Study On The Stochastic Simulation Algorithm For Biochemical Reaction Systems With Delays

Life activity within the cell is a very complex process, contains thousands of interac-tive networks. Modeling and simulation those interactive networks is an important issueto study the phenomena of life. The intracellular life activities are a dynamic evolution-ary process with time and space. The study of randomness in gene regulatory networksbecomes a key issue because of the randomness of the chemical reaction in cells, the lownumbers of some gene, such as RNA, and so on.In this thesis, we focus on the Monte Carlo simulation of the evolutionary trajec-tories of biochemical reaction systems. The earliest research on this problem is the S-SA(Stochastic Simulation Algorithm) proposed by Gillespie in1976. It can simulatereaction events one after another along the time line, thus obtaining a trajectory of thesystem state that is exact in the statistical sense. Since then, it is widely used in biochem-ical simulation after it put forth. However, when a system gets complex, the enormouscomputational burden and the slow simulation speed on some issues made the scholarto seek the more efcient simulation methods. In2001, Gillespie presented an approxi-mating method called τ-leaping algorithm, which significantly improved the simulationspeeds. This also gives a lot of follow-up, and our work is mainly to improve these al-gorithms for the simulation speed and accuracy, and to integrate them into the diferenttypes of systems.In the stochastic simulation algorithm, the choice of the step is critical. For theexisting step selection strategy often obtains a smaller step size, if some reactants haveless number. This made the algorithm cannot accelerate the simulation speed. The crit-ical reaction is redefined in this thesis. This made the critical reactions more suitable todefine the reactions which have negative reactants. The new step selection strategy isproposed based on the definition. This made accelerate algorithm can be used even if thenumbers of some species in biochemical systems are small. The simulation results showthat the acceleration τ-leaping algorithm given in this paper can efectively improve thesimulation speed under the same simulation precision.Delay is a common phenomenon in biochemical reaction system. Delay reactionis being divided into consuming reactions and non-consuming reactions at present. Atthe consuming delay reactions, its reactants can still be involved in the other reactions.The fire of other reactions might afect the current delay reaction. Because of the mutualinfluence of the reactions, the diferences between the molecules should be represented inorder to seek a more accurate simulation when the system contains non-consuming delayreactions. The method is making a mark to each molecule, and this will be a very difcult task. We proposed a new marker method, which only marking the key molecular, greatlysimplifying the data and procedures scale, so improve the efciency of the simulation.When the system has a large number of reaction molecules, we can ignore the dif-ferences between individual molecules, and use the accelerated simulation method to thedelay reaction system. An event wait queue is made to schedule the reactions would befired. The data of the queue will increase as the simulation goes on. If the number ofdelayed reaction in the system is relatively large or the delay time is considerably longerthan the leaping time, which will inevitably afect the simulation speed. The updatemethod for the wait queue is proposed in this thesis. It can efectively reduce the sizeof the queue as well as shorten the storage and access time. The ID-leaping algorithmbased on it is efective to improve the speed of simulation.After integration of some complex delay reaction systems with, the multiple de-lay biochemical reactions will produce. Compared to the MD-SSA, we proposed theMD-leaping algorithm. The algorithm accelerates the simulation speed by building aquadruple structure based on diferent delay time-delay for the multi-delayed reactions.The algorithm in this paper extends the D-leaping method and solves the problem of ac-celerating the simulation of multi-delayed biochemical reaction system for the first time.The results of two specific biochemical reaction systems show that this algorithm can bewidely used in multiple delay biochemical reaction system, and can efectively improvethe efciency.