Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2012 Oct 7;137(13):134110. doi: 10.1063/1.4756796.
An algorithm is presented to maintain rigid structures in Verlet based cartesian molecular dynamics (MD) simulations. After each unconstrained MD step, the coordinates of selected particles are corrected to maintain rigid structures through an iterative procedure of rotation matrix computation. This algorithm, named as SHAPE and implemented in CHARMM program suite, avoids the calculations of Lagrange multipliers, so that the complexity of computation does not increase with the number of particles in a rigid structure. The implementation of this algorithm does not require significant modification of propagation integrator, and can be plugged into any cartesian based MD integration scheme. A unique feature of the SHAPE method is that it is interchangeable with SHAKE for any object that can be constrained as a rigid structure using multiple SHAKE constraints. Unlike SHAKE, the SHAPE method can be applied to large linear (with three or more centers) and planar (with four or more centers) rigid bodies. Numerical tests with four model systems including two proteins demonstrate that the accuracy and reliability of the SHAPE method are comparable to the SHAKE method, but with much more applicability and efficiency.
提出了一种算法，用于在基于 Verlet 的笛卡尔分子动力学（MD）模拟中保持刚性结构。在每个无约束的 MD 步骤之后，通过旋转矩阵计算的迭代过程来修正选定粒子的坐标，以保持刚性结构。该算法名为 SHAPE，实现在 CHARMM 程序套件中，避免了拉格朗日乘数的计算，因此计算复杂度不会随刚性结构中的粒子数量增加而增加。该算法的实现不需要对传播积分器进行重大修改，并且可以插入任何基于笛卡尔的 MD 积分方案中。SHAPE 方法的一个独特特点是，它可以与 SHAKE 互换使用，用于任何可以使用多个 SHAKE 约束约束为刚性结构的对象。与 SHAKE 不同，SHAPE 方法可应用于大型线性（三个或更多中心）和平面（四个或更多中心）刚体。对包括两个蛋白质在内的四个模型系统的数值测试表明，SHAPE 方法的准确性和可靠性与 SHAKE 方法相当，但适用性和效率更高。
