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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.

SUBMITTER: Chakravorty A

PROVIDER: S-EPMC5881404 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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

Chakravorty Arghya A Jia Zhe Z Peng Yunhui Y Tajielyato Nayere N Wang Lisi L Alexov Emil E

Frontiers in molecular biosciences 20180327

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 ...[more]

PMID: 29637074

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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.

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.

Dataset Information

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

Publications

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

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