Biological applications of the theory of birth-and-death processes

In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer, and somatic evolution of cancers. We further describe how empirical data, e.g., distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. It is concluded that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological process, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.Comment: 29 pages, 4 figures; submitted to "Briefings in Bioinformatics

Universal Features in the Genome-level Evolution of Protein Domains

Protein domains are found on genomes with notable statistical distributions, which bear a high degree of similarity. Previous work has shown how these distributions can be accounted for by simple models, where the main ingredients are probabilities of duplication, innovation, and loss of domains. However, no one so far has addressed the issue that these distributions follow definite trends depending on protein-coding genome size only. We present a stochastic duplication/innovation model, falling in the class of so-called Chinese Restaurant Processes, able to explain this feature of the data. Using only two universal parameters, related to a minimal number of domains and to the relative weight of innovation to duplication, the model reproduces two important aspects: (a) the populations of domain classes (the sets, related to homology classes, containing realizations of the same domain in different proteins) follow common power-laws whose cutoff is dictated by genome size, and (b) the number of domain families is universal and markedly sublinear in genome size. An important ingredient of the model is that the innovation probability decreases with genome size. We propose the possibility to interpret this as a global constraint given by the cost of expanding an increasingly complex interactome. Finally, we introduce a variant of the model where the choice of a new domain relates to its occurrence in genomic data, and thus accounts for fold specificity. Both models have general quantitative agreement with data from hundreds of genomes, which indicates the coexistence of the well-known specificity of proteomes with robust self-organizing phenomena related to the basic evolutionary ``moves'' of duplication and innovation

Birth/birth-death processes and their computable transition probabilities with biological applications

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth(death)/birth-death process, a tractable bivariate extension of the birth-death process. We develop an efficient and robust algorithm to calculate the transition probabilities of birth(death)/birth-death processes using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution

The development of computational methods for large-scale comparisons and analyses of genome evolution

The last four decades have seen the development of a number of experimental methods for the deduction of the whole genome sequences of an ever-increasing number of organisms. These sequences have in the first instance, allowed their investigators the opportunity to examine the molecular primary structure of areas of scientific interest, but with the increased sampling of organisms across the phylogenetic tree and the improved quality and coverage of genome sequences and their associated annotations, the opportunity to undertake detailed comparisons both within and between taxonomic groups has presented itself. The work described in this thesis details the application of comparative bioinformatics analyses on inter- and intra-genomic datasets, to elucidate those genomic changes, which may underlie organismal adaptations and contribute to changes in the complexity of genome content and structure over time. The results contained herein demonstrate the power and flexibility of the comparative approach, utilising whole genome data, to elucidate the answers to some of the most pressing questions in the biological sciences today.As the volume of genomic data increases, both as a result of increased sampling of the tree of life and due to an increase in the quality and throughput of the sequencing methods, it has become clear that there is a necessity for computational analyses of these data. Manual analysis of this volume of data, which can extend beyond petabytes of storage space, is now impossible. Automated computational pipelines are therefore required to retrieve, categorise and analyse these data. Chapter two discusses the development of a computational pipeline named the Genome Comparison and Analysis Toolkit (GCAT). The pipeline was developed using the Perl programming language and is tightly integrated with the Ensembl Perl API allowing for the retrieval and analyses of their rich genomic resources. In the first instance the pipeline was tested for its robustness by retrieving and describing various components of genomic architecture across a number of taxonomic groups. Additionally, the need for programmatically independent means of accessing data and in particular the need for Semantic Web based protocols and tools for the sharing of genomics resources is highlighted. This is not just for the requirements of researchers, but for improved communication and sharing between computational infrastructure. A prototype Ensembl REST web service was developed in collaboration with the European Bioinformatics Institute (EBI) to provide a means of accessing Ensembl’s genomic data without having to rely on their Perl API. A comparison of the runtime and memory usage of the Ensembl Perl API and prototype REST API were made relative to baseline raw SQL queries, which highlights the overheads inherent in building wrappers around the SQL queries. Differences in the efficiency of the approaches were highlighted, and the importance of investing in the development of Semantic Web technologies as a tool to improve access to data for the wider scientific community are discussed.Data highlighted in chapter two led to the identification of relative differences in the intron structure of a number of organisms including teleost fish. Chapter three encompasses a published, peer-reviewed study. Inter-genomic comparisons were undertaken utilising the 5 available teleost genome sequences in order to examine and describe their intron content. The number and sizes of introns were compared across these fish and a frequency distribution of intron size was produced that identified a novel expansion in the Zebrafish lineage of introns in the size range of approximately 500-2,000 bp. Further hypothesis driven analyses of the introns across the whole distribution of intron sizes identified that the majority, but not all of the introns were largely comprised of repetitive elements. It was concluded that the introns in the Zebrafish peak were likely the result of an ancient expansion of repetitive elements that had since degraded beyond the ability of computational algorithms to identify them. Additional sampling throughout the teleost fish lineage will allow for more focused phylogenetically driven analyses to be undertaken in the future.In chapter four phylogenetic comparative analyses of gene duplications were undertaken across primate and rodent taxonomic groups with the intention of identifying significantly expanded or contracted gene families. Changes in the size of gene families may indicate adaptive evolution. A larger number of expansions, relative to time since common ancestor, were identified in the branch leading to modern humans than in any other primate species. Due to the unique nature of the human data in terms of quantity and quality of annotation, additional analyses were undertaken to determine whether the expansions were methodological artefacts or real biological changes. Novel approaches were developed to test the validity of the data including comparisons to other highly annotated genomes. No similar expansion was seen in mouse when comparing with rodent data, though, as assemblies and annotations were updated, there were differences in the number of significant changes, which brings into question the reliability of the underlying assembly and annotation data. This emphasises the importance of an understanding that computational predictions, in the absence of supporting evidence, may be unlikely to represent the actual genomic structure, and instead be more an artefact of the software parameter space. In particular, significant shortcomings are highlighted due to the assumptions and parameters of the models used by the CAFE gene family analysis software. We must bear in mind that genome assemblies and annotations are hypotheses that themselves need to be questioned and subjected to robust controls to increase the confidence in any conclusions that can be drawn from them.In addition functional genomics analyses were undertaken to identify the role of significantly changed genes and gene families in primates, testing against a hypothesis that would see the majority of changes involving immune, sensory or reproductive genes. Gene Ontology (GO) annotations were retrieved for these data, which enabled highlighting the broad GO groupings and more specific functional classifications of these data. The results showed that the majority of gene expansions were in families that may have arisen due to adaptation, or were maintained due to their necessary involvement in developmental and metabolic processes. Comparisons were made to previously published studies to determine whether the Ensembl functional annotations were supported by the de-novo analyses undertaken in those studies. The majority were not, with only a small number of previously identified functional annotations being present in the most recent Ensembl releases.The impact of gene family evolution on intron evolution was explored in chapter five, by analysing gene family data and intron characteristics across the genomes of 61 vertebrate species. General descriptive statistics and visualisations were produced, along with tests for correlation between change in gene family size and the number, size and density of their associated introns. There was shown to be very little impact of change in gene family size on the underlying intron evolution. Other, non-family effects were therefore considered. These analyses showed that introns were restricted to euchromatic regions, with heterochromatic regions such as the centromeres and telomeres being largely devoid of any such features. A greater involvement of spatial mechanisms such as recombination, GC-bias across GC-rich isochores and biased gene conversion was thus proposed to play more of a role, though depending largely on population genetic and life history traits of the organisms involved. Additional population level sequencing and comparative analyses across a divergent group of species with available recombination maps and life history data would be a useful future direction in understanding the processes involved