Methods for construction and analysis of computational models in systems biology : applications to the modelling of the heat shock response and the self-assembly of intermediate filaments

Systems biology is a new, emerging and rapidly developing, multidisciplinary research field that aims to study biochemical and biological systems from a holistic perspective, with the goal of providing a comprehensive, system- level understanding of cellular behaviour. In this way, it addresses one of the greatest challenges faced by contemporary biology, which is to compre- hend the function of complex biological systems. Systems biology combines various methods that originate from scientific disciplines such as molecu- lar biology, chemistry, engineering sciences, mathematics, computer science and systems theory. Systems biology, unlike “traditional” biology, focuses on high-level concepts such as: network, component, robustness, efficiency, control, regulation, hierarchical design, synchronization, concurrency, and many others. The very terminology of systems biology is “foreign” to “tra- ditional” biology, marks its drastic shift in the research paradigm and it indicates close linkage of systems biology to computer science. One of the basic tools utilized in systems biology is the mathematical modelling of life processes tightly linked to experimental practice. The stud- ies contained in this thesis revolve around a number of challenges commonly encountered in the computational modelling in systems biology. The re- search comprises of the development and application of a broad range of methods originating in the fields of computer science and mathematics for construction and analysis of computational models in systems biology. In particular, the performed research is setup in the context of two biolog- ical phenomena chosen as modelling case studies: 1) the eukaryotic heat shock response and 2) the in vitro self-assembly of intermediate filaments, one of the main constituents of the cytoskeleton. The range of presented approaches spans from heuristic, through numerical and statistical to ana- lytical methods applied in the effort to formally describe and analyse the two biological processes. We notice however, that although applied to cer- tain case studies, the presented methods are not limited to them and can be utilized in the analysis of other biological mechanisms as well as com- plex systems in general. The full range of developed and applied modelling techniques as well as model analysis methodologies constitutes a rich mod- elling framework. Moreover, the presentation of the developed methods, their application to the two case studies and the discussions concerning their potentials and limitations point to the difficulties and challenges one encounters in computational modelling of biological systems. The problems of model identifiability, model comparison, model refinement, model inte- gration and extension, choice of the proper modelling framework and level of abstraction, or the choice of the proper scope of the model run through this thesis.

Genetic regulatory networks in avian B cells

Biology is turning into an information science. The science of systems biology seeks to understand the genetic networks that govern organism development and functions. In this study the chicken was used as a model organism in the study of B cell regulatory factors. These studies open new avenues for plasma cell research by connecting the down regulation of the B cell gene expression program directly to the initiation of plasma cell differentiation. The unique advantages of the DT40 avian B cell model system, specifically its high homologous recombination rate, were utilized to study gene regulation in Pax5 knock out cell lines and to gain new insights into the B cell to plasma cell transitions that underlie the secretion of antibodies as part of the adaptive immune response. The Pax5 transcription factor is central to the commitment, development and maintenance of the B cell phenotype. Mice lacking the Pax5 gene have an arrest in development at the pro-B lymphocyte stage while DT40 cells have been derived from cells at a more mature stage of development. The DT40 Pax5-/- cells exhibited gene expression similarities with primary chicken plasma cells. The expression of the plasma cell transcription factors Blimp-1 and XBP-1 were significantly upregulated while the expression of the germinal centre factor BCL6 was diminished in Pax5-/- cells, and this alteration was normalized by Pax5 re-introduction. The Pax5-deficient cells further manifested substantially elevated secretion of IgM into the supernatant, another characteristic of plasma cells. These results for the first time indicated that the downregulation of the Pax5 gene in B cells promotes plasma cell differentiation. Cross-species meta-analysis of chicken and mouse Pax5 gene knockout studies uncovers genes and pathways whose regulatory relationship to Pax5 has remained unchanged for over 300 million years. Restriction of the hematopoietic stem cell fate to produce T, B and NK cell lineages is dependent on the Ikaros and its molecular partners, the closely related Helios and Aiolos. Ikaros family members are zinc finger proteins which act as transcriptional repressors while helping to activate lymphoid genes. Helios in mice is expressed from the hematopoietic stem cell level onwards, although later in development its expression seems to predominate in the T cell lineage. This study establishes the emergence and sequence of the chicken Ikaros family members. Helios expression in the bursa of Fabricius, germinal centres and B cell lines suggested a role for Helios in the avian B-cell lineage, too. Phylogenetic studies of the Ikaros family connect the expansion of the Ikaros family, and thus possibly the emergence of the adaptive immune system, with the second round of genome duplications originally proposed by Ohno. Paralogs that have arisen as a result of genome-wide duplications are sometimes termed ohnologs – Ikaros family proteins appear to fit that definition. This study highlighted the opportunities afforded by the genome sequencing efforts and somatic cell reverse genetics approaches using the DT40 cell line. The DT40 cell line and the avian model system promise to remain a fruitful model for mechanistic insight in the post-genomic era as well.

Molecular Mechanisms of Sexual Dimorphism in Threespine Stickleback

Sexual dimorphism is commonly understood as differences in external features, such as morphological features or coloration. However, it can more broadly encompass behavior and physiology and at the core of these differences is the genetic mechanism – mRNA and protein expression. How, and which, molecular mechanisms influence sexually dimorphic features is not well understood thus far. DNA, RNA and proteins are the template required to create the phenotype of an individual, and they are connected to each other via processes of transcription and translation. As the genome of males and females are almost identical with the exception of the few genes on the sex chromosome or the sex-determining alleles (in the case of organisms without sex chromosomes), it is likely that many of the downstream processes resulting in sexual dimorphism are produced by changes in gene regulation and result from a regulatory cascade and not from a vastly different gene composition. Thus, in this thesis a systems biology approach is used to understand sexual dimorphism at all molecular levels and how different genomic features, e.g. sex chromosome evolution, can affect the interplay of these molecules. The threespine stickleback, Gasterosteus aculeatus, is used as the model to investigate molecular mechanisms of sexual dimorphism. It has well-characterized ecology and behavior, especially in the breeding season when sexual dimorphism is high. Moreover, threespine stickleback has a recently evolved Y chromosome in the early stages of sex chromosome evolution, characterized by a lack of recombination leading to degeneration (i.e. gene loss). The aim of my thesis is to investigate how the genotype links to the molecular phenotype and relates to differences in molecular expression between males and females. Based on previous research on sex differences in mRNA expression, I investigated sex-biased protein expression in adult fish outside the breeding season to see if differences persisted after translation. As sex-biased expression also prevailed in the proteome and previous transcription expression seemed to be related to the sex chromosomes, I investigated the genome level with a particular focus on the sex-chromosomes. I characterized the status of Y chromosome degeneration in the threespine stickleback and its effects on gene function. Furthermore, since the degeneration process leaves genes in a single copy in males, I examined whether the resulting dosage difference of messenger RNA for hemizygous genes is compensated as it is in other organisms. In addition, threespine sticklebacks have wellcharacterized behavioral differences related to the male’s social status during the breeding season. To understand the connection between the genotype and behavior, I examined gene expression patterns related to breeding behavior using dominant and subordinate males as well as female

Quantitative refinement of reaction-based biomodels

In the field of molecular biology, scientists adopted for decades a reductionist perspective in their inquiries, being predominantly concerned with the intricate mechanistic details of subcellular regulatory systems. However, integrative thinking was still applied at a smaller scale in molecular biology to understand the underlying processes of cellular behaviour for at least half a century. It was not until the genomic revolution at the end of the previous century that we required model building to account for systemic properties of cellular activity. Our system-level understanding of cellular function is to this day hindered by drastic limitations in our capability of predicting cellular behaviour to reflect system dynamics and system structures. To this end, systems biology aims for a system-level understanding of functional intraand inter-cellular activity. Modern biology brings about a high volume of data, whose comprehension we cannot even aim for in the absence of computational support. Computational modelling, hence, bridges modern biology to computer science, enabling a number of assets, which prove to be invaluable in the analysis of complex biological systems, such as: a rigorous characterization of the system structure, simulation techniques, perturbations analysis, etc. Computational biomodels augmented in size considerably in the past years, major contributions being made towards the simulation and analysis of large-scale models, starting with signalling pathways and culminating with whole-cell models, tissue-level models, organ models and full-scale patient models. The simulation and analysis of models of such complexity very often requires, in fact, the integration of various sub-models, entwined at different levels of resolution and whose organization spans over several levels of hierarchy. This thesis revolves around the concept of quantitative model refinement in relation to the process of model building in computational systems biology. The thesis proposes a sound computational framework for the stepwise augmentation of a biomodel. One starts with an abstract, high-level representation of a biological phenomenon, which is materialised into an initial model that is validated against a set of existing data. Consequently, the model is refined to include more details regarding its species and/or reactions. The framework is employed in the development of two models, one for the heat shock response in eukaryotes and the second for the ErbB signalling pathway. The thesis spans over several formalisms used in computational systems biology, inherently quantitative: reaction-network models, rule-based models and Petri net models, as well as a recent formalism intrinsically qualitative: reaction systems. The choice of modelling formalism is, however, determined by the nature of the question the modeler aims to answer. Quantitative model refinement turns out to be not only essential in the model development cycle, but also beneficial for the compilation of large-scale models, whose development requires the integration of several sub-models across various levels of resolution and underlying formal representations.

Computational models for and from biology : simple gene assembly and reaction systems

The advancement of science and technology makes it clear that no single perspective is any longer sufficient to describe the true nature of any phenomenon. That is why the interdisciplinary research is gaining more attention overtime. An excellent example of this type of research is natural computing which stands on the borderline between biology and computer science. The contribution of research done in natural computing is twofold: on one hand, it sheds light into how nature works and how it processes information and, on the other hand, it provides some guidelines on how to design bio-inspired technologies. The first direction in this thesis focuses on a nature-inspired process called gene assembly in ciliates. The second one studies reaction systems, as a modeling framework with its rationale built upon the biochemical interactions happening within a cell. The process of gene assembly in ciliates has attracted a lot of attention as a research topic in the past 15 years. Two main modelling frameworks have been initially proposed in the end of 1990s to capture ciliates’ gene assembly process, namely the intermolecular model and the intramolecular model. They were followed by other model proposals such as templatebased assembly and DNA rearrangement pathways recombination models. In this thesis we are interested in a variation of the intramolecular model called simple gene assembly model, which focuses on the simplest possible folds in the assembly process. We propose a new framework called directed overlap-inclusion (DOI) graphs to overcome the limitations that previously introduced models faced in capturing all the combinatorial details of the simple gene assembly process. We investigate a number of combinatorial properties of these graphs, including a necessary property in terms of forbidden induced subgraphs. We also introduce DOI graph-based rewriting rules that capture all the operations of the simple gene assembly model and prove that they are equivalent to the string-based formalization of the model. Reaction systems (RS) is another nature-inspired modeling framework that is studied in this thesis. Reaction systems’ rationale is based upon two main regulation mechanisms, facilitation and inhibition, which control the interactions between biochemical reactions. Reaction systems is a complementary modeling framework to traditional quantitative frameworks, focusing on explicit cause-effect relationships between reactions. The explicit formulation of facilitation and inhibition mechanisms behind reactions, as well as the focus on interactions between reactions (rather than dynamics of concentrations) makes their applicability potentially wide and useful beyond biological case studies. In this thesis, we construct a reaction system model corresponding to the heat shock response mechanism based on a novel concept of dominance graph that captures the competition on resources in the ODE model. We also introduce for RS various concepts inspired by biology, e.g., mass conservation, steady state, periodicity, etc., to do model checking of the reaction systems based models. We prove that the complexity of the decision problems related to these properties varies from P to NP- and coNP-complete to PSPACE-complete. We further focus on the mass conservation relation in an RS and introduce the conservation dependency graph to capture the relation between the species and also propose an algorithm to list the conserved sets of a given reaction system.

Mechanistic population Models in Biology: Model Derivation and Application

In general, models of ecological systems can be broadly categorized as ’top-down’ or ’bottom-up’ models, based on the hierarchical level that the model processes are formulated on. The structure of a top-down, also known as phenomenological, population model can be interpreted in terms of population characteristics, but it typically lacks an interpretation on a more basic level. In contrast, bottom-up, also known as mechanistic, population models are derived from assumptions and processes on a more basic level, which allows interpretation of the model parameters in terms of individual behavior. Both approaches, phenomenological and mechanistic modelling, can have their advantages and disadvantages in different situations. However, mechanistically derived models might be better at capturing the properties of the system at hand, and thus give more accurate predictions. In particular, when models are used for evolutionary studies, mechanistic models are more appropriate, since natural selection takes place on the individual level, and in mechanistic models the direct connection between model parameters and individual properties has already been established. The purpose of this thesis is twofold. Firstly, a systematical way to derive mechanistic discrete-time population models is presented. The derivation is based on combining explicitly modelled, continuous processes on the individual level within a reproductive period with a discrete-time maturation process between reproductive periods. Secondly, as an example of how evolutionary studies can be carried out in mechanistic models, the evolution of the timing of reproduction is investigated. Thus, these two lines of research, derivation of mechanistic population models and evolutionary studies, are complementary to each other.