Research On Stochastic Simulation Algorithm In Biochemical Reaction System

Cell life activity is a very complex process,which is regulated by biochemical reactions such as protein and gene expression interaction,and its biochemical reactions show obvious randomness.An important way to model and simulate biochemical reaction system is to study system biology.In this process,discreteness and randomness play an important role.In this paper,we mainly discuss the stochastic simulation algorithm of biochemical reactions in Markov and non Markov processes.In the Markov process,on the basis of introducing the theory of stochastic process,starting from the basic hypothesis of biochemical reaction system,this paper introduces various mathematical descriptions of biochemical reaction internal noise,external stochastic disturbance and reaction process including time lag,including chemical master equation,chemical rate equation,chemical Langevin equation and related numerical simulation methods,including stochastic simulation algorithm(SSA)and jump algorithm.As a "accurate" simulation method for biochemical reaction system,stochastic simulation algorithm(SSA)has been widely used in various researches,especially in the field of biology.However,due to the complexity of biological systems,the simulation speed of stochastic simulation algorithm(SSA)is very slow due to the huge amount of computation,which makes people urgently seek more efficient and fast simulation methods,so there is a jump algorithm,which greatly improves the simulation speed and precision.In biochemical reaction,the chemical master equation is the most basic equation to describe biochemical reaction,although it can make statistical description for many processes.if the system is large and has high dimension,it is very difficult to solve the chemical master equation accurately.So we can deduce all kinds of approximate equations of chemical master equation under different conditions,such as chemical rate equation,chemical Langevin equation and so on.When the random fluctuation can be neglected,the chemical rate equation can well describe the dynamic behavior of the system.When the random fluctuation is large,the chemical Langevin equation can give a reasonable description of the random behavior of the system under certain conditions.Therefore,it is very important to study how to select the appropriate equation to describe the dynamics of the system when modeling a given biochemical reaction system Meaning.Time delay is a common phenomenon in biochemical reaction system.It explains the non Markov properties of many stochastic processes,which play a key role in many problems of molecular biology involving biochemical reaction or transport.In this paper,an accurate and general framework is introduced,which can generate the statistical correct implementation of non Markov discrete stochastic process systems.Under the restriction of a large number of processes,we provide an approximate and simple simulation algorithm,which works exactly the same as the original Gillespie method.The difference is that the instantaneous rate of events depends on the time after the event last occurred.In order to simulate the reaction process more accurately,we need to reflect the differences between molecules in the simulation process.When the number of reactant molecules in the system is large,we can ignore the differences between individual molecules,but when the scale of the system is large or the time lag is long,the scale of waiting sequence will become quite large,So it will take a lot of time to read and process them.In this paper,the algorithm is proposed.Based on the non Markov random algorithm,comparing with the improved Anderson algorithm,we can find that although it is only approximate,our numerical simulation in this paper shows that the algorithm can reappear the event interval time very accurately even for a small number of processes,and the deviation is very small for the process.The simulation algorithm based on this method can effectively improve the simulation speed and accuracy,and be applied to the biological system.