531] In some embodiments, a single locus likelihood function comprises a binomial distribution and a multi-locus likelihood function is as follows: L(β, λ, π; n1, n2) = Π i [∑ gi BN(n 1i |n i ,·p(g i ,λ,β))·P(g i |π)]

[0532] In some embodiments, the contributors include two contributors, and the likelihood function is: L(β, λ, π; n1, n2) = Π i ∑ g1i，g2i BN(n 1i |n i , p 1i (g 1i , g 2i ,λ,β))·P(g 1i , g 2i |π)

[0533] where L(β, λ, π; n1, n2) is the likelihood of observing the allele count vector n1 to n2 for alleles 1 and 2 given the parameters β and π; p 1i (g 1i , g 2i , λ, β) are probability parameters, which are regarded as p1′ in Table 3, indicating the probability of the genotypes of the two contributors (g 1i , g 2i ) is the probability of allele 1 at locus i; and P(g 1i , g 2i |π) is the a priori joint probability of observing the two contributor genotypes given the population allele frequencies (π).

[0534] In some embodiments, the genotypes of all contributors are known, and the likelihood function is expressed as L(β, λ; n1, n2) = Π i n i ! / (n 1i ! n 2i ! )p 1i n1i p 2i n2i , where p ai =∑ d＝0...D-1g dai β d / [∑ d＝0...D-1 β d ·(∑ a＝1 , 2g dai )]. If all markers are on autosomes, then p ai =1 / 2·∑ d＝0...D-1 g dai β d In matrix notation, this is p←g / 2·β.

[0535] The iterative weighted linear regression method is developed by constructing a cost function that has the same gradient as the gradient of log[L(β; n1, n2)] at each iteration when β = β0:

[0536] E=1 / 2·∑ i n i / [p 1i (β0)·(1-p 1i (β0))]·(n 1i / n i -p 1i (β)) 2 .

[0537] In matrix notation, this is E = 1 / 2·(rp) T ·W 2 (rp), where W = diag([n / (p0·(1-p0))] 1 / 2 ) is a diagonal matrix, and p0=g / 2·β0.

[0538] Given the inputs: r, n, g and λ, perform iterative weighted linear regression by performing the following steps

[0539] Step 1. Initialize β to a probability vector of uniform length D β←[1 / D] D

[0540] Step 2. Correction of computational errors in the genotype matrix g: G←[(1-λ)g+λ(2-g)] / 2

[0541] Step 3: Repeat steps a to e until convergence.

[0542] Step a: Update the expected allele 1 fraction using the previously calculated contributor fraction: p←G·β

[0543] Step b. Calculate the weight of weighted regression W←diag([n / (p·(1-p))] 1 / 2 )

[0544] Step c. Solve the weighted linear regression: β←(W·G) -1 ·(W·r)

[0545] Step d. Ensure non-negativity: For each contributor i, β i ←max(β i ,0)

[0546] Step e. Normalize the probability vector: β←β / ∑ i β i - Normalization

[0547] Estimating confidence intervals

[0548] The lower bound of the confidence interval of the estimate is determined based on the Cramer-Rao inequality: var(θ ML )≥1 / I(θ ML ), where θ ML is the maximum likelihood estimate of the parameter θ, and I(θ ML ) is θ ML Fisher information at . Based on this, the variances of β and c in the above likelihood function can be estimated. Following the Cramér-Rao bound, the standard error is estimated as sqrt(1 / H), where H is the Hessian matrix that can be approximated and estimated using the BFGS-quasi-Newton method.

[0549] We use the following reparameterization to estimate β and c during numerical optimization,

[0550] β=1 / (1+e -η ),

[0551] c=e κ .

[0552] Let I(η) and I(κ) be the Fisher information under parameterization η and κ, then the Fisher information of the original parameters is

[0553] I(β)=I(η)(1 / (β(1-β)) 2

[0554] I(c)=I(k)(1 / c) 2 .

[0555] Therefore, based on the numerical optimization method for estimating the standard deviation, this embodiment has the following transformation,

[0556] std(β)=std(η)·β·(1-β)

[0557] std(β)=std(η)·c.

[0558] sample

[0559] As used herein, a sample comprises "cell-free" (e.g., cfDNA) or cell-bound (e.g., cellular DNA) nucleic acids. Cell-free nucleic acids, including cell-free DNA, can be obtained from biological samples by various methods known in the art, including, but not limited to, plasma, serum, and urine (see, e.g., Fan et al., Proc Natl Acad Sci 105: 16266-16271

[2008] ; Koide et al., Prenatal Diagnosis 25: 604-607

[2005] ; Chen et al., Nature Medicine 2: 1033-1035

[1996] ; Lo et al., Lancet 350: 485-487

[1997] ; Botezatu et al., Clin Chem. 46: 1078-1084, 2000; and Su et al., J Mol. Diagn. 6: 101-107

[2004] ). In order to separate cell-free DNA from cells in a sample, various methods can be used, including but not limited to fractionation, centrifugation (e.g., density gradient centrifugation), DNA-specific precipitation or high-throughput cell sorting and / or other separation methods. Commercially available kits for manual and automatic separation of cfDNA are available (Roche Diagnostics, Indianapolis, IN, Qiagen, Valencia, CA, Macherey-Nagel, Duren, DE). Biological samples containing cfDNA have been used to determine whether there is a chromosomal abnormality, such as trisomy 21, by sequencing assays that can detect chromosomal aneuploidy and / or multiple polymorphisms.

[0560] In various embodiments, DNA present in the sample can be enriched specifically or non-specifically before use (e.g., before preparing a sequencing library). Non-specific enrichment of sample DNA refers to whole genome amplification of sample genomic DNA fragments, which can be used to increase the level of sample DNA before preparing a DNA sequencing library. Non-specific enrichment can be the selective enrichment of one of the two genomes present in a sample containing more than one genome. For example, non-specific enrichment can be the selectivity of cancer genomes in plasma samples, which can be obtained by known methods to increase the relative ratio of cancer to normal DNA in the sample. Alternatively, non-specific enrichment can be the non-selective amplification of two genomes present in the sample. For example, non-specific amplification can be the amplification of cancer and normal DNA in a sample, and the sample contains a mixture of DNA from cancer and normal genomes. The method of whole genome amplification is known in the art. Degenerate oligonucleotide-triggered PCR (DOP), primer extension PCR technology (PEP) and multiple displacement amplification (MDA) are examples of whole genome amplification methods. In some embodiments, a sample containing a mixture of cfDNA from different genomes is not enriched for cfDNA of the genome present in the mixture. In other embodiments, a sample comprising a mixture of cfDNA from different genomes is non-specifically enriched for any one genome present in the sample.

[0561] For example, as described above, samples containing nucleic acids to which the methods described herein are applied generally include biological samples ("test samples"). In some embodiments, the nucleic acids to be analyzed are purified or isolated by any of a number of well-known methods.

[0562] Thus, in certain embodiments, the sample comprises or consists of: purified or isolated polynucleotides, or it may comprise a sample such as a tissue sample, a biological fluid sample, a cell sample, etc. Suitable biological fluid samples include, but are not limited to, blood, plasma, serum, sweat, tears, sputum, urine, sputum, ear flow, lymph, saliva, cerebrospinal fluid, wound exudate (ravages), bone marrow suspension, vaginal flow, transcervical lavage, brain fluid, ascites, milk, secretions of the respiratory tract, intestinal and urogenital tracts, amniotic fluid, milk, and leukocyte samples. In some embodiments, the sample is a sample that is easily obtained by a non-invasive process, such as blood, plasma, serum, sweat, tears, sputum, urine, sputum, ear flow, saliva, or feces. In certain embodiments, the sample is a peripheral blood sample, or a plasma and / or serum fraction of a peripheral blood sample. In other embodiments, the biological sample is a swab or smear, a biopsy specimen, or a cell culture. In another embodiment, the sample is a mixture of two or more biological samples, for example, the biological sample can include two or more biological fluid samples, tissue samples and cell culture samples. As used herein, the terms "blood", "plasma" and "serum" clearly encompass fractions or processed portions thereof. Similarly, in the case of samples obtained from biopsies, swabs, smears, etc., "sample" clearly encompasses processed fractions or portions obtained from biopsies, swabs, smears, etc.

[0563] In certain embodiments, samples can be obtained from sources including, but not limited to, samples from different individuals, samples from different developmental stages of the same or different individuals, samples from different diseased individuals (e.g., individuals suffering from cancer or suspected of having a genetic disease), samples from normal individuals, samples obtained at different stages of an individual's disease, samples obtained from individuals undergoing different treatments for a disease, samples from individuals exposed to different environmental factors, samples from individuals with susceptibility to a pathology, samples from individuals exposed to an infectious pathogen (e.g., HIV), etc.

[0564] In an illustrative but non-limiting embodiment, the sample is a recipient sample obtained from a recipient of an organ transplant, such as a plasma sample from a recipient, which includes cfDNA derived from the recipient and cfDNA derived from tissue or organs transplanted from a donor. In this case, the sample can be analyzed using the method described herein to quantify the recipient and donor DNA portions. The recipient sample can be a tissue sample, a biological fluid two-body sample, or a cell sample. As a non-limiting example, biological fluids include blood, plasma, serum, sweat, tears, sputum, urine, sputum, ear flow, lymph, saliva, cerebrospinal fluid, wound exudate, bone marrow suspension, vaginal flow, cervical lavage, brain fluid, ascites, milk, respiratory tract, intestinal and urogenital tract secretions and white blood cell samples.

[0565] In another illustrative but non-restrictive embodiment, the recipient sample is a mixture of two or more biological samples, for example, the biological sample can include two or more biological fluid samples, tissue samples and cell culture samples. In some embodiments, the sample is a sample that is easy to obtain by a non-invasive process, such as blood, blood plasma, serum, sweat, tears, sputum, urine, milk, sputum, ear flow, saliva and feces. In some embodiments, the biological sample is a peripheral blood sample, and / or its blood plasma and serum part. In other embodiments, the biological sample is a swab or smear, a biopsy sample or a cell culture sample. As mentioned above, the terms "blood", "blood plasma" and "serum" clearly cover its fraction or processing part. Similarly, in the case of obtaining a sample from a biopsy, a swab, a smear, etc., "sample" clearly covers the processed fraction or part obtained from a biopsy, a swab, a smear, etc.

[0566] In certain embodiments, samples can also be obtained from tissues, cells or other sources containing polynucleotides cultured in vitro. Cultured samples can be taken from cultures (e.g., tissues or cells) maintained under different culture media and conditions (e.g., pH, pressure or temperature), cultures (e.g., tissues or cells) maintained over different lengths of time, cultures (e.g., tissues or cells) treated with different factors or reagents (e.g., candidate drugs or modulators), or cultures of different types of tissues and / or cells.

[0567] Methods for isolating nucleic acids from biological sources are well known and will vary depending on the nature of the source. As required by the methods described herein, those skilled in the art can easily isolate nucleic acids from sources. In some cases, it may be advantageous to fragment the nucleic acid molecules in the nucleic acid sample. Fragmentation can be random or specific, such as achieved by digestion with restriction endonucleases. Random fragmentation methods are well known in the art and include, for example, limited DNA enzyme digestion, alkali treatment, and physical shearing. In one embodiment, the sample nucleic acid is obtained in the form of cfDNA, which is not fragmented.

[0568] Sequencing library preparation

[0569] In one embodiment, the method described herein can utilize next generation sequencing technology (NGS), which allows multiple samples to be sequenced as genomic molecules (i.e., single sequencing) or a combined sample (e.g., multiple sequencing) comprising indexed genomic molecules in a sequencing run. These methods can generate reads of up to hundreds of millions of DNA sequences. In a plurality of embodiments, the sequence of genomic nucleic acids and / or the genomic nucleic acids of the index can be determined using the next generation sequencing technology (NGS) described herein, for example. In a plurality of embodiments, one or more processors as described herein can be used to perform analysis of a large amount of sequence data obtained using NGS.

[0570] In various embodiments, the use of such sequencing techniques does not involve the preparation of sequencing libraries.

[0571] However, in certain embodiments, the sequencing methods considered herein relate to the preparation of sequencing libraries. In an illustrative method, the preparation of sequencing libraries relates to the production of random collections of adaptor-modified DNA fragments (e.g., polynucleotides) ready to be sequenced. The sequencing libraries of polynucleotides can be prepared from DNA or RNA, including equivalents and analogs of DNA or cDNA, such as DNA or cDNA of complementary or copied DNA produced from RNA templates, by the action of reverse transcriptase. Polynucleotides can originate in double-stranded form (e.g., dsDNA, such as genomic DNA fragments, cDNA, PCR amplification products, etc.), or in certain embodiments, polynucleotides can originate in single-stranded form (e.g., ssDNA, RNA, etc.) and have been converted to dsDNA form. For example, in certain embodiments, single-stranded mRNA molecules can be copied into double-stranded cDNA suitable for preparing sequencing libraries. The precise sequence of a primary polynucleotide molecule is generally unimportant to the library preparation method and can be known or unknown. In one embodiment, the polynucleotide molecule is a DNA molecule. More particularly, in certain embodiments, the polynucleotide molecule represents the entire genetic complement of an organism or substantially the entire genetic complement of an organism, and is a genomic DNA molecule (e.g., cellular DNA, cell-free DNA (cfDNA), etc.), typically including intron sequences and exon sequences (coding sequences), as well as non-coding regulatory sequences, such as promoter and enhancer sequences. In certain embodiments, the primary polynucleotide molecule comprises a human genomic DNA molecule, such as a cfDNA molecule present in the peripheral blood of a pregnant subject.

[0572] The preparation of sequencing libraries for some NGS sequencing platforms is facilitated by using polynucleotides containing a specific range of fragment sizes. The preparation of such libraries generally involves fragmentation of large polynucleotides (e.g., cellular genomic DNA) to obtain polynucleotides of the desired size range.

[0573] Fragmentation can be achieved by any of a variety of methods known to those skilled in the art. For example, fragmentation can be achieved by mechanical means, including but not limited to nebulization, sonication, and hydrodynamic shearing. However, mechanical fragmentation typically cleaves the DNA backbone at CO, PO, and CC bonds, resulting in a heterogeneous mix of blunt ends and 3′- and 5′-overhangs with broken CO, PO, and / or CC bonds (e.g., see Alnemri and Liwack, J Biol. Chem 265:17323-17333

[1990] ; Richards and Boyer, J Mol Biol 11:327-240

[1965] ), which may need to be repaired because they may lack the 5′-phosphate required for subsequent enzymatic reactions, such as the ligation of sequencing adapters required to prepare sequencing DNA.

[0574] In contrast, cfDNA typically exists in fragments of less than about 300 base pairs, and therefore, fragmentation is generally not required for generating sequencing libraries using cfDNA samples.

[0575] Typically, whether polynucleotides are forcibly fragmented (e.g., in vitro fragmentation) or exist naturally as fragments, they are converted to blunt-ended DNA with a 5'-phosphate and a 3'-hydroxyl group. Standard protocols, such as those for sequencing using the Illumina platform described elsewhere herein, instruct the user to end-repair sample DNA, to purify the end-repaired products prior to dA tailing, and to purify the dA-tailed products prior to the adapter ligation step of library preparation.

[0576] The various embodiments of the sequence library preparation methods described herein eliminate the need to perform one or more steps that are typically mandatory by standard protocols to obtain modified DNA products that can be sequenced by NGS. The abbreviated method (ABB method), the 1-step method, and the 2-step method are examples of methods for preparing sequencing libraries, which can be found in patent application 13 / 555,037 filed on July 20, 2012, which is incorporated by reference in its entirety.

[0577] Sequencing methods

[0578] As indicated above, the prepared samples (eg, sequencing libraries) are sequenced as part of the process of quantifying and deconvoluting the DNA mixture sample. Any of a variety of sequencing techniques can be used.

[0579] Several sequencing technologies are commercially available, such as the hybridization sequencing platform from Affymetrix (Sunnyvale, California) and the synthesis sequencing platform from 454 Life Sciences (Bradford, Connecticut), Illumina / Solexa (from Hayward, California) and Helicos Biosciences (Cambridge, Massachusetts), and the ligation sequencing platform from Applied Biosystems (Foster City, California). In addition to performing single molecule sequencing using synthesis sequencing from Helicos Biosciences, other single molecule sequencing technologies include, but are not limited to, SMRT from Pacific Biosciences. TM Technology, ION TORRENT TM technologies and nanopore sequencing, for example, developed by Oxford Nanopore Technologies.

[0580] Although the automated Sanger method is considered a "first generation" technique, Sanger sequencing, including automated Sanger sequencing, can also be used in the methods described herein. Other suitable sequencing methods include, but are not limited to, nucleic acid imaging techniques, such as atomic force microscopy (AFM) or transmission electron microscopy (TEM). Illustrative sequencing techniques are described in more detail below.

[0581] In one illustrative but non-limiting embodiment, the methods described herein include using Illumina's synthetic sequencing and reversible terminator-based sequencing chemistry (e.g., as described in Bentley et al., Nature 6: 53-59

[2009] ), to obtain sequence information of nucleic acids in a test sample, such as cfDNA in a recipient sample, including donor DNA and recipient DNA, cfDNA, or cell DNA of a subject being screened for cancer, etc. The template DNA can be genomic DNA, such as cell DNA or cfDNA. In some embodiments, genomic DNA from isolated cells is used as a template and is fragmented into a length of several hundred base pairs. In other embodiments, cfDNA is used as a template, and fragmentation is not required because cfDNA exists as short fragments. For example, fetal cfDNA circulates in the bloodstream in fragments of about 170 base pairs (bp) in length (Fan et al., Clinical Chemistry 56: 1279-1286

[2010] ), and fragmentation of DNA is not required before sequencing. Circulating tumor DNA also exists as short fragments with a size distribution that peaks at approximately 150-170 bp. Illumina’s sequencing technology relies on attaching fragmented genomic DNA to a flat, optically transparent surface to which oligonucleotide anchors are bound. The template DNA is end-repaired to generate 5′-phosphorylated blunt ends, and the polymerase activity of the Klenow fragment is used to add a single A base to the 3′ end of the blunt phosphorylated DNA fragment. This addition prepares the DNA fragment for ligation to an oligonucleotide adapter, which has an overhang of a single T base at its 3′ end to increase ligation efficiency. The adapter oligonucleotide is complementary to the flow cell anchor oligonucleotide (not to be confused with the anchor / anchor read in repeat amplification analysis). Under limiting dilution conditions, adapter-modified single-stranded template DNA is added to the flow cell and immobilized by hybridization to the anchor oligonucleotide. The attached DNA fragments are extended and bridge amplified to create an ultra-high-density sequencing flow cell with hundreds of millions of clusters, each containing approximately 1000 copies of the same template. In one embodiment, the randomly fragmented genomic DNA is amplified using PCR before being subjected to cluster amplification. Alternatively, a genome library preparation without amplification (e.g., PCR-free) is used, and cluster amplification is used alone to enrich the randomly fragmented genomic DNA (Kozarewa et al., Nature Methods, Issue 6: 291-295

[2009] ). The template is sequenced using a powerful four-color DNA synthesis sequencing technology that uses a reversible terminator and a removable fluorescent dye. Highly sensitive fluorescence detection can be achieved using laser excitation and total internal reflection optics. Short sequence reads of about tens to hundreds of base pairs are aligned with a reference genome, and a specially developed data analysis pipeline software is used to identify the unique mapping of short sequence reads to the reference genome.After the first read is complete, the template can be regenerated in situ to perform a second read from the other end of the fragment. Thus, single-end or double-end sequencing of DNA fragments can be used.

[0582] Multiple embodiments of the present disclosure can use synthetic sequencing that allows paired end sequencing.In some embodiments, the sequencing of the synthesis platform of Illumina involves clustering of fragments.Clustering is the process that each fragment molecule is amplified isothermally.In some embodiments, as the example described here, the fragment has two different adapters attached to the two ends of the fragment, and the adapter allows the fragment to hybridize with two different oligonucleotides on the surface of the flow cell swimming lane.The fragment further includes or is connected to two index sequences at the two ends of the fragment, and the index sequence provides a label to identify different samples in multiple sequencing.In some sequencing platforms, the fragment to be sequenced is also referred to as an insert.

[0583] In some embodiments, the flow cell used for clustering in the Illumina platform is a slide with lanes. Each lane is a glass channel coated with two types of oligonucleotides. The first of the two types of oligonucleotides on the surface makes hybridization possible. The oligonucleotide is complementary to the first adapter on one end of the fragment. The polymerase produces a complementary strand of the hybridized fragment. The double-stranded molecule is denatured, and the original template strand is washed away. The remaining strand is parallel to many other remaining strands and is cloned and amplified by bridging application.

[0584] In bridge amplification, the chains overlap and the second adapter region on the second end of the chain hybridizes to a second type of oligonucleotide on the surface of the flow cell. The polymerase generates a complementary chain, forming a double-stranded bridge molecule. This double-stranded molecule is denatured, resulting in two single-stranded molecules tethered to the flow cell by two different oligonucleotides. The process is then repeated over and over again and occurs simultaneously for millions of clusters, resulting in clonal amplification of all fragments. After bridge amplification, the reverse strand is cut and washed away, leaving only the forward strand. The 3′ end is blocked to prevent unwanted priming.

[0585] After clustering, sequencing begins with extension of the first sequencing primer to generate the first read. In each cycle, fluorescently labeled nucleotides compete for addition to the growing chain. Only one is incorporated based on the sequence of the template. After each nucleotide is added, the cluster is excited by a light source and emits a characteristic fluorescent signal. The number of cycles determines the length of the read. The emission wavelength and signal intensity determine the base calls. For a given cluster, all identical chains are read simultaneously. Hundreds of millions of clusters are sequenced in a massively parallel manner. After the first read is completed, the products of the read are washed away.

[0586] In the next step of the protocol involving two index primers, the Index 1 primer is introduced and hybridized to the Index 1 region on the template. The Index region provides identification of the fragments, which is used to demultiplex the samples during multiplex sequencing. The Index 1 read is generated similarly to the first read. After the Index 1 read is completed, the product of the read is washed away and the 3' end of the strand is deprotected. The template strand is then overlapped and bound to the second oligonucleotide on the flow cell. The Index 2 sequence is read in the same manner as Index 1. The Index 2 read product is then washed out at the completion of this step.

[0587] After reading the two indexes, read 2 is initiated by extending the second flow cell oligonucleotide using a polymerase to form a double-stranded bridge. The double-stranded DNA is denatured and the 3′ end is blocked. The initial positive strand is cut and washed away, leaving the reverse strand. Read 2 begins with the introduction of the read 2 sequencing primer. As with read 1, the sequencing steps are repeated until the desired length is reached. The read 2 product is washed away. This entire process generates millions of reads representing all fragments. Sequences from the merged sample library are separated based on the unique index introduced during sample preparation. For each sample, similar fragment reads for base calls are locally clustered. The forward and reverse reads are paired to create continuous sequences. These continuous sequences are aligned to the reference genome for variant identification.

[0588] The synthetic sequencing examples described above involve paired-end reads, which are used in many embodiments of the disclosed methods. Paired-end sequencing involves two reads at both ends of a fragment. When a pair of reads is mapped to a reference sequence, the base pair distance between the two reads can be determined, which can then be used to determine the length of the fragment from which the read was obtained. In some cases, one of a pair of end reads of a fragment spanning two bands will align to one band, while the other will align it to an adjacent band. This becomes less and less common as the bands become longer or the reads become shorter. Various methods can be used to interpret the band membership of these fragments. For example, they can be omitted when determining the fragment size frequency of the band; they can be counted for two adjacent bands; they can be assigned to the band containing the larger number of base pairs of the two bands; or they can be assigned to both bands with a weight related to the portion of the base pairs in each band.

[0589] Paired end reads can use inserts of different lengths (i.e., different fragment sizes to be sequenced). As the default meaning in the present disclosure, paired end reads are used to refer to reads obtained from various insertion lengths. In some cases, it is used to distinguish short insertion paired end reads from long insertion paired end reads, the latter also referred to as partner pair reads. In some embodiments involving partner pair reads, two biotin-linked adapters are first attached to the two ends of a relatively long insert (e.g., several kb). Then, the biotin-linked adapter connects the two ends of the insert to form a circular molecule. Sub-fragments containing biotin-linked adapters can then be obtained by further fragmenting the circular molecule. Sub-fragments including the reverse order of the two ends of the original fragment can then be sequenced by the same method as the above-mentioned short insertion paired end sequencing. More detailed information on partner pair sequencing using the Illumina platform is shown in the online publication at the following URL, which is incorporated by reference in its entirety: res|·|illumina|.|com / documents / products / technotes / technote_nextera_matepair_data_processing. Additional information regarding paired-end sequencing can be found in U.S. Pat. No. 7,601,499 and U.S. Patent Publication No. 2012 / 0,053,063, which are incorporated by reference for materials regarding paired-end sequencing methods and apparatus.

[0590] After sequencing the DNA fragments, the sequence reads of a predetermined length, such as 100bp, are mapped to a known reference genome or compared thereto. The reads mapped or compared and their corresponding positions on the reference sequence are also referred to as tags. In one embodiment, the reference genome sequence is the NCBI36 / hg18 sequence, which can be obtained on the World Wide Web at genome dot ucsc dotedu / cgi-bin / hgGateway? org=Human&db=hg18&hgsid=166260105). Alternatively, the reference genome sequence is GRCh37 / hg19, which can be obtained on the World Wide Web at genome dot ucsc dot edu / cgi-bin / hgGateway. Other public sequence information sources include GenBank, dbEST, dbSTS, EMBL (European Molecular Biology Laboratory) and DDBJ (DNA Database of Japan). There are many computer algorithms that can be used to align sequences, including but not limited to BLAST (Altschul et al., 1990), BLITZ (MPsrch) (Sturrock & Collins, 1993), FASTA (Person & Lipman, 1988), BOWTIE (Langmead et al., Genome Biology 10: R25.1-R25.10

[2009] ), or ELAND (Illumina, San Diego, CA, USA). In one embodiment, one end of the clonally expanded copy of the plasma cfDNA molecule is sequenced and processed by bioinformatics alignment analysis on an Illumina Genome Analyzer using the Efficient Large-Scale Alignment of Nucleotide Databases (ELAND) software.

[0591] In one illustrative but non-limiting embodiment, the methods described herein include single molecule sequencing technology using Helicos TrueTrue Molecule Sequencing (tSMS) technology (e.g., as described in Harris TD et al., Science 320: 106-109

[2008] ) to obtain sequence information of nucleic acids in a test sample, such as cfDNA in a recipient sample, including recipient and donor DNA, cfDNA, or cellular DNA in subjects screened for cancer, etc. In the tSMS technology, a DNA sample is cut into chains of approximately 100 to 200 nucleotides, and then a polyA sequence is added to the 3′ end of each DNA chain. Each chain is labeled by adding fluorescently labeled adenosine nucleotides. The DNA chains are then hybridized to a flow cell containing millions of oligo T capture sites fixed to the surface of the flow cell. In certain embodiments, the density of the template can be approximately 100 million templates / cm 2The flow cell is then loaded into the instrument (e.g. HeliScope TM Sequencer), and the laser illuminates the surface of the circulation cell to show the position of each template. A CCD camera can map the position of the template on the circulation cell surface. The template fluorescent label is then cut and washed away. The sequencing reaction begins by introducing DNA polymerase and fluorescently labeled nucleotides. Oligo T nucleic acid is used as a primer. The polymerase incorporates the labeled nucleotides into the primer in a template-guided manner. The polymerase and unincorporated nucleotides are removed. By imaging the surface of the circulation cell, templates that have been directed to incorporate fluorescently labeled nucleotides can be identified. After imaging, the cutting step will remove the fluorescent label, and then the process is repeated with other fluorescently labeled nucleotides until the desired read length is achieved. Sequence information is collected in each nucleotide addition step. Whole genome sequencing performed by single molecule sequencing technology excludes or generally avoids PCR-based amplification in the preparation of the sequencing library, and the method allows the sample to be measured directly rather than a copy of the sample.

[0592] In another illustrative but non-limiting embodiment, the method described herein includes using 454 sequencing (Roche) (e.g., as described in Margulies, M. et al., Nature 437: 376-380

[2005] ) to obtain sequence information of nucleic acids in a test sample, such as cfDNA in a recipient test sample, including recipient and donor DNA, cfDNA or cell DNA in a subject screened for cancer, etc. 454 sequencing generally involves two steps. In the first step, the DNA is sheared into fragments of about 300-800 base pairs, and then the fragments are blunt-ended. Oligonucleotide adapters are then attached to the ends of the fragments. The adapters are used as primers for amplification and sequencing of the fragments. The fragments can be attached to DNA capture beads, such as streptavidin-coated beads, using, for example, adapter B containing a 5′-biotin tag. The fragments attached to the beads are PCR amplified in droplets of an oil-water emulsion. The result is that there are multiple copies of the cloned amplified DNA fragments on each bead. In the second step, the beads are captured in a hole (e.g., a picoliter-sized hole). Pyrophosphate sequencing is performed in parallel for each DNA fragment. The addition of one or more nucleotides generates a light signal that is recorded in a sequencer by a CCD camera. The signal intensity is proportional to the number of nucleotides incorporated. Pyrophosphate sequencing utilizes pyrophosphate (PPi), which is released after the addition of nucleotides. In the presence of 5' adenosine 5'phosphosulfate, PPi is converted to ATP by ATP sulfurylase. Luciferase uses ATP to convert luciferin to oxyluciferin, and the reaction generates light that can be measured and analyzed.

[0593] In another illustrative but non-limiting embodiment, the methods described herein include using SOLiDTM Technology (Applied Biosystems) to obtain sequence information of nucleic acids in test samples, such as cfDNA in recipient test samples, cfDNA or cellular DNA in subjects screened for cancer, etc. TM In ligation sequencing, genomic DNA is sheared into fragments and adapters are attached to the 5' and 3' ends of the fragments to generate a fragment library. Alternatively, internal adapters can be introduced by connecting adapters to the 5' and 3' ends of the fragments, circularizing the fragments, digesting the circularized fragments to generate internal adapters and attaching adapters to the 5' and 3' ends of the resulting fragments to generate a partner pairing library. Next, a clonal bead population is prepared in a microreactor containing beads, primers, templates, and PCR components. After PCR, the template is denatured and the beads are enriched to separate beads with extended templates. The template on the selected beads is 3' modified, which allows binding to a slide. The sequence can be determined by sequentially hybridizing and connecting partially random oligonucleotides to bases (or base pairs) determined by the center identified by a specific fluorophore. After recording the color, the connected oligonucleotides are cut and removed, and the process is then repeated.

[0594] In another illustrative but non-limiting embodiment, the methods described herein include using Pacific Biosciences' Single Molecule Real-Time (SMRT TM ) sequencing technology, to obtain sequence information of nucleic acids in test samples, such as cfDNA in recipient test samples, cfDNA or cellular DNA in subjects screened for cancer, etc. In SMRT sequencing, the continuous incorporation of dye-labeled nucleotides is imaged during DNA synthesis. Single DNA polymerase molecules are attached to the bottom surface of each zero-mode wavelength detector (ZMW detector), which obtains sequence information when phosphorylated nucleotides are incorporated into the growing primer chain. The ZMW detector includes a restriction structure that enables the incorporation of single nucleotides by DNA polymerase against the background observation of fluorescent nucleotides that diffuse rapidly in and out of the ZMW (e.g., in microseconds). It usually takes several milliseconds to incorporate nucleotides into the growing chain. During this period, the fluorescent label is excited and produces a fluorescent signal, and the fluorescent label is cut off. The measurement of the corresponding fluorescence of the dye indicates which base is incorporated. Repeat this process to provide a sequence.

[0595] In another illustrative but non-limiting embodiment, the method described herein includes using nanopore sequencing (e.g., as described in Soni GV and Meller A. Clinical Chemistry 53: 1996-2001

[2007] ) to obtain sequence information of nucleic acids in a test sample, such as cfDNA in a maternal or recipient test sample, cfDNA or cellular DNA in a subject screened for cancer, etc. Nanopore sequencing DNA analysis technology is developed by many companies, including, for example, Oxford Nanopore Technologies (Oxford, UK), Sequenom, NABsys, etc. Nanopore sequencing is a single-molecule sequencing technology by which single-molecule DNA can be directly sequenced as it passes through a nanopore. A nanopore is a small hole, typically about 1 nanometer in diameter. The nanopore is immersed in a conductive fluid and an electric potential (voltage) is applied thereto, resulting in a small amount of current being generated due to the conduction of ions through the nanopore. The amount of current flowing is sensitive to the size and shape of the nanopore. When a DNA molecule passes through a nanopore, each nucleotide on the DNA molecule blocks the nanopore to varying degrees, thereby changing the magnitude of the current passing through the nanopore to varying degrees. Therefore, this change in the current as the DNA molecule passes through the nanopore provides a read of the DNA sequence.

[0596] In another illustrative but non-limiting embodiment, the method described herein includes using a chemically sensitive field effect transistor (chemFET) array (e.g., as described in U.S. Patent Application Publication No. 2009 / 0026082) to obtain sequence information of nucleic acids in a test sample, such as cfDNA in a recipient test sample, cfDNA or cellular DNA in a subject being screened for cancer, etc. In one example of this technology, a DNA molecule can be placed in a reaction chamber, and the template molecule can be hybridized with a sequencing primer bound to a polymerase. The incorporation of one or more triphosphates into a new nucleic acid chain at the 3′ end of the sequencing primer can be recognized by a chemFET as a change in current. The array can have multiple chemFET sensors. In another example, a single nucleic acid can be attached to a bead, and the nucleic acid can be amplified on the bead, and each bead can be transferred to each reaction chamber on the chemFET array, each chamber having a chemFET sensor, and the nucleic acid can be sequenced.

[0597] In another embodiment, the method includes using transmission electron microscopy (TEM) to obtain nucleic acids in a test sample, such as sequence information of cfDNA in a recipient test sample. The method, known as individual molecule placement rapid nanotransfer (IMPRNT), includes single-atom resolution transmission electron microscopy imaging of high molecular weight (150kb or greater) DNA selectively labeled with heavy atom markers, and arranging these molecules on an ultra-thin film in an ultra-dense (3nm chain to chain) parallel array with consistent base spacing. Electron microscopes are used to image molecules on film to determine the position of heavy atom markers and to extract base sequence information from DNA. The method is further described in PCT patent publication WO 2009 / 046445. The method allows sequencing of a complete human genome in less than ten minutes.

[0598] In another embodiment, the DNA sequencing technology is ion torrent single molecule sequencing, which combines semiconductor technology with simple sequencing chemistry to translate chemically encoded information (A, C, G, T) directly into digital information (0, 1) on a semiconductor chip. In fact, when nucleotides are incorporated into the DNA chain by polymerase, hydrogen ions are released as byproducts. Ion torrent uses a high-density array of micro-machined holes to perform this biochemical process in a massively parallel manner. There is a different DNA molecule in each hole. Below the hole is an ion-sensitive layer, and below the ion-sensitive layer is an ion sensor. When a nucleotide (such as C) is added to the DNA template and then incorporated into the DNA chain, a hydrogen ion will be released. The charge of this ion will change the pH of the solution, which can be detected by the ion sensor of ion torrent. The sequencer is essentially the world's smallest solid-state pH meter - the base is detected, directly converted from chemical information to digital information. Then, the ion personal genome machine (PGM) TM ) The sequencer floods the chip with one nucleotide after another. If the next nucleotide flooding the chip does not match, no voltage change will be recorded and no base will be detected. If there are two identical bases on the DNA strand, the voltage will double and the chip will record two identical bases detected. Direct detection allows nucleotide incorporation to be recorded in seconds.

[0599] In another embodiment, the method includes obtaining nucleic acids in a test sample by hybridization sequencing, such as sequence information of cfDNA in a recipient test sample. Hybridization sequencing includes contacting a plurality of polynucleotide sequences with a plurality of polynucleotide probes, wherein each of the plurality of polynucleotide probes can be optionally bound to a substrate. The substrate may be a flat surface comprising an array of known nucleotide sequences. The hybridization pattern of the array can be used to determine the polynucleotide sequences present in the sample. In other embodiments, each probe is bound to a bead, such as a magnetic bead, etc. Hybridization with the beads can be determined and used to identify a plurality of polynucleotide sequences within the sample.

[0600] In some embodiments of the method described herein, the sequence tag mapped comprises about 20bp, about 25bp, about 30bp, about 35bp, about 40bp, about 45bp, about 50bp, about 55bp, about 60bp, about 65bp, about 70bp, about 75bp, about 80bp, about 85bp, about 90bp, about 95bp, about 100bp, about 110bp, about 120bp, about 130, about 140bp, about 150bp, about 200bp, about 250bp, about 300bp, about 350bp, about 400bp, about 450bp, or about 500bp sequencing reads. It is expected that technological progress will make the single-end read greater than 500bp possible, thereby allowing the read greater than about 1000bp when generating paired end reads. In one embodiment, the sequence tag mapped comprises the sequence read of 36bp. Sequence tag mapping is achieved by comparing the sequence of the tag with the reference sequence to determine the chromosomal origin of the sequenced nucleic acid (e.g., cfDNA) molecule, and no specific genetic sequence information is required. A small degree of mismatch (0-2 mismatches per sequence tag) can be allowed to account for minor polymorphisms that may exist between the reference genome and the genome in the mixed sample.

[0601] Typically, multiple sequence tags are obtained per sample. In some embodiments, at least about 1×10 sequences containing 75 bp reads can be obtained by mapping the reads to a reference genome per sample. 5 sequence tags.

[0602] The accuracy required to correctly quantify a DNA mixture sample depends on the variation in the number of sequence tags mapped to the reference genome between samples in a sequencing run (inter-run variability) and the variation in the number of sequence tags mapped to the reference genome in different sequencing runs (inter-run variability). Additional variation may result from using different protocols to extract and purify nucleic acids, prepare sequencing libraries, and use different sequencing platforms.

[0603] Device and system for deconvolution and quantification of nucleic acid mixtures from multiple sources

[0604] Various computer programs are usually used to perform the analysis of sequencing data and the diagnosis derived therefrom. Therefore, some embodiments adopt the processing of data stored in one or more computer systems or other processing systems or transmitted therethrough. Embodiments disclosed herein also relate to devices for performing these operations. The device can be specially constructed for the desired purpose, or it can be a general-purpose computer (or a group of computers) selectively activated or reconfigured by a computer program and / or data structure stored in a computer. In some embodiments, a group of processors performs some or all of the listed analysis operations collaboratively (for example, via a network or cloud computing) and / or in parallel. A processor or a group of processors for performing the method described herein can be of various types, including microcontrollers and microprocessors, such as programmable devices (for example, CPLD and FPGA) and non-programmable devices, such as gate array ASICs or general-purpose microprocessors.

[0605] In addition, some embodiments relate to tangible and / or non-transient computer-readable media or computer program products, which include program instructions and / or data (including data structures) for performing various computer-implemented operations. Examples of computer-readable media include, but are not limited to, semiconductor memory devices, magnetic media such as disk drives, tapes, optical media such as CDs, magneto-optical media, and hardware devices specifically configured to store and execute program instructions, such as read-only memory devices (ROM) and random access memory (RAM). Computer-readable media can be directly controlled by end users, or media can be indirectly controlled by end users. Examples of directly controlled media include media located at user facilities and / or media that are not shared with other entities. Examples of indirectly controlled media include media that users can access indirectly via external networks and / or via services that provide shared resources (such as "clouds"). Examples of program instructions include machine code, such as machine code generated by a compiler, and files containing higher-level code that can be executed by a computer using an interpreter.

[0606] In various embodiments, data or information used in the disclosed methods and apparatus are provided in an electronic format. Such data or information may include reads and labels derived from nucleic acid samples, counts or densities of such labels aligned to specific regions of reference sequences (e.g., aligned to chromosomes or chromosome fragments), reference sequences (including reference sequences that provide only or primarily polymorphisms), detections such as SNV or aneuploidy detections, consulting advice, diagnosis, etc. As used herein, data or other information provided in an electronic format may be used for storage on a machine and for transmission between machines. Typically, data in an electronic format is provided in digital form and may be stored as bits and / or bytes in various data structures, lists, databases, etc. The data may be embodied electronically, optically, or the like.

[0607] One embodiment provides a kind of computer program product, for generating the output indicating the presence or absence of SNV or aneuploidy associated with cancer in the test sample.The computer product may include instructions for executing any one or more of the above-mentioned methods for determining chromosome abnormality.As explained, the computer product may include non-transient and / or tangible computer-readable medium with computer executable or compilable logic (e.g., instruction) recorded thereon, so that the processor can quantify the DNA mixture sample.In one example, the computer product includes a computer-readable medium, and the computer-readable medium includes a computer executable or compilable logic (e.g., instruction) recorded thereon, so that the processor can quantify the DNA mixture sample.

[0608] Sequence information from the sample under consideration can be mapped to a chromosome reference sequence to identify a plurality of sequence tags for each of any one or more chromosomes of interest. In various embodiments, the reference sequence is stored in a database such as a relational database or an object database.

[0609] It should be understood that it is impractical, or even impossible in most cases, for an unassisted person to perform the computational operations of the methods disclosed herein. For example, mapping a single 30 bp read in a sample to any human chromosome may take years of effort without the aid of a computing device.

[0610] The method disclosed herein can be performed using a system for quantifying a DNA mixture sample. The system includes: (a) a sequencer for receiving nucleic acid from a test sample and providing nucleic acid sequence information from the sample; (b) a processor; and (c) one or more computer-readable storage media, which store instructions for executing on the processor to perform the method for quantifying a DNA mixture sample.

[0611] In some embodiments, the method is indicated by a computer-readable medium having stored thereon computer-readable instructions for executing a method for quantifying a DNA mixture sample. Thus, one embodiment provides a computer program product comprising one or more computer-readable non-transitory storage media having stored thereon computer-executable instructions, which, when executed by one or more processors of a computer system, cause the computer system to implement a method for quantifying a DNA mixture sample. The method includes: (a) extracting nucleic acid molecules from a nucleic acid sample; (b) amplifying the extracted nucleic acid molecules; (c) sequencing the amplified nucleic acid molecules using a nucleic acid sequencer to generate nucleic acid sequence reads; (d) mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence by one or more processors; (e) using the mapped nucleic acid sequence reads and determining by one or more processors the allele counts of the nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci; and (f) using a probabilistic mixture model and quantifying by one or more processors one or more fractions of nucleic acid from one or more contributors in the nucleic acid sample, wherein using the probabilistic mixture model includes applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and wherein the probabilistic mixture model models the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci using a probability distribution that takes into account errors in the nucleic acid sequence read sequences and counts.

[0612] In some embodiments, the instruction may further include automatically recording information related to the method in the patient's medical record for the human subject providing the recipient test sample. The patient's medical record may be maintained by, for example, a laboratory, a physician's office, a hospital, a health maintenance organization, an insurance company, or a personal medical record website. In addition, based on the result of the analysis implemented by the processor, the method may further include prescribing, starting, and / or changing treatment of the human subject from which the recipient test sample has been obtained. This may involve carrying out one or more other tests or analyses on other samples collected from the subject.

[0613] The disclosed method can also be performed using a computer processing system, which is suitable for or configured to perform a method for quantifying a DNA mixture sample. One embodiment provides a computer processing system, which is suitable for or configured to perform the method described herein. In one embodiment, the device includes a sequencing device, which is suitable for or configured to sequence at least a portion of a nucleic acid molecule in a sample to obtain the type of sequence information described in this other places. The device may also include a component for processing a sample. Such components are described in other places here.

[0614] Sequence or other data can be directly or indirectly input to a computer or stored on a computer readable medium. In one embodiment, a computer system is directly coupled to a sequencing device, and this sequencing device reads and / or analyzes the nucleotide sequence from a sample. The sequence or other information from this type of instrument is provided via the interface in the computer system. Alternatively, the sequence of system processing is provided from a sequence storage source (such as a database or other storage repository). Once it can be used for a processing device, a memory device or a large-capacity storage device at least temporarily buffers or stores the nucleotide sequence. In addition, a memory device can store the label counts of various chromosomes or genomes, etc. Memory can also store various routines and / or programs for analyzing and presenting sequences or mapping data. This type of program / routine can include programs for performing statistical analysis, etc.

[0615] In one example, a user provides a sample to a sequencing device. Data is collected and / or analyzed by a sequencing device connected to a computer. Software on the computer allows data collection and / or analysis. Data can be stored, displayed (via a monitor or other similar device) and / or sent to another location. The computer can be connected to the Internet, which is used to transmit data to a handheld device used by a remote user (e.g., a physician, scientist, or analyst). It should be understood that data can be stored and / or analyzed before transmission. In some embodiments, raw data is collected and sent to a remote user or device that will analyze and / or store data. Transmission can be performed via the Internet, or via satellite or other connections. Alternatively, data can be stored on a computer-readable medium, and the medium can be shipped to an end user (e.g., via mail). Remote users can be in the same or different geographical locations, including but not limited to buildings, cities, states, countries, or continents.

[0616] In some embodiments, the method also includes collecting data about multiple polynucleotide sequences (for example, read order, label and / or reference chromosome sequence), and sending the data to a computer or other computing system. For example, a computer can be connected to laboratory equipment, such as a sample collection device, a nucleotide amplification device, a nucleotide sequencing device or a hybridization device. Then, the computer can collect the applicable data collected by the laboratory equipment. Data can be stored on a computer at any step, for example, before sending, during sending, or in conjunction with real-time information collection during or after sending. Data can be stored on a computer-readable medium that can be extracted from a computer. The collected or stored data can be, for example, transferred to a remote location from a computer via a local area network or a wide area network such as the Internet. As described below, various operations can be performed on the data transmitted at a remote location.

[0617] The types of electronically formatted data that may be stored, transmitted, analyzed, and / or manipulated in the systems, apparatus, and methods disclosed herein are as follows:

[0618] The reads obtained by sequencing the nucleic acids in the test sample

[0619] Tags obtained by aligning reads to a reference genome or one or more other reference sequences

[0620] Reference genome or sequence

[0621] Allele count - the count or number of tags for each allele and region in a reference genome or other reference sequence

[0622] Determined contributor nucleic acid fractions and associated confidence intervals

[0623] Diagnosis (clinical condition associated with detection)

[0624] Recommendations for further testing resulting from detection and / or diagnosis

[0625] Treatment and / or surveillance plan derived from detection and / or diagnosis

[0626] These various types of data can be obtained, stored, transmitted, analyzed, and / or manipulated at one or more locations using different devices. The processing options span a wide spectrum. At one end of the spectrum, all or much of this information is stored and used at the location where the test sample is processed, such as a doctor's office or other clinical location. At the other extreme, the sample is obtained at one location, can be processed and optionally sequenced at a different location, read alignment and detection are performed at one or more different locations, and a diagnosis, recommendation, and / or plan is prepared at another location (which may be the location where the sample was obtained).

[0627] In a number of embodiments, reads are generated with a sequencing device and then transmitted to a remote site where they are processed to generate calls. For example, at the remote location, reads are compared to reference sequences to generate tags, which are counted and assigned to chromosomes or fragments of interest. Also at the remote location, doses are used to generate calls.

[0628] The processing operations that can be adopted at different locations are as follows:

[0629] Sample collection

[0630] Sample processing before sequencing

[0631] Sequencing

[0632] Analyze sequence data and quantify DNA mixture samples

[0633] diagnosis

[0634] Report the diagnosis and / or detection to the patient or healthcare provider

[0635] Develop a plan for further treatment, testing, and / or monitoring

[0636] Execution plan

[0637] consult

[0638] Any one or more operations in these operations can be automatically performed as described in this other place.Usually, the order-checking and analysis of sequence data and the quantitative of DNA mixture samples will be performed by calculation.Other operations can be performed manually or automatically.

[0639] Examples of locations where sample collection can be performed include medical practitioners' offices, clinics, patients' homes (places where sample collection tools or test kits are provided), and mobile medical vehicles. Examples of locations where sample processing can be performed before sequencing include medical practitioners' offices, clinics, patients' homes (places where sample processing devices or test kits are provided), mobile medical vehicles, and facilities of DNA analysis providers. Examples of locations where sequencing can be performed include medical practitioners' offices, clinics, medical practitioners' offices, clinics, patients' homes (places where sample sequencing devices and / or test kits are provided), mobile medical vehicles, and facilities of DNA analysis providers. A dedicated network connection can be provided at the location where sequencing is performed for transmitting sequence data (usually read sequences) in an electronic format. Such connections can be wired or wireless, and have and can be configured to send data to sites that can process and / or aggregate data before being transmitted to a processing site. Data aggregators can be maintained by health organizations such as health maintenance organizations (HMOs).

[0640] The analysis and / or derivation operation can be performed at any one of the aforementioned locations, or alternatively at another remote site dedicated to the service of calculating and / or analyzing nucleic acid sequence data. Such locations include, for example, facilities such as clusters of general server farms, DNA analysis service businesses, etc. In some embodiments, the computing equipment used to perform the analysis is rented or leased. The computing resource can be a part of the Internet accessible set of processors, such as the processing resources commonly known as clouds. In some cases, the calculation is performed in parallel or on a large scale by a group of mutually related or unrelated processors. The processing can be completed using distributed processing such as cluster computing, grid computing, etc. In such embodiments, the cluster or grid of computing resources jointly forms a super virtual computer composed of multiple processors or computers, and the multiple processors or computers work together to perform the analysis and / or derivation described herein. As described herein, these technologies and more conventional supercomputers can be used to process sequence data. Each is a parallel computing form that relies on a processor or a computer. In the case of grid computing, these processors (usually the entire computer) are connected by a conventional network protocol (such as Ethernet) through a network (dedicated, public or Internet). In contrast, a supercomputer has many processors connected by a local high-speed computer bus.

[0641] In certain embodiments, the diagnosis is generated at the same location as the analytical operation. In other embodiments, it is performed at different locations. In certain examples, the report diagnosis is performed at the location of sampling, although not necessarily so. The example of the location that can generate or report diagnosis and / or execute the plan includes the office of medical practitioners, clinics, computer-accessible Internet sites and handheld devices, such as mobile phones, tablet computers, smart phones, etc. with wired or wireless connections of the network. The example of the location of the execution consultation includes the office of health practitioners, clinics, computer-accessible Internet sites, handheld devices, etc.

[0642] In some embodiments, sample collection, sample processing, and sequencing operations are performed at a first location, and analysis and derivation operations are performed at a second location. However, in some cases, sample collection is collected at one location (e.g., a health practitioner's office or clinic), and sample processing and sequencing are performed at a different location, which is optionally the same location where analysis and derivation are performed.

[0643] In a number of embodiments, the order of the operations listed above can be triggered by user or entity starting sample collection, sample processing and / or sequencing. After one or more of these operations begin to be performed, other operations will naturally follow. For example, sequencing operations can cause reads to be automatically collected and sent to a processing device, which then usually automatically and possibly performs sequence analysis and quantifies DNA mixture samples without further user intervention. In some embodiments, the result of the processing operation may then be automatically passed to a system component or entity that reports information to a health professional and / or patient as a diagnosis in a reformatted manner. As explained, such information can also be automatically processed to produce a treatment, test and / or monitoring plan, possibly together with consulting information. Therefore, starting early operations can trigger an end-to-end sequence in which diagnosis, planning, consulting and / or other information useful to a physical condition are provided to health professionals, patients or other interested parties. This can be achieved even if the parts of the entire system are physically separated and may be far away from the location of, for example, a sample and a sequencing device.

[0644] Figure 4 A typical computer system according to certain embodiments is shown in a simple box format, which can be used as a computing device when the computer system is appropriately configured or designed. Computer system 2000 includes any number of processors 2002 (also referred to as central processing units or CPUs) coupled to storage devices, which include main storage devices 2006 (usually random access memory or RAM), main storage devices 2004 (usually read-only memory or ROM). CPU 2002 can be of various types, including microcontrollers and microprocessors such as programmable devices (e.g., CPLD and FPGA), and non-programmable devices such as gate array ASICs or general-purpose microprocessors. In the depicted embodiment, main storage device 2004 is used to transmit data and instructions to CPU unidirectionally, and main storage device 2006 is generally used to transmit data and instructions in a bidirectional manner. Both main storage devices can include any suitable computer-readable medium, such as the above-mentioned medium. Mass storage device 2008 is also bidirectionally coupled to main storage device 2006, and provides additional data storage capacity, and can include any of the above-mentioned computer-readable media. The mass storage device 2008 can be used to store programs, data, etc., and is typically an auxiliary storage medium such as a hard disk. Typically, such programs, data, etc. are temporarily copied to the main memory 2006 for execution on the CPU 2002. It will be understood that the information retained in the mass storage device 2008 can be combined as part of the main storage device 2004 in a standard manner where appropriate. Certain mass storage devices such as CD-ROM 2014 can also pass data unidirectionally to the CPU or the main storage device.

[0645] CPU 2002 is also coupled to interface 2010, which is connected to one or more input / output devices, such as nucleic acid sequencer (2020), video monitor, tracking ball, mouse, keyboard, microphone, touch-sensitive display, transducer card reader, magnetic tape or paper tape reader, tablet computer, stylus, voice or handwriting recognition peripheral device, USB port or other well-known input device, such as other computers. Finally, CPU 2002 can optionally be connected to external devices, such as databases, computers or telecommunications networks using external connections (as shown in 2012). Through such connections, it can be expected that CPU may receive information from the network, or may output information to the network during the execution of the method steps described herein. In some embodiments, instead of or in addition to via interface 2010, nucleic acid sequencer (2020) can also be linked to CPU 2002 via network connection 2012 communication.

[0646] In one embodiment, a system such as computer system 2000 is used as a data import, data association, and query system capable of performing some or all of the tasks described herein. Information and programs including data files may be provided via network connection 2012 for researchers to access or download. Alternatively, such information, programs, and files may be provided to researchers on a storage device.

[0647] In a specific embodiment, the computer system 2000 is directly coupled to a data acquisition system, such as a microarray, a high throughput screening system, or a nucleic acid sequencer (2020) that captures data from a sample. Data from such a system is provided via an interface 2010 for analysis by the system 2000. Alternatively, data processed by the system 2000 is provided from a data storage source such as a database or other repository of relevant data. Once in the device 2000, a memory device such as a main storage device 2006 or a mass storage device 2008 buffers or stores the relevant data at least temporarily. The memory may also store various routines and / or programs for importing, analyzing, and presenting data, including sequence reads, UMIs, codes for determining sequence reads, overlapping sequence reads, and correcting errors in reads, etc.

[0648] In some embodiments, the computer used herein may include a user terminal, which may be any type of computer (e.g., desktop computer, laptop computer, tablet computer, etc.), media computing platform (e.g., cable, satellite set-top box, digital video recorder, etc.), handheld computing device (e.g., PDA, email client, etc.), mobile phone, or any other type of computing or communication platform.

[0649] In certain embodiments, the computer used here can also include a server system communicated with a user terminal, and the server system can include a server device or a decentralized server device, and can include a mainframe computer, a minicomputer, a supercomputer, a personal computer, or a combination thereof. Without departing from the scope of the present invention, multiple server systems can also be used. The user terminal and the server system can communicate with each other through a network. The network can include, for example, a wired network, such as a LAN (local area network), a WAN (wide area network), a MAN (metropolitan area network), an ISDN (integrated services digital network), etc., and a wireless network, such as a wireless LAN, a CDMA, a Bluetooth and a satellite communication network, etc., without limiting the scope of the present invention.

[0650] Figure 5 One embodiment of a decentralized system for generating a detection or diagnosis from a test sample is shown. Sample collection location 01 is used to obtain a test sample from a patient, such as a pregnant woman or a presumed cancer patient. The sample is then provided to a processing and sequencing location 03, where the test sample can be processed and sequenced as described above. Location 03 includes a device for processing the sample and a device for sequencing the processed sample. As described elsewhere herein, the result of sequencing is a collection of reads, which are typically provided in an electronic format and provided to a network, such as the Internet, which is accessed through a computer program. Figure 5 Indicated by reference numeral 05.

[0651] The sequence data is provided to a remote location 07 where analysis and call generation is performed. This location may include one or more powerful computing devices, such as computers or processors. After the computing resources at location 07 complete the analysis and generate a call based on the received sequence information, the call is relayed back to the network 05. In some embodiments, not only is a call generated at location 07, but an associated diagnosis is also generated. The call and / or diagnosis is then transmitted over the network and returned to the sample collection location 01, such as Figure 5 As explained, this is just one of many variations on how the various operations associated with generating a call or diagnosis are divided between various locations. One common variation involves providing sample collection, processing, and sequencing in a single location. Another variation involves providing processing and sequencing at the same location as analysis and call generation.

[0652] Figure 6 Details the options for performing various operations at different locations. Figure 6 In the most granular sense shown in , each of the following operations is performed at a separate location: sample collection, sample processing, sequencing, read alignment, calling, diagnosis, and reporting and / or planning.

[0653] In one embodiment that aggregates some of these operations, sample processing and sequencing are performed in one location, and read alignment, calling, and diagnostics are performed at separate locations. Figure 6 The portion identified by reference character A. Figure 6 In another embodiment identified by character B in FIG, sample collection, sample processing, and sequencing are all performed at the same location. In this embodiment, read alignment and detection are performed at a second location. Finally, diagnosis and reporting and / or planning are performed at a third location. Figure 6 In the embodiment depicted by letter C in FIG, sample collection is performed at a first location, sample processing, sequencing, read alignment, detection, and diagnosis are all performed together at a second location, and reporting and / or planning is performed at a third location. Figure 6 In the embodiment marked D, sample collection is performed at a first location, sample processing, sequencing, read alignment and detection are all performed at a second location, and diagnosis and reporting and / or plan management are performed at a third location.

[0654] One embodiment provides a system for analyzing simple nucleotide variants associated with tumors in cell-free DNA (cfDNA), the system comprising a sequencer for receiving a nucleic acid sample and providing nucleic acid sequence information from the nucleic acid sample; a processor; and a machine-readable storage medium comprising instructions for execution on the processor, the instructions comprising: code for mapping nucleic acid sequence reads to one or more polymorphic loci on a reference sequence; code for determining allele counts of nucleic acid sequence reads of one or more alleles at one or more polymorphic loci using the mapped nucleic acid sequence reads; and code for quantifying one or more fractions of nucleic acid of one or more contributors in the nucleic acid sample using a probabilistic mixture model, wherein using the probabilistic mixture model comprises applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and the probabilistic mixture model uses a probability distribution to model the allele counts of the nucleic acid sequence reads at one or more polymorphic loci, the probability distribution taking into account errors in the nucleic acid sequence reads.

[0655] In some embodiments of any system provided herein, the sequencer is configured to perform next generation sequencing (NGS). In some embodiments, the sequencer is configured to perform large-scale parallel sequencing using synthetic sequencing by reversible dye terminators. In other embodiments, the sequencer is configured to perform connection sequencing. In other embodiments, the sequencer is configured to perform single molecule sequencing.

[0656] Experimental

[0657] Example 1

[0658] This example uses data obtained from actual DNA mixture samples to illustrate that some embodiments can provide higher accuracy and reliability, as well as lower empirical bias, when quantifying DNA mixture samples compared to conventional techniques that do not use the probabilistic methods disclosed herein.

[0659] DNA mixture samples included two DNAs from the genome (contributor), and the minor fractions in different samples were 0.1%, 0.2%, 0.4%, and 2%. Some samples contained 3ng of input DNA, and other samples contained 10ng. Samples were processed with two experimental procedures labeled Nack or Nack2 to indicate two primer designs with different numbers of target loci for the two designs. Some samples were processed using the MiSeq sequencing platform, and others were processed using the MiniSeq platform.

[0660] Sample data were analyzed using three different methods. Table 8 shows the mean value of the coefficient of variation (CV, defined as standard_deviation_of_predictions / true_fraction) values ​​of multiple mixture fractions using three different methods of various samples and experimental processes and the mean value of the coefficient of variation + deviation values ​​of multiple mixture fractions (CVB, usually expressed as CV (RMSD) and defined as RMSD / true_fraction). The first method applies a probability model that includes a binomial distribution for modeling sequencing errors. The first method corresponds to some embodiments described as the Seq model above. The data of the first method (Seq) are shown in the third row of Table 8. The second method applies a probabilistic mixture model, including the probability distribution of explaining DNA extraction errors, PCR amplification errors, and sequencing errors. The second method corresponds to some embodiments described as the "extraction-PCR-Seq model" above. The fourth row of Table 8 shows the data of the second method (EPS).

[0661] The third method corresponds to the benchmark method NaiveLM or also called KGT.NaiveLM as described above. It uses a basic linear regression formula to determine the DNA fraction of a contributor. The fifth row of Table 8 shows the data for the third method (NaiveLM).

[0662] It is worth noting that the genotype information of the contributors was not used to quantify the contributor scores in the Seq or EPS methods, but it was used in the NaiveLM method. Although the Seq method and the EPS method do not require the use of the genotype information of the contributors, they produce more reliable results as indicated by the smaller coefficient of variation values ​​compared to the NaiveLM method. In addition, the Seq method and the EPS method have lower bias, as indicated by the smaller CVB values ​​compared to the NaiveLM method. The best results among the three methods are marked in bold in Table 8. In short, the two methods using the probability mixture model produce more reliable, accurate and less biased results than the linear regression method.

[0663] Table 8. CV and CVB performance metrics of two public methods (Seq and EPS) compared with a baseline method (NaiveLM) on four different datasets.

[0664]

[0665] Example 2

[0666] There are multiple free parameters, such as the average length of the DNA template, the average length of the amplicon, and the molecular weight of the human genome, which are used together with the input DNA amount to estimate the effective input DNA amount and read count. Reasonable adjustment of these parameters can ensure less bias and robust prediction performance. This example studies how the average length of the DNA template affects the performance of various methods of the above-mentioned quantitative DNA mixture.

[0667] This example uses simulated cfDNA (mcfDNA) to simulate real cfDNA. In order to obtain the correct real cfDNA correction factor, we need to 1) generate a similar standard mixture using real cfDNA extracted from two individuals; 2) perform gDNA spike-in in the experiment of the actual cfDNA mixture.

[0668] Source genome

[0669] mcfDNA: mcfDNA from a test cell line for which the Nack4 target site has no CNV.

[0670] cfDNA: cfDNA from healthy people, not from the mother

[0671] gDNA: gDNA from the tested cell line or one of the normal cell lines

[0672] Mixture composition design

[0673] Mix 1: 75% cfDNA or mcfDNA, 25% gDNA

[0674] Mix 2: 50% cfDNA or mcfDNA, 50% gDNA

[0675] Mix 3: 25% cfDNA or mcfDNA, 75% gDNA

[0676] Mix 4: 10% cfDNA or mcfDNA, 90% gDNA

[0677] Each mixture had 3 replicates.

[0678] Mixed strategies

[0679] 1. Quantify cfDNA and gDNA templates;

[0680] 2. Mix cfDNA and gDNA templates in ratios of 3:1, 1:1, 1:3, and 1:9;

[0681] 3. Perform PCR on the mixed template.

[0682] The obtained mixture and its composition are shown in Table 9.

[0683] Table 9. Simulated and real DNA mixtures and estimated mixture fractions, reflecting the effect of cfDNA / mcfDNA length on their relative effectiveness as PCR templates. Each type of mixture had three replicates.

[0684] Mixture Fraction mcfDNA+gDNA cfDNA+gDNA Mixture 1 (75%) 82.9％，84.0％，84.9％ 68.6％，68.8％，69.1％ Mixture 3 (25%) 14.2％，14.5％，14.4％ 20.5％，20.2％，20.0％ Mix 4 (10%) 5.37％，5.51％，5.40％ 8.94％，8.86％，9.09％

[0685] Figure 7 The CVB performance of various methods at different choices of cfDNA length parameters are shown. The following lengths were evaluated: 120 bp, 130 bp, 140 bp, 150 bp, 160 bp, 216 bp, 300 bp, 409 bp and 100 k bp. Different shades of the bars indicate different mcfDNA lengths.

[0686] The different methods are marked below.

[0687] S: Probabilistic model that takes into account errors due to sequencing. No benchmark genome is used as input (D and R genomes are not known).

[0688] EPS: A probabilistic model that takes into account errors due to DNA extraction, PCR, and sequencing. Does not use a benchmark genome as input.

[0689] PUGT.EPS00: A generic implementation of the EPS model that allows known, unknown, and partially known benchmarks. Does not use a benchmark genome as input.

[0690] PUGT.EPS: A general implementation of the EPS model that allows known, unknown, and partially known benchmarks. Uses a benchmark genome as input.

[0691] KGT.IterLM: Iterative linear model. Uses a benchmark genome as input.

[0692] KGT.Seq: A probabilistic model that takes into account errors due to sequencing. Uses a benchmark genome as input.

[0693] KGT.NaiveLM: Baseline method, naive linear model with known genotypes. Uses a benchmark genome as input.

[0694] The EPS model has the best performance (indicated by the arrow) at the default DNA length parameter of 160 bp, both when the benchmark genome is available and when it is not available.

[0695] Furthermore, even if the practitioner perturbs the DNA length parameter from 160 bp to 120 bp or to 216 bp, the quantitative performance of the EPS method remains excellent. This indicates the robustness of the method to the cfDNA length parameter. This range is much wider than the parameters used in the above embodiments, which are 160 bp for mcfDNA and 165 bp for cfDNA.

[0696] The performance ranking between different methods is:

[0697] PUGT.EPS (using the benchmark genome) > KGT.seq or KGT.IterLM (using the benchmark genome) > PUGT.EPS or EPS (not using the benchmark genome) > S (not using the benchmark genome) > KGT.Naive (using the benchmark genome).

[0698] It is noteworthy that the three EPS methods have significantly lower CVBs than the naive linear model with known genotypes, indicating that the EPS methods have improved accuracy and reduced bias over the conventional linear model methods. Note that the conventional methods are only applicable to mixture samples with known reference genomes.

[0699] In addition, under the default DNA length parameters, the methods described in the present disclosure have lower limit of blank (LOB) and higher analytical sensitivity than the methods using the conventional linear model. As shown in Table 10, the limit of blank (LOB) of the four disclosed methods is less than 0.1%, but the LOB of the conventional naive linear model method is 0.42%.

[0700] Table 10. LOBs of different methods

[0701] method S PUGT.EPS00 PUGT.EPS KGT.seq KGT.NaiveLM LOB 0.05％ 0.08％ 0.06％ 0.03％ 0.42％

[0702] Example 3

[0703] This example uses data obtained from simulated cfDNA (mcfDNA) and actual genomic DNA (gDNA) to investigate the sensitivity of some published methods and compares them to a known method, KIMERDx, that uses qPCR technology.

[0704] Table 11 shows the LOQs for the two probit models labeled as follows.

[0705] EPS: A probabilistic model that takes into account errors due to DNA extraction, PCR, and sequencing. Does not use a benchmark genome as input.

[0706] PUGT.EPS: A general implementation of the EPS model that allows known, unknown, and partially known benchmarks. Uses a benchmark genome as input.

[0707] LOQ or limit of quantitation is a measure of the sensitivity of quantitation. It is defined as the smallest donor fraction that can be determined with a coefficient of variation (CV) of no more than 20%.

[0708] Under mcfDNA conditions simulating cfDNA samples from solid organ transplant patients (the first two rows of data in Table 11), DNA mixture samples from two contributors were generated. Each sample included 3ng DNA. The probability methods PUGT.EPS (using the benchmark genotype) and EPS (not using the benchmark genotypes of the recipient and donor before transplantation) were applied to 5 samples x 3 replicates. When only 3ng of input DNA was used, the two probability methods achieved LOQs of ≤0.2%, indicating that both published methods have high sensitivity.

[0709] Under the gDNA conditions simulating blood gDNA samples from bone marrow transplant patients (the third row of data in Table 11), a DNA mixture sample of two contributors was generated. Each sample included 10ng DNA. The PUGT.EPS method was used to analyze 5 samples x 3 replicates. When using 10ng input DNA, the PUGT.EPS method achieved a LOQ of ≤0.1%, which, as expected, was lower than the LOQ under mefDNA conditions using 3ng input DNA.

[0710] Under another gDNA condition (four rows of data in Table 11), a DNA mixture sample of five contributors was generated. Each sample included a total amount of 10ng of DNA. The PUGT.EPS method was used to analyze 5 samples x 3 replicates. The PUGT.EPS method achieved a LOQ of ≤0.35%. Even in such a difficult situation (with five contributors), the method obtained a LOQ significantly lower than 1%.

[0711] Table 11. Sensitivity of the published methods

[0712] Sample type LOQ Sample size method mcfDNA 3ng, 2 contributors 0.2％ 5 samples x3 PUGT.EPS mcfDNA 3ng, 2 contributors 0.2％ 5 samples x3 EPS (no benchmark) gDNA 10ng, 2 contributors 0.1％ 5 samples x3 PUGT.EPS gDNA 10ng, 5 contributors 0.35％ 4 samples x3 PUGT.EPS

[0713] Table 12 shows the sensitivity (LOQ) values ​​of the KIMERDx method using qPCR technology for a mixture sample of only two contributors. The KIMERDx method was used to analyze different amounts of input gDNA. To achieve a LOQ of 0.1%, 66ng of input gDNA was required. In contrast, the PUGT.EPS method only requires <=10ng of input DNA to achieve the same level of sensitivity. With 10ng of input gDNA, KIMERDx will reach a LOQ of 0.7% compared to <0.1% for PUGT.EPS.

[0714] Table 12. Sensitivity of the qPCR KIMERDx method

[0715] LOQ Cell number Input DNA (ng) 0.05％ 20000 132 0.1％ 10000 66 1％ 1000 7 2％ 500 3 5％ 200 1

[0716] Thus, this example illustrates that the disclosed probabilistic methods require significantly less input DNA to achieve the same level of sensitivity compared to prior art methods. In contrast, the disclosed methods achieve significantly higher sensitivity at low input DNA amounts. Due to their increased sensitivity, these methods may allow faster sample processing, require less reagents and improve the accuracy of DNA mixture quantification.

[0717] Existing chimerism assays are not applicable to solid organ transplantation surveillance, for which our method is designed. The disclosed method improves the sensitivity of DNA mixture quantification, which is particularly beneficial in applications where the amount of input DNA is limited, which covers all solid organ transplantation situations. The use of cfDNA for solid organ transplantation surveillance is challenging because the amount of cfDNA extracted from a typical blood sample is usually <10 ng, which is much lower than the amount of gDNA that can be extracted. At the same time, cfDNA is much less effective as a PCR template compared to an equal amount of gDNA.

[0718] Existing methods are also not suitable for transplants with more than one donor, for which our disclosed method still achieves high sensitivity. Transplants with more than one donor frequently occur in bone marrow transplants and are also common in organ transplants with blood transfusions and in patients with previous organ transplants.

[0719] Example 4

[0720] Conventional methods for mosaicism analysis utilize capillary electrophoresis (CE) fragment analysis or quantitative polymerase chain reaction (qPCR) analysis of short tandem repeats (STRs) or small insertions and deletions (Indels). These methods have many method-related disadvantages, including limit of quantitation, dynamic range, number of targets, workflow, analysis, and reproducibility. An alternative to these conventional methods is to utilize next-generation sequencing (NGS) targeting hundreds of SNPs to quantitatively assess mosaicism with low limits of quantitation, wide dynamic range, simple workflow, automated analysis, and robust reproducibility.

[0721] Conventional chimerism analysis using CE

[0722] Target: STR

[0723] STRs are loci found throughout the genome. They consist of short sequences, usually between 2 and 8 nucleotides, most commonly 4, which are repeated in tandem (e.g. gata tandem repeats as gatatagatagatagata). The number of repeats varies between 4 and 40 repeats, making the length of a typical STR less than 400 total nucleotides. The number of repeats varies widely within a population. These two characteristics of STRs, their relatively short total length and high variability, make them an attractive target for human identification in forensics. The short length is important for poor quality forensic samples, as it is difficult to amplify larger regions with these types of samples. The high variability within a population is an attractive feature because a relatively small number is required to make a positive identification. Although more than 100 STRs have been well characterized in the human genome, most applications use fewer than 30 STRs.

[0724] Assay design

[0725] PCR primers are designed in conserved flanking regions around the STRs. Primers can be multiplexed with four fluorophores containing 4 to 7 STRs of varying lengths. This means that multiplexing supports 10 to 21 unique STRs. The CE system measures relative fluorescence units and elapsed time for detection to generate an electropherogram of each STR. Most laboratories utilize the full multiplex to generate a pre-transplant baseline genotype for both the recipient and the donor. The pre-transplant genotypes are compared to each other to select informative markers, markers for which the recipient and donor have unique alleles. Chimeric samples can be analyzed with the entire multiplex or with a single monoplex of informative STRs. Monoplex assays generally provide the highest level of sensitivity, but many laboratories prefer to perform multiplex assays.

[0726] Workflow

[0727] Extract DNA from peripheral blood, bone marrow, or cell lineages using magnetic beads or flow cytometry.

[0728] Perform PCR amplification of target STRs, including fluorescent labeling.

[0729] Separation and detection of STR-PCR amplicons is performed by electrophoresis (most commonly on CE instruments). CE systems measure relative fluorescence units and elapsed time to detect the electropherogram for each allele present in the sample.

[0730] The person performing the analysis examines the electropherogram for each informative marker to determine the relative frequency of the donor relative to the recipient. In cases with multiple informative markers, the average frequency is usually taken as the final measure of chimerism, after accounting for the variable performance of the different markers.

[0731] The time from DNA extraction to data analysis was approximately 7 hours, with hands-on time of approximately 2 hours. Analysis of the data was highly variable, with analysis of a single chimeric sample taking anywhere from 15 minutes to two hours, depending on the number of informative markers, the variability between markers, and the complexity of stochastic peak subtraction.

[0732] limitation

[0733] There are three major limitations to CE analysis of STR regions for mosaicism analysis.

[0734] First, individual electrophoretic peaks are often difficult to analyze, and the chimera percentages from multiple peaks within the same sample often vary by 10-15%. Due to this variability, analysis of a single sample often takes hours, and the results are still semi-quantitative.

[0735] Second, the method’s limit of quantitation (LOQ), often referred to as the limit of detection (LOD) or sensitivity, ranges from 1% to 5%. This wide range exists because each STR will have its own LOQ, depending on the PCR enzyme’s stuttering or “slippage” on the STR and the variable performance of the fluorophore.

[0736] Third, although more than 100 STR targets are well characterized in the genome, including more than 21 STRs in an assay is not reliable. This is because multiplexing many specific primer pools into a single assay is very difficult to make robust and reliable. Therefore, chimeric mixtures from closely related individuals may have difficulty identifying informative markers, and the cases of many donors may be difficult to analyze.

[0737] These limitations may be significant in clinical use. For example, a chimeric result of 99% would be reported as 100%.

[0738] Routine mosaic analysis using qPCR

[0739] Target: Indel

[0740] Indels are insertions or omissions of 1 to 10,000 nucleotide bases. Millions of indels are found in the human genome, making it the second largest contributor to human genomic variation after SNPs. Similar to STRs, many indels are short and can be easily amplified even from highly degraded DNA and small amounts of DNA. In addition, there are a large number of indels available in different lengths, at different allele frequencies, and they are widely distributed throughout the genome. These characteristics of indels make them attractive targets for human identification and mosaic analysis.

[0741] Assay design

[0742] PCR primers are designed to amplify indels and are designed as single, small multiplex (about 3 targets) or large multiplex (30-40 targets). It has been shown that 30-40 appropriately selected indels are needed to distinguish individuals from each other. Using commercially available test kits, 30 to 40 indel targets are run before transplantation donor and recipient benchmark samples with 3 indel multiple repeats or single indels placed on 96-well plates. This step identifies informative targets, where donors and recipients have different alleles. Then, at least two informative targets are selected for each donor-recipient pair for use in chimeric analysis.

[0743] Each insertion and deletion is targeted by a set of fluorescently labeled primers that hybridize the target DNA. As the amplicon is cycled through PCR, the increased fluorescence is directly proportional to the number of amplicon present. Quantification is determined by reaching the required PCR cycle number for the threshold cycle (Ct) value. Informative markers are usually selected to amplify the genome of the minor contributor, which is usually the recipient in the case of stem cell transplantation. Quantity is then determined by comparing the Ct value of the post-transplant sample, the matching pre-transplant benchmark, and the reference control sample.

[0744] Workflow

[0745] Extract DNA from peripheral blood, bone marrow, or cell lineages using magnetic beads or flow cytometry.

[0746] Quantify and dilute the purified DNA to achieve the target concentration.

[0747] Perform benchmark genotyping by testing donor and recipient pre-transplant samples for each indel target in the system. In a mini-multiplex system, this would include 10 separate reactions with 2-3 indel targets in each reaction. In a singleplex system, this would require 46 separate reactions with a single indel target in each reaction. Each benchmark sample run must also include a positive control and a no-template control. This means that a mini-multiplex system can accommodate 8 benchmark samples per 96-well plate, while a singleplex system can accommodate 2 per plate.

[0748] Add 10 ng of reference DNA to each reaction well (100 ng total for mini multiplex reactions and 460 ng for singleplex reactions)

[0749] Prepare PCR Master Mix and add it to each reaction well.

[0750] Add amplification primers to the appropriate wells (8x10 for mini-multiplex, 2x46 for singleplex)

[0751] • The plate was sealed, vortexed, centrifuged, and then loaded onto the qPCR instrument.

[0752] The results are loaded into dedicated software.

[0753] • Compare the recipient and donor benchmarks in the software and select informative markers for chimerism analysis. Typically, two informative targets are selected for each transplant recipient / donor pair.

[0754] For each target to be amplified, the pre-transplant reference sample for the minor contributor must be run in triplicate, each post-transplant chimeric sample must be run in triplicate, a positive control for each two reaction wells, and a no-template control for each target. In other words, to perform a single post-transplant chimerism analysis, 60 ng (6 wells) of reference DNA must be run, 60 ng (6 wells) of pre-transplant reference DNA must be run, and 60 ng (6 wells) of post-transplant chimeric DNA must be run. This is a total of 21 wells to generate data from 2 targets.

[0755] Prepare PCR Master Mix and add it to each reaction well.

[0756] Add amplification primers to appropriate wells (7 wells per sample - 3 wells before transplantation, 3 wells after transplantation, and 1 well for a no template control)

[0757] • The plate was sealed, vortexed, centrifuged, and then loaded onto the qPCR instrument.

[0758] The results are loaded into dedicated software.

[0759] The total time required from extracted DNA to genotyping data for informative marker selection was approximately 3 hours, with 1.5 hours hands-on time. After selecting informative markers and extracting DNA from chimeric samples, an additional 3 hours plus 1.5 hours hands-on time were required to generate chimeric data.

[0760] limitation

[0761] There are three major limitations to qPCR-based mosaic analysis of indel targets.

[0762] First, each chimerism analysis requires 60 ng of a pre-transplant recipient reference sample. This is in addition to 100-500 ng of reference DNA, which is also required for initial genotyping. For programs that perform chimerism analysis frequently, the pre-transplant reference sample may be exhausted, thereby limiting the ability to run the assay for long periods of time.

[0763] Second, the requirement to perform chimeric analysis as a single-plex reaction complicates the overall system, requiring dozens of unique assays to be maintained in inventory. Additionally, the cost per reaction typically limits the analysis to only two targets per donor-recipient pair, and these targets may be different for each donor-recipient pair, making the setup prone to error.

[0764] Third, although the LOQ used for qPCR was very low, the dynamic range of qPCR-based chimerism was compromised and chimerism prediction was unreliable when minor contributors were greater than 30%.

[0765] Novel Chimerism Analysis by NGS

[0766] Target: SNP

[0767] SNPs are single nucleotide positions where there is variation within a human population or within a specific population to a measurable degree. dbSNP is a SNP database managed by the National Center for Biotechnology Information (NCBI) and currently includes more than 170 million human SNPs, of which nearly 25 million have been validated. This means that SNPs are responsible for the vast majority of variation in the human population, with an average of one SNP per 1000 nucleotide bases. SNPs can be biallelic (two observed alleles), triallelic (three observed alleles) or tetraallelic (four observed alleles). When the minor allele has a frequency of at least 1% in a group of random individuals in the population, a single base variation can be considered a SNP. Due to the low mutation rate, small amplicon size and compatibility with high-throughput sequencing technologies of SNPs, they are ideal targets for mosaic analysis.

[0768] Assay design

[0769] In various populations around the world, SNPs were selected as double alleles with approximately 50 / 50 allele frequencies. In addition, SNPs with low mutation rates and no linkage disequilibrium with the SNP library were selected. Finally, the design capabilities of SNPs were evaluated from two aspects: minimizing primer-primer interactions and the uniformity of PCR amplification and sequencing coverage. The total number of SNPs was determined based on the ability to distinguish first-degree relatives of all populations in the world.

[0770] A single PCR step amplifies the DNA, isolates the amplicons of interest, and incorporates flow cell adapters (oligonucleotide sequences that are the reverse of the oligonucleotide sequences on the Illumina flow cell, allowing sample amplicons to bind to the flow cell), sequencing primers (oligonucleotide sequences that serve as the start site for Illumina sequencing by synthesis (SBS) process), and index barcode sequences (oligonucleotide sequences that allow multiple samples to be run simultaneously).

[0771] The NGS system sequences each amplicon hundreds to thousands of times. In the pre-transplant baseline sample, this information is used to genotype each contributor. In the post-transplant mosaic sample, the read counts for each nucleotide at the SNP position can be used with or without the baseline genotype to accurately estimate the mosaicism percentage for each contributor, up to five total contributors.

[0772] Workflow

[0773] Extract DNA from peripheral blood, bone marrow, or cell lineages using magnetic beads or flow cytometry.

[0774] Quantify and dilute the purified DNA to achieve the target concentration.

[0775] • Add a unique index barcode to each sample DNA.

[0776] Add the master mix to each sample, mix, seal, and centrifuge.

[0777] Perform PCR amplification.

[0778] • Pool all samples into a single well and then perform PCR cleanup.

[0779] Quantify, dilute and denature the purified pool.

[0780] The final pool (also called library) is loaded into the sequencer, and sequencing begins.

[0781] Import sequencing data into chimerism-specific analysis software for automated quality control and chimerism analysis.

[0782] The time required from extracted DNA to loading the sequencer is less than 3 hours, of which less than 2 hours are hands-on time. The sequencing run takes 9 to 13 hours, depending on the number of samples run simultaneously. After the sequencing data is collected, data analysis can be performed without manual intervention, thus automating the analysis and reducing human errors.

[0783] limitation

[0784] There is a major limitation to NGS-based mosaicism analysis using SNPs: NGS-based sample processing and sequencing takes longer than CE- and qPCR-based mosaicism analysis, but the hands-on time is comparable. NGS-based library preparation can be completed in the afternoon and sequencing can be completed overnight. This allows for a 24-hour turnaround for samples received in the morning. However, because sequencing can be multiplexed, this method can combine multiple samples for sequencing, increasing the overall efficiency of sample processing.

[0785] Summarize

[0786] NGS-based chimerism analysis using SNP targets is an efficient, accurate and reliable method that can overcome many of the limitations associated with conventional chimerism analysis methods. Results are truly quantitative and can be generated automatically without laborious manual inspection of electropherograms and stuttering subtraction. NGS-based chimerism analysis has a wide dynamic range, low LOQ, and does not degrade performance at high levels of mixed chimerism. NGS systems use more than 200 SNP targets and multiplex them into a single reaction. This allows the use of donors with more than one donor and very closely related donor-recipient pairs. The indexing capabilities and throughput of the NGS system allow benchmark and chimeric samples to be run simultaneously, with only one assay and accessories stored in inventory, and little chance of human error in the workflow.

[0787] Example 5

[0788] This example shows that some embodiments are superior to conventional methods due to the throughput of NGS sequencers, the design of assays with incredibly high uniformity, and the use of SNPs as targets. The disclosed methods can analyze many more targets than conventional methods, which are limited to <30 targets. The process allows multiplexing of many samples to improve efficiency. These methods are quantitative and can all be completed cost-effectively.

[0789] An experiment will have the method performance in some embodiments of known or unknown benchmark genomes to compare.Table 12 shows the DNA quantification of four samples with different recipient parts in three benchmark conditions (benchmark known, benchmark unknown, and recipient known but unknown to donor).The result shows that the method can be performed at different recipient parts with or without benchmark, and the performance is similar.When the benchmark is known, the method tends to produce results with less confidence interval (and higher reliability).

[0790] Table 12. DNA quantification of known and unknown references

[0791]

[0792]

[0793] Figure 8 The DNA fraction (Y-axis) and the actual DNA fraction (X-axis) determined by some embodiments are compared. The horizontal line indicates the value of the actual fraction. The chimeric sample includes a cfDNA mixture of simulated cfDNA (Catalog No. 12498714289) provided by Horizon Discovery. As shown in the figure, the predicted minor contributor fraction is quite close to the actual minor contributor fraction at 0.1%, 0.2%, 0.4% and 2%.

[0794] Fig. 9 The coefficient of variation (CV) of 16 conditions for determining the limit of quantification (LOQ) in some embodiments is shown. LOQ is defined as the lowest concentration at which the analyte can be reliably detected with an imprecision (CV) of less than 20%. This measurement takes into account analytical sensitivity (i.e., detection limit) and reproducibility (i.e., precision). Four different groups of bars represent different minor contributor fractions of 0.1%, 0.2%, 0.4%, and 2%. The four bars in the group represent four input DNA conditions from left to right: 10ng gDNA, 3ng gDNA, 10ng cfDNA, and 3ng cfDNA. At each minor contributor fraction, there is a pattern consistent with expectations - samples with fewer numbers result in higher CVs, while cfDNA results in higher CVs.

[0795] All but one condition (0.1% minor contributor fraction, 3 ng of cfDNA) could detect the analyte with an imprecision (CV) less than 20%. In other words, one condition (3 ng cfDNA) had a LOQ of 0.2% and the remaining conditions had a LOQ of 0.1%.

[0796] The above data are summarized in Table 13. It clearly shows that all four input DNA conditions had LOQ values ​​less than 0.2%, with all but the most challenging input condition (3 ng cfDNA) having a LOQ of 0.1%.

[0797] Table 13. Limits of quantitation for some embodiments using different DNA inputs

[0798] Input DNA Limit of Quantitation 10ng cfDNA <0.1％ 3ng cfDNA <0.2％ 10ng gDNA <0.1％ 3ng gDNA <0.1％

[0799] discuss

[0800] Conventional chimerization approaches using qPCR or CE technologies sacrifice ease of use, target quantity, sensitivity, or dynamic range.

[0801] The method implemented multiplexes samples in a single assay. This allows pre-transplant benchmark samples and post-transplant chimeric samples to be run side by side using the same assay and in the same sequencing run. The method can be performed with or without a benchmark with almost the same performance.

[0802] qPCR and CE chimerism methods can provide a certain level of multiplexing for pre-transplant benchmark samples, but these methods have a performance drop for post-transplant chimerism quantification when the target is multiplexed. This means that benchmark samples and chimeric samples must be run separately, and the entire system may require at least a dozen unique assays.

[0803] While qPCR is sensitive for microchimerism detection, it lacks a reliable dynamic range for mixed chimerism. CE-based chimerism analysis provides a wide dynamic range for mixed chimerism detection, but lacks sensitivity for microchimerism. The disclosed method provides both a reliable lower limit of quantification (LOQ) and a wide dynamic range, allowing one solution to cover all different types of chimerism.

Claims

1. A method for quantifying a nucleic acid sample comprising nucleic acids from two or more contributors, wherein the genotypes of the two or more contributors are unknown, the method comprising: (a) extracting nucleic acid molecules from the nucleic acid sample; (b) amplifying the extracted nucleic acid molecules; (c) sequencing the amplified nucleic acid molecules from the nucleic acid sample using a nucleic acid sequencer to generate nucleic acid sequence reads; (d) using computer-implemented hashing to identify reads in the nucleic acid sequence reads that match any sequence in a plurality of unbiased target sequences, and mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence, wherein the plurality of unbiased target sequences comprises five classes of sequences that encompass each polymorphic site in the plurality of polymorphic sites: (i) a reference target sequence that is a subsequence of the reference sequence, the reference target sequence having a reference allele having a reference nucleotide at a polymorphic site; (ii) alternative target sequences, each having an alternative allele having an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) a mutated reference target sequence, which includes all possible sequences, each possible sequence differing from the reference target sequence by only one nucleotide at a site that is not a non-polymorphic site; (iv) mutated alternative target sequences, which include all possible sequences, each possible sequence differing from the alternative target sequence by only one nucleotide at a site that is not a non-polymorphic site; and (v) unexpected allele target sequences, each sequence having an unexpected allele different from the reference allele and the alternative allele, and each sequence having a sequence different from the previous four categories of sequences; (e) determining allele counts of the nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci using the mapped nucleic acid sequence reads; and (f) quantifying one or more fractions of nucleic acids from the two or more contributors in the nucleic acid sample using a probabilistic mixture model, wherein using the probabilistic mixture model comprises applying the probabilistic mixture model to the allele counts of nucleic acid sequence reads, and wherein the probabilistic mixture model models the allele counts of nucleic acid sequence reads at the one or more polymorphic loci using a probability distribution that takes into account errors in the nucleic acid sequence reads and without using genotype information of the contributors to quantify the contributor fractions.

2. The method of claim 1, further comprising determining, using the probabilistic mixture model and by one or more processors, one or more genotypes of the two or more contributors at the one or more polymorphic loci.

3. The method of claim 1, further comprising determining the risk of a recipient contributor rejecting a tissue or organ transplanted from a donor contributor using the one or more fractions of nucleic acid from the two or more contributors.

4. The method according to claim 1, wherein: The nucleic acid molecule comprises a DNA molecule or an RNA molecule.

5. The method according to claim 1, wherein: The nucleic acid sample comprises nucleic acid from one or more contaminant genomes and a genome of interest.

6. The method according to claim 1, wherein: The two or more contributors comprise one or more donors of a transplant and a recipient of said transplant, and wherein said nucleic acid sample comprises a sample obtained from said recipient.

7. The method according to claim 6, wherein: The transplant includes an allogeneic or a xenogeneic transplant.

8. The method according to claim 6, wherein: The nucleic acid sample comprises a biological sample obtained from the recipient.

9. The method according to claim 1, wherein: The nucleic acid sample comprises a biological sample obtained from a cell culture.

10. The method according to claim 1, wherein: The extracted nucleic acid molecules comprise cell-free nucleic acid.

11. The method according to claim 1, wherein: The extracted nucleic acid molecules include cellular DNA.

12. The method according to claim 1, wherein: The one or more polymorphic loci comprise one or more biallelic polymorphic loci.

13. The method according to claim 1, wherein: The one or more alleles at the one or more polymorphic loci comprise one or more single nucleotide polymorphism (SNP) alleles.

14. The method according to claim 1, wherein: The probabilistic mixture model uses a single-locus likelihood function to model allele counts at a single polymorphic locus, and the single-locus likelihood function includes M(n 1i ,n 2i |p 1i ,i) in n 1i is the allele count of allele 1 at locus i, n 2i is the allele count of allele 2 at locus i, p 1i is the expected fraction of allele 1 at locus i, and θ includes one or more model parameters.

15. The method according to claim 14, wherein: The p 1i Modeled as the following function: (i) the genotype of the contributor at locus i, or g i =(g 11i , ..., g D1i ), which is a vector of the number of copies of allele 1 at locus i in contributors 1…D; (ii) a read count error caused by the sequencing operation in (c), or λ; as well as (iii) the nucleic acid fraction of the contributor in the nucleic acid sample, or β = (β1, ..., β D ), where D is the number of contributors.

16. The method according to claim 15, wherein: The contributors include two or more contributors, and p 1i = p(g i ,λ,β)←[(1-λ)g i +λ(2-g i )] / 2·β, where · is the vector dot product operator.

17. The method according to claim 15, wherein: Zero, one, or more genotypes of the contributor are unknown.

18. The method according to claim 17, wherein: (f) involves marginalizing over multiple possible combinations of genotypes to enumerate p 1i , wherein the p 1i is a probability parameter.

19. The method of claim 17, further comprising determining a genotype configuration at each of the one or more polymorphic loci, the genotype configuration comprising two alleles for each of the two or more contributors.

20. The method according to claim 15, wherein: The single locus likelihood function comprises a first binomial distribution.

21. The method according to claim 20, wherein: The first binomial distribution is expressed as follows: n 1i ~BN(n i ,p 1i ) in n 1i is the allele count of the nucleic acid sequence read of allele 1 at locus i; as well as n i is the total read count at locus i, which is equal to the total genome copy number n".

22. The method according to claim 21, wherein: (f) involves maximizing a multi-locus likelihood function calculated from multiple single-locus likelihood functions.

23. The method according to claim 22, wherein: (f) include: calculating a plurality of multi-locus likelihood values ​​using the plurality of latent score values ​​and the multi-locus likelihood function of the allele counts of the nucleic acid sequence reads determined in (e); identifying one or more potential score values ​​associated with a maximum multi-locus likelihood value; and One or more fractions of nucleic acid from the two or more contributors in the nucleic acid sample are quantified as the identified potential fraction values.

24. The method according to claim 22, wherein: The multi-locus likelihood function includes: L(β,θ,λ,π;n1,n2)=Π i [Σg i M(n 1i ,n 2i |p(g i ,λ,β),θ)·P(g i |p)] in L(β, θ, λ, π; n1, n2) is the likelihood of observing allele count vectors n1 and n2 for alleles 1 and 2; p(g i , λ, β) is based on the contributor genotype g at locus i i The expected fraction or probability of observing allele 1 at locus i; P(g i |π) is the observed genotype g at locus i given the population allele frequency (π). i The prior probability of ; and Σg i represents the summation of multiple possible combinations of the contributor genotypes.

25. The method according to claim 24, wherein: The multi-locus likelihood function includes: L(β,λ,π;n1,n2)=Π i [Σg i BN(n 1i |n i ,·p(g i ,λ,β))·P(g i |π)].

26. The method according to claim 25, wherein: The contributors include two contributors, and the likelihood function includes: L(β,λ,π;n1,n2)=Π i S g1ig2i BN(n 1i |n i ,p 1i (g 1i ,g 2i ,λ,β)·P(g 1i ,g 2i |p) in L(β, λ, π; n1, n2) is the likelihood of observing the allele count vector n1 to n2 for alleles 1 and 2 given the parameters β and π; p 1i (g 1i , g 2i , λ, β) are probability parameters indicating the probability of 1i , g 2i )’s probability of allele 1 at locus i; and P(g 1i , g 2i |π) is the a priori joint probability of observing the two contributor genotypes given the population allele frequencies (π).

27. The method according to claim 26, wherein: Using the marginal distribution P(g 1i |π) and P(g 2i |π) to calculate the prior joint probability.

28. The method according to claim 27, wherein: The a priori joint probability is calculated using the genetic relationship between the two contributors.

29. The method of claim 24, wherein: The probabilistic mixture model takes into account the error in the number of nucleic acid molecule copies caused by the extraction of the nucleic acid molecules from the nucleic acid sample performed in (a), and the read count error caused by the sequencing operation in (c).

30. The method of claim 29, wherein: The probabilistic mixture model uses a second binomial distribution to model the allele counts of the extracted nucleic acid molecules for the alleles at the one or more polymorphic loci.

31. The method according to claim 30, wherein: The second binomial distribution is expressed as follows: n 1i "~BN(n i ",p 1i ) in n 1i " is the allele count of the extracted nucleic acid molecule of allele 1 at locus i; n i " is the total nucleic acid molecule count at locus i; as well as p iu is a probability parameter indicating the probability of allele 1 at locus i.

32. The method according to claim 31, wherein: The first binomial distribution is expressed in terms of allele fraction n 1i " / n i "As a condition.

33. The method of claim 32, wherein: The first binomial distribution is reparameterized as follows: n 1i ~BN(n i ,n 1i " / n i ") in n 1i is the allele count of the nucleic acid sequence read of allele 1 at locus i; n i "is the total number of nucleic acid molecules at locus i, which is equal to the total genome copy number n"; n i is the total read count at locus i; as well as n 1i " is the number of extracted nucleic acid molecules of allele 1 at locus i.

34. The method of claim 33, wherein: The probability mixture model uses the first beta distribution to show that n 1i The distribution of " / n".

35. The method of claim 34, wherein: The first beta distribution has a mean and variance that match the mean and variance of the second binomial distribution.

36. The method of claim 34, wherein: Locus i is modeled as bi-allelic, and the first Beta distribution is expressed as follows: n i1 " / n"~Beta((n"-1)p 1i ,(n"-1)p 2i ) in p 1i is a probability parameter indicating the probability of allele 1 at locus i; as well as p 2i is a probability parameter indicating the probability of allele 2 at locus i.

37. The method of claim 34, wherein: (f) comprising combining the first binomial distribution for modeling sequencing read counts and the first beta distribution for modeling the number of extracted nucleic acid molecules to obtain the single locus likelihood function following a first beta-binomial distribution.

38. The method of claim 37, wherein: The first beta-binomial distribution has the following form: n 1i ~BB(n i ,(n"-1)·p 1i ,(n"-1)·p 2i ), Or in the form of: n 1i ~BB(n i ,n"·p 1i ,n"·p 2i )。 39. The method of claim 38, wherein: The multi-locus likelihood function includes: L(β,n",λ,π;n1,n2)=Π i [Σg i BB(n 1i |n i ,(n"-1)·p 1i ,(n”-1)·p 2i ); P(g i |p)] where L(β, n", λ, π; n1, n2) is the likelihood of observing the allele count vectors n1 and n2 for alleles 1 and 2 at all loci, and p 1i = p(g i ,λ,β),p 2i =1–p 1i .

40. The method of claim 39, wherein: The contributors include two contributors, and the multi-locus likelihood function includes: L(β,n",λ,π;n1,n2)= Π i Σ g1ig2i BB(n 1i ,n 2i |n i ,(n"−1)·p 1i (g 1i ,g 2i ,λ,β),(n"-1)·p 2i (g 1i ,g 2i ,λ,β))·P(g 1i ,g 2i |π) Where L(β, n", λ, π; n1, n2) is the likelihood of observing the allele count vector n1 of allele 1 at all loci and the allele count vector n2 of allele 2 at all loci given the parameters β, n", λ and π; p 1i (g 1i , g 2i , λ, β) are probability parameters indicating the probability of 1i , g 2i )’s probability of allele 1 at locus i; p 2i (g 1i , g 2i , λ, β) are probability parameters indicating the probability of 1i , g 2i )’s probability of allele 2 at locus i; and P(g 1i , g 2i |π) is the first contributing genotype (g) of allele 1 observed at locus i given the population allele frequency (π). 1i ) and the second contributor genotype of allele 1 (g 2i ) is the prior joint probability of .

41. The method of claim 33, wherein: (f) comprising estimating the total number of genome copies n" extracted from the plurality of extracted nucleic acid molecules.

42. The method according to claim 41, wherein: The estimated total genome copy number n" extracted is adjusted according to the fragment size of the extracted nucleic acid molecules.

43. The method of claim 24, wherein: The probabilistic mixture model takes into account the nucleic acid molecule count error caused by the amplification of the nucleic acid molecules performed in (b) and the read count error caused by the sequencing operation in (c).

44. The method of claim 43, wherein the amplification process of (b) is modeled as follows: x t+1 =x t +y t+1 in x t+1 is the number of nucleic acid copies of a given allele after cycle t+1 of amplification; x t is the number of nucleic acid copies of a given allele after cycle t of amplification; y t+1 is a new copy generated in cycle t+1, and it follows the binomial distribution y t+1 ~BN(x t , r t+1 );as well as r t+1 is the amplification rate at cycle t+1.

45. The method of claim 43, wherein: The probabilistic mixture model uses a second Beta distribution to model the allele fractions of the amplified nucleic acid molecules for the alleles at the one or more polymorphic loci.

46. ​​The method of claim 45, wherein: Locus i is biallelic, and the second Beta distribution is expressed as follows: n 1i ' / (n 1i '+n 2i ')~Beta(n"·ρ i ·p 1i ,n"·r i ·p 2i ) in n 1i ' is the allele count of the amplified nucleic acid molecule of allele 1 at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of allele 2 at locus i; n" is the total nucleic acid molecule count at any locus; ρ i is a constant related to the average amplification rate r; p 1i is the probability of allele 1 at locus i; as well as p 2i is the probability of allele 2 at locus i.

47. The method of claim 46, wherein: ρ i is (1+r) / (1-r) / [1-(1+r) -t ], and r is the average amplification rate for each cycle.

48. The method of claim 46, wherein: ρ i Expressed as (1+r) / (1-r).

49. The method of claim 46, wherein: (f) comprising combining the first binomial distribution and the second beta distribution to obtain n following a second beta-binomial distribution 1i The single locus likelihood function.

50. The method of claim 49, wherein: The second beta-binomial distribution has the following form: n 1i ~BB(n i ,n”·ρ i ·p 1i ,n”·ρ i ·p 2i ) in n 1i is the allele count of the nucleic acid sequence reads of allele 1 at locus i; p 1i is a probability parameter indicating the probability of allele 1 at locus i; as well as p 2i is a probability parameter indicating the probability of allele 2 at locus i.

51. The method of claim 50, wherein: (f) comprising, by assuming that the one or more polymorphic loci have the same amplification rate, reparameterizing the second beta-binomial distribution to: n 1i ~BB(n i ,n"·(1+r) / (1-r)·p 1i ,n"·(1+r) / (1-r)·p 2i ) where r is the amplification rate.

52. The method of claim 51, wherein: The multi-locus likelihood function includes: L(β,n",r,λ,π;n1,n2)=Π i [Σg i BB(n 1i |n i ,n"·(1+r) / (1-r)·p 1i , n"·(1+r) / (1-r)·p 2i )·P(g i |π)]。 53. The method of claim 51, wherein: The contributors include two contributors, and the multi-locus likelihood function includes: L(β,n",r,λ,π;n1,n2)= Π i Σ g1ig2i [BB(n 1i |n i ,n"·(1+r) / (1-r)·p 1i (g 1i ,g 2i ,λ,β),n"·(1+r) / (1-r)·p 2i (g 1i ,g 2i ,λ,β))·P(g 1i ,g 2i |π)] Where L(β, n", r, λ, π; n1, n2) is the likelihood of observing the allele count vector n1 of allele 1 at all loci and the allele count vector n2 of allele 2 at all loci given the parameters β, n", r, λ and π.

54. The method of claim 50, wherein: (f) comprising reparameterizing the second beta-binomial distribution by defining the relative amplification rate of each polymorphic locus as proportional to the total reads of the locus as: n 1i ~BB(n i ,c'·n i ·p 1i ,c'·n i ·p 2i ) in c' is the parameter to be optimized; and n i is the total read sequence at locus i.

55. The method of claim 54, wherein: The multi-locus likelihood function includes: L(β,n",c',λ,π;n1,n2)=Π i [Σg i BB(n 1i |n i ,c'·n i ·p 1i ,c'·n i ·p 2i )·P(g i |π)].

56. The method of claim 24, wherein: The probabilistic mixture model takes into account the errors in the number of nucleic acid molecules caused by the extraction of the nucleic acid molecules performed in (a) and the amplification of the nucleic acid molecules performed in (b), as well as the read count errors caused by the sequencing operation in (c).

57. The method of claim 56, wherein: The probabilistic mixture model uses a third beta distribution to model the allele fractions of the amplified nucleic acid molecules for the alleles at the one or more polymorphic loci, taking into account the sampling errors caused by extracting the nucleic acid molecules performed in (a) and amplifying the nucleic acid molecules performed in (b).

58. The method of claim 57, wherein locus i is biallelic and the third Beta distribution has the form: n 1i ' / (n 1i '+n 2i ')~Beta(n”·(1+r i ) / 2·p 1i ,n”·(1+r i ) / 2·p 2i ) in n 1i ' is the allele count of the amplified nucleic acid molecule of allele 1 at locus i; n 2i ' is the allele count of the amplified nucleic acid molecule of allele 2 at locus i; n” is the total nucleic acid molecule count; r i is the average amplification rate of locus i; p 1i is the probability of allele 1 at locus i; and p 2i is the probability of allele 2 at locus i.

59. The method of claim 58, wherein: (f) comprising combining the first binomial distribution and the third beta distribution to obtain n following a third beta-binomial distribution 1i The single locus likelihood function.

60. The method of claim 59, wherein: The third beta-binomial distribution has the following form: n 1i ~BB(n i ,n”·(1+r i ) / 2·p 1i ,n”·(1+r i ) / 2·p 2i ) where r i is the amplification rate.

61. The method of claim 60, wherein: The multi-locus likelihood function includes: L(β,n",r,λ,π;n1,n2)= P i [Σg i BB(n 1i |n i ,n”·(1+r) / 2·p 1i ,n”·(1+r) / 2·p 2i )·P(g i |π)], where r is the amplification rate assumed to be equal for all loci.

62. The method of claim 60, wherein: The contributors include two contributors, and wherein the multi-locus likelihood function comprises: L(β,n",r,λ,π;n1,n2)=Π i Σ g1ig2i BB(n 1i |n i ,n”·(1+r) / 2·p 1i (g 1i , g 2i ,λ,β),n”·(1+r) / 2·p 2i (g 1i ,g 2i ,λ,β))·P(g 1i ,g 2i |p) Where L(n1, n2|β, n", r, λ, π) is the observed allele count vector n1 of allele 1 and the observed allele count vector n2 of allele 2 given the parameters β, n", r, λ and π.

63. The method of claim 1, further comprising: (g) estimating one or more confidence intervals for one or more fractions of nucleic acids of the two or more contributors using a Hessian matrix of log-likelihoods applying numerical differentiation.

64. The method of claim 1, further comprising estimating a sequencing error rate λ at a variant site based on the frequency of the unexpected allele target sequence observed in (v).

65. The method of claim 1, wherein: (e) comprising using the identified reads and their matched unbiased target sequences to determine the allele counts of the nucleic acid sequence reads for the alleles at the one or more polymorphic loci.

66. The method of claim 1, wherein: The plurality of unbiased target sequences include sequences that are truncated to have the same length as the nucleic acid sequence reads.

67. The method of claim 1, wherein: The plurality of unbiased target sequences include sequences stored in one or more hash tables, and the read sequence is identified using the hash tables.

68. A system for quantifying a nucleic acid sample comprising nucleic acids from two or more contributors, wherein the genotypes of the two or more contributors are unknown, the system comprising: (a) a sequencer configured to (i) receive nucleic acid molecules extracted from the nucleic acid sample, (ii) amplify the extracted nucleic acid molecules, and (iii) sequence the amplified nucleic acid molecules under conditions that produce nucleic acid sequence reads; as well as (b) a computer comprising one or more processors configured to: Using computer-implemented hashing to identify reads in the nucleic acid sequence reads that match any sequence of a plurality of unbiased target sequences, mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence, wherein the plurality of unbiased target sequences includes five classes of sequences that encompass each polymorphic site in the plurality of polymorphic sites: (i) a reference target sequence that is a subsequence of the reference sequence, the reference target sequence having a reference allele having a reference nucleotide at a polymorphic site; (ii) alternative target sequences, each having an alternative allele having an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) a mutated reference target sequence, which includes all possible sequences, each possible sequence differing from the reference target sequence by only one nucleotide at a site that is not a non-polymorphic site; (iv) mutated alternative target sequences, which include all possible sequences, each possible sequence differing from the alternative target sequence by only one nucleotide at a site that is not a non-polymorphic site; and (v) unexpected allele target sequences, each sequence having an unexpected allele different from the reference allele and the alternative allele, and each sequence having a sequence different from the previous four categories of sequences; using the mapped nucleic acid sequence reads, determining allele counts for the nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci; and quantifying one or more fractions of nucleic acid from the two or more contributors in the nucleic acid sample using a probabilistic mixture model, in Using the probabilistic mixture model comprises applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and The probabilistic mixture model models the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci using a probability distribution that takes into account errors in the nucleic acid sequence reads and does not use the genotype information of the contributors to quantify the contributor fraction.

69. The system of claim 68, further comprising means for extracting nucleic acid molecules from the nucleic acid sample.

70. The system of claim 68, wherein: The probability distribution includes the following first binomial distribution: n 1i ~BN(n i ,p 1i ) in n 1i is the allele count of the nucleic acid sequence read of allele 1 at locus i; n i is the total read count at locus i, which is equal to the total genome copy number n"; as well as p 1i is the probability parameter indicating the probability of allele 1 at locus i.

71. A computer program product, comprising a non-transitory machine-readable medium storing program code, the program code, when executed by one or more processors of a computer system, causes the computer system to implement a method for quantifying a nucleic acid sample comprising nucleic acids of two or more contributors, wherein the genotypes of the two or more contributors are unknown, the program code comprising: Code for mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence using a computer-implemented hash to identify reads in the nucleic acid sequence reads that match any sequence of a plurality of unbiased target sequences, wherein the plurality of unbiased target sequences includes five classes of sequences covering each polymorphic locus in the plurality of polymorphic loci: (i) a reference target sequence that is a subsequence of the reference sequence, the reference target sequence having a reference allele having a reference nucleotide at a polymorphic site; (ii) alternative target sequences, each having an alternative allele having an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) a mutated reference target sequence, which includes all possible sequences, each possible sequence differing from the reference target sequence by only one nucleotide at a site that is not a non-polymorphic site; (iv) mutated alternative target sequences, which include all possible sequences, each possible sequence differing from the alternative target sequence by only one nucleotide at a site that is not a non-polymorphic site; and (v) unexpected allele target sequences, each sequence having an unexpected allele different from the reference allele and the alternative allele, and each sequence having a sequence different from the previous four categories of sequences; code for determining allele counts of nucleic acid sequence reads of one or more alleles at the one or more polymorphic loci using the mapped nucleic acid sequence reads; and code for quantifying one or more fractions of nucleic acid from the two or more contributors in the nucleic acid sample using a probabilistic mixture model, in Using the probabilistic mixture model comprises applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, and The probabilistic mixture model models the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci using a probability distribution that takes into account errors in the nucleic acid sequence reads and does not use the genotype information of the contributors to quantify the contributor fraction.

72. A method implemented at a computer system comprising one or more processors and a system memory for quantifying a nucleic acid sample comprising nucleic acids of two or more contributors, wherein the genotypes of the two or more contributors are unknown, the method comprising: (a) receiving, by the one or more processors, nucleic acid sequence reads obtained from the nucleic acid sample; (b) using a computer-implemented hash by the one or more processors to identify reads in the nucleic acid sequence reads that match any sequence of a plurality of unbiased target sequences, and mapping the nucleic acid sequence reads to one or more polymorphic loci on a reference sequence, wherein the plurality of unbiased target sequences comprises five classes of sequences that encompass each polymorphic site in the plurality of polymorphic sites: (i) a reference target sequence that is a subsequence of the reference sequence, the reference target sequence having a reference allele having a reference nucleotide at a polymorphic site; (ii) alternative target sequences, each having an alternative allele having an alternative nucleotide at the polymorphic site, the alternative nucleotide being different from the reference nucleotide; (iii) a mutated reference target sequence, which includes all possible sequences, each possible sequence differing from the reference target sequence by only one nucleotide at a site that is not a non-polymorphic site; (iv) mutated alternative target sequences, which include all possible sequences, each possible sequence differing from the alternative target sequence by only one nucleotide at a site that is not a non-polymorphic site; and (v) unexpected allele target sequences, each sequence having an unexpected allele different from the reference allele and the alternative allele, and each sequence having a sequence different from the previous four categories of sequences; (c) using the mapped nucleic acid sequence reads and determining, by the one or more processors, allele counts of the nucleic acid sequence reads for one or more alleles at the one or more polymorphic loci; and (d) quantifying, by the one or more processors, one or more fractions of nucleic acids from the two or more contributors in the nucleic acid sample and confidence levels for the fractions using a probabilistic mixture model, wherein using the probabilistic mixture model comprises applying the probabilistic mixture model to the allele counts of the nucleic acid sequence reads, Wherein, the probabilistic mixture model uses a probability distribution to model the allele counts of the nucleic acid sequence reads at the one or more polymorphic loci, wherein the probability distribution takes into account errors in the mapped nucleic acid sequence reads and does not use the genotype information of the contributors to quantify the contributor scores.

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