Spatial aspects in biological system simulations.

Mathematical models of the dynamical properties of biological systems aim to improve our understanding of the studied system with the ultimate goal of being able to predict system responses in the absence of experimentation. Despite the enormous advances that have been made in biological modeling and simulation, the inherently multiscale character of biological systems and the stochasticity of biological processes continue to present significant computational and conceptual challenges. Biological systems often consist of well-organized structural hierarchies, which inevitably lead to multiscale problems. This chapter introduces and discusses the advantages and shortcomings of several simulation methods that are being used by the scientific community to investigate the spatiotemporal properties of model biological systems. We first describe the foundations of the methods and then describe their relevance and possible application areas with illustrative examples from our own research. Possible ways to address the encountered computational difficulties are also discussed.