METHOD FOR THE POISSON-BOLTZMANN EQUATION

提出了一种快速并行边界元方法。 线性化泊松方程的高效而稳健的数值解 玻尔兹曼方程在生物分子静电研究中的应用 离子强度效应很重要的问题。在这样的情况下 分析，所有N个边界元素表示介质边界 在生物分子表面上相互作用，从而包括 具有0(N2)个存储和0(N3)个CPU成本的多体问题 传统的解决方法。这两种成本都大幅降低到 0(N)通过结合快速多极算法(FMA)和高效的 迭代的无矩阵求解过程。到目前为止，所有FAST BE分析 仅限于泊松方程的解(零离子 力量)。因此，这里提出的一项关键技术改进是使用 FMA用于计算表面元素间的德拜-休克尔相互作用 在整个盐浓度范围内。充分利用，充分利用 可用的计算资源，FAST固有的并行性 将对BE分析进行开发，并面向操作 在分布式系统上。这两种情况的结果都会显示出来 易于分析的模型问题，也适用于代表性的 生物分子系统用于验证预期的计算性能 和精确度。 建议的商业应用 SBIR工作的成功完成将使 政府、学术界和产业界先进的串并快速 用于生物分子静电问题的BE软件 浸泡在离子溶液中的组件。从使用中获得的知识 在静电问题中如此强大的计算工具持有 有希望揭示静电相互作用对 生物过程与结构类药物开发的新领域 设计。

A fast parallel boundary element (BE) method is proposed for the efficient and robust numerical solution of the linearized Poisson- Boltzmann equation for application to biomolecular electrostatic problems where ionic strength effects are important. In such an analysis, all N boundary elements representing the dielectric boundary at the biomolecular surface interact with each other and thus comprise a many-body problem with 0(N2) storage and 0(N3) CPU costs in conventional solution methods. Both costs are drastically reduced to 0(N) by combining fast multipole algorithms (FMAs) with an efficient iterative matrix-free solution procedure. To date all fast BE analysis have been limited to the solution of the Poisson equation (zero ionic strength). Thus, a key technical advance proposed here is to employ a FMA to calculate the Debye-Huckel interactions between surface elements over the entire range of salt concentration. To make full use of available computational resources, the inherent parallelisum of the fast BE analysis will be exploited and the software oriented for operation upon distributed systems. Results will be presented for both analytically tractable model problems and also for representative biomolecular systems to verify the anticipated computational performance and accuracy. PROPOSED COMMERCIAL APPLICATION The successful completion of the SBIR effort, will make available to government, academia and industry an advanced serial and parallel fast BE software which will be used in electrostatic problems of biomolecular assemblies immersed in ionic solution. The knowledge gained from using such powerful computational tools in electrostatic problems hold the promises of revealing the effects of electrostatic interactions on biological processes and opening new venues for structure-based drug design.