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The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.
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On delivering polar solvation free energy of proteins from energy minimized structures using a regularized super‐Gaussian Poisson–Boltzmann model
Abstract The biomolecules interact with their partners in an aqueous media; thus, their solvation energy is an important thermodynamics quantity. In previous works (J. Chem. Theory Comput. 14(2): 1020–1032), we demonstrated that the Poisson–Boltzmann (PB) approach reproduces solvation energy calculated via thermodynamic integration (TI) protocol if the structures of proteins are kept rigid. However, proteins are not rigid bodies and computing their solvation energy must account for their flexibility. Typically, in the framework of PB calculations, this is done by collecting snapshots from molecular dynamics (MD) simulations, computing their solvation energies, and averaging to obtain the ensemble‐averaged solvation energy, which is computationally demanding. To reduce the computational cost, we have proposed Gaussian/super‐Gaussian‐based methods for the dielectric function that use the atomic packing to deliver smooth dielectric function for the entire computational space, the protein and water phase, which allows the ensemble‐averaged solvation energy to be computed from a single structure. One of the technical difficulties associated with the smooth dielectric function presentation with respect to polar solvation energy is the absence of a dielectric border between the protein and water where induced charges should be positioned. This motivated the present work, where we report a super‐Gaussian regularized Poisson–Boltzmann method and use it for computing the polar solvation energy from single energy minimized structures and assess its ability to reproduce the ensemble‐averaged polar solvation on a dataset of 74 high‐resolution monomeric proteins.
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- PAR ID:
- 10552932
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 46
- Issue:
- 1
- ISSN:
- 0192-8651
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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