Approaches for the exact reduction of large-scale biochemical models

Mathematical models are a fundamental tool used in many branches of science and engineering to gain insights into the dynamics of systems. In Systems Biology [122], these models facilitate the analysis of complex biochemical networks that describe molecular interactions at different level in living organisms. In the last years, several efforts have been dedicated to the characterization of biological systems [98, 127, 128, 165, 209], specific interaction mechanisms [10, 15, 44, 45] and biological phenomena such as oscillations and bistability [80, 119, 147, 175]. As result, the use of mathematical models of biological processes have shown to be an useful asset in the development of several medical applications including drug design and target therapy [55, 110, 179, 197]. There are two main problems to solve when working with these types of models. The first one is the typically large computational cost required for their analysis, which is giving in part to the large number of configurations in which components such as proteins, or genes are present in the living cell. The second problem is related to the difficulty in calibrating large models, since they are generally associated with many parameters whose experimental estimation in living cells is notoriously difficult to make. In this dissertation we explore several approaches for the reduction of biological systems, paying special attention to the interpretability of the aggregated system. In general, we are interested in techniques that produce an exact reduction, i.e., algorithms that given an input chemical network, produce a smaller network (consisting of fewer species and reactions) that preserves the output dynamics of interest to the modeler, e.g. [137, 201]. We present a framework for the automatic analysis of largescale quantitative repositories of biological models, with special support for models written in the well-known SBML [103] specifications. For networks with stochastic dynamics, we provide equivalences at the level of the Markov chain that can be applied to several models including biological networks and epidemic processes on complex networks. In addition, we approach the simplification of biochemical models by focusing on their steady-state behaviour [2], a stable condition attained by the biological system when the influence of the initial condition can be disregarded. Here, we discuss a method for the computation of equilibrium points, with the guarantee of yielding the unique equilibrium of the ODE under defined graph-theoretical conditions. Overall, this dissertation provides a detailed analysis of techniques for the reduction of quantitative models of biochemical reaction networks, together with the interpretation of the biological and functional characteristics of the reductions obtained over a wide collection of case studies from the literature. Interestingly, the inspection of the obtained reductions has revealed reducible motifs, i.e., structures embedded in the structure of the network that are often compressed in the models analyzed. These findings provide the intuition that these techniques can abstract beyond the behavior of the system to capture structural/functional segments of the network that can be simplified with no (or little) effect in the dynamics of the model