Research On Simulation Algorithms Of Stochastic Biological Processes Based On Stochastic Petri Nets

The development of system biology has made biological modeling and computer simulation techniques to be powerful tools for simulating biological processes, which supports the researches on medicine and pharmacy forcefully. Recent past has seen several successful methods for modeling and simulation of complex biological systems like metabolic control pathways, genetic regulatory networks and cell signaling pathways. Furthermore, stochastic modeling has emerged as a physically more realistic alternative for modeling in vivo reactions.In order to model and simulate biological systems accurately and effectively, we have developed a software system for biological simulation based on stochastic Petri nets, which is named CELLMATLAB, and implemented various stochastic algorithms used to simulate the biological processes represented with stochastic Petri nets in the systems.The thesis mainly implements three types of different simulation algorithms, namely exact stochastic simulation algorithm (SSA), stochastic tau-leaping method and hybrid simulation method, and then points out their advantages and existing limitations. SSA provide an awfully precise description of time evolution for the system, but it's computationally expensive; stochastic tau-leaping method can produce significant gains in simulation speed, but with certain losses in accuracy, and has a narrow range of applications; hybrid simulation method is between the foregoing two methods, and it's especially applicable for stiff systems.Though there are certain differences between these methods, their variables are all the numbers of molecules. For the large complex systems, especially stiff systems whose reaction rates and numbers of molecules differ by several orders of magnitude, it's somewhat impractical to express the states of systems with numbers. Hence, this thesis proposes an improved hybrid simulation method, which is to dynamically partition the system into regimes of continuous and discrete reactions according to concentrations of molecular species and rates of reactions, and then to model them with a set of ordinary differential equations (ODEs) describing the temporal evolution of concentrations and exact stochastic simulation algorithm respectively. For species with high numbers, it's more practical to describe the state with concentrations, and to approximate it as a continuous process. For low species, the state is still described with numbers, and species are regarded as discrete individuals. Due to the invert relationship between deterministic rate constants and stochastic rate constants, it's completely feasible to adjust the used methods according to the states of reactants. The dynamically hybrid simulation method not only can reflect the continuity for species with high numbers but also capture the fluctuation for low species in time. Thus, for large complex systems, the hybrid method would be more accurate than deterministic simulation and less computational cost than stochastic simulation.Lastly, the thesis takes the simple model with four reactions, model of intracellular viral kinetics and the heat-shock model as examples, not only verifying the efficiency and accurate of various algorithms but also demonstrating the applicability and correctness of the improved algorithm proposed in this thesis, which is especially applicable for simulating the systems with stiffness.