NGS Based Haplotype Assembly Using Matrix Completion

We apply matrix completion methods for haplotype assembly from NGS reads to develop the new HapSVT, HapNuc, and HapOPT algorithms. This is performed by applying a mathematical model to convert the reads to an incomplete matrix and estimating unknown components. This process is followed by quantizing and decoding the completed matrix in order to estimate haplotypes. These algorithms are compared to the state-of-the-art algorithms using simulated data as well as the real fosmid data. It is shown that the SNP missing rate and the haplotype block length of the proposed HapOPT are better than those of HapCUT2 with comparable accuracy in terms of reconstruction rate and switch error rate. A program implementing the proposed algorithms in MATLAB is freely available at https://github.com/smajidian/HapMC

Minimum error correction-based haplotype assembly: considerations for long read data

The single nucleotide polymorphism (SNP) is the most widely studied type of genetic variation. A haplotype is defined as the sequence of alleles at SNP sites on each haploid chromosome. Haplotype information is essential in unravelling the genome-phenotype association. Haplotype assembly is a well-known approach for reconstructing haplotypes, exploiting reads generated by DNA sequencing devices. The Minimum Error Correction (MEC) metric is often used for reconstruction of haplotypes from reads. However, problems with the MEC metric have been reported. Here, we investigate the MEC approach to demonstrate that it may result in incorrectly reconstructed haplotypes for devices that produce error-prone long reads. Specifically, we evaluate this approach for devices developed by Illumina, Pacific BioSciences and Oxford Nanopore Technologies. We show that imprecise haplotypes may be reconstructed with a lower MEC than that of the exact haplotype. The performance of MEC is explored for different coverage levels and error rates of data. Our simulation results reveal that in order to avoid incorrect MEC-based haplotypes, a coverage of 25 is needed for reads generated by Pacific BioSciences RS systems.Comment: 17 pages, 6 figure

PWHATSHAP: efficient haplotyping for future generation sequencing

Background: Haplotype phasing is an important problem in the analysis of genomics information. Given a set of DNA fragments of an individual, it consists of determining which one of the possible alleles (alternative forms of a gene) each fragment comes from. Haplotype information is relevant to gene regulation, epigenetics, genome-wide association studies, evolutionary and population studies, and the study of mutations. Haplotyping is currently addressed as an optimisation problem aiming at solutions that minimise, for instance, error correction costs, where costs are a measure of the con dence in the accuracy of the information acquired from DNA sequencing. Solutions have typically an exponential computational complexity. WhatsHap is a recent optimal approach which moves computational complexity from DNA fragment length to fragment overlap, i.e. coverage, and is hence of particular interest when considering sequencing technology's current trends that are producing longer fragments.  Results: Given the potential relevance of ecient haplotyping in several analysis pipelines, we have designed and engineered pWhatsHap, a parallel, high-performance version of WhatsHap. pWhatsHap is embedded in a toolkit developed in Python and supports genomics datasets in standard le formats. Building on WhatsHap, pWhatsHap exhibits the same complexity exploring a number of possible solutions which is exponential in the coverage of the dataset. The parallel implementation on multi-core architectures allows for a relevant reduction of the execution time for haplotyping, while the provided results enjoy the same high accuracy as that provided by WhatsHap, which increases with coverage.  Conclusions: Due to its structure and management of the large datasets, the parallelisation of WhatsHap posed demanding technical challenges, which have been addressed exploiting a high-level parallel programming framework. The result, pWhatsHap, is a freely available toolkit that improves the eciency of the analysis of genomics information

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

Haplotype Assembly and Small Variant Calling using Emerging Sequencing Technologies

Short read DNA sequencing technologies from Illumina have made sequencing a human genome significantly more affordable, greatly accelerating studies of biological function and the association of genetic variants to disease. These technologies are frequently used to detect small genetic variants such as single nucleotide variants (SNVs) using a reference genome. However, short read sequencing technologies have several limitations. First, the human genome is diploid and short reads contain limited information for assembling haplotypes, or the sequences of alleles on homologous chromosomes. Moreover, there is significant input DNA required, which poses challenges for analyzing single cells. Further, there is limited ability to detect genetic variants inside long duplicated sequences that occur in the genome. As a result, there has been widespread development of novel methods to overcome these deficiencies using short reads. These include clone based sequencing, linked read sequencing, and proximity ligation sequencing, as well as various single cell sequencing methods. There are also entirely new sequencing technologies from Pacific Biosciences and Oxford Nanopore Technologies that produce significantly longer reads. While these emerging methods and technologies demonstrate improvements compared to short reads, they also have properties and error modalities that pose unique computational challenges. Moreover, there is a shortage of bioinformatics methods for accurate small variant detection and haplotype assembly using these approaches compared to short reads. This dissertation aims to address this problem with the introduction of several new algorithms for highly accurate haplotype assembly and SNV calling. First, it introduces HapCUT2, an algorithm that can rapidly assemble haplotypes using a broad range of sequencing technologies. Second, it introduces an algorithm for variant calling and haplotyping using SISSOR, a recently introduced microfluidics based technology for sequencing single cells. Finally, it introduces Longshot, an algorithm for detecting and phasing SNVs using error-prone long read technologies. In each case, the algorithms are benchmarked using multiple real whole-genome sequencing datasets and are found to be highly accurate. The methods introduced in this dissertation contribute to the goal of sequencing diploid genomes accurately and completely for a broad range of scientific and clinical purposes

Coding mechanisms for communication and compression : analysis of wireless channels and DNA sequencing

textThis thesis comprises of two related but distinct components: Coding arguments for communication channels and information-theoretic analysis for haplotype assembly. The common thread for both problems is utilizing information and coding theoretic principles in understanding their underlying mechanisms. For the first class of problems, I study two practical challenges that prevent optimal discrete codes utilizing in real communication and compression systems, namely, coding over analog alphabet and fading. In particular, I use an expansion coding scheme to convert the original analog channel coding and source coding problems into a set of independent discrete subproblems. By adopting optimal discrete codes over the expanded levels, this low-complexity coding scheme can approach Shannon limit perfectly or in ratio. Meanwhile, I design a polar coding scheme to deal with the unstable state of fading channels. This novel coding mechanism of hierarchically utilizing different types of polar codes has been proved to be ergodic capacity achievable for several fading systems, without channel state information known at the transmitter. For the second class of problems, I build an information-theoretic view for haplotype assembly. More precisely, the recovery of the target pair of haplotype sequences using short reads is rephrased as the joint source-channel coding problem. Two binary messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of highthroughput sequencing. The focus is on determining the required number of reads for reliable haplotype reconstruction.Electrical and Computer Engineerin

Algorithms For Haplotype Inference And Block Partitioning

The completion of the human genome project in 2003 paved the way for studies to better understand and catalog variation in the human genome. The International HapMap Project was started in 2002 with the aim of identifying genetic variation in the human genome and studying the distribution of genetic variation across populations of individuals. The information collected by the HapMap project will enable researchers in associating genetic variations with phenotypic variations. Single Nucleotide Polymorphisms (SNPs) are loci in the genome where two individuals differ in a single base. It is estimated that there are approximately ten million SNPs in the human genome. These ten million SNPS are not completely independent of each other - blocks (contiguous regions) of neighboring SNPs on the same chromosome are inherited together. The pattern of SNPs on a block of the chromosome is called a haplotype. Each block might contain a large number of SNPs, but a small subset of these SNPs are sufficient to uniquely dentify each haplotype in the block. The haplotype map or HapMap is a map of these haplotype blocks. Haplotypes, rather than individual SNP alleles are expected to effect a disease phenotype. The human genome is diploid, meaning that in each cell there are two copies of each chromosome - i.e., each individual has two haplotypes in any region of the chromosome. With the current technology, the cost associated with empirically collecting haplotype data is prohibitively expensive. Therefore, the un-ordered bi-allelic genotype data is collected experimentally. The genotype data gives the two alleles in each SNP locus in an individual, but does not give information about which allele is on which copy of the chromosome. This necessitates computational techniques for inferring haplotypes from genotype data. This computational problem is called the haplotype inference problem. Many statistical approaches have been developed for the haplotype inference problem. Some of these statistical methods have been shown to be reasonably accurate on real genotype data. However, these techniques are very computation-intensive. With the international HapMap project collecting information from nearly 10 million SNPs, and with association studies involving thousands of individuals being undertaken, there is a need for more efficient methods for haplotype inference. This dissertation is an effort to develop efficient perfect phylogeny based combinatorial algorithms for haplotype inference. The perfect phylogeny haplotyping (PPH) problem is to derive a set of haplotypes for a given set of genotypes with the condition that the haplotypes describe a perfect phylogeny. The perfect phylogeny approach to haplotype inference is applicable to the human genome due to the block structure of the human genome. An important contribution of this dissertation is an optimal O(nm) time algorithm for the PPH problem, where n is the number of genotypes and m is the number of SNPs involved. The complexity of the earlier algorithms for this problem was O(nm^2). The O(nm) complexity was achieved by applying some transformations on the input data and by making use of the FlexTree data structure that has been developed as part of this dissertation work, which represents all the possible PPH solution for a given set of genotypes. Real genotype data does not always admit a perfect phylogeny, even within a block of the human genome. Therefore, it is necessary to extend the perfect phylogeny approach to accommodate deviations from perfect phylogeny. Deviations from perfect phylogeny might occur because of recombination events and repeated or back mutations (also referred to as homoplasy events). Another contribution of this dissertation is a set of fixed-parameter tractable algorithms for constructing near-perfect phylogenies with homoplasy events. For the problem of constructing a near perfect phylogeny with q homoplasy events, the algorithm presented here takes O(nm^2+m^(n+m)) time. Empirical analysis on simulated data shows that this algorithm produces more accurate results than PHASE (a popular haplotype inference program), while being approximately 1000 times faster than phase. Another important problem while dealing real genotype or haplotype data is the presence of missing entries. The Incomplete Perfect Phylogeny (IPP) problem is to construct a perfect phylogeny on a set of haplotypes with missing entries. The Incomplete Perfect Phylogeny Haplotyping (IPPH) problem is to construct a perfect phylogeny on a set of genotypes with missing entries. Both the IPP and IPPH problems have been shown to be NP-hard. The earlier approaches for both of these problems dealt with restricted versions of the problem, where the root is either available or can be trivially re-constructed from the data, or certain assumptions were made about the data. We make some novel observations about these problems, and present efficient algorithms for unrestricted versions of these problems. The algorithms have worst-case exponential time complexity, but have been shown to be very fast on practical instances of the problem