Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA.
J Comput Chem. 2010 Oct;31(13):2428-33. doi: 10.1002/jcc.21535.
Reaction kinetics on free energy surfaces with small activation barriers can be computed directly with the Smoluchowski equation. The procedure is computationally expensive even in a few dimensions. We present a propagation method that considerably reduces computational time for a particular class of problems: when the free energy surface suddenly switches by a small amount, and the probability distribution relaxes to a new equilibrium value. This case describes relaxation experiments. To achieve efficient solution, we expand the density matrix in a basis set obtained by singular value decomposition of equilibrium density matrices. Grid size during propagation is reduced from (100-1000)(N) to (2-4)(N) in N dimensions. Although the scaling with N is not improved, the smaller basis set nonetheless yields a significant speed up for low-dimensional calculations. To demonstrate the practicality of our method, we couple Smoluchowsi dynamics with a genetic algorithm to search for free energy surfaces compatible with the multiprobe thermodynamics and temperature jump experiment reported for the protein alpha(3)D.
在具有小活化能垒的自由能表面上的反应动力学可以直接用 Smoluchowski 方程来计算。即使在几个维度上，这个过程的计算量也非常大。我们提出了一种传播方法，该方法大大减少了特定一类问题的计算时间：当自由能表面突然发生小的变化，并且概率分布松弛到新的平衡值时。这种情况描述了弛豫实验。为了实现有效的解决方案，我们在由平衡密度矩阵的奇异值分解得到的基集中展开密度矩阵。在传播过程中，网格大小从 (100-1000)(N) 减少到 (2-4)(N)，在 N 维中。尽管与 N 的比例关系没有改善，但较小的基集仍然为低维计算提供了显著的加速。为了展示我们的方法的实用性，我们将 Smoluchowsi 动力学与遗传算法相结合，以搜索与多探针热力学和温度跳跃实验相兼容的自由能表面，该实验是针对蛋白质 alpha(3)D 报告的。
