FAST INTEGRAL METHOD FOR THE POISSON-BOLTZMANN EQUATION

第一阶段的工作成功地开发了一种快速边界元方法（BEM）来求解浸入离子溶液中的生物分子的线性泊松-玻尔兹曼方程（PBE）。与以前的快速边界元模型不同，这些模型仅限于泊松方程（对应于零离子强度），新的边界元模型适应离子强度效应，因此代表了生物分子建模的重大进步。在易于接近的工作站上，成功地解决了涉及多达8万个边界要素的问题。在第二阶段，这种新能力将扩展到求解非线性PBE，有效地将PBE解与分子动力学（MD）代码耦合，并模拟相对运动中的多个分子。还将纳入旨在进一步提高精度和减少计算需求的建模增强功能，包括用于密切表面电荷相互作用的新颖局部校正方法。第二阶段开发的快速并行边界元分析将扩展以适应这些新功能。为了促进强大的商业化前景，输入/输出将被配置为与现有的MD和分子表面生成代码接口。快速BEM PBE求解器将应用于以前无法进入的大规模生物分子系统，重点是推进基础生物学研究，并展示快速非线性PBE分析的建模能力。建议的商业应用：成功完成第二阶段的工作将产生新的强大的计算工具，以解决由线性/非线性泊松/泊松/玻尔兹曼偏微分方程控制的大量应用。由此产生的软件工具将允许政府、学术界和工业界的研究人员在工作站或个人电脑上对大型生物系统进行精确的静电建模研究。从这些研究中获得的知识对制药和生物医学界是有价值的。

The Phase I effort successfully developed a fast boundary element method (BEM) to solve the linear Poisson-Boltzmann equation (PBE) for biomolecules immersed in ionic solution. Unlike previous fast BEMs which were limited to the Poisson equation (corresponding to zero ionic strength), the new BEM accommodates ionic strength effects and thus represents a major advance in biomolecular modeling. Problems involving up to 80,000 boundary elements were successfully carried out upon readily accessibly workstations. In Phase II, this new capability will be extended to solve the nonlinear PBE, efficiently couple the PBE solutions to molecular dynamics (MD) codes and model multiple molecules in relative motion. Modeling enhancements designed to further improve accuracy and reduce computational requirements will also be incorporated, including a novel local correction method for close surface-charge interactions. The fast parallel BEM analysis developed in Phase II will be extended to accommodate these new capabilities. To promote strong commercialization prospects, the input/output will be configured to interface with existing MD and molecular surface generation codes. The fast BEM PBE solver will be applied to large-scale biomolecular systems that have been previous inaccessible with emphasis upon advancing basic biological research and demonstrating the modeling capabilities of the fast nonlinear PBE analysis. PROPOSED COMMERCIAL APPLICATIONS: Successful completion of the Phase II effort will result in new powerful computational tools to address an enormous range of applications governed by the linear/nonlinear Poisson/Poisson/Boltzmann PDEs. The resulting software tools will allow researchers in government, academia and industry to carry out accurate electrostatic modeling studies of the large-scale biological systems on workstations or PCs. The knowledge gained from such studies will be valuable to the pharmaceutical and biomedical community.