Department of Computer Sciences and Genome Center , University of California , Davis , California 95616 , United States.
J Chem Theory Comput. 2018 Jul 10;14(7):3903-3919. doi: 10.1021/acs.jctc.8b00338. Epub 2018 Jun 20.
Computational methods ranging from all-atom molecular dynamics simulations to coarse-grained normal-mode analyses based on simplified elastic networks provide a general framework to studying molecular dynamics. Despite recent successes in analyzing very large systems with up to 100 million atoms, those methods are currently limited to studying small- to medium-size molecular systems when used on standard desktop computers, because of computational limitations. The hope to circumvent those limitations rests on the development of improved algorithms with novel implementations that mitigate their computationally challenging parts. In this paper, we have addressed the computational challenges associated with computing coarse-grained normal modes of very large molecular systems, focusing on the calculation of the eigenpairs of the Hessian of the potential energy function from which the normal modes are computed. We have described and implemented a new method for handling this Hessian based on tensor products. This new formulation is shown to reduce space requirements and to improve the parallelization of its implementation. We have implemented and tested four different methods for computing some eigenpairs of the Hessian, namely, the standard, robust Lanczos method, a simple modification of this method based on polynomial filtering, a functional-based method recently proposed for normal-mode analyses of viruses, and a block Chebyshev-Davidson method with inner-outer restart. We have shown that the latter provides the most efficient implementation when computing eigenpairs of extremely large Hessian matrices corresponding to large viral capsids. We have also shown that, for those viral capsids, a large number of eigenpairs is actually needed, on the order of thousands, noticing however that this large number is still a small fraction of the total number of possible eigenpairs (a few percent).
计算方法包括从全原子分子动力学模拟到基于简化弹性网络的粗粒正则模态分析，为研究分子动力学提供了一个通用框架。尽管最近在分析多达 1 亿个原子的非常大的系统方面取得了成功，但由于计算限制，这些方法目前仅限于在标准台式计算机上研究中小规模的分子系统。希望规避这些限制的希望在于开发具有新颖实现的改进算法，以减轻其具有挑战性的计算部分。在本文中，我们解决了计算非常大的分子系统的粗粒正则模态所涉及的计算挑战，重点是计算正则模态所依据的势能函数的 Hessian 的特征对。我们描述并实现了一种基于张量积的处理这种 Hessian 的新方法。该新公式被证明可以减少空间要求并提高其实现的并行化程度。我们已经实现并测试了计算 Hessian 的一些特征对的四种不同方法，即标准的、鲁棒的 Lanczos 方法、基于多项式滤波的此方法的简单修改、最近为病毒的正则模态分析提出的基于函数的方法以及带有内-外重启的块 Chebyshev-Davidson 方法。我们表明，当计算对应于大型病毒衣壳的非常大的 Hessian 矩阵的特征对时，后者提供了最有效的实现。我们还表明，对于那些病毒衣壳，实际上需要大量的特征对，大约数千个，但是请注意，这个大量仍然只是可能的特征对总数的一小部分（百分之几）。
