Department of Chemistry, Chung-Ang University, Seoul 156-756, Korea.
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
J Chem Theory Comput. 2012 Apr 10;8(4):1415-25. doi: 10.1021/ct200785q. Epub 2012 Mar 16.
We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we find that the variance in the number of reaction events is dependent on the square of the mean number of the reaction events when the size of measurement time is small on the relaxation time scale of rate coefficient fluctuations, which does not conform to renewal statistics. On the other hand, when the size of the measurement time interval is much greater than the relaxation time of rate coefficient fluctuations, the variance becomes linearly proportional to the mean reaction number in accordance with renewal statistics. Gillespie's stochastic simulation method is generalized for the reaction system with a rate coefficient fluctuation. The simulation results confirm the correctness of the analytic results for the time dependent mean and variance of the reaction event number distribution. On the basis of the obtained results, we propose a method of quantitative analysis for the reaction event counting statistics of reaction systems with rate coefficient fluctuations, which enables one to extract information about the magnitude and the relaxation times of the fluctuating reaction rate coefficient, without a bias that can be introduced by assuming a particular kinetic model of conformational dynamics and the conformation dependent reactivity. An exact relationship is established between a higher moment of the reaction event number distribution and the multitime correlation of the reaction rate for the reaction system with a nonequilibrium initial state distribution as well as for the system with the equilibrium initial state distribution.
我们研究了基本生物聚合物反应的反应事件计数统计（RECS），其中速率系数取决于生物聚合物的状态和周围环境，并在具有动态异质性的反应系统的 RECS 中发现了普遍的动力学相变。通过对基本生物聚合物反应的一般模型的精确分析，我们发现当测量时间的大小在速率系数波动的弛豫时间尺度上很小时，反应事件数的方差取决于反应事件数的平均值的平方，这不符合更新统计。另一方面，当测量时间间隔的大小远大于速率系数波动的弛豫时间时，方差与更新统计一致，与平均反应数呈线性比例。我们推广了具有速率系数波动的反应系统的 Gillespie 随机模拟方法。模拟结果证实了反应事件数分布的时间相关平均值和方差的解析结果的正确性。基于获得的结果，我们提出了一种用于具有速率系数波动的反应系统的反应事件计数统计的定量分析方法，该方法可以提取有关波动反应速率系数的大小和弛豫时间的信息，而不会引入通过假设构象动力学和构象依赖性反应的特定动力学模型而引入的偏差。对于具有非平衡初始态分布的反应系统以及具有平衡初始态分布的系统，建立了反应事件数分布的更高阶矩与反应速率的多时间相关之间的精确关系。
