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Large Eigenvalue Problems in Coarse-Grained Dynamic Analyses of Supramolecular Systems
Journal of Chemical Theory and Computation ( IF 5.5 ) Pub Date : 2018-06-06 00:00:00 , DOI: 10.1021/acs.jctc.8b00338
Patrice Koehl 1
Affiliation  

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).

中文翻译:

超分子系统粗粒动力学分析中的大特征值问题

从全原子分子动力学模拟到基于简化弹性网络的粗粒度正态分析的计算方法,为研究分子动力学提供了一个总体框架。尽管最近在分析具有1亿个原子的超大型系统方面取得了成功,但是由于计算上的限制,这些方法目前仅限于研究在标准台式计算机上使用的中小型分子系统。克服这些限制的希望在于开发改进的算法,并采用新颖的实现方式来减轻其计算上的困难。在本文中,我们解决了与计算非常大的分子系统的粗粒度正态模相关的计算难题,着重于计算势能函数的黑森本征对,从中计算出正常模式。我们已经描述并实现了一种基于张量积处理此Hessian的新方法。事实证明,这种新公式可减少空间需求并提高其实现的并行性。我们已经实现并测试了四种用于计算Hessian本征对的不同方法,即标准鲁棒Lanczos方法,基于多项式过滤对该方法的简单修改,最近针对病毒的正常模式分析而提出的基于功能的方法,以及带有内部-外部重新启动功能的块Chebyshev-Davidson方法。我们已经表明,当计算与大病毒衣壳相对应的极大黑森矩阵的特征对时,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,这个数目仍然只是可能的特征对总数的一小部分(百分之几)。
更新日期:2018-06-06
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