ArticleJournal of mathematical biology2009
Geometric and potential driving formation and evolution of biomolecular surfaces.
Article in Journal of mathematical biology, 2009. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 46 papers.
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46 citing papers in PubMed.
- On generalizing the induced surface charge method to heterogeneous Poisson-Boltzmann models for electrostatic free energy calculation.Journal of computational physics · 2026Article
- Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential.Journal of computational physics · 2024Article
- On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary.Mathematical biosciences and engineering : MBE · 2021Article
- A review of mathematical representations of biomolecular data.Physical chemistry chemical physics : PCCP · 2020Review
- Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states.Journal of mathematical biology · 2019Article
- Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations.Journal of chemical theory and computation · 2018Article
- Divide-and-conquer strategy for large-scale Eulerian solvent excluded surface.Communications in information and systems · 2018Article
- Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening.PLoS computational biology · 2018Article
- Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.The Journal of chemical physics · 2017Article
- Object-oriented Persistent Homology.Journal of computational physics · 2016Article
- 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
- Multidimensional persistence in biomolecular data.Journal of computational chemistry · 2015Article
- LS-VISM: A software package for analysis of biomolecular solvation.Journal of computational chemistry · 2015Article
- On the energy components governing molecular recognition in the framework of continuum approaches.Frontiers in molecular biosciences · 2015Review
- A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.Chemical physics letters · 2014Article
- Persistent homology analysis of protein structure, flexibility, and folding.International journal for numerical methods in biomedical engineering · 2014Article
- A unified discontinuous Galerkin framework for time integration.Mathematical methods in the applied sciences · 2014Article
- Variational Implicit Solvation with Poisson-Boltzmann Theory.Journal of chemical theory and computation · 2014Article
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5 authors.
Funding
Abstract
This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent-solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank-Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.
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