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

05301 Abstracts Collection -- Exact Algorithms and Fixed-Parameter Tractability

From 24.07.05 to 29.07.05, the Dagstuhl Seminar 05301 ``Exact Algorithms and Fixed-Parameter Tractability\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. This is a collection of abstracts of the presentations given during the seminar

The Binary Perfect Phylogeny with Persistent characters

The binary perfect phylogeny model is too restrictive to model biological events such as back mutations. In this paper we consider a natural generalization of the model that allows a special type of back mutation. We investigate the problem of reconstructing a near perfect phylogeny over a binary set of characters where characters are persistent: characters can be gained and lost at most once. Based on this notion, we define the problem of the Persistent Perfect Phylogeny (referred as P-PP). We restate the P-PP problem as a special case of the Incomplete Directed Perfect Phylogeny, called Incomplete Perfect Phylogeny with Persistent Completion, (refereed as IP-PP), where the instance is an incomplete binary matrix M having some missing entries, denoted by symbol ?, that must be determined (or completed) as 0 or 1 so that M admits a binary perfect phylogeny. We show that the IP-PP problem can be reduced to a problem over an edge colored graph since the completion of each column of the input matrix can be represented by a graph operation. Based on this graph formulation, we develop an exact algorithm for solving the P-PP problem that is exponential in the number of characters and polynomial in the number of species.Comment: 13 pages, 3 figure

Algorithms for Analysis of Heterogeneous Cancer and Viral Populations Using High-Throughput Sequencing Data

Next-generation sequencing (NGS) technologies experienced giant leaps in recent years. Short read samples reach millions of reads, and the number of samples has been growing enormously in the wake of the COVID-19 pandemic. This data can expose essential aspects of disease transmission and development and reveal the key to its treatment. At the same time, single-cell sequencing saw the progress of getting from dozens to tens of thousands of cells per sample. These technological advances bring new challenges for computational biology and require the development of scalable, robust methods to deal with a wide range of problems varying from epidemiology to cancer studies. The first part of this work is focused on processing virus NGS data. It proposes algorithms that can facilitate the initial data analysis steps by filtering genetically related sequencing and the tool investigating intra-host virus diversity vital for biomedical research and epidemiology. The second part addresses single-cell data in cancer studies. It develops evolutionary cancer models involving new quantitative parameters of cancer subclones to understand the underlying processes of cancer development better

A list of parameterized problems in bioinformatics

In this report we present a list of problems that originated in bionformatics. Our aim is to collect information on such problems that have been analyzed from the point of view of Parameterized Complexity. For every problem we give its definition and biological motivation together with known complexity results.Postprint (published version

Predicting Horizontal Gene Transfers with Perfect Transfer Networks

Horizontal gene transfer inference approaches are usually based on gene sequences: parametric methods search for patterns that deviate from a particular genomic signature, while phylogenetic methods use sequences to reconstruct the gene and species trees. However, it is well-known that sequences have difficulty identifying ancient transfers since mutations have enough time to erase all evidence of such events. In this work, we ask whether character-based methods can predict gene transfers. Their advantage over sequences is that homologous genes can have low DNA similarity, but still have retained enough important common motifs that allow them to have common character traits, for instance the same functional or expression profile. A phylogeny that has two separate clades that acquired the same character independently might indicate the presence of a transfer even in the absence of sequence similarity. We introduce perfect transfer networks, which are phylogenetic networks that can explain the character diversity of a set of taxa. This problem has been studied extensively in the form of ancestral recombination networks, but these only model hybridation events and do not differentiate between direct parents and lateral donors. We focus on tree-based networks, in which edges representing vertical descent are clearly distinguished from those that represent horizontal transmission. Our model is a direct generalization of perfect phylogeny models to such networks. Our goal is to initiate a study on the structural and algorithmic properties of perfect transfer networks. We then show that in polynomial time, one can decide whether a given network is a valid explanation for a set of taxa, and show how, for a given tree, one can add transfer edges to it so that it explains a set of taxa

Analysis and Visualization of Local Phylogenetic Structure within Species

While it is interesting to examine the evolutionary history and phylogenetic relationship between species, for example, in a sort of tree of life, there is also a great deal to be learned from examining population structure and relationships within species. A careful description of phylogenetic relationships within species provides insights into causes of phenotypic variation, including disease susceptibility. The better we are able to understand the patterns of genotypic variation within species, the better these populations may be used as models to identify causative variants and possible therapies, for example through targeted genome-wide association studies (GWAS). My thesis describes a model of local phylogenetic structure, how it can be effectively derived under various circumstances, and useful applications and visualizations of this model to aid genetic studies. I introduce a method for discovering phylogenetic structure among individuals of a population by partitioning the genome into a minimal set of intervals within which there is no evidence of recombination. I describe two extensions of this basic method. The first allows it to be applied to heterozygous, in addition to homozygous, genotypes and the second makes it more robust to errors in the source genotypes. I demonstrate the predictive power of my local phylogeny model using a novel method for genome-wide genotype imputation. This imputation method achieves very high accuracy - on the order of the accuracy rate in the sequencing technology - by imputing genotypes in regions of shared inheritance based on my local phylogenies. Comparative genomic analysis within species can be greatly aided by appropriate visualization and analysis tools. I developed a framework for web-based visualization and analysis of multiple individuals within a species, with my model of local phylogeny providing the underlying structure. I will describe the utility of these tools and the applications for which they have found widespread use.Doctor of Philosoph

Inferring tumour evolution from single-cell and multi-sample data

Tumour development has long been recognised as an evolutionary process during which cells accumulate mutations and evolve into a mix of genetically distinct cell subpopulations. The resulting genetic intra-tumour heterogeneity poses a major challenge to cancer therapy, as it increases the chance of drug resistance. To study tumour evolution in more detail, reliable approaches to infer the life histories of tumours are needed. This dissertation focuses on computational methods for inferring trees of tumour evolution from single-cell and multi-sample sequencing data. Recent advances in single-cell sequencing technologies have promised to reveal tumour heterogeneity at a much higher resolution, but single-cell sequencing data is inherently noisy, making it unsuitable for analysis with classic phylogenetic methods. The first part of the dissertation describes OncoNEM, a novel probabilistic method to infer clonal lineage trees from noisy single nucleotide variants of single cells. Simulation studies are used to validate the method and to compare its performance to that of other methods. Finally, OncoNEM is applied in two case studies. In the second part of the dissertation, a comprehensive collection of existing multi-sample approaches is used to infer the phylogenies of metastatic breast cancers from ten patients. In particular, shallow whole-genome, whole exome and targeted deep sequencing data are analysed. The inference methods comprise copy number and point mutation based approaches, as well as a method that utilises a combination of the two. To improve the copy number based inference, a novel allele-specific multi-sample segmentation algorithm is presented. The results are compared across methods and data types to assess the reliability of the different methods. In summary, this thesis presents substantial methodological advances to understand tumour evolution from genomic profiles of single cells or related bulk samples