Structured biological modelling: a method for the analysis and simulation of biological systems applied to oscillatory intracellular calcium waves

Abstract

In biology signal and information processing networks are widely known. Due to their inherent complexity and non-linear dynamics the time evolution of these systems can not be predicted by simple plausibility arguments. Fortunately, the power of modern computers allows the simulation of complex biological models. Therefore the problem becomes reduced to the question of how to develop a consistent mathematical model which comprises the essentials of the real biological system. As an interface between the phenomenological description and a computer simulation of the system the proposed method of Structured Biological Modelling (SBM) uses top-down levelled dataflow diagrams. They serve as a powerful tool for the analysis and the mathematical description of the system in terms of a stochastic formulation. The stochastic treatment, regarding the time evolution of the system as a stochastic process governed by a master equation, circumvents most difficulties arising from high dimensional and non-linear systems. As an application of SBM we develop a stochastic computer model of intracellular oscillatory Ca 2+ waves in non-excitable cells. As demonstrated on this example, SBM can be used for the design of computer experiments which under certain conditions can be used as cheap and harmless counterparts to the usual time-consuming biological experiments.