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.

A Farewell to Flat Biology. Three-dimensional Cell Culture Models in Cancer Drug Target Identification and Validation

Cells of epithelial origin, e.g. from breast and prostate cancers, effectively differentiate into complex multicellular structures when cultured in three-dimensions (3D) instead of conventional two-dimensional (2D) adherent surfaces. The spectrum of different organotypic morphologies is highly dependent on the culture environment that can be either non-adherent or scaffold-based. When embedded in physiological extracellular matrices (ECMs), such as laminin-rich basement membrane extracts, normal epithelial cells differentiate into acinar spheroids reminiscent of glandular ductal structures. Transformed cancer cells, in contrast, typically fail to undergo acinar morphogenic patterns, forming poorly differentiated or invasive multicellular structures. The 3D cancer spheroids are widely accepted to better recapitulate various tumorigenic processes and drug responses. So far, however, 3D models have been employed predominantly in the Academia, whereas the pharmaceutical industry has yet to adopt a more widely and routine use. This is mainly due to poor characterisation of cell models, lack of standardised workflows and high throughput cell culture platforms, and the availability of proper readout and quantification tools. In this thesis, a complete workflow has been established entailing well-characterised 3D cell culture models for prostate cancer, a standardised 3D cell culture routine based on high-throughput-ready platform, automated image acquisition with concomitant morphometric image analysis, and data visualisation, in order to enable large-scale high-content screens. Our integrated suite of software and statistical analysis tools were optimised and validated using a comprehensive panel of prostate cancer cell lines and 3D models. The tools quantify multiple key cancer-relevant morphological features, ranging from cancer cell invasion through multicellular differentiation to growth, and detect dynamic changes both in morphology and function, such as cell death and apoptosis, in response to experimental perturbations including RNA interference and small molecule inhibitors. Our panel of cell lines included many non-transformed and most currently available classic prostate cancer cell lines, which were characterised for their morphogenetic properties in 3D laminin-rich ECM. The phenotypes and gene expression profiles were evaluated concerning their relevance for pre-clinical drug discovery, disease modelling and basic research. In addition, a spontaneous model for invasive transformation was discovered, displaying a highdegree of epithelial plasticity. This plasticity is mediated by an abundant bioactive serum lipid, lysophosphatidic acid (LPA), and its receptor LPAR1. The invasive transformation was caused by abrupt cytoskeletal rearrangement through impaired G protein alpha 12/13 and RhoA/ROCK, and mediated by upregulated adenylyl cyclase/cyclic AMP (cAMP)/protein kinase A, and Rac/ PAK pathways. The spontaneous invasion model tangibly exemplifies the biological relevance of organotypic cell culture models. Overall, this thesis work underlines the power of novel morphometric screening tools in drug discovery.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

New [18F]Tracers for Alzheimer's Disease Imaging. Labeling Synthesis And Biological Testing

Alzheimer’s disease (AD) is the most common form of dementia. Characteristic changes in an AD brain are the formation of β-amyloid protein (Aβ) plaques and neurofibrillary tangles, though other alterations in the brain have also been connected to AD. No cure is available for AD and it is one of the leading causes of death among the elderly in developed countries. Liposomes are biocompatible and biodegradable spherical phospholipid bilayer vesicles that can enclose various compounds. Several functional groups can be attached on the surface of liposomes in order to achieve long-circulating target-specific liposomes. Liposomes can be utilized as drug carriers and vehicles for imaging agents. Positron emission tomography (PET) is a non-invasive imaging method to study biological processes in living organisms. In this study using nucleophilic 18F-labeling synthesis, various synthesis approaches and leaving groups for novel PET imaging tracers have been developed to target AD pathology in the brain. The tracers were the thioflavin derivative [18F]flutemetamol, curcumin derivative [18F]treg-curcumin, and functionalized [18F]nanoliposomes, which all target Aβ in the AD brain. These tracers were evaluated using transgenic AD mouse models. In addition, 18F-labeling synthesis was developed for a tracer targeting the S1P3 receptor. The chosen 18F-fluorination strategy had an effect on the radiochemical yield and specific activity of the tracers. [18F]Treg-curcumin and functionalized [18F]nanoliposomes had low uptake in AD mouse brain, whereas [18F]flutemetamol exhibited the appropriate properties for preclinical Aβ-imaging. All of these tracers can be utilized in studies of the pathology and treatment of AD and related diseases.

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.

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.