Kinetic modeling of biological systems

The dynamics of how the constituent components of a natural system interact defines the spatio-temporal response of the system to stimuli. Modeling the kinetics of the processes that represent a biophysical system has long been pursued with the aim of improving our understanding of the studied system. Due to the unique properties of biological systems, in addition to the usual difficulties faced in modeling the dynamics of physical or chemical systems, biological simulations encounter difficulties that result from intrinsic multi-scale and stochastic nature of the biological processes.This chapter discusses the implications for simulation of models involving interacting species with very low copy numbers, which often occur in biological systems and give rise to significant relative fluctuations. The conditions necessitating the use of stochastic kinetic simulation methods and the mathematical foundations of the stochastic simulation algorithms are presented. How the well-organized structural hierarchies often seen in biological systems can lead to multi-scale problems and the possible ways to address the encountered computational difficulties are discussed. We present the details of the existing kinetic simulation methods and discuss their strengths and shortcomings. A list of the publicly available kinetic simulation tools and our reflections for future prospects are also provided.