Salis Howard, Kaznessis Yiannis N
Department of Chemical Engineering and Materials Science, and Digital Technology Center, University of Minnesota, Minneapolis, Minnesota 55455, USA.
J Chem Phys. 2005 Dec 1;123(21):214106. doi: 10.1063/1.2131050.
Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.
随机化学动力学能更准确地描述“小”化学系统（如生物细胞）的动力学。许多实际系统存在动力学刚性，这使得精确随机模拟算法或其他动力学蒙特卡罗方法的大部分时间都用于执行频繁发生的反应事件。先前的方法通过推导一个演化方程（如化学主方程）来描述松弛的快速动力学，并利用该方程的解来确定慢动力学，从而成功应用了一种概率稳态近似。然而，由于化学主方程的解仅限于小型、精心挑选或线性的反应网络，因此一种替代的无方程方法将非常有用。我们提出了一种概率稳态近似，它能分离任意反应网络的时间尺度，检测边际分布向准稳态的收敛，直接对基础分布进行采样，并使用这些样本准确预测系统在未来时刻的状态，包括慢动力学的影响。该数值方法能准确求解快速和慢速反应动力学，对于刚性系统，还能将计算时间减少几个数量级。所发展的理论对基础稳态分布的形状或形式不做任何近似，仅假设其具有遍历性。我们通过多个有趣的例子，包括一个高度非线性的蛋白质 - 蛋白质相互作用网络，展示了该方法的准确性和效率。所发展的理论可应用于任何类型的动力学蒙特卡罗模拟，以更有效地模拟动力学刚性系统，包括现有的精确、近似或混合随机模拟技术。
