Computational Methods for Analysing Long-run Dynamics of Large Biological Networks

Systems biology combines developments in the fields of computer science, mathematics, engineering, statistics, and biology to study biological networks from a holistic point of view in order to provide a comprehensive, system level understanding of the underlying system. Recent developments in biological laboratory techniques have led to a slew of increasingly complex and large biological networks. This poses a challenge for formal representation and analysis of those large networks efficiently. To understand biology at the system level, the focus should be on understanding the structure and dynamics of cellular and organismal function, rather than on the characteristics of isolated parts of a cell or organism. One of the most important focuses is the long-run dynamics of a network, as they often correspond to the functional states, such as proliferation, apoptosis, and differentiation. In this thesis, we concentrate on how to analyse long-run dynamics of biological networks. In particular, we examine situations where the networks in question are very large. In the literature, quite a few mathematical models, such as ordinary differential equations, Petri nets, and Boolean networks (BNs), have been proposed for representing biological networks. These models provide different levels of details and have different advantages. Since we are interested in large networks and their long-run dynamics, we need to use ``coarse-grained" level models that focus on the system behaviour of the network while neglecting molecular details. In particular, we use probabilistic Boolean networks (PBNs) to describe biological networks. By focusing on the wiring of a network, a PBN not only simplifies the representation of the network, but it also captures the important characteristics of the dynamics of the network. Within the framework of PBNs, the analysis of long-run dynamics of a biological network can be performed with regard to two aspects. The first aspect lies in the identification of the so-called attractors of the constituent BNs of a PBN. An attractor of a BN is a set of states, inside which the network will stay forever once it goes in; thus capturing the network's long-term behaviour. A few methods have been discussed for computing attractors in the literature. For example, the binary decision diagram based approach and the satisfiability based approach. These methods, however, are either restricted by the network size, or can only be applied to synchronous networks where all the elements in the network are updated synchronously at each time step. To overcome these issues, we propose a decomposition-based method. The method works in three steps: we decompose a large network into small sub-networks, detect attractors in sub-networks, and recover the attractors of the original network using the attractors of the sub-networks. Our methods can be applied to both asynchronous networks, where only one element in the network is updated at each time step, and synchronous networks. Experimental results show that our proposed method is significantly faster than the state-of-the-art methods. The second aspect lies in the computation of steady-state probabilities of a PBN with perturbations. The perturbations of a PBN allow for a random, with a small probability, alteration of the current state of the PBN. In a PBN with perturbations, the long-run dynamics is characterised by the steady-state probability of being in a certain set of states. Various methods for computing steady-state probabilities can be applied to small networks. However, for large networks, the simulation-based statistical methods remain the only viable choice. A crucial issue for such methods is the efficiency. The long-run analysis of large networks requires the computation of steady-state probabilities to be finished as soon as possible. To reach this goal, we apply various techniques. First, we revive an efficient Monte Carlo simulation method called the two-state Markov chain approach for making the computations. We identify an initialisation problem, which may lead to biased results of this method, and propose several heuristics to avoid this problem. Secondly, we develop several techniques to speed up the simulation of PBNs. These techniques include the multiple central processing unit based parallelisation, the multiple graphic processing unit based parallelisation, and the structure-based parallelisation. Experimental results show that these techniques can lead to speedups from ten times to several hundreds of times. Lastly, we have implemented the above mentioned techniques for identification of attractors and the computation of steady-state probabilities in a tool called ASSA-PBN. A case-study for analysing an apoptosis network with this tool is provided

Qualitative networks: a symbolic approach to analyze biological signaling networks

BACKGROUND: A central goal of Systems Biology is to model and analyze biological signaling pathways that interact with one another to form complex networks. Here we introduce Qualitative networks, an extension of Boolean networks. With this framework, we use formal verification methods to check whether a model is consistent with the laboratory experimental observations on which it is based. If the model does not conform to the data, we suggest a revised model and the new hypotheses are tested in-silico. RESULTS: We consider networks in which elements range over a small finite domain allowing more flexibility than Boolean values, and add target functions that allow to model a rich set of behaviors. We propose a symbolic algorithm for analyzing the steady state of these networks, allowing us to scale up to a system consisting of 144 elements and state spaces of approximately 10(86 )states. We illustrate the usefulness of this approach through a model of the interaction between the Notch and the Wnt signaling pathways in mammalian skin, and its extensive analysis. CONCLUSION: We introduce an approach for constructing computational models of biological systems that extends the framework of Boolean networks and uses formal verification methods for the analysis of the model. This approach can scale to multicellular models of complex pathways, and is therefore a useful tool for the analysis of complex biological systems. The hypotheses formulated during in-silico testing suggest new avenues to explore experimentally. Hence, this approach has the potential to efficiently complement experimental studies in biology

Advances in Functional Decomposition: Theory and Applications

Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The first two algorithms compute simple-disjoint and disjoint-support decompositions. They are based on representing the target function by a Reduced Ordered Binary Decision Diagram (BDD). Unlike other BDD-based algorithms, the presented ones can deal with larger target functions and produce more decompositions without requiring expensive manipulations of the representation, particularly BDD reordering. The third algorithm also finds disjoint-support decompositions, but it is based on a technique which integrates circuit graph analysis and BDD-based decomposition. The combination of the two approaches results in an algorithm which is more robust than a purely BDD-based one, and that improves both the quality of the results and the running time. The fourth algorithm uses circuit graph analysis to obtain non-disjoint decompositions. We show that the problem of computing non-disjoint decompositions can be reduced to the problem of computing multiple-vertex dominators. We also prove that multiple-vertex dominators can be found in polynomial time. This result is important because there is no known polynomial time algorithm for computing all non-disjoint decompositions of a Boolean function. The fifth algorithm provides an efficient means to decompose a function at the circuit graph level, by using information derived from a BDD representation. This is done without the expensive circuit re-synthesis normally associated with BDD-based decomposition approaches. Finally we present two publications that resulted from the many detours we have taken along the winding path of our research

Revision of Boolean Logical Models of Biological Regulatory Networks using Answer-Set Programming

Biological regulatory networks are one of the most prominent tools used to represent complex, regulatory cellular processes. Creating computational models of these networks is key to better comprehend the corresponding cellular processes, as they allow for the reproduction of known behaviors, the testing of hypotheses, and the identification of predictions in silico. However, given that the process of constructing and revising such models is mainly a manual one, it is prone to error, and would therefore benefit from automation. An attempt at solving this problem has already been made using a mixture of Answer Set Programming (ASP) and C++. The previous attempt automated the process of revising these models, by using ASP to verify whether a Boolean logical model of a biological regulatory network was consistent with a given set of experimental observations and, in case of inconsistencies, used C++ to implement an algorithm capable of searching for possible sets of repair operations to render the model consistent. In our work we propose an alternative solution for this problem, a solution that fully leverages ASP which, being a declarative language tailored for this type of difficult search problems, has demonstrated to be a great tool to use both for consistency checking as well as model repair. This is in view of the fact that ASP offers a more intuitive and elaboration-tolerant programming style, which facilitates the processes of understanding, and modifying the code behind the model revision process. This, coupled with the powerful and exhaustively optimized solving capabilities provided by the state of the art ASP system clingo, has shown that there is great potential in adopting a fully ASP-based approach to aid in the automation of the revision of Boolean logical models. In this thesis we present the tool that we have developed to automate the process of revising Boolean logical models of Biological Regulatory Network(s) (BRN), which uses ASP to search for inconsistencies and perform repairs on these models.As redes reguladoras biológicas são das ferramentas mais proeminentes usadas para representar processos celulares regulatórios complexos. A criação de modelos computacionais destas redes é fundamental para entender melhor os processos celulares correspondentes, pois permitem reproduzir comportamentos conhecidos, testar hipóteses e identificar previsões in silico. Porém, dado que o processo de construção e revisão destes modelos é principalmente manual, torna-se propenso a erros e, logo, beneficiaria de automação. Já foi feita uma tentativa de resolução deste problema usando uma mistura de Programação por Conjuntos de Resposta (ASP) com C++. A tentativa anterior automatizou o processo de revisão destes modelos, usando ASP para verificar se um modelo lógico booleano de uma rede regulatória é consistente com um determinado conjunto de observações experimentais e, caso inconsistências se verifiquem, é utilizado um algoritmo desenvolvido em C++ capaz de encontrar possíveis conjuntos de operações de reparo para tornar o modelo consistente. No nosso trabalho, propomos uma solução alternativa para este problema, que tira completo partido da utilização ASP que, sendo uma linguagem declarativa adaptada a este tipo de problemas de busca difíceis, demonstrou ser uma excelente ferramenta a utilizar tanto para a verificação da consistência como para a reparação de modelos. Tal deve-se ao facto de ASP oferecer um estilo de programação mais intuitivo e tolerante à elaboração, o que facilita os processos de compreensão, e a modificação do código por detrás do processo de revisão de modelos. Isto, juntamente com as poderosas e otimizadas capacidades de resolução de problemas de busca oferecidas pelo sistema ASP de última geração clingo, demonstrou que existe um grande potencial na adopção de um sistema totalmente baseado em ASP para ajudar na automatização da revisão destes modelos. Nesta tese apresentamos a ferramenta que desenvolvemos para automatizar o processo de revisão de modelos lógicos booleanos de redes reguladoras biológicas (BRN), que utiliza ASP para procurar inconsistências e efectuar reparações nestes modelos

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems