Computational Analysis of Large-Scale Multi-affine ODE Models

A biological system as considered in systems biology is understood in the form of a network of interactions among individual biochemical species. Complexity of these networks is inherently enormous, even for simple (e.g., procaryotic) organisms. When modeling and analyzing dynamics of these networks, i.e., exploring how the species evolve in time, we have to fight even another level of complexity -- the enormous state space. In this paper we deal with a class of biological models that can be described in terms of multi-affine dynamic systems. First, we present a prototype tool for parallel (distributed) analysis of multi-affine systems discretized into rectangles that adapts the approach of Belta et.al. Secondly, we propose heuristics that significantly increase applicability of the approach to large biological models. Effects of different settings of the heuristics is firstly compared on a set of experiments performed on small models. Subsequently, experiments on large models are provided as well.