Numerical Methods that Solve the PBE for Biomolecular Electrostatics

通过结合几种创新的数值方法，修改后的泊松-玻尔兹曼方程（mPBE）的解将比目前可能的速度快一个数量级。这项工作建立在以前开发的高效泊松-玻尔兹曼求解器的基础上，并将其扩展到计算要求更高的mPBE。在第一阶段，mPBE求解器的初步版本将被开发和测试的生物分子配置，其中泊松-玻尔兹曼方程是已知的打破，如高电荷的生物分子在多价盐环境。在第二阶段，该模型将进一步完善，纳入一个静电建模软件包，并用于研究生物重要的系统，需要基于mPBE的物理建模水平。该软件的发布将使研究人员和生物技术企业能够在现成的计算机上模拟高度带电的生物分子。具体目标。第一阶段的具体目标如下。(1)选择适当的mPBE理论，既捕获高电荷生物分子的重要物理行为（例如，体积排阻、有限离子尺寸、分子表面的图像效应），并使用先进的数值方法实现快速计算性能，并制定数值求解策略。(2)实施目标（1）中的方法，并对生成的软件进行初步测试。(3)使用快速mPBE求解器进行初步研究，以评估复杂形状生物聚合物在多价盐溶液中的盐依赖性行为。研究设计。第一阶段研究计划通过使用精心定制的计算方法对一般形状的生物分子进行有效的mPBE计算，解决了整个第一阶段和第二阶段奋进的高风险因素。因此，第一阶段关注的是制定，软件实现和测试的mPBE求解器。方法.将重新配置现有软件的组件，以进行基于mPBE的计算。其主要组成部分是一个自适应笛卡尔网格，它结合了层次，八叉树分解的域和一个无奇异性表示的潜在的解决方案，以尽量减少网格点计数，从而计算成本。一个新的，自洽的外边界处理也被用来减少域的大小。将探讨各种网格和多重网格选择，以加快对波动潜力的评估。长期目标。计算方法将被纳入一个软件包，提供一套静电模型与不同的计算性能和建模保真度选项。该软件将通过已建立的分子建模供应商分发。与现有MD代码和可视化软件的接口也将允许替代分配路径。与NIGMS研究所使命的健康相关性和相关性。这项工作解决了日益增长的需要快速和准确的计算机模拟生物学的重要进程。

By combining several innovative numerical methods, solutions to the modified Poisson-Boltzmann equation (mPBE) will be computed an order of magnitude faster than currently possible. The effort builds upon a previously developed efficient Poisson-Boltzmann solver and extends it to tackle the computationally more demanding mPBE. In Phase I, a preliminary version of the mPBE solver will be developed and tested for biomolecular configurations where the Poisson-Boltzmann equation is known to break down, such as highly charged biomolecules in multivalent salt environments. In Phase II, this model will be further refined, incorporated into an electrostatics modeling software package and used to study biologically significant systems requiring the mPBE-based level of physics modeling. Distribution of this software will allow researchers and biotech business to simulate highly charged biomolecules upon readily available computers. Specific Aims. The Phase I specific aims are as follows. (1) Select the appropriate mPBE theory that both captures the important physical behavior of highly charged biomolecules (e.g., volume exclusion, finite ion size, image effects at the molecular surface) and achieves fast computational performance using advanced numerical methods, and formulate numerical solution strategies. (2) Implement the approach in Aim (1) and conduct preliminary testing of the resulting software. (3) Conduct preliminary studies using the fast mPBE solver to assess the salt-dependent behavior of complex-shape biopolymers in multivalent salt solutions. Research Design. The Phase I research plan addresses the high-risk elements of the overall Phase I and II endeavor by demonstrating efficient mPBE calculations for generally-shaped biomolecules using carefully tailored computational methods. Thus, Phase I is concerned with the formulation, software implementation and testing of the mPBE solver. Methods. Components from existing software will be reconfigured for mPBE-based calculations. The main component is an adaptive Cartesian grid, which combines a hierarchical, octree decomposition of the domain and a singularity-free representation of the potential solution to minimize grid point count and thus computational cost. A new, self-consistent outer boundary treatment is also used to reduce domain size. Various mesh and multigrid options will be explored to expedite evaluation of the fluctuation potentials. Long Term Objectives. The computational methods will be incorporated into a software package offering a suite of electrostatics models with diverse computational performance and modeling fidelity options. The software will be distributed through an established molecular modeling vendor. Interfaces with existing MD codes and visualization software will also allow alternate distribution paths. Health Relatedness and relevance to Mission of the NIGMS Institute. This effort addresses the growing need for fast and accurate computer simulation of biologically important processes.