A Novel Computational Method for Diffuse Interface Models of Implicit Solvation of Biomolecules

在过去的二十年里，隐式溶剂模型因其低计算成本和相对较高的精度而在生物分子模拟领域具有极其重要的意义，在文献中有成千上万的示范应用。隐式溶剂模型的准确性取决于溶质-溶剂界面的几何描述和分子附近定义的溶剂介电分布。该模型在实际生成的溶质-溶剂光滑边界条件下的成功应用，将大大提高隐式溶剂模型的精度和效率。这项研究将直接集成到现有的隐式溶剂软件和可视化包中，以确保在化学、物理和生物领域建立的研究人员用户社区的广泛使用。此外，本文还将提出一种适用于数学生物学空间多尺度建模的非常规扩散界面模型的计算方法。这项工作的成功开展将成为研究离散模型和连续模型描述的区域之间过渡的有价值的计算工具。这一结果将对广泛的科学领域产生潜在影响，例如癌症研究和药物设计的多尺度建模。本项目的目标是开发一种新的生物分子隐式溶剂化扩散界面模型的计算方法。这种计算方法在数学上是严格的，在计算上是有效的，可以通过自由能最小化来产生物理上真实的溶质-溶剂光滑边界。为此，提出了一种创新的结构，将一个受有界允许函数约束的变分问题转化为一个等价的无约束问题，从而可以直接应用传统的欧拉-拉格朗日方程。这一新的计算公式将使用先进的计算算法来实现，以确保其准确性、稳定性和效率，并将通过几个常见的生物分子建模任务进行验证。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In the past two decades, implicit solvent models are of tremendous importance to the biomolecularmodeling community with thousands of exemplary applications in the literature due to their lowcomputational cost and relatively high accuracy. The accuracy of implicit solvent models dependson the geometric description of the solute-solvent interface and the solvent dielectric profile thatis defined near the molecules. Successful implementations of the proposed model in this project withrealistically generated solute-solvent smooth boundaries will greatly improve the accuracy andefficiency of these implicit solvent models. This investigation will be directly integrated into existingimplicit solvent software and visualization packages to ensure extensive usages by an establisheduser community of researchers in chemistry, physics, and biology. Moreover, the proposed work will present an unconventional computational method for diffuse interface models applied to spatial multiscale modeling in mathematical biology. Successful development of the proposed work will become a valuable computationaltool for studying the transition between regions described by discrete and continuum models. The outcome will have potential impacts across a wide range of scientific fields such as multiscalemodeling in cancer research and drug design. The goal of this project is to develop a novel computational method for diffuse interface models ofimplicit solvation of biomolecules. The computational approach will be mathematically rigorous andcomputationally efficient to generate physically realistic solute-solvent smooth boundaries by freeenergy minimization. To this end, an innovative construction is proposed to transform a variationalproblem subject to bounded admissible functions into an equivalent unconstrained problem sothat the traditional Euler-Lagrange Equation can be applied directly. This new computationalformulation will be implemented with advanced computational algorithms to ensure their accuracy,stability, and efficiency, and it will be validated by several common biomolecular modeling tasks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.