Numerical Methods that Solve the PBE for Biomolecular Electrostatics

通过结合几种创新的数值方法，修正泊松-玻尔兹曼方程（mPBE）的解将比目前可能的计算速度快一个数量级。这项工作建立在以前开发的高效泊松-玻尔兹曼解算器的基础上，并将其扩展到解决计算要求更高的mPBE。在第一阶段，将开发mPBE解算器的初步版本，并测试泊松-玻尔兹曼方程被打破的生物分子构型，例如多价盐环境中的高电荷生物分子。在第二阶段，该模型将进一步完善，整合到静电建模软件包中，用于研究需要基于mpbe的物理建模水平的具有生物学意义的系统。该软件的分发将允许研究人员和生物技术企业在现成的计算机上模拟高电荷的生物分子。具体的目标。第一阶段的具体目标如下。(1)选择合适的mPBE理论，既能捕捉高电荷生物分子的重要物理行为（如体积排斥、有限离子大小、分子表面的图像效应），又能利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Aim(1)中的方法，并对生成的软件进行初步测试。(3)利用快速mPBE求解器进行初步研究，评估复杂形状生物聚合物在多价盐溶液中的盐依赖行为。研究设计。I期研究计划通过使用精心定制的计算方法，展示对一般形状生物分子的高效mPBE计算，解决了整个I期和II期工作的高风险因素。因此，第一阶段关注的是mPBE求解器的制定、软件实现和测试。方法。现有软件中的组件将被重新配置，用于基于mpbe的计算。主要组成部分是自适应笛卡尔网格，它结合了域的分层八叉树分解和潜在解的无奇点表示，以最小化网格点计数，从而减少计算成本。一种新的、自洽的外边界处理也被用于减小域的尺寸。将探讨各种网格和多网格选择，以加快对波动潜力的评估。长期目标。计算方法将被整合到一个软件包中，提供一套具有不同计算性能和建模保真度选项的静电模型。该软件将通过一个成熟的分子建模供应商进行分发。与现有MD代码和可视化软件的接口也将允许替代分发路径。健康相关性和与NIGMS研究所使命的相关性。这一努力解决了对生物重要过程的快速和准确的计算机模拟的日益增长的需求。

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.