Diffused Solute-Solvent Interface with Poisson--Boltzmann Electrostatics: Free-Energy Variation and Sharp-Interface Limit

Li, B O; Liu, Yuan

doi:10.1137/15m100701x

Cited by 14 publications

(24 citation statements)

References 44 publications

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“…Our results on force convergence are then stated in terms of the weak convergence of corresponding stress tensors. Our work is closely related to the analysis in [21] and [20]. In [21], Li and Zhao study a similar but simpler phase-field model in which the electrostatic free energy is described by the Coulomb-field approximation [8,33], without the need of solving a dielectric Poisson or Poisson-Boltzmann equation.…”

Section: Main Results and Connections To Existing Studiesmentioning

confidence: 99%

“…where v n is the normal velocity of the sharp boundary. We shall use some of the results on the Poisson-Boltzmann electrostatics obtained in [20].…”

Section: Main Results and Connections To Existing Studiesmentioning

confidence: 99%

“…In the last term of electrostatic free energy, the dielectric coefficient ε = ε(φ) is constructed to be a smooth function, taking the values ε p and ε w in the solute region {φ ≈ 1} and solvent region {φ ≈ 0}, respectively [20,31]. The first variation of the functional F ξ [φ] is given by [20,31]…”

Section: A Phase-field Variational Model Of Solvationmentioning

confidence: 99%

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Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

Dai

2017

Arch Rational Mech Anal

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We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals-CahnHilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the PoissonBoltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics-its potential, free energy, and dielectric boundary force-with respect to the perturbation of dielectric boundary. We also prove the Γ-convergence of the phase-field free-energy functionals to their sharpinterface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals-Cahn-Hilliard functionals with minimal assumptions.

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Section: Main Results and Connections To Existing Studiesmentioning

confidence: 99%

“…where v n is the normal velocity of the sharp boundary. We shall use some of the results on the Poisson-Boltzmann electrostatics obtained in [20].…”

Section: Main Results and Connections To Existing Studiesmentioning

confidence: 99%

Section: A Phase-field Variational Model Of Solvationmentioning

confidence: 99%

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Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

Dai

2017

Arch Rational Mech Anal

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“…In our recent mathematical work, 102 we derived rigorously the first variation δ φ F ξ [φ] and also proved that in the sharp-interface limit as ξ → 0, our phasefield relaxation dynamics converges to the sharp-interface VISM relaxation dynamics. Here, we first present the main steps in the calculation of first variation for the electrostatic part of the free energy.…”

Section: Introductionmentioning

confidence: 80%

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson–Boltzmann electrostatics

Sun

Wen

Zhao³

et al. 2015

The Journal of Chemical Physics

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Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods. C 2015 AIP Publishing LLC. [http://dx

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“…The last term is the electrostatic energy, where U ele is the electrostatic energy density and the integral is again taken over the solvent region. For the PB electrostatics, one needs to solve a phase-field dielectric boundary PB equation to obtain the electrostatic energy density U ele [10,31,37]. Here, we shall consider the CFA, which yields a good approximation of the electrostatic free energy when the ionic effect is less significant.…”

Section: Introductionmentioning

confidence: 99%

A new phase-field approach to variational implicit solvation of charged molecules with the Coulomb-field approximation

Zhao

Sun

et al. 2018

Communications in Mathematical Sciences

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We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals Γ-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson-Boltzmann equation for the electrostatic interaction. *

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Diffused Solute-Solvent Interface with Poisson--Boltzmann Electrostatics: Free-Energy Variation and Sharp-Interface Limit

Cited by 14 publications

References 44 publications

Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson–Boltzmann electrostatics

A new phase-field approach to variational implicit solvation of charged molecules with the Coulomb-field approximation

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