Savva Giannis D, Stamatakis Michail
Thomas Young Centre and Department of Chemical Engineering, University College London, Roberts Building, Torrington Place, London WC1E 7JE, U.K.
J Phys Chem A. 2025 Feb 13;129(6):1726-1740. doi: 10.1021/acs.jpca.4c05963. Epub 2025 Feb 5.
Reaction kinetics in biological systems are often subject to stochastic effects due to the low populations of reacting molecules, necessitating the adoption of kinetic Monte Carlo methods for their study. Such methods, however, can be computationally expensive, especially in the case of stiff systems, where some reactions are executed at much higher frequencies than others. We present an algorithm that reduces the reaction rate constants of the fast processes on-the-fly, thereby saving computational time, while keeping the approximation error within desirable limits. The algorithm couples the Modified Next Reaction Method for simulating stochastic systems with the Common Random Number framework and calculates accurate metrics for both the computational cost and approximation error by generating multiple sets of trajectories that correspond to increasingly reduced (downscaled) reaction rate constants. The optimum downscale factor is chosen via optimization of two conflicting objectives: (a) maximizing the speedup and (b) minimizing the approximation error introduced, and it is straightforward to tune the performance of the method, favoring accuracy versus speed or vice versa. Our approach is demonstrated on a biology-inspired well-mixed stiff system and is shown to accelerate the stochastic simulation thereof from 66 h down to 90 min, achieving a speed-up factor of 44×, without distorting the dynamics of the system studied.
由于生物系统中反应分子数量较少，其反应动力学往往受到随机效应的影响，因此需要采用动力学蒙特卡罗方法进行研究。然而，此类方法计算成本较高，特别是对于刚性系统而言，其中一些反应的执行频率比其他反应高得多。我们提出了一种算法，该算法可以即时降低快速过程的反应速率常数，从而节省计算时间，同时将近似误差控制在理想范围内。该算法将用于模拟随机系统的改进型下一步反应方法与公共随机数框架相结合，并通过生成多组对应于逐渐降低（缩减）的反应速率常数的轨迹，计算出计算成本和近似误差的准确指标。通过对两个相互冲突的目标进行优化来选择最佳缩减因子：（a）最大化加速比；（b）最小化引入的近似误差，并且很容易调整该方法的性能，偏向于准确性与速度，反之亦然。我们的方法在一个受生物学启发的充分混合的刚性系统上得到了验证，结果表明该方法能将随机模拟从66小时加速至90分钟，加速因子达到44倍，且不会扭曲所研究系统的动力学。
