Joint genotype inference with germline and somatic mutations
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Abstract
The joint sequencing of related genomes has become an important means to discover rare variants. Normal-tumor genome pairs are routinely sequenced together to find somatic mutations and their associations with different cancers. Parental and sibling genomes reveal de novo germline mutations and inheritance patterns related to Mendelian diseases.
Acute lymphoblastic leukemia (ALL) is the most common paediatric cancer and the leading cause of cancer-related death among children. With the aim of uncovering the full spectrum of germline and somatic genetic alterations in childhood ALL genomes, we conducted whole-exome re-sequencing on a unique cohort of over 120 exomes of childhood ALL quartets, each comprising a patient's tumor and matched-normal material, and DNA from both parents. We developed a general probabilistic model for such quartet sequencing reads mapped to the reference human genome. The model is used to infer joint genotypes at homologous loci across a normal-tumor genome pair and two parental genomes.
We describe the algorithms and data structures for genotype inference, model parameter training. We implemented the methods in an open-source software package (QUAD GT) that uses the standard file formats of the 1000 Genomes Project. Our method's utility is illustrated on quartets from the ALL cohort.
Keywords
Acute Lymphoblastic Leukemia Somatic Mutation Germline Mutation Parental Genotype Base CallBackground
Acute lymphoblastic leukemia (ALL) is the most common paediatric cancer and the leading cause of cancer-related death among children. Advances in the understanding of the pathobiology of ALL have led to risk-targeted treatment regimes and increased survival rates, but treatment is still far from optimal. Childhood ALL arises after the acquisition of a series of DNA sequence abnormalities. These initiating events, or so-called driver mutations, ultimately confer a selective growth advantage, and are causally implicated in cancer development. A central goal of cancer genome analysis is the identification of cancer genes that, by definition, carry driver mutations.
Next-generation sequencing (NGS) technologies [1] have enabled the genome-wide identification of human disease-related variants. Analysis pipelines have been established for the large-scale sequencing of individual tumor genomes [2]. Briefly, short sequencing reads are collected from the tumor sample, mapped to the reference genome assembly, and the set of aligned reads are used to infer variations across the genome at homologous loci covered with multiple reads. The sequence variants in the tumor genome may be the result of somatic mutations, or constitutional variants preserved in the somatic lineage. In order to distinguish somatic mutations from conserved variants, it is necessary to sequence normal and tumor samples side by side. The Cancer Genome Atlas Network [3] catalogues somatic mutations in different cancers using such normal-tumor pairs.
While sequencing an entire human genome is still too expensive for the average research laboratory, various target-enrichment techniques [8] are available for sequencing only regions of interest. In particular, sequencing the so-called exome covering all gene-coding regions, has been a routine step in medical applications [9]. Through our ongoing paediatric oncogenomics study, we conducted whole exome deep re-sequencing of a unique cohort of over 120 exomes of childhood ALL quartets, consisting of the patient's tumor and matched-normal material as well as DNA from both parents.
Existing software tools
Various bioinformatics tools have been developed for genotyping individual genomes from sequencing data, including SNVMix [10], VarScan [11], and The Genome Analysis Toolkit GATK [12, 13]. A couple of methods have been developed for the purpose of joint genotyping of paired normal-tumor samples, including SomaticSniper [14], MutationSeq [15], and JointSNVMix [16]. SomaticSniper and MutationSeq employ machine-learning techniques for variant classification; JointSNVMix is based on a full Bayesian model incorporating prior genotype distributions, somatic mutations, and sequencing base call errors. The Strelka software package [17] infers joint tumor-normal genotypes in a Bayesian model that also considers tumor sampling impurity: DNA collected from the tumor sample is usually "contaminated" to some degree with the normal tissue, and therefore the sequencing reads come from a mixture of normal and tumor genomes. To our knowledge, no existing variant caller incorporates somatic and germline mutation models simultaneously to handle quartet data as in our data sets.
Our contribution
We infer the four genotypes jointly in a framework that respects the rules of inheritance in the germline and somatic lineages. Aside from assigning belief to de novo and somatic mutations, we hypothesized, constrained patterns in one lineage have an indirect beneficial effect on the inference in other lineages. In particular, the "triangulation" of the normal genome by related genomes means that genotypes and lineage-specific mutations can be resolved more reliably: information from the parental genotypes reinforce the inference of somatic mutations, and tumor sequencing reads help to recognize constitutional mutations. We present a Bayesian framework that incorporates prior parental genotypes, inherited, de novo and somatic mutations, as well as tumor-sampling impurity and sequencing errors. All model parameters are estimated in an expectation-maximization algorithm [18].
Methods
Probabilistic model
Base calls are assumed to be independent between different loci. The input for genotype inference at a single locus consists of nucleotide base calls made with their accompanying sequencing error probabilities.
Parental genotype priors
Let π[x] denote the frequency of each allele x ∈ {A; C; G; T} at a given locus. The prior allele frequencies are computed by using a standard DNA substitution model quantifying the divergence from the reference genome assembly. Assuming the simple Jukes-Cantor model with a reference nucleotide genotype $y,\phantom{\rule{0.3em}{0ex}}\pi \left[x\right]=\nu /3$ for $x\ne y$ and $\Pi \left[y\right]=1-v$, where v is the parental genome's divergence from the reference. More general divergence models and known SNP frequencies can be accommodated by using $\pi \left[x\right]={\sum}_{y\in \left\{\text{A},\text{C},\text{G},\text{T}\right\}}{\pi}_{\text{ref}}\left[y\right]{v}_{y\to x}$, where ${V}_{x\to y}$ is the model's substitution probability from $x$ to $y$ and ${\mathrm{\Pi}}_{\mathsf{\text{ref}}}$ is a known allele frequency.
(In other words, γ is numerically analogous to the so-called inbreeding coefficient, or F-statistic.) It is easy to verify that haploid allele frequencies are the same at any γ setting.
Mutations and inheritance
The child's normal genotype is determined by Mendelian inheritance and de novo point mutations with probabilities v_{ x }_{→y}that occur within the parental germlines. For simplicity, germline mutations in a parental lineage (g_{F,} g_{M} for father and mother, respectively) are conceived of as mutations that result in a diploid genotype$\left({g}_{\text{F}}^{\prime},{g}_{\text{M}}^{\prime}\right)$, which then determine the child's normal genotype by Mendel's laws.
Germline mutations follow standard molecular evolution model for substitutions in DNA. Let X denote the parent's normal allele at a locus, and X' denote the same allele at the end of the germline before gametogenesis. The mutation model specifies the probabilities that apply to every locus ${v}_{x\to {x}^{\prime}}=\mathbb{P}\left\{{X}^{\prime}=x|X=x\right\}$. Let $\chi \left({g}_{\text{F}}^{\prime},{g}_{\text{M}}^{\prime}\to {g}_{\text{N}}\right)$ denote the probability of normal genotype g_{N} given the mutated parental genotypes ${g}_{\text{F}}^{\prime},{g}_{\text{M}}^{\prime}$. Then χ may be 0, 1, 1/2 or 1/4, depending on the common alleles between the three genotypes.
Tumor genotype
The tumor genome undergoes mutations following the same type of molecular evolution model as the one used for germline mutations, but has its own parameters.
Sequencing errors
Allele sampling and sample impurity
Aligned sequencing reads randomly sample the haploid alleles at a given locus. Let y_{ k } be the true allele for base call z_{ k }. The locus' diploid genotype determines the frequency $\rho \left[y\right]=\mathbb{P}\left\{{y}_{k}=y\right\}$ for each possible allele y. At a homozygous locus xx, ρ[y] = 1 and ρ[x'] = 0 for all x' ≠ x. At a heterozygous locus xx', ρ[y] = 1/2, ρ[x'] = 1/2 and ρ[x"] = 0 for all x" ≠ x, x'.
Likelihood for aligned reads given the genotypes
Hence, $\mathbb{P}\left\{{Z}_{k}={z}_{k}\right\}={\sum}_{y}\mathbb{P}\left\{{Z}_{k}={z}_{k}|{Y}_{k}=y\right\}\mathbb{P}\left\{{Y}_{k}=y\right\}={\sum}_{y}{p}_{k}\left(y\right)\rho \left[y\right]$.
Complete likelihood
The four factors are defined by (4), via the allele frequencies ρ that are determined by genotypes and tumor sampling purity, as discussed above (see Allele sampling and sample impurity).
Algorithmic techniques and data structures
Our algorithmic solutions address the efficient calculation of the likelihood formula of (5), and its use in an Expectation-Maximization (EM) framework for model parameter setting. First, we examine a straightforward decomposition of the likelihood formula dictated by the assumed probabilistic graphical model.
For the EM algorithm, we need to recompute likelihoods and posterior probabilities in a number of iterations, which can be directly achieved by storing all sequencing reads in memory, but such an approach may be costly. We scrutinize the computation of read likelihoods, in order to arrive at an economical data structure, also discussed in some detail, that eliminates the need to store all base calls in memory.
Likelihood decomposition
Read likelihoods
If no reads call z, then T_{ β }[z] = 1. Equation (10) becomes L_{ z }(ρ) = T_{ ρ }_{[z]}[z]. For pure diploid samples, ρ[z] may be 0, 1 or 1/2, corresponding to the possible subproducts for diploid samples E[y] = T_{0}[y] (sequencing error), C[y] = T_{1}[y] (homozygote yy), and H[y] = T_{1/2}[y] (heterozygote with y). Likelihood formulas become even more economical with normalized subproducts C'[y] = C[y]/E[y], H'[y] = H[y]/E[y], and scaling factor $E={\prod}_{y}E\left[y\right]={\prod}_{k}\frac{1}{3}{\epsilon}_{k}.$
Data structure for storing base calls
Storing individual base calls at each locus is costly, because the sequencing coverage may be large across the four samples. It suffices, however, to store the partial likelihood factors appearing in Equations (11), (12) and (14). In particular, for each locus with mapped base calls, it is enough to store the sample-specific H'[x], C'[x], and ${T}_{\beta}^{\prime}\left[x\right]$ values for each called base x and the six possible values of β, in addition to a single scaling value E. For a sample with m base calls at the locus, (1 + 8m) variables thus suffice, independently of read coverage. The stored partial likelihoods are reused throughout the iterations optimizing the model parameters at a fixed tumor purity level ω.
Recurrent base calls
In our experience, loci with identical sets of base calls reoccur at an appreciable frequency, especially at lower coverages (less than about 15×) that characterize exon boundaries in exome sequencing. We exploit recurrent patterns in the piled-up base calls to achieve even better memory usage and speed. Namely, we sort the base calls $\mathcal{R}$ at a given locus for a given sample (by allele and quality score), and use run-length encoding to achieve a compact characterization $h\left(\mathcal{R}\right)$. The encoding is not used for higher coverages or widely varying quality scores, where h would take too many bits. Information-theoretic considerations [21] suggest that compactly encoded $\mathcal{R}$ occur more often ($h$ is our proxy for Kolmogorov complexity). Short codes $h$ are placed in a small hash table to find recurrent calls (in our experiments with 20-30× total coverage by AB SOLiD sequencing reads, 20-30% savings can be achieved this way).
Parameter optimization and genotype inference
Then the child's normal genotype has posterior probabilities ${p}_{\mathsf{\text{N}}}\left[g\right]=\frac{{\mathsf{\text{U}}}_{\mathsf{\text{N}}}\left[g\right]\cdot {\mathsf{\text{L}}}_{\mathsf{\text{N}}}\left[g\right]}{L}$.
Model parameters are optimized using the EM algorithm [18]. In one iteration, likelihoods and various posterior probabilities are computed across all loci in the so-called E-step, which are then used to set the model parameters for the next iteration in the so-called M-step. The iterations continue until convergence is achieved. Among the optimized model parameters, the parental genotype priors, the germline and tumor mutation parameters are optimized through multiple iterations using the same set of precalculated partial likelihoods.
where N is the number of loci, ${p}_{j}\left({g}_{\mathsf{\text{N}}},\phantom{\rule{0.3em}{0ex}}{g}_{\mathsf{\text{T}}}\right)$ is the posterior probability for a normal-tumor genotype pair at locus j, and α(g, g') is the expected number of substitutions for the two alleles given the diploid genotypes.
In order to set the tumor purity ω, the partial likelihoods need to be recomputed (for different T_{ β } values) by reading the input read-mapping files at each iteration. At the same time, we compute a calibrated map $\mu :\left\{0,1,\phantom{\rule{2.77695pt}{0ex}}\dots ,\phantom{\rule{2.77695pt}{0ex}}93\right\}\mapsto \left[0,1\right]$ from reported base-calling qualities to sequencing errors in the same framework. Note that both μ and ω have well-estimated initial values (μ starts with the canonical Phred-scaled values, and ω is estimated experimentally).
Decomposing zygosity and divergence
For the purposes of parameter inference, consider the following machine realizing the formulas for the parental genotype priors of (1). Upon receiving a heterozygous genotype xy, it flips either allele to output homozygous xx or yy with γ /2 probability each. Otherwise, with probability (1 - γ), the output is the same heterozygote xy. Homozygous genotypes are output without any change. Clearly, if the input genotype distribution is for Hardy-Weinberg, then the machine's output is distributed by the probabilities of (1). Accordingly, the divergence and heterozygosity parameters for the parental genotype prior ϕ are inferred by treating the machine's input genotype as a hidden variable. Expected frequencies for divergent input genotypes are used to estimate the divergence parameter, and expected frequencies for heterozygous → homozygous "flips" are used to estimate γ.
Sequencing data
Exome sequencing
Coverage statistics for two quartets used in validation experiments.
Exome sequencing (AB SOLiD system) | |||||
---|---|---|---|---|---|
Total | Normal | Tumor | Father | Mother | |
Quartet A (chromosome 12 only) | |||||
Sites: | 11 458 426 | ||||
Reads: | 5 530 702 | 1 454 529 | 1 396 361 | 1 117 647 | 1 562 165 |
Depth: | 23.0 | 6.0 | 5.8 | 4.6 | 6.6 |
Experimental tumor purity: | 0.63 | ||||
QUAD GT's purity estimate: | 0.41 | ||||
Quartet B (all chromosomes) | |||||
Sites: | 425 344 130 | ||||
Reads: | 134 574 732 | 38 156 404 | 34 580 382 | 29 997 426 | 31 840 520 |
Depth: | 23.0 | 5.4 | 5.1 | 6.5 | 5.9 |
Experimental tumor purity: | 0.97 | ||||
QUAD GT's purity estimate: | 0.44 | ||||
Whole-genome sequencing (Illumina HiSeq 2000) | |||||
Quartet B (whole genome) | |||||
Total | Normal | Tumor | |||
Depth: | 123.8 | 48.6 | 75.2 | ||
Illumina's purity estimate: | 0.46 |
Whole-genome sequencing
Tumor and normal DNA samples from Quartet B were submitted to Illumina, Inc, for deep whole-genome sequencing using the standard operating procedures of the HiSeq 2000 sequencing platform. Table 1 summarizes coverage statistics and tumor impurity. The whole-genome data was further analyzed for somatic mutations with CASAVA and Strelka [17] by Illumina, Inc.
Implementation
We incorporated the presented methods into an open-source Java software package called QUAD GT, using the standard file formats of the 1000 Genomes Project (SAM v1.4 [20] for input and VCF v4.1 [22] for output). Any of the input files may be missing, which makes QUAD GT suitable to analyze sets with just normal-tumor samples, or just parental-offspring trios.
The probabilistic framework enabled us to couple the inference with confidence measures in the form of quality scores computed from posterior probabilities. The quality scores accompany sample-specific genotype calls (VCF's GQ field), as well as the joint genotyping for the four samples (VCF's QUAL column). The posterior probabilities for germline and somatic mutations are calculated, as well, by summing across all pertinent genotype assignments. The program specifically introduces ambiguity in the genotyping calls to meet prescribed quality scores: a definite x/y base call in a sample is replaced by x/. or ./y, and then by ./. in a greedy manner, in order to achieve high specificity.
Parallelization
The E-step of the optimization, where sums of posterior probabilities are calculated across loci, is well-suited to parallelization. In our implementation, we use a hash key computed at each locus to assign the calculations to different computing threads running in parallel.
Availability
The QUAD GT software package is publicly available at http://www.iro.umontreal.ca/~csuros/quadgt/.
Results and discussion
We used two quartet data sets (A and B) to compare independent and joint variant detection. Figure 1 summarizes the coverage statistics for the quartets. Exome-sequencing reads at 5-6× coverage per sample were mapped to the human reference, and we inferred genome variants using our software package QUAD GT. The entire analysis pipeline for one quartet set, including model training and genotyping, took about 12 hours (wall-clock time) on standard multi-core computer workstations with 16 Gbytes of memory.
Exome-sequencing data from Quartet A was used to assess the concordance of genotyping calls by QUAD GT and a well-established variant caller, The Genome Analysis Toolkit [12]. We used independently produced whole-genome (WG) sequencing reads for the normal-tumor pair in Quartet B (with 124× total coverage, see Table 1) to gauge the two variant callers' sensitivity.
Concordance experiments
Comparison of calls made by the Genome Analysis Toolkit and QUAD GT on Quartet A.
Normal genome | |
Heterozygous SNPs (ref/alt) | Homozygous SNPs (alt/alt) |
called by both QUAD GT and GATK: 2100 | called by both QUAD GT and GATK: 945 |
called by GATK only: 60 | called by GATK only: 500 |
QUAD GT calls ref/ref: 4 | QUAD GT calls ref/ref: 0 |
QUAD GT calls alt/alt: 9 | QUAD GT calls ref/alt: 206 |
called by QUAD GT only: 839 | called by QUAD GT only: 17 |
GATK calls alt/alt: 206 | GATK calls ref/alt: 9 |
De novo mutations | |
called by both QUAD GT and GATK: 4 | |
called by GATK only: 327 | |
called by QUAD GT only: 0 | |
Tumor genome | |
Heterozygous SNPs (ref/alt) | Homozygous SNPs (alt/alt) |
called by both QUAD GT and GATK: 2032 | called by both QUAD GT and GATK: 938 |
called by GATK only: 41 | called by GATK only: 504 |
QUAD GT calls ref/ref: 3 | QUAD GT calls ref/ref: 0 |
QUAD GT calls alt/alt: 7 | QUAD GT calls ref/alt: 224 |
called by QUAD GT only: 989 | called by QUAD GT only: 17 |
GATK calls alt/alt: 224 | GATK calls ref/alt: 7 |
Somatic mutations | |
called by both QUAD GT and GATK: 8 | |
called by GATK only: 512 | |
called by QUAD GT only: 6 |
Sensitivity assessment
Whole-genome somatic loci and exome genotyping on Quartet B.
Locus | WG genotyping | Exome base calls (A:C:G:T) | QuadGT call | |||||||
---|---|---|---|---|---|---|---|---|---|---|
mutation | quality | N | T | F | M | N | T | F | M | |
chr4:85818319 | GG > AG | 68 | 0:0:8:0 | 2:0:6:0 | 0:0:9:0 | 0:0:9:0 | 0/0 | 0/0 | 0/0 | 0/0 |
chr6:29965983 | TT > CT | 17 | 0:1:0:27 | 0:1:0:25 | 0:3:0:0 | 0:0:0:43 | 0/0 | 0/0 | 0/1 | 0/0 |
chr8:10078796 | GG > CG | 15 | 0:2:1:0 | 0:2:3:0 | 0:5:2:0 | 0:2:4:0 | 0/1 | 0/1 | 0/1 | 0/1 |
chr12:25289551 | CC > TC | 29 | 0:37:0:1 | 0:31:0:2 | 0:57:0:0 | 1:45:0:0 | 0/0 | 0/0 | 0/0 | 0/0 |
Exome somatic calls supported by whole-genome data.
Locus | Whole-genome | Exome | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
mutation | score | Quality score | Rank | Base calls | (A:C:G:T) | ||||||
qGT | GATK | qGT | GATK | Normal | Tumor | Father | Mother | ||||
1 | chr20:577556 | GG > AG | 61 | 282 | 99,99 | 1 | 1 | 0:0:90:0 | 27:0:64:0 | 1:0:104:0 | 1:0:90:0 |
2 | chr18:26965596 | AA > GA | 87 | 282 | 99,99 | 1 | 1 | 77:0:1:2 | 63:1:20:0 | 106:0:0:0 | 84:0:0:0 |
3 | chr9:139897201 | GG > AG | 59 | 91 | 66,99 | 16 | 73 | 0:0:23:0 | 6:0:18:0 | 0:0:24:0 | 0:0:21:0 |
4 | chr2:88942555 | GG > TG | 93 | 53 | - | 84 | - | 0:0:29:0 | 0:0:5:3 | 0:0:36:0 | 0:0:26:0 |
5 | chr2:88942554 | AA > CA | 93 | 52 | - | 86 | - | 30:0:0:0 | 0:0:6:3 | 0:0:36:0 | 0:0:26:0 |
6 | chr7:150399212 | CC > TC | 93 | 48 | 60,99 | 98 | 104 | 0:20:0:0 | 1:6:0:9 | 0:14:0:0 | 0:13:0:0 |
7 | chrX:129017457 | CC > AC | 41 | 46 | 45,99 | 109 | 221 | 0:15:0:0 | 5:6:0:0 | 0:16:0:0 | 0:12:0:0 |
8 | chr16:3681082 | CC > TC | 89 | 44 | 30,82 | 118 | 629 | 0:10:0:0 | 0:10:0:4 | 0:19:0:0 | 0:11:0:0 |
9 | chr10:107013067 | CC > AC | 30 | 36 | - | 186 | - | 0:52:0:0 | 5:57:0:1 | 0:74:0:0 | 0:72:1:0 |
10 | chr8:72396806 | TT > CT | 59 | 24 | - | 398 | - | 0:0:0:6 | 0:3:0:13 | 0:0:0:20 | 0:0:0:11 |
11 | chrX:21779651 | GG > TG | 89 | 21 | 36,99 | 483 | 412 | 2:0:13:0 | 0:0:7:8 | 0:0:9:0 | 0:0:14:0 |
12 | chr5:125673987 | CC > TC | 97 | 14 | 6,70 | 790 | 7393 | 0:2:0:0 | 0:7:0:3 | 0:6:0:0 | 0:5:0:0 |
13 | chr12:10156011 | GG > AG | 89 | 8 | - | - | - | 0:0:16:0 | 3:0:8:0 | 0:0:28:0 | 0:0:9:0 |
14 | chr19:43602412 | GG > AG | 32 | 5 | - | - | - | 0:0:10:0 | 2:0:10:0 | 0:1:17:0 | 0:0:10:0 |
15 | chr6:112619582 | GG > AG | 68 | 3 | - | - | - | 0:0:5:0 | 2:1:5:0 | 0:0:6:0 | 0:0:5:0 |
Table 4 suggests that the joint variant-calling in QUAD GT leads to better sensitivity than GATK, which does not consider the relations between the genomes. In particular, 9 out of 276 (3%) SOMATIC calls by QUAD GT with quality score at least 30 have support in the WG data, whereas only 7 of GATK's 667 (1%) divergent genotypes of same quality threshold are validated. At a quality score cutoff of 20, 12 out of 555 (2%) and 7 out of 1312 (0.5%) are validated QUAD GT and GATK predictions.
Conclusions
Sequencing multiple genomes with known pedigrees or clonal relationships has a great promise for understanding the development of particular diseases. Our experiments with sequenced quartets of parents and normal-tumor pairs illustrate that the joint calls improve the reliability of inferred de novo and somatic mutations. The constraints imposed by the known relationships greatly improve the consistency of calls between different samples, and ultimately help to delineate the single nucleotide polymorphisms that can be associated with the disease.
A future release of the software is now under development that incorporates more nuanced substitution models with variable rates, transition-transversion ratios and nucleotide composition, as well as site-specific priors relying on public variant databases and gene annotations.
Notes
Acknowledgements
The authors are indebted to the patients and their parents for participating in this study. This study was supported by research funds provided by the Terry Fox Research Institute, the Canadian Institutes for Health Research, and Canada's National Sciences and Engineering Research Council. JFS is the recipient of a Cole Foundation studentship. RV is the recipient of a post-doctoral research fellowship from the Government of Canada through the "Foreign Affairs and International Trade Canada." DS holds the François-Karl-Viau Research Chair in Pediatric Oncogenomics.
Declarations
Funding for the publication of this article was provided by a grant from the National Sciences and Engineering Research Council.
This article has been published as part of BMC Bioinformatics Volume 14 Supplement 5, 2013: Proceedings of the Third Annual RECOMB Satellite Workshop on Massively Parallel Sequencing (RECOMB-seq 2013). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcbioinformatics/supplements/14/S5.
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