The Stochastic Simulation Computing For Intracellular Biochemically Reacting Systems

Modeling and simulating the biochemically reacting systems is an important pathway to research systems biology. The stochastic simulation of biochemically reacting systems attracts a large number of interest, since discreteness and stochasticity are important in systems formed by living cells where some key reactant molecules may be present in small numbers.The recently introduced probability-weighted stochastic simulation approach can efficiently simulate chemically reacting systems which have widely varying rate constants by applying a weighted Monte Carlo approach. Presented here is an improved procedure which adaptively determines the weighted factor and becomes more efficient and applicable. Numerical results show that the proposed method can be applied to the biochemically reacting systems with significant improvement on efficiency over existing approaches.Furthermore, most of the existed methods didn't contain the efficient output analysis, but focused on the direct improvement of the algorithms. Only recently, Lipshtat proposed the "all possible steps" (APS) approach for all the time course to reduce the number of runs which is required for reliable estimation of moments. This method obtains the statistical character of one species in the whole time course. However, we often need to know the statistical character of all species in some time. We develop the "final all possible steps" (FAPS) method, which obtains the reliable statistics of all species in any time during the time course with fewer simulation times. Moreover, the FAPS method can be incorporated into the leap methods, which makes the simulation of larger systems more efficient. Numerical results indicate that the proposed methods can be applied to a wide range of biochemically reacting systems with a high-precision level and obtain a significant improvement on efficiency over the existed methods.Some biochemical processes such as transcription and translation do not occur instantaneously but have considerably delays associated with them. There have been some versions of exact delay stochastic simulation algorithms (DSSAs) to solve these biochemically reacting systems with delays. In these simulations, averaging over a great deal of simulations is needed for reliable statistical characters. Here we present an accelerating approach, called the "delay final all possible steps" (DFAPS) approach, which does not alter the course of stochastic simulation, but reduces the required running times and is more efficient than the DSSAs. Numerical simulation results indicate that the proposed method can be applied to a wide range of biochemically reacting systems with delays and obtain a significant improvement on efficiency and accuracy over the existed methods.But intracellular biochemical reactions substantially lie in cells with gravity, electric charge and spatial structure, where the distribution of species isn't always homogenous, so there is the effect of diffusive processes on biochemically reacting systems. The biochemical reactions in inhomogeneous mesoscopic space can be researched by stochastically simulating the reaction-diffusive master equation.We propose the improved next subvolume method (INSM). INSM improves the exact stochastic simulation algorithm- the next subvolume method, which is proposed by Elf et al. This algorithm can reflect the impact of inner structure of cell on the reaction and distribution or diffusion of different materials. And it can reduce computation intense in some conditions which has been validated by the numerical results.