Treecode-Accelerated Implicit Solvent Models for Biomolecular Simulations

目前的生物分子模拟无法达到研究蛋白质折叠等构象变化所需的长时间尺度。主要的障碍之一是计算蛋白质周围的溶剂水分子之间的静电力的高昂成本。为了解决这个问题，本项目采用了一个隐式溶剂模型，其中静电势满足泊松-玻尔兹曼(PB)方程。由于分子表面的几何复杂性、介电函数的不连续性以及计算区域的无界，PB方程的数值解是一个挑战。研究人员将通过开发边界积分PB解算器来克服这些困难，该解算器使用一种新的笛卡尔树码算法来筛选库仑相互作用。树码加速的PB解算器将在基准例子上进行测试，例如球面的Kirkwood解，并将结果与使用其他PB解算器获得的结果进行比较。除了静电势之外，该程序还将扩展到计算其他重要的量，如动力学所需的溶剂化自由能和溶剂化力。当前生物分子模拟面临的一个障碍是计算系统中分子之间的自感应静电力的费用。单靠计算机硬件的进步并不能达到研究长期分子动力学所必需的改进。因此，该项目的重点是改进这些计算机模拟中使用的数学算法。除了实现更准确和更高效的生物分子模拟外，所开发的算法还将在静电力发挥作用的其他应用中潜在地有用，例如在燃料电池中模拟电荷传输。该项目将通过支持一名博士后的研究，帮助培训科学工作人员，该博士后将由PI指导。

Current biomolecular simulations are unable to reach the long time scales needed to study conformation changes such as protein folding. One of the main obstacles is the high cost of computing the electrostatic forces among the solvent water molecules surrounding the protein. To address this issue, this project adopts an implicit solvent model in which the electrostatic potential satisfies the Poisson-Boltzmann (PB) equation. Numerical solution of the PB equation poses a challenge due to the geometric complexity of the molecular surface, the discontinuity in the dielectric function, and the unbounded computational domain. The investigators will overcome these difficulties by developing a boundary integral PB solver using a new Cartesian treecode algorithm for screened Coulomb interactions. The treecode-accelerated PB solver will be tested on benchmark examples such as Kirkwood's solution for a spherical surface, and the results will be compared with those obtained using other PB solvers. In addition to the electrostatic potential, the code will be extended to compute other important quantities such as the solvation free energy and solvation forces needed for dynamics. One obstacle facing current biomolecular simulations is the expense of computing the self-induced electrostatic forces among the molecules in the system. Advances in computer hardware alone won't achieve the improvements necesssary for studying long time molecular dynamics. This project therefore focuses on improving the mathematical algorithms used in these computer simulations. In addition to enabling more accurate and efficient biomolecular simulations, the algorithms developed will be potentially useful in other applications where electrostatic forces play a role, for example in modeling charge transport in fuel cells. The project will contribute to training the scientific workforce by supporting the research of a postdoc who will be mentored by the PI.