ArticleJournal of computational physics2010
Differential geometry based solvation model I: Eulerian formulation.
Article in Journal of computational physics, 2010. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 67 papers.
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Who cites it
67 citing papers in PubMed.
- Multiscale Differential Geometry Learning for Protein Flexibility Analysis.Journal of computational chemistry · 2025Article
- Optimal Dielectric Boundary for Binding Free Energy Estimates in the Implicit Solvent.Journal of chemical information and modeling · 2024Article
- Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains.The journal of physical chemistry. B · 2024Article
- Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential.Journal of computational physics · 2024Article
- Improving the Accuracy of Physics-Based Hydration-Free Energy Predictions by Machine Learning the Remaining Error Relative to the Experiment.Journal of chemical theory and computation · 2024Article
- Methodology-Centered Review of Molecular Modeling, Simulation, and Prediction of SARS-CoV-2.Chemical reviews · 2022Review
- Multidimensional Global Optimization and Robustness Analysis in the Context of Protein-Ligand Binding.Journal of chemical theory and computation · 2020Article
- A review of mathematical representations of biomolecular data.Physical chemistry chemical physics : PCCP · 2020Review
- Short solvent model for ion correlations and hydrophobic association.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
- DG-GL: Differential geometry-based geometric learning of molecular datasets.International journal for numerical methods in biomedical engineering · 2019Article
- Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation.Chemical reviews · 2018Review
- Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations.Journal of chemical theory and computation · 2018Article
- Improvements to the APBS biomolecular solvation software suite.Protein science : a publication of the Protein Society · 2018Article
- Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly.Frontiers in molecular biosciences · 2018Review
- Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening.PLoS computational biology · 2018Article
- Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions.The journal of physical chemistry. B · 2016Article
- Object-oriented Persistent Homology.Journal of computational physics · 2016Article
- Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins.Methods in enzymology · 2016Review
- A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics.The Journal of chemical physics · 2015Article
- Parameter optimization in differential geometry based solvation models.The Journal of chemical physics · 2015Article
7 more citing papers are in PubMed but not listed here.
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3 authors.
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Abstract
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.
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