Gaussian-Based Smooth Dielectric Function: A Surface-Free Approach for Modeling Macromolecular Binding in Solvents

Abstract

Conventional modeling techniques to model macromolecular solvation and its effect on binding in the framework of Poisson-Boltzmann based implicit solvent models make use of a geometrically defined surface to depict the separation of macromolecular interior (low dielectric constant) from the solvent phase (high dielectric constant). Though this simplification saves time and computational resources without significantly compromising the accuracy of free energy calculations, it bypasses some of the key physio-chemical properties of the solute-solvent interface, e.g., the altered flexibility of water molecules and that of side chains at the interface, which results in dielectric properties different from both bulk water and macromolecular interior, respectively. Here we present a Gaussian-based smooth dielectric model, an inhomogeneous dielectric distribution model that mimics the effect of macromolecular flexibility and captures the altered properties of surface bound water molecules. Thus, the model delivers a smooth transition of dielectric properties from the macromolecular interior to the solvent phase, eliminating any unphysical surface separating the two phases. Using various examples of macromolecular binding, we demonstrate its utility and illustrate the comparison with the conventional 2-dielectric model. We also showcase some additional abilities of this model, viz. to account for the effect of electrolytes in the solution and to render the distribution profile of water across a lipid membrane.

DelPhi Suite: New Developments and Review of Functionalities

“…Such approach results in a smooth dielectric function that reflects the following physical expectations: low‐packed macromolecular regions as protein's surface are assigned higher dielectric constant compared with the hydrophobic core; the cavities inside the macromolecule are assigned dielectric constants higher than the rest of macromolecule but smaller than bulk water; and there is a smooth transition of the dielectric constant from macromolecule to water, to reflect that surface waters are not so free to move compared with bulk waters. This approach is particularly useful in modeling protein–protein binding and pKa's modeling …”

Modeling electrostatics in molecular biology: A tutorial of DelPhi and associated resources [Article v1.0]

“…One should use the traditional two-dielectric if modeling involves rigid structures (energy minimized or snapshots from MD simulations). The Gaussian approach is applicable for cases when one wants to use single structure to generate ensemble average quantity (see [5] for more details).…”

“…This implementation of PBE will be termed two-dielectric PBE. In parallel, we have implemented a Gaussian-based smooth dielectric function in DelPhi that treats the solute and solvent on the same footage and the entire computational space is described via continuous dielectric function [5][6][7][8]. Thus, the macromolecules are considered to be inhomogeneous objects and there is no sharp boundary between solute-solvent.…”

BION-2: Predicting Positions of Non-Specifically Bound ions on Protein Surface by a Gaussian-based Treatment of Electrostatic Environment

“…In this work we report a new development of BION [21,22], the BION-2, which is a method and a web server to predict non-specifically surface-bound ions. The development takes advantage of a Gaussian-based smooth dielectric function in DelPhi [25][26][27][28][29]. This allows the energy function that evaluates the possibility that a given site holds an ion to be made of two important components: (a) electrostatic energy of interaction between the candidate ion and the charges of the macromolecules and (b) de-solvation penalty the ion should pay by approaching the macromolecular surface.…”