Collaborative Research: A new diffuse-interface approach to ensemble average solvation energy: modeling, analysis and computation

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In the quantitative analysis of biological processes, the complex interactions between the solute and solvent are typically described by solvation energies: the free energy of transferring the solute or biomolecule (e.g., proteins, DNA, RNA) from the vacuum to a solvent environment of interest (e.g., water at a certain ionic strength). Compared with explicit solvent models, which treat both the solute and the solvent as individual molecules, implicit solvent models, which average the effect of solvent phase as continuum media, are much more efficient and thus can handle much larger systems. Central to the construction of implicit solvent models is an interface separating the solute and solvent domains. However, commonly used interface definitions are ad hoc partitions and thus either non-negligibly overestimate or underestimate the solvation free energies. Variational implicit solvation models (VISM) have emerged as a successful approach to calculate the disposition of the solute-solvent interface by optimizing a solvation energy functional coupling the discrete description of the biomolecule and the continuum description of the solvent. The objective of this collaborative research project is to enhance the precision and computational efficiency of solvation energy prediction by means of VISM. The project will involve novel developments in mathematical models and numerical algorithms that can better reflect the interactions between biological macromolecules and the surrounding ionic environment. In addition, the project will provide opportunities for students to be involved in this collaborative research.Research has shown that neglecting the inherent randomness associated with solute-solvent interfaces, resulting from atom vibrations or thermodynamic fluctuations, can lead to substantial errors in predicting solvation energies. Since experimentally observed solvation energies are ensemble averages, the primary objective of this research is to develop a diffuse-interface VISM capable of capturing the ensemble average solvation energy (EASE). EASE represents the weighted average of solvation energies computed from all possible microstates of the solute-solvent system. In the routine calculation of EASE, one needs to carry out explicit solvent simulations, such as molecular dynamics (MD), to obtain thousands of solute-solvent configurations (snapshots) and perform energy calculations for each snapshot. Leveraging tools from statistical mechanics and geometric measure theory, this project aims to develop an innovative diffuse-interface VISM that rigorously reproduces EASE by utilizing a single diffuse interface profile instead of thousands of individual snapshots. Furthermore, while diffuse-interface VISMs offer improved accuracy compared to implicit solvent models utilizing predetermined interfaces, the computational cost associated with determining the interface poses a significant challenge. This limitation hampers the application of diffuse-interface VISMs to large molecular systems. Therefore, the second goal of this research is to develop accelerated numerical algorithms for solvation energy computation within the framework of diffuse-interface VISMs. By capitalizing on the structure of the proposed diffuse-interface VISM functional, a novel optimization algorithm will be devised that combines the augmented Lagrangian method with an inexact Newton scheme. This innovative approach will markedly enhance computational efficiency. Lastly, the analysis of the proposed model will provide novel techniques for studying the regularity of solutions to total variation minimization problems. The analytic techniques developed within the scope of this research project may also have broader relevance and applicability within the mathematical community.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.