PDB_Hydro: incorporating dipolar solvents with variable density in the Poisson-Boltzmann treatment of macromolecule electrostatics

Abstract

We describe a new way to calculate the electrostatic properties of macromolecules which eliminates the assumption of a constant dielectric value in the solvent region, resulting in a Generalized Poisson–Boltzmann–Langevin equation (GPBLE). We have implemented a web server () that both numerically solves this equation and uses the resulting water density profiles to place water molecules at preferred sites of hydration. Surface atoms with high or low hydration preference can be easily displayed using a simple PyMol script, allowing for the tentative prediction of the dimerization interface in homodimeric proteins, or lipid binding regions in membrane proteins. The web site includes options that permit mutations in the sequence as well as reconstruction of missing side chain and/or main chain atoms. These tools are accessible independently from the electrostatics calculation, and can be used for other modeling purposes. We expect this web server to be useful to structural biologists, as the knowledge of solvent density should prove useful to get better fits at low resolution for X-ray diffraction data and to computational biologists, for whom these profiles could improve the calculation of interaction energies in water between ligands and receptors in docking simulations.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

“…The relative pros and cons of the PB and DPBL equations have been described in detail; 12,13,25,26,[29][30][31]43,55 here we focus on the properties of the PDE solvers, namely, convergence rate, computing time, and memory requirements. As the emphasis of the paper is on solving the DPBL equation, we show first that the increased complexity of the equation is a small price to pay compared to the wealth of information derived from its solution, in particular the possibility to look at hydration.…”

“…[39][40][41][42] We recently proposed a simple formalism based on statistical thermodynamics that allows us to circumvent this limitation. 29,30,43 In this formalism, we represent the solvent as an assembly of freely orientable dipoles of constant modulus p 0 and bulk concentration c dip . These dipoles as well as all counterions are distributed on a lattice surrounding the solutes to simulate the excluded volume effects ͑see Fig.…”

“…We recently developed an extension to the PB equation in which the solvent is described as an assembly of interacting dipoles on a lattice gas to account for the nonuniform dielectric property of the solvent. [29][30][31] Here we describe how we solve the corresponding equations, dubbed dipolar Poisson-Boltzmann-Langevin ͑DPBL͒ equations. This paper is organized as follows.…”

Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization

“…Our approach draws upon several recent field-theoretical studies that treat the solvent as a lattice gas of dipoles [18][19][20][21]. In particular, Koehl et al developed a Poisson-BoltzmannLangevin approach for ion solvation in aqueous solutions [19][20][21], taking into account the permanent dipoles of water molecules and density variation near the ions; the theory contains adjustable parameters that are optimized to model aqueous systems. In earlier works, Warshel and coworkers [22,23] studied the charge solvation of biomolecules in an aqueous solution.…”

“…First, instead of a lattice gas model as in Refs. [18][19][20][21], we consider a continuum model in which the liquid nature of the medium is accounted for by incompressibility and the volume of the molecules. Second, we include the molecular polarizability and permanent dipoles using the same unified framework.…”