Hybrid Computational Models and Robust Numerical Methods for Electrostatic Interactions in Biomolecules

该项目开发了生物分子系统中静电相互作用的混合计算模型和鲁棒数值方法。计算模型是在不同的层次上构建的。它们包括具有原子细节的变分平均场模型，特别是离子尺寸效应，以及用于处理单个离子的蒙特卡罗模拟模型。这些模型与先进的变分方法相结合，用于生物分子的溶剂化。设计并分析了求解相关椭圆界面问题和计算介电边界力的鲁棒数值方法。开发了特殊的接口代数多重网格方法和图形处理单元（GPU）实现，以加速相关的大规模计算。数值分析着重于所提格式的准确性，特别是边界力近似的准确性。生物分子，如蛋白质和DNA是原子的集合，其中很大一部分是带电的。带电的生物分子使溶剂（水或盐水）极化并产生离子，这些离子是溶液中可移动的带电粒子。静电或电荷-电荷相互作用产生强大的力，这些力决定了潜在生物系统的结构、动力学和功能。例如，静电相互作用影响药物分子与目标分子的结合方式，这反过来决定了药物在治疗疾病过程中的有效性。本项目旨在通过现代数学理论和计算工具的发展，在分子水平上理解生物系统的基本原理，推进计算数学的研究。这个项目的成功可能有助于降低实验通常需要的高成本，并加快药物发现的过程。此外，这种高度跨学科的研究为不同水平的学生提供了在计算数学和分子生物科学的界面上接受训练的机会。这种培训对于在竞争激烈的国际环境中保持我们的科研实力至关重要。

This project develops hybrid computational models and robust numerical methods for electrostatic interactions in biomolecular systems. The computational models are constructed at different levels. They include variational mean-field models with atomistic details, particularly ionic size effects, and Monte Carlo simulation models for treating individual ions. These models are coupled with an advanced, variational approach to the solvation of biomolecules. A robust numerical method for solving the related elliptic interface problem and calculating the dielectric boundary force is designed and analyzed. Special interface algebraic multigrid methods and the GPU (Graphics Processing Unit) implementation are developed to accelerate the related large-scale computations. Numerical analysis focuses on the accuracy of the proposed schemes, particularly that of the boundary force approximation.Biomolecules such as proteins and DNA are assemblies of atoms of which a significant portion are charged. Charged biomolecules polarize the solvent (water or salted water) and produce ions that are mobile charged particles in the solution. The electrostatic or charge-charge interaction gives rise to strong forces that determine the structure, dynamics, and function of underlying biological systems. For instance, the electrostatic interaction affects how a drug molecule binds to a target molecule, which in turn determines how effective the drug is in the process of curing a disease. Through the development of modern mathematical theories and computational tools, this project aims at understanding the fundamental principles of biological systems at the molecular level and advancing the research of computational mathematics. The success of this project can potentially help reduce the high cost often needed for experiments and speed up the process of drug discovery. In addition, this highly interdisciplinary research brings opportunities for students at different levels to receive training at the interface of computational mathematics and molecular biological science. Such training is critical to keeping our strength in scientific research in an competitive international environment.