摘要：

Stochastic modelling and simulation is a very important research area in systems biology. The stochastic simulation algorithm (SSA) is a powerful numerical method to describe the intrinsic noise in molecular systems. Due to the complexity of biological networks, more sophisticated modelling methodologies are still needed to describe various biological behaviours. Among them, memory is a ubiquitous phenomenon in biological systems in which the present system state is not entirely determined by the current conditions but also depends on the time evolutionary path of the system. These conditional chemical reactions contradict to the extant stochastic approaches for modeling chemical kinetics and have increasingly posed significant challenges to stochastic modelling. To tackle the challenge, the delay-SSA and memory-SSA have been designed to study the effects of multi-step reactions and conditional chemical reactions, respectively, in an efficient way. This talk will discuss these three numerical methods and demonstrate how to use the memory-SSA to realize bursting gene expression that has been observed in single cells recently.