Collaborative Research: On calculating polar solvation and binding energies for non-rigid proteins in the Poisson-Boltzmann theory: modeling, analysis and application

About This Grant

Electrostatic free energy (EFE) calculations are indispensable for the quantitative analysis of biological processes, as they characterize the polar interactions between charged biomolecules such as proteins, DNA and RNA, and their surrounding ionic solvent environments. As one of the most widely used implicit solvent models, the Poisson-Boltzmann (PB) model computes EFE as the difference between PB energies of biomolecules in two reference states, typically vacuum and solvent. The success of classical PB theory relies on two restrictive assumptions: (i) biomolecules remain rigid and do not change shape when moving between states, and (ii) identical computational procedures are used for both states. However, under physiological conditions, proteins are inherently flexible and undergo conformational changes during solvation and binding. This project aims to overcome the rigidity limitation by introducing a generalized PB theory that accommodates non-rigid biomolecular structures. This enables PB models to handle shape changes in key biological processes such as solvation and binding. The proposed algorithms will be implemented in DelPhi, an open-source PB package, and they will be applied to other popular PB solvers in the form of post-processing patches. The new computational tools will be distributed free of charge to academic users, making them accessible to the broader biological research community. In addition, this project will provide interdisciplinary research and training opportunities for undergraduate and graduate students in biophysical modeling, computation and mathematical analysis. Outreach and dissemination activities will be developed to engage broader audiences and foster public understanding of how computational science contributes to human health and biomedical innovation. The limitations of the classic PB theory essentially stem from the fact that EFE computed by the PB model involves self-energy terms, that is, the singular charge at an atom center will interact with the potential induced by itself, which yields infinite energy values at each atom center. The rigidity assumption and identical numerical discretizations in two reference states enables the cancellation of these infinitely large self-energies terms between states. This project introduces a novel partition of the PB energy functional to separate the singular self-energies from the regular parts, so that the self-energy difference due to conformational changes can be analytically formulated and is free of singularities in subsequent numerical computation. This approach applies to both sharp-interface and diffuse-interface PB models, and it employs distinct strategies for regularization and non-regularization approaches in the numerical treatment of the PB equation. The proposed PB theory represents the first computational method capable of accurate EFE prediction for non-rigid biomolecules. This innovation provides a more precise physical modeling of solvation and binding processes and yields more accurate polar solvation and binding energy predictions. The proposed research will have a broader impact to the field of molecular biosciences, by providing improved binding energy estimations to several PB applications in drug design and mutation predictions. This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences and the Chemical Theory, Models and Computational Methods Program in the Division of Chemistry. 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.