Collaborative Research: A Regularized Poisson Boltzmann Model for Fast Computation of the Ensemble Average Polar Solvation Energy

这一合作研究项目将开发数学模型和模拟工具，用于研究大生物分子(例如蛋白质)与模拟水环境的周围水分子之间的相互作用。描述这种相互作用的能量计算是复杂的，因为生物分子的结构并不完全固定或刚性，而且周围的水分子也在不断地运动。因此，为了提供与实验可测量的能量相当的量，必须在相应的数学描述中考虑这些构象变化。在这个项目中，将通过将适当的生物物理考虑与数学进步相结合，形成一个新的理论模型，使模拟能够模拟大分子和水原子构象变化的影响。拟议的数学发展将使分子生物科学和生物物理学的研究人员受益。此外，所提出的模型和算法将在Delphi中实现，该工具免费分发给学术用户，以确保数学、化学、物理和生物从业人员的广泛使用。此外，这个项目将为本科生和研究生提供生物建模、计算和数学分析的跨学科研究和培训机会。实验可观察到的溶剂化能是集合平均。然而，这种能量的直接泊松-玻尔兹曼(PB)计算需要生成数以千计的快照的典型结构系综，这在计算上非常昂贵。如果能够通过非均相介电分布模拟大分子构象变化的影响，采用单一结构来计算系综平均溶剂化能，可以大大节省计算时间。在这个项目中，一个包含三个关键创新的新型超高斯PB模型将被建立：(1)在连续介质静电偏微分方程(PDE)中结合大分子与环境相关的原子特征；(2)发展一种新的正则化公式来处理奇异电荷，通过严格的数学分析开发新的椭圆PDE：部分电荷和水分子(在空腔内、键合在蛋白质上和在大块溶剂中)将不再像当前的高斯模型那样被建模为均匀的空间区域，而是将反映整个溶质-溶剂系统的灵活性；以及(3)对于真空和水环境中的大分子，不需要确定尖锐的分子表面。将进行模型基准测试和生物应用测试以进行验证，生成的工具将被整合到广泛使用的Delphi程序包中，用于计算系综平均溶剂化能。该项目由数学科学部数学生物学项目部、化学理论、模型和计算方法项目部以及既定的促进竞争性研究计划(EPSCoR)共同支持。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。

This collaborative research project will develop mathematical models and simulation tools for studying the interactions between large biological molecules, for example proteins, and surrounding water molecules modeling an aqueous environment. The energy computation for characterizing such interactions is complex because the structures of biomolecules are not completely fixed or rigid, and the surrounding water molecules are also in constant motion. Thus, to deliver quantities that are comparable with experimentally-measurable energies, one must account for these conformational changes in the corresponding mathematical description. A new theoretical model will be formulated in this project by combining appropriate biophysical considerations with mathematical advances, allowing simulations to mimic the effect of conformational changes in both macromolecule and water atoms. The proposed mathematical development will benefit researchers in molecular biosciences and biophysics. Moreover, the proposed models and algorithms will be implemented in DelPhi, which is distributed free of charge to academic users, to ensure extensive usage by practitioners from mathematics, chemistry, physics, and biology. In addition, this project will provide interdisciplinary research and training opportunities for undergraduate and graduate students in biological modeling, computation and mathematical analysis.Experimentally-observable solvation energies are ensemble averaged. However, direct Poisson-Boltzmann (PB) calculations of such energies require the generation of a representative ensemble of structures in terms of thousands of snapshots, which is computationally very expensive. Tremendous savings in computational time can be achieved if one can calculate the ensemble average solvation energy by employing a single structure by mimicking the effect of conformation changes of macromolecules via heterogeneous dielectric distributions. In this project, a novel super-Gaussian PB model will be formulated embodying three key innovations: (1) incorporation of environment-dependent atomic characteristics of macromolecules within the continuum electrostatic partial differential equation (PDE); (2) development of a novel, regularized formulation to treat singular charges, with new elliptic PDEs developed through rigorous mathematical analysis: partial charges and water molecules (inside cavities, bonded to the protein, and in bulk solvent) will no longer be modeled as homogeneous spatial regions as in the current Gaussian model, but will reflect the flexibility of the entire solute-solvent system; and (3) elimination of the need to determine a sharp molecular surface, for macromolecules in both vacuum and water environments. Model benchmarking and biological applications tests will be carried out for validation, and the resulting tool will be incorporated into the widely-used DelPhi program package for computing ensemble-average solvation energies. This project is supported jointly by the Division of Mathematical Sciences Mathematical Biology Program, the Division of Chemistry Chemical Theory, Models and Computational Methods Program, and the Established Program to Stimulate Competitive Research (EPSCoR).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.