Haplotype Inference on Pedigrees with Recombinations, Errors, and Missing Genotypes via SAT solvers

The Minimum-Recombinant Haplotype Configuration problem (MRHC) has been highly successful in providing a sound combinatorial formulation for the important problem of genotype phasing on pedigrees. Despite several algorithmic advances and refinements that led to some efficient algorithms, its applicability to real datasets has been limited by the absence of some important characteristics of these data in its formulation, such as mutations, genotyping errors, and missing data. In this work, we propose the Haplotype Configuration with Recombinations and Errors problem (HCRE), which generalizes the original MRHC formulation by incorporating the two most common characteristics of real data: errors and missing genotypes (including untyped individuals). Although HCRE is computationally hard, we propose an exact algorithm for the problem based on a reduction to the well-known Satisfiability problem. Our reduction exploits recent progresses in the constraint programming literature and, combined with the use of state-of-the-art SAT solvers, provides a practical solution for the HCRE problem. Biological soundness of the phasing model and effectiveness (on both accuracy and performance) of the algorithm are experimentally demonstrated under several simulated scenarios and on a real dairy cattle population.Comment: 14 pages, 1 figure, 4 tables, the associated software reHCstar is available at http://www.algolab.eu/reHCsta

Unlocking the bottleneck in forward genetics using whole-genome sequencing and identity by descent to isolate causative mutations

Forward genetics screens with N-ethyl-N-nitrosourea (ENU) provide a powerful way to illuminate gene function and generate mouse models of human disease; however, the identification of causative mutations remains a limiting step. Current strategies depend on conventional mapping, so the propagation of affected mice requires non-lethal screens; accurate tracking of phenotypes through pedigrees is complex and uncertain; out-crossing can introduce unexpected modifiers; and Sanger sequencing of candidate genes is inefficient. Here we show how these problems can be efficiently overcome using whole-genome sequencing (WGS) to detect the ENU mutations and then identify regions that are identical by descent (IBD) in multiple affected mice. In this strategy, we use a modification of the Lander-Green algorithm to isolate causative recessive and dominant mutations, even at low coverage, on a pure strain background. Analysis of the IBD regions also allows us to calculate the ENU mutation rate (1.54 mutations per Mb) and to model future strategies for genetic screens in mice. The introduction of this approach will accelerate the discovery of causal variants, permit broader and more informative lethal screens to be used, reduce animal costs, and herald a new era for ENU mutagenesis.The High-Throughput Genomics Group at the Wellcome Trust Centre for Human Genetics is funded by Wellcome Trust grant reference 090532/Z/09/Z and MRC Hub grant G0900747 91070. This study was supported by Wellcome Trust Strategic Award 082030 (CCG), Wellcome Trust Studentship 094446/Z/10/Z (KRB), the Oxford NIHR Biomedical Research Centre, and the MRC Human Immunology Unit (RJC). AJR and GL were supported by Wellcome Trust grant 090532/Z/ 09/Z, CCG and AE by a Major initiative Award from the Clive and Vera Ramaciotti Foundation, and AE by an NHMRC Career Development Award. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Haplotypes versus genotypes on pedigrees

Abstract. Genome sequencing will soon produce haplotype data for individuals. For pedigrees of related individuals, sequencing appears to be an attractive alternative to genotyping. However, methods for pedigree analysis with haplotype data have not yet been developed, and the computational complexity of such problems has been an open question. Furthermore, it is not clear in which scenarios haplotype data would provide better estimates than genotype data for quantities such as recombination rates. To answer these questions, a reduction is given from genotype problem instances to haplotype problem instances, and it is shown that solving the haplotype problem yields the solution to the genotype problem, up to constant factors or coefficients. The pedigree analysis problems we will consider are the likelihood, maximum probability haplotype, and minimum recombination haplotype problems. Two algorithms are introduced: an exponential-time hidden Markov model (HMM) for haplotype data where some individuals are untyped, and a linear-time algorithm for pedigrees having haplotype data for all individuals. Recombination estimates from the general haplotype HMM algorithm are compared to recombination estimates produced by a genotype HMM. Having haplotype data on all individuals produces better estimates. However, having several untyped individuals can drastically reduce the utility of haplotype data. Pedigree analysis, both linkage and association studies, has a long history of important contributions to genetics, including disease-gene finding and some of the first genetic maps for humans. Recent contributions include fine-scale recombination maps in humans [4], regions linked to Schizophrenia that might be missed by genome-wide association studies [11], and insights into the relationship between cystic fibrosis and fertility [13]. Algorithms for pedigree problems are of great interest to the computer science community, in part because of connections to machine learning algorithms, optimization methods, and combinatorics [7, 16

Bayesian Inference for Retrospective Population Genetics Models Using Markov Chain Monte Carlo Methods

Genetics, the science of heredity and variation in living organisms, has a central role in medicine, in breeding crops and livestock, and in studying fundamental topics of biological sciences such as evolution and cell functioning. Currently the field of genetics is under a rapid development because of the recent advances in technologies by which molecular data can be obtained from living organisms. In order that most information from such data can be extracted, the analyses need to be carried out using statistical models that are tailored to take account of the particular genetic processes. In this thesis we formulate and analyze Bayesian models for genetic marker data of contemporary individuals. The major focus is on the modeling of the unobserved recent ancestry of the sampled individuals (say, for tens of generations or so), which is carried out by using explicit probabilistic reconstructions of the pedigree structures accompanied by the gene flows at the marker loci. For such a recent history, the recombination process is the major genetic force that shapes the genomes of the individuals, and it is included in the model by assuming that the recombination fractions between the adjacent markers are known. The posterior distribution of the unobserved history of the individuals is studied conditionally on the observed marker data by using a Markov chain Monte Carlo algorithm (MCMC). The example analyses consider estimation of the population structure, relatedness structure (both at the level of whole genomes as well as at each marker separately), and haplotype configurations. For situations where the pedigree structure is partially known, an algorithm to create an initial state for the MCMC algorithm is given. Furthermore, the thesis includes an extension of the model for the recent genetic history to situations where also a quantitative phenotype has been measured from the contemporary individuals. In that case the goal is to identify positions on the genome that affect the observed phenotypic values. This task is carried out within the Bayesian framework, where the number and the relative effects of the quantitative trait loci are treated as random variables whose posterior distribution is studied conditionally on the observed genetic and phenotypic data. In addition, the thesis contains an extension of a widely-used haplotyping method, the PHASE algorithm, to settings where genetic material from several individuals has been pooled together, and the allele frequencies of each pool are determined in a single genotyping.Perinnöllisyystieteessä eli genetiikassa tutkitaan perinnöllisen aineksen rakennetta, toimintaa ja muuntelua sekä muita yksilöiden väliseen vaihteluun vaikuttavia tekijöitä eliökunnassa. Nykyisten laboratoriomenetelmien avulla on mahdollista kerätä eliöistä yhä tarkempia ja laajempia molekyylitason aineistoja. Tällaisten aineistojen käsittelemiseksi tarvitaan tilastollisia malleja, jotka hyödyntävät mahdollisimman tarkasti käytettävissä olevaa tietämystä biologisista prosesseista, joiden tuloksena kerätyt aineistot ovat muodostuneet. Tässä väitöskirjassa kehitetään Bayesläisen tilastotieteen malleja eräille geneettisille prosesseille sekä sovelletaan malleja esimerkkiaineistoihin. Pääpaino on yksilöiden yhteisen lähihistorian mallittamisessa. Yksinkertaisimmillaan lähtökohtana on joukko nykyhetken yksilöitä, joiden perinnöllinen aines oletetaan tunnetuksi tietyissä merkkigeenikohdissa laboratoriossa suoritettujen genotyyppimittausten perusteella. Tilastollista mallia käytetään arvioimaan todennäköisyyksiä erilaisille yksilöitä yhdistäville lähihistorioille, jotka kuvataan sukupuurakenteiden sekä merkkigeenien periytymisreittien avulla. Tarkasteltavat aikajaksot ovat enintään kymmeniä sukupolvia. Väitöskirjassa myös hyödynnetään lähihistoriamallia geenikartoitussovelluksessa, jonka tavoitteena on paikallistaa sellaisia kohtia genomista, joilla on vaikutusta tiettyyn yksilöistä mitattuun tai havaittuun ominaisuuteen. Muita sovelluskohteita ovat populaatiorakenteen arviointi sekä yksilöiden välisten sukulaisuusasteiden arviointi

Parsimony-based genetic algorithm for haplotype resolution and block partitioning

This dissertation proposes a new algorithm for performing simultaneous haplotype resolution and block partitioning. The algorithm is based on genetic algorithm approach and the parsimonious principle. The multiloculs LD measure (Normalized Entropy Difference) is used as a block identification criterion. The proposed algorithm incorporates missing data is a part of the model and allows blocks of arbitrary length. In addition, the algorithm provides scores for the block boundaries which represent measures of strength of the boundaries at specific positions. The performance of the proposed algorithm was validated by running it on several publicly available data sets including the HapMap data and comparing results to those of the existing state-of-the-art algorithms. The results show that the proposed genetic algorithm provides the accuracy of haplotype decomposition within the range of the same indicators shown by the other algorithms. The block structure output by our algorithm in general agrees with the block structure for the same data provided by the other algorithms. Thus, the proposed algorithm can be successfully used for block partitioning and haplotype phasing while providing some new valuable features like scores for block boundaries and fully incorporated treatment of missing data. In addition, the proposed algorithm for haplotyping and block partitioning is used in development of the new clustering algorithm for two-population mixed genotype samples. The proposed clustering algorithm extracts from the given genotype sample two clusters with substantially different block structures and finds haplotype resolution and block partitioning for each cluster

Accurate HLA type inference using a weighted similarity graph

Abstract Background The human leukocyte antigen system (HLA) contains many highly variable genes. HLA genes play an important role in the human immune system, and HLA gene matching is crucial for the success of human organ transplantations. Numerous studies have demonstrated that variation in HLA genes is associated with many autoimmune, inflammatory and infectious diseases. However, typing HLA genes by serology or PCR is time consuming and expensive, which limits large-scale studies involving HLA genes. Since it is much easier and cheaper to obtain single nucleotide polymorphism (SNP) genotype data, accurate computational algorithms to infer HLA gene types from SNP genotype data are in need. To infer HLA types from SNP genotypes, the first step is to infer SNP haplotypes from genotypes. However, for the same SNP genotype data set, the haplotype configurations inferred by different methods are usually inconsistent, and it is often difficult to decide which one is true. Results In this paper, we design an accurate HLA gene type inference algorithm by utilizing SNP genotype data from pedigrees, known HLA gene types of some individuals and the relationship between inferred SNP haplotypes and HLA gene types. Given a set of haplotypes inferred from the genotypes of a population consisting of many pedigrees, the algorithm first constructs a weighted similarity graph based on a new haplotype similarity measure and derives constraint edges from known HLA gene types. Based on the principle that different HLA gene alleles should have different background haplotypes, the algorithm searches for an optimal labeling of all the haplotypes with unknown HLA gene types such that the total weight among the same HLA gene types is maximized. To deal with ambiguous haplotype solutions, we use a genetic algorithm to select haplotype configurations that tend to maximize the same optimization criterion. Our experiments on a previously typed subset of the HapMap data show that the algorithm is highly accurate, achieving an accuracy of 96% for gene HLA-A, 95% for HLA-B, 97% for HLA-C, 84% for HLA-DRB1, 98% for HLA-DQA1 and 97% for HLA-DQB1 in a leave-one-out test. Conclusions Our algorithm can infer HLA gene types from neighboring SNP genotype data accurately. Compared with a recent approach on the same input data, our algorithm achieved a higher accuracy. The code of our algorithm is available to the public for free upon request to the corresponding authors

A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree

BACKGROUND: When studying genetic diseases in which genetic variations are passed on to offspring, the ability to distinguish between paternal and maternal alleles is essential. Determining haplotypes from genotype data is called haplotype inference. Most existing computational algorithms for haplotype inference have been designed to use genotype data collected from individuals in the form of a pedigree. A haplotype is regarded as a hereditary unit and therefore input pedigrees are preferred that are free of mutational events and have a minimum number of genetic recombinational events. These ideas motivated the zero-recombinant haplotype configuration (ZRHC) problem, which strictly follows the Mendelian law of inheritance, namely that one haplotype of each child is inherited from the father and the other haplotype is inherited from the mother, both without any mutation. So far no linear-time algorithm for ZRHC has been proposed for general pedigrees, even though the number of mating loops in a human pedigree is usually very small and can be regarded as constant. RESULTS: Given a pedigree with n individuals, m marker loci, and k mating loops, we proposed an algorithm that can provide a general solution to the zero-recombinant haplotype configuration problem in O(kmn + k(2)m) time. In addition, this algorithm can be modified to detect inconsistencies within the genotype data without loss of efficiency. The proposed algorithm was subject to 12000 experiments to verify its performance using different (n, m) combinations. The value of k was uniformly distributed between zero and six throughout all experiments. The experimental results show a great linearity in terms of execution time in relation to input size when both n and m are larger than 100. For those experiments where n or m are less than 100, the proposed algorithm runs very fast, in thousandth to hundredth of a second, on a personal desktop computer. CONCLUSIONS: We have developed the first deterministic linear-time algorithm for the zero-recombinant haplotype configuration problem. Our experimental results demonstrated the linearity of its execution time in relation to the input size. The proposed algorithm can be modified to detect inconsistency within the genotype data without loss of efficiency and is expected to be able to handle recombinant and missing data with further extension

Causal Inference in Genetic Trio Studies

We introduce a method to rigorously draw causal inferences---inferences immune to all possible confounding---from genetic data that include parents and offspring. Causal conclusions are possible with these data because the natural randomness in meiosis can be viewed as a high-dimensional randomized experiment. We make this observation actionable by developing a novel conditional independence test that identifies regions of the genome containing distinct causal variants. The proposed Digital Twin Test compares an observed offspring to carefully constructed synthetic offspring from the same parents in order to determine statistical significance, and it can leverage any black-box multivariate model and additional non-trio genetic data in order to increase power. Crucially, our inferences are based only on a well-established mathematical description of the rearrangement of genetic material during meiosis and make no assumptions about the relationship between the genotypes and phenotypes

Estimating genealogies from linked marker data: a Bayesian approach

<p>Abstract</p> <p>Background</p> <p>Answers to several fundamental questions in statistical genetics would ideally require knowledge of the ancestral pedigree and of the gene flow therein. A few examples of such questions are haplotype estimation, relatedness and relationship estimation, gene mapping by combining pedigree and linkage disequilibrium information, and estimation of population structure.</p> <p>Results</p> <p>We present a probabilistic method for genealogy reconstruction. Starting with a group of genotyped individuals from some population isolate, we explore the state space of their possible ancestral histories under our Bayesian model by using Markov chain Monte Carlo (MCMC) sampling techniques. The main contribution of our work is the development of sampling algorithms in the resulting vast state space with highly dependent variables. The main drawback is the computational complexity that limits the time horizon within which explicit reconstructions can be carried out in practice.</p> <p>Conclusion</p> <p>The estimates for IBD (identity-by-descent) and haplotype distributions are tested in several settings using simulated data. The results appear to be promising for a further development of the method.</p