时滞生化反应系统的随机模拟算法研究
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摘要
细胞内的生命活动是一个非常复杂的过程,包含了成千上万个相互作用的网络,因此对这些相互作用网络进行建模和仿真是研究生命现象的一个重要的课题.而细胞内的生命活动又是一个随时空演化的动态过程,细胞内化学反应的随机性,细胞中某些基因、核糖核酸等低数目的原因,使得随机性的研究成为基因调控网络研究的一个重点问题.
本文中我们主要讨论运用蒙特卡洛方法模拟生化反应演化轨道的问题.对这个问题的最早研究为Gillespie于1976年提出的,用于模拟生化反应的精确算法SSA.因为该算法能逐个模拟反应系统中随时间变化的每一个反应,能够给出统计上精确的系统演化随机轨迹,因此一经提出,即在生物学领域得到了广泛的应用.然而,由于生物系统的复杂性,在很多问题上SSA的巨大的运算量和缓慢的模拟速度,促使人们寻求更高效的模拟方法.于是, Gillespie在2001年又提出了τ-leaping算法,使得模拟速度大幅提升,由此也引发了大量的后续工作.我们主要的工作就是对这类算法的改进,提高它的模拟速度和精度,并且将它们整合到各种不同类型的系统中去.
在随机模拟算法中,步长的选择是非常关键的一个环节.对于现有的步长选择策略,当系统中某些反应物数目较少时,往往会得到较小的步长,不能使用加速算法.本文重新定义了临界反应,使其更合理地界定了可能出现负分子组分的反应,对反应做了更细化的分类,并给出了新的步长选择策略,使得即使有小分子数目的反应物出现时,系统仍可以采取τ-leaping算法.仿真结果表明本文给出的加速τ-leaping算法能够在保证精度的同时有效地提高模拟速度.
时滞是生化反应系统中普遍存在的现象,现阶段通常把时滞反应分为消耗时滞反应与非消耗时滞反应.非消耗时滞反应中,反应物在时滞反应发生后仍可参与到其它反应中,而其它反应的发生可能会影响到当前的时滞反应.因为这种反应之间的相互影响,当系统中含有非消耗时滞反应时,为了更精确地模拟其反应过程,在模拟过程中需要体现分子之间的差异,因此选择对每个分子进行标记,这将是一个非常艰巨的任务.本文提出的标记方法,只针对关键分子进行标记,大大简化了数据规模以及操作程序,从而提高了模拟效率.
当系统中反应物分子数目较大时,我们可以忽略个别分子的差异,对时滞反应系统采取加速模拟的方法.加速模拟过程中通常需要建立一个事件等待序列,来预定将要发生的反应.但是当系统的规模较大或者时滞时间较长时,等待序列的规模也会变得相当庞大,从而对它们的读取与处理将会花费大量的时间.我们提出了一种新的等待序列更新方法,能够有效地控制等待序列的规模,减少存储空间和存取时间.基于该方法提出的ID-leaping算法能够有效地提高模拟速度,并且应用到生物系统中去.
对一些复杂的时滞系统进行整合后,会构成多重时滞生化反应,本文针对已有的MD-SSA提出了相应的加速算法MD-leaping.该算法通过对多重时滞反应系统建立以不同时滞时间为主体的四元结构体,使得在每一个跳跃时间步长内可以同时模拟多个生化反应,提高了模拟速度. MD-leaping算法是D-leaping算法的拓展,它首次解决了多重时滞生化反应系统的加速模拟问题.通过对生化反应系统的模拟,表明该算法可以广泛地应用于多重时滞生化反应系统,并且与已有的多重时滞系统的非加速算法相比运行效率有显著提高.
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.
本文中我们主要讨论运用蒙特卡洛方法模拟生化反应演化轨道的问题.对这个问题的最早研究为Gillespie于1976年提出的,用于模拟生化反应的精确算法SSA.因为该算法能逐个模拟反应系统中随时间变化的每一个反应,能够给出统计上精确的系统演化随机轨迹,因此一经提出,即在生物学领域得到了广泛的应用.然而,由于生物系统的复杂性,在很多问题上SSA的巨大的运算量和缓慢的模拟速度,促使人们寻求更高效的模拟方法.于是, Gillespie在2001年又提出了τ-leaping算法,使得模拟速度大幅提升,由此也引发了大量的后续工作.我们主要的工作就是对这类算法的改进,提高它的模拟速度和精度,并且将它们整合到各种不同类型的系统中去.
在随机模拟算法中,步长的选择是非常关键的一个环节.对于现有的步长选择策略,当系统中某些反应物数目较少时,往往会得到较小的步长,不能使用加速算法.本文重新定义了临界反应,使其更合理地界定了可能出现负分子组分的反应,对反应做了更细化的分类,并给出了新的步长选择策略,使得即使有小分子数目的反应物出现时,系统仍可以采取τ-leaping算法.仿真结果表明本文给出的加速τ-leaping算法能够在保证精度的同时有效地提高模拟速度.
时滞是生化反应系统中普遍存在的现象,现阶段通常把时滞反应分为消耗时滞反应与非消耗时滞反应.非消耗时滞反应中,反应物在时滞反应发生后仍可参与到其它反应中,而其它反应的发生可能会影响到当前的时滞反应.因为这种反应之间的相互影响,当系统中含有非消耗时滞反应时,为了更精确地模拟其反应过程,在模拟过程中需要体现分子之间的差异,因此选择对每个分子进行标记,这将是一个非常艰巨的任务.本文提出的标记方法,只针对关键分子进行标记,大大简化了数据规模以及操作程序,从而提高了模拟效率.
当系统中反应物分子数目较大时,我们可以忽略个别分子的差异,对时滞反应系统采取加速模拟的方法.加速模拟过程中通常需要建立一个事件等待序列,来预定将要发生的反应.但是当系统的规模较大或者时滞时间较长时,等待序列的规模也会变得相当庞大,从而对它们的读取与处理将会花费大量的时间.我们提出了一种新的等待序列更新方法,能够有效地控制等待序列的规模,减少存储空间和存取时间.基于该方法提出的ID-leaping算法能够有效地提高模拟速度,并且应用到生物系统中去.
对一些复杂的时滞系统进行整合后,会构成多重时滞生化反应,本文针对已有的MD-SSA提出了相应的加速算法MD-leaping.该算法通过对多重时滞反应系统建立以不同时滞时间为主体的四元结构体,使得在每一个跳跃时间步长内可以同时模拟多个生化反应,提高了模拟速度. MD-leaping算法是D-leaping算法的拓展,它首次解决了多重时滞生化反应系统的加速模拟问题.通过对生化反应系统的模拟,表明该算法可以广泛地应用于多重时滞生化反应系统,并且与已有的多重时滞系统的非加速算法相比运行效率有显著提高.
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.
引文
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