Kinetic Descriptions of Chemical and Biological Systems:

Analysis and simulation of multiscale stochastic intracellular bio-chemical reacting networks

Di Liu

Michigan State University


Intracellular reacting networks involving gene regulation often exhibits multiscale properties. That includes multiple reacting rates, multiple population magnitudes and multi-stability. Direct Stochastic Simulation Algorithm (SSA) would turn out to be inefficient dealing with such systems. Schemes such as Nested SSA and Tau-leaping method have proved to be effective for certain asymptotic regimes. Based on the framework of transition path theory (TPT), we extended the probability current between two adjacent reacting states to single reacting states as well as reacting trajectories, thereby give the definition of transition state (TS) as states with maximum velocity strength. I will present recent results on the convergence analysis and applications of the algorithms.