Numerical studies of Implicit Tau Leaping methods for stochastic biochemical systems

Deterministic models of chemical reactions systems have been used successfully in studying chemical kinetics problems. However, in biochemical systems (e.g. cellular systems in biology), small molecular population sizes of some key reacting species can lead to results that cannot be predicted by the traditional deterministic models. It has been found that such processes involve intrinsic randomness that can be better modeled by stochastic models. Chemical Master Equation (CME) is an accurate stochastic model of well-stirred biochemical systems. We investigate reliable and efficient simulation methods for the CME, namely the implicit tau-leaping method. The tau-leaping algorithms were tested on several models of practical interest such as the Schl¨ogl model and the Goldbeter-Koshland switch and compared to the exact methods. We observed that, for systems not reaching steady state, the implicit tau-leaping strategy is accurate.