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Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi.

ABSTRACT: The standard treatment of ions in the framework of the Poisson-Boltzmann equation relies on molecular surfaces, which are commonly constructed along with the Stern layer. The molecular surface determines where ions can be present. In the Gaussian-based smooth dielectric function in DelPhi, smooth boundaries between the solute and solvent take the place of molecular surface. Therefore, this invokes the question of how to model mobile ions in the water phase without a definite solute-solvent boundary. This article reports a natural extension of the Gaussian-based smooth dielectric function approach that treats mobile ions via Boltzmann distribution with an added desolvation penalty. Thus, ion concentration near macromolecules is governed by the local electrostatic potential and the desolvation penalty (from being partially desolvated). The approach is tested against the experimental salt dependence of binding free energy on 7 protein-protein complexes and 12 DNA-protein complexes, resulting in Pearson correlations of 0.95 and 0.88, respectively. © 2017 Wiley Periodicals, Inc.

SUBMITTER: Jia Z

PROVIDER: S-EPMC5495612 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

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Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi.

Jia Zhe Z Li Lin L Chakravorty Arghya A Alexov Emil E

Journal of computational chemistry 20170611 22

The standard treatment of ions in the framework of the Poisson-Boltzmann equation relies on molecular surfaces, which are commonly constructed along with the Stern layer. The molecular surface determines where ions can be present. In the Gaussian-based smooth dielectric function in DelPhi, smooth boundaries between the solute and solvent take the place of molecular surface. Therefore, this invokes the question of how to model mobile ions in the water phase without a definite solute-solvent bound ...[more]

PMID: 28602026

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Project description:Our group has implemented a smooth Gaussian-based dielectric function in DelPhi (J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) which models the solute as an object with inhomogeneous dielectric permittivity and provides a smooth transition of dielectric permittivity from surface-bound water to bulk solvent. Although it is well-understood that the protein hydrophobic core is less polarizable than the hydrophilic protein surface, less attention is paid to the polarizability of water molecules inside the solute and on its surface. Here, we apply explicit water simulations to study the behavior of water molecules buried inside a protein and on the surface of that protein and contrast it with the behavior of the bulk water. We selected a protein that is experimentally shown to have five cavities, most of which are occupied by water molecules. We demonstrate through molecular dynamics (MD) simulations that the behavior of water in the cavity is drastically different from that in the bulk. These observations were made by comparing the mean residence times, dipole orientation relaxation times, and average dipole moment fluctuations. We also show that the bulk region has a nonuniform distribution of these tempo-spatial properties. From the perspective of continuum electrostatics, we argue that the dielectric "constant" in water-filled cavities of proteins and the space close to the molecular surface should differ from that assigned to the bulk water. This provides support for the Gaussian-based smooth dielectric model for solving electrostatics in the Poisson-Boltzmann equation framework. Furthermore, we demonstrate that using a well-parametrized Gaussian-based model with a single energy-minimized configuration of a protein can also reproduce its ensemble-averaged polar solvation energy. Thus, we argue that the Gaussian-based smooth dielectric model not only captures accurate physics but also provides an efficient way of computing ensemble-averaged quantities.

Project description:Calculations of electrostatic potential and solvation free energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model realistically in a two-dielectric setting. In fact, the detection of water molecules in a protein cavity remains to be an experimental challenge. This introduces an uncertainty, which affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterizes empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transferred from water phase to vacuum. An important feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces to a piecewise constant of the two-dielectric model. Mathematically, an effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both water filled and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in biomolecular electrostatic analysis.

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Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi.

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Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi.

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