Simulation of biochemical networks

Abstract

Advances in experimental techniques of molecular biology motivate attempts to mathematically model complex biochemical reaction networks occurring in the cell. Usually, the models are so complex that they cannot be solved analytically and so computer simulations must be employed. Biochemical reaction networks may be expressed as a system of differential equations, thus allowing standard algorithms and software packages to be used in the simulation. Frequently, the lack of precise model parameters prevents quantitative studies of the system dynamics. In such cases, qualitative simulations using logical formalism or the study of flux distribution of the stationary state may be performed. The methods mentioned above are deterministic and do not take into account stochastic fluctuations resulting from the fact that biochemical processes occur in very small volumes. Various Monte Carlo approaches are used to account for the stochastic effects in the dynamics of biochemical reaction networks. Recent advances in these methods allow simulations of systems composed of reactions varying by many orders of magnitude in their rates and the number of molecules involved. Simulations explicitly incorporating positional information on the spatial clustering of membrane receptors have also been performed.