Zhao Ruijun, Shen Juanfang, Skeel Robert D
Department of Computer Science, Purdue University, West Lafayette, IN, 47907-2107.
J Chem Theory Comput. 2010 Aug 10;6(8):2411-2423. doi: 10.1021/ct900689m.
Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective variables chosen so that paths cluster in collective variable space. The computational task becomes that of computing the "center" of such a cluster. A good way to define the center employs the concept of a committor, whose value at a point in collective variable space is the probability that a trajectory at that point will reach B before A. The committor "foliates" the transition region into a set of isocommittors. The maximum flux transition path is defined as a path that crosses each isocommittor at a point which (locally) has the highest crossing rate of distinct reactive trajectories. This path is based on the same principle as the minimum resistance path of Berkowitz et al (1983), but it has two advantages: (i) the path is invariant with respect to a change of coordinates in collective variable space and (ii) the differential equations that define the path are simpler. It is argued that such a path is nearer to an ideal path than others that have been proposed with the possible exception of the finite-temperature string method path. To make the calculation tractable, three approximations are introduced, yielding a path that is the solution of a nonsingular two-point boundary-value problem. For such a problem, one can construct a simple and robust algorithm. One such algorithm and its performance is discussed.
对于生物分子系统的两个亚稳态A和B，问题在于计算从A到B的可能转变路径。如果针对一组经过选择的约化集体变量进行这种计算，会更具信息量且更易于处理，这样路径会在集体变量空间中聚集。计算任务就变成了计算这样一个聚集的“中心”。定义中心的一个好方法是采用反应概率的概念，其在集体变量空间中某一点的值是该点处的轨迹在到达A之前到达B的概率。反应概率将转变区域“叶状化”为一组等反应概率线。最大通量转变路径被定义为一条在（局部）具有不同反应轨迹最高交叉率的点穿过每条等反应概率线的路径。这条路径基于与Berkowitz等人（1983年）的最小阻力路径相同的原理，但它有两个优点：（i）该路径在集体变量空间的坐标变化下是不变的；（ii）定义该路径的微分方程更简单。有人认为，除了有限温度弦方法路径可能是个例外，这样的路径比其他已提出的路径更接近理想路径。为了使计算易于处理，引入了三种近似，得到一条是一个非奇异两点边值问题解的路径。对于这样一个问题，可以构造一个简单且稳健的算法。讨论了一种这样的算法及其性能。
