Constrained hidden Markov models for population-based haplotyping

Peer reviewe

Inference with Constrained Hidden Markov Models in PRISM

A Hidden Markov Model (HMM) is a common statistical model which is widely used for analysis of biological sequence data and other sequential phenomena. In the present paper we show how HMMs can be extended with side-constraints and present constraint solving techniques for efficient inference. Defining HMMs with side-constraints in Constraint Logic Programming have advantages in terms of more compact expression and pruning opportunities during inference. We present a PRISM-based framework for extending HMMs with side-constraints and show how well-known constraints such as cardinality and all different are integrated. We experimentally validate our approach on the biologically motivated problem of global pairwise alignment

Laskennallisia menetelmiä haplotyypien ennustamiseen ja paikallisten rinnastusten merkittävyyden arviointiin

This thesis which consists of an introduction and four peer-reviewed original publications studies the problems of haplotype inference (haplotyping) and local alignment significance. The problems studied here belong to the broad area of bioinformatics and computational biology. The presented solutions are computationally fast and accurate, which makes them practical in high-throughput sequence data analysis. Haplotype inference is a computational problem where the goal is to estimate haplotypes from a sample of genotypes as accurately as possible. This problem is important as the direct measurement of haplotypes is difficult, whereas the genotypes are easier to quantify. Haplotypes are the key-players when studying for example the genetic causes of diseases. In this thesis, three methods are presented for the haplotype inference problem referred to as HaploParser, HIT, and BACH. HaploParser is based on a combinatorial mosaic model and hierarchical parsing that together mimic recombinations and point-mutations in a biologically plausible way. In this mosaic model, the current population is assumed to be evolved from a small founder population. Thus, the haplotypes of the current population are recombinations of the (implicit) founder haplotypes with some point--mutations. HIT (Haplotype Inference Technique) uses a hidden Markov model for haplotypes and efficient algorithms are presented to learn this model from genotype data. The model structure of HIT is analogous to the mosaic model of HaploParser with founder haplotypes. Therefore, it can be seen as a probabilistic model of recombinations and point-mutations. BACH (Bayesian Context-based Haplotyping) utilizes a context tree weighting algorithm to efficiently sum over all variable-length Markov chains to evaluate the posterior probability of a haplotype configuration. Algorithms are presented that find haplotype configurations with high posterior probability. BACH is the most accurate method presented in this thesis and has comparable performance to the best available software for haplotype inference. Local alignment significance is a computational problem where one is interested in whether the local similarities in two sequences are due to the fact that the sequences are related or just by chance. Similarity of sequences is measured by their best local alignment score and from that, a p-value is computed. This p-value is the probability of picking two sequences from the null model that have as good or better best local alignment score. Local alignment significance is used routinely for example in homology searches. In this thesis, a general framework is sketched that allows one to compute a tight upper bound for the p-value of a local pairwise alignment score. Unlike the previous methods, the presented framework is not affeced by so-called edge-effects and can handle gaps (deletions and insertions) without troublesome sampling and curve fitting.Tässä väitöskirjassa esitetään uusia, tarkkoja ja tehokkaita laskennallisia menetelmiä populaation haplotyyppien ennustamiseen genotyypeistä sekä sekvenssien paikallisten rinnastusten merkittävyyden arviointiin. Käytetyt menetelmät perustuvat mm. dynaamiseen ohjelmointiin, jossa pienimmät osaongelmat ratkaistaan ensin ja näistä pienistä ratkaisuosista kootaan suurempien osaongelmien ratkaisuja. Organismin genomi on yleensä koodattu solun sisään DNA:han, yksinkertaistaen jonoon (sekvenssiin) emäksiä A, C, G ja T. Genomi on jäsentynyt kromosomeihin, jotka sisältävät tietyissä paikoissa esiintyviä muutoksia, merkkijaksoja. Diploidin organismin, kuten ihmisen, kromosomit (autosomit) esiintyvät pareittain. Yksilö perii parin toisen kromosomin isältään ja toisen äidiltään. Haplotyyppi on yksilön tietyissä paikoissa esiintyvien merkkijaksojen jono tietyssä kromosomiparin kromosomissa. Haplotyyppien mittaaminen suoraan on vaikeaa, mutta genotyypit ovat helpommin mitattavia. Genotyypit kertovat, mitkä kaksi merkkijaksoa kromosomin vastaavissa kohdissa esiintyy. Haplotyyppiaineistoja käytetään yleisesti esimerkiksi genettisten tautien tutkimiseen. Tämän vuoksi haplotyyppien laskennallinen ennustaminen genotyypeistä on tärkeä tutkimusongelma. Syötteenä ongelmassa on siis näyte tietyn populaation genotyypeistä, joista tulisi ennustaa haplotyypit jokaiselle näytteen yksilölle. Haplotyyppien ennustaminen genotyypeistä on mahdollista, koska haplotyypit ovat samankaltaisia yksilöiden välillä. Samankaltaisuus johtuu evoluution prosesseista, kuten periytymisestä, luonnonvalinnasta, migraatiosta ja isolaatiosta. Tässä väitöskirjassa esitetään kolme menetelmää haplotyypien määritykseen. Näistä tarkin menetelmä, nimeltään BACH, käyttää vaihtuva-asteista Markov-mallia ja bayesilaista tilastotiedettä haplotyyppien ennnustamiseen genotyyppiaineistosta. Menetelmän malli pystyy mallintamaan tarkasti geneettistä kytkentää eli fyysisesti lähekkäin sijaitsevien merkkijaksojen riippuvuutta. Tämä kytkentä näkyy haplotyyppijonojen lokaalina samankaltaisuutena. Paikallista rinnastusta käytetään esimerkiksi etsittäessä eri organismien genomien sekvensseistä samankaltaisia kohtia, esimerkiksi vastaavia geenejä. Paikallisen rinnastuksen hakualgoritmit löytävät vain samankaltaisimman kohdan, mutta eivät kerro, onko löydös tilastollisesti merkittävä. Yleinen tapa määrittää rinnastuksen tilastollista merkittävyyttä on laskea rinnastuksen hyvyydelle (pisteluvulle) p-arvo, joka kertoo rinnastuksen tilastollisen merkittävyyden. Väitöskirjan menetelmä paikallisten rinnastusten merkittävyyden laskemiseksi laskee sekvenssien paikalliselle rinnastukselle odotusarvon, joka antaa yleisesti käytettävälle p‐arvolle tiukan ylärajan. Vaikka malli on yksinkertainen, empiirisissä testeissä menetelmän antaman odotusarvon yksinkertainen johdannainen osoittautuu sangen tarkaksi p‐arvon estimaatiksi. Lähestymistavan etuna on, että sen avulla rinnastuksen aukot (poistot ja lisäykset) voidaan mallintaa suoraviivaisella tavalla

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

HaploRec : efficient and accurate large-scale reconstruction of haplotypes

Peer reviewe

A model-based approach to selection of tag SNPs

BACKGROUND: Single Nucleotide Polymorphisms (SNPs) are the most common type of polymorphisms found in the human genome. Effective genetic association studies require the identification of sets of tag SNPs that capture as much haplotype information as possible. Tag SNP selection is analogous to the problem of data compression in information theory. According to Shannon's framework, the optimal tag set maximizes the entropy of the tag SNPs subject to constraints on the number of SNPs. This approach requires an appropriate probabilistic model. Compared to simple measures of Linkage Disequilibrium (LD), a good model of haplotype sequences can more accurately account for LD structure. It also provides a machinery for the prediction of tagged SNPs and thereby to assess the performances of tag sets through their ability to predict larger SNP sets. RESULTS: Here, we compute the description code-lengths of SNP data for an array of models and we develop tag SNP selection methods based on these models and the strategy of entropy maximization. Using data sets from the HapMap and ENCODE projects, we show that the hidden Markov model introduced by Li and Stephens outperforms the other models in several aspects: description code-length of SNP data, information content of tag sets, and prediction of tagged SNPs. This is the first use of this model in the context of tag SNP selection. CONCLUSION: Our study provides strong evidence that the tag sets selected by our best method, based on Li and Stephens model, outperform those chosen by several existing methods. The results also suggest that information content evaluated with a good model is more sensitive for assessing the quality of a tagging set than the correct prediction rate of tagged SNPs. Besides, we show that haplotype phase uncertainty has an almost negligible impact on the ability of good tag sets to predict tagged SNPs. This justifies the selection of tag SNPs on the basis of haplotype informativeness, although genotyping studies do not directly assess haplotypes. A software that implements our approach is available

In Silico Haplotyping, Genotyping and Analysis of Resequencing Data using Markov Models.

Searches for the elusive genetic mechanisms underlying complex diseases have long challenged human geneticists. Recently, genome-wide association studies (GWAS) have successfully identified many complex disease susceptibility loci by genotyping a subset of several hundred thousand common genetic variants across many individuals. With the rapid deployment of next-generation sequencing technologies, it is anticipated that future genetic association studies will be able to more comprehensively survey genetic variation, both to identify new loci that were missed in the original round of genome-wide association studies and to finely characterize the contributions of identified loci. GWAS, whether in the current genotyping-based form or in the anticipated sequencing-based form, pose a range of computational and analytical challenges. I first propose and implement a computationally efficient hidden Markov model that can rapidly reconstruct the two chromosomes carried by each individual in a study. To achieve this goal, the methods combine partial genotype or sequence data for each individual with additional information on additional individuals. Comparisons with standard haplotypers in both simulated and real datasets show that the proposed method is at least comparable and more computational efficient. I next extend my method for imputing genotypes at untyped SNP loci. Specifically, I consider how my approach can be used to assess several million common variants that are not directly genotyped in a typical association study but for which data are available in public databases. I describe how the extended method performs in a wide range of simulated and real settings. Finally, I consider how low-depth shot-gun resequencing data on a large number of individuals can be combined to provide accurate estimates of individual sequences. This approach should speed up the advent of large-scale genome resequencing studies and facilitate the identification of rare variants that contribute to disease susceptibility and that cannot be adequately assessed with current genotyping-based GWAS approaches. My methods are flexible enough to accommodate phased haplotype data, genotype data, or re-sequencing data as input and can utilize public resources such as the HapMap consortium and the 1000 Genomes Project that now include data on several million genetic variants typed on hundreds of individuals.Ph.D.BiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64640/1/ylwtx_1.pd