Approaches for the exact reduction of large-scale biochemical models

Mathematical models are a fundamental tool used in manybranches of science and engineering to gain insights into thedynamics of systems. In Systems Biology [122], these modelsfacilitate the analysis of complex biochemical networks thatdescribe molecular interactions at different level in living organisms.In the last years, several efforts have been dedicatedto the characterization of biological systems [98, 127, 128, 165,209], specific interaction mechanisms [10, 15, 44, 45] and biologicalphenomena such as oscillations and bistability [80,119, 147, 175]. As result, the use of mathematical models ofbiological processes have shown to be an useful asset in thedevelopment of several medical applications including drugdesign and target therapy [55, 110, 179, 197].There are two main problems to solve when working withthese types of models. The first one is the typically large computationalcost required for their analysis, which is giving inpart to the large number of configurations in which componentssuch as proteins, or genes are present in the living cell.The second problem is related to the difficulty in calibratinglarge models, since they are generally associated with manyparameters whose experimental estimation in living cells isnotoriously difficult to make.In this dissertation we explore several approaches for the reductionof biological systems, paying special attention to theinterpretability of the aggregated system. In general, we areinterested in techniques that produce an exact reduction, i.e.,algorithms that given an input chemical network, produce asmaller 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 largescalequantitative repositories of biological models, with specialsupport for models written in the well-known SBML [103]specifications. For networks with stochastic dynamics, weprovide equivalences at the level of the Markov chain thatcan be applied to several models including biological networksand epidemic processes on complex networks. In addition,we approach the simplification of biochemical modelsby focusing on their steady-state behaviour [2], a stable conditionattained by the biological system when the influenceof the initial condition can be disregarded. Here, we discussa method for the computation of equilibrium points, with theguarantee of yielding the unique equilibrium of the ODE underdefined graph-theoretical conditions.Overall, this dissertation provides a detailed analysis of techniquesfor the reduction of quantitative models of biochemicalreaction networks, together with the interpretation of thebiological and functional characteristics of the reductions obtainedover a wide collection of case studies from the literature.Interestingly, the inspection of the obtained reductionshas revealed reducible motifs, i.e., structures embedded in thestructure of the network that are often compressed in the modelsanalyzed. These findings provide the intuition that thesetechniques can abstract beyond the behavior of the system tocapture structural/functional segments of the network thatcan be simplified with no (or little) effect in the dynamics ofthe model.