Information Theoretic Analysis of the Structure-Dynamics Relationships in Complex Biological Systems

Complex systems and networks is an emerging scientific field, with applications in every area of human enquiry, for which a solid theoretical, computational and experimental foundation is lacking. As our technological capability of generating and gathering vast amounts of data from such systems is increasing, precise methods are needed to describe, analyse and synthesize such systems. Systems biology is a prime example of an interdisciplinary field aiming at tackling the complexity of biological organisms and dedicated to understanding their organizing principles and to devising efficient intervention strategies for curing diseases.A very important topic in the study of complex systems and networks is to uncover the laws that govern their structure-dynamics relationships. A complete description of the system’s behaviour as a whole can only be achieved if the structure and the dynamics are investigated together, as well as the intricate ways in which they influence each other. The understanding of structure-dynamics relationships is a key step in the control of complex systems and networks. For example, in biology, understanding these relationships in organisms would enable us to find more precise drug targets and to design better drugs to cure diseases. In gene regulatory networks, it would help devise control strategies to change the network from faulty states that correspond to disease states, to normal states that give the healthy phenotype. When we observe a dynamical behaviour that is different from the normal, healthy one, the knowledge about the structure-dynamics relationships would help us identify which part of the structure gives rise to such behaviour. Then, we would know where and how to change the structure, to return the system to its normal dynamics, that is, to obtain a desired dynamical behaviour.A feasible way of investigating the structure-dynamics relationships is by measuring the amount of information that is communicated in the system and by analysing the patterns of information propagation within its elements. These objectives can be achieved by means of information theory. To this end, with concepts from Kolmogorov complexity and from Shannon’s information theory, we create novel analysis methods of the structure-dynamics relationships in two models of complex systems: an executable model of the human immune systems and the random Boolean network model of gene regulatory networks.In these endeavours, the information-theoretic means of identifying and measuring the information propagation in complex systems and networks needs to be improved and extended. Research is needed into the theoretical foundations of information theory, to refine existing equations and to introduce new ones that can give more accurate results in the investigation of the propagation of information and its applications to the structure-dynamics relationships. To this end, we bring analytical contributions to the generalization of Shannon’s information theory, named Rényi’s information theory. Thus, we continue the development of the theoretical foundations of information theory, for new and better applications in complex systems science and engineering.The goal of this thesis is to characterize various aspects of the structure-dynamics relationships in models of complex biological systems, by means of information theory. Moreover, our goal is to prove that information theory is a model independent analysis framework that can be applied to any class of models. We pursue our objective, by analysing two different classes of models: an executable model of the human immune system and the random Boolean network model of gene regulatory networks.In the executable model of the regulation of cytokines within the human immune system, our aim is to develop computationally feasible analysis methods that can extract meaningful biological information from the complex encoding of the dynamical behaviour of different perturbations of the wild type system. We aim at classifying several structural perturbations of the system, using only their dynamical information. We endeavour to create methods that can make predictions about the structural parameters that should be changed in order to obtain a desired dynamical behaviour. These conclusions have direct applications to the fine-tuning of the real-world biological experiments performed on the system, of whose computational model we analyse. The benefits of our predictions would be increased efficiency and increased reduction of the time required to optimize the parameters of the real-world biological experiments.In the random Boolean network model of gene regulatory networks, our goal is to develop an experimental order parameter that can characterize the dynamical regime of the network, from the dynamical behaviour that simulates that obtained from the measurements of real-world biological experiments. Moreover, we aim at proving that structural information is hidden in the dynamics of random Boolean networks and that it can be extracted with methods from information theory. We study ensembles of random Boolean networks from two distinct structural classes, which take into account the stochasticity present in real biological systems.Another goal of this study is to bring analytical contributions to the field of Rényi’s information theory, which is a generalization of Shannon’s information theory. Recently, it has found novel applications in the study of the structure-dynamics relationships in complex systems and networks