Evaluation of the influence of the internal aqueous solvent structure on electrostatic interactions at the protein-solvent interface by nonlocal continuum electrostatic approach

Effects of the dielectric properties of the ceramic-solvent interface on the binding of proteins to oxide ceramics: a non-local electrostatic approach

The rapid development of nanoscience and nanotechnology has raised many fundamental questions that significantly impede progress in these fields. In particular, understanding the physicochemical processes at the interface in aqueous solvents requires the development and application of efficient and accurate methods. In the present work we evaluate the electrostatic contribution to the energy of model protein-ceramic complex formation in an aqueous solvent. We apply a non-local (NL) electrostatic approach that accounts for the effects of the short-range structure of the solvent on the electrostatic interactions of the interfacial systems. In this approach the aqueous solvent is considered as a non-ionic liquid, with the rigid and strongly correlated dipoles of the water molecules. We have found that an ordered interfacial aqueous solvent layer at the protein- and ceramic-solvent interfaces reduces the charging energy of both the ceramic and the protein in the solvent, and significantly increases the electrostatic contribution to their association into a complex. This contribution in the presented NL approach was found to be significantly shifted with respect to the classical model at any dielectric constant value of the ceramics. This implies a significant increase of the adsorption energy in the protein-ceramic complex formation for any ceramic material. We show that for several biocompatible ceramics (for example HfO2, ZrO2, and Ta2O5) the above effect predicts electrostatically induced protein-ceramic complex formation. However, in the framework of the classical continuum electrostatic model (the aqueous solvent as a uniform dielectric medium with a high dielectric constant ∼80) the above ceramics cannot be considered as suitable for electrostatically induced complex formation. Our results also show that the protein-ceramic electrostatic interactions can be strong enough to compensate for the unfavorable desolvation effect in the process of protein-ceramic complex formation.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Variational approach for nonpolar solvation analysis

Solvation analysis is one of the most important tasks in chemical and biological modeling. Implicit solvent models are some of the most popular approaches. However, commonly used implicit solvent models rely on unphysical definitions of solvent-solute boundaries. Based on differential geometry, the present work defines the solvent-solute boundary via the variation of the nonpolar solvation free energy. The solvation free energy functional of the system is constructed based on a continuum description of the solvent and the discrete description of the solute, which are dynamically coupled by the solvent-solute boundaries via van der Waals interactions. The first variation of the energy functional gives rise to the governing Laplace-Beltrami equation. The present model predictions of the nonpolar solvation energies are in an excellent agreement with experimental data, which supports the validity of the proposed nonpolar solvation model.

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields

A self-consistent method is presented for the calculation of the local dielectric permittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute/liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum protein electrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for on-the-fly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with field-dependent dielectric response.

Water-exclusion and liquid-structure forces in implicit solvation

A continuum model of solvation is proposed to describe (i) long-range electrostatic effects of water exclusion resulting from incomplete and anisotropic hydration in crowded environments and (ii) short-range effects of liquid-structure forces on the hydrogen-bond interactions at solute/water interfaces. The model is an extension of the phenomenological screened coulomb potential-based implicit model of solvation. The developments reported here allow a more realistic representation of highly crowded and spatially heterogeneous environments, such as those in the interior of a living cell. Only the solvent is treated as a continuum medium. It is shown that the electrostatic effects of long-range water-exclusion can strongly affect protein-protein binding energies and are then related to the thermodynamics of complex formation. Hydrogen-bond interactions modulated by the liquid structure at interfaces are calibrated based on systematic calculations of potentials of mean force in explicit water. The electrostatic component of the model is parametrized for monovalent, divalent and trivalent ions. The conceptual and practical aspects of the model are discussed based on simulations of protein complexation and peptide folding. The current implementation is ~1.5 times slower than the gas-phase force field and exhibits good parallel performance.

Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach

Using a nonlocal electrostatic approach that incorporates the short-range structure of the contacting media, we evaluated the electrostatic contribution to the energy of the complex formation of two model proteins. In this study, we have demonstrated that the existence of an ordered interfacial water layer at the protein-solvent interface reduces the charging energy of the proteins in the aqueous solvent, and consequently increases the electrostatic contribution to the protein binding (change in free energy upon the complex formation of two proteins). This is in contrast with the finding of the continuum electrostatic model, which suggests that electrostatic interactions are not strong enough to compensate for the unfavorable desolvation effects.

Steric and electrostatic complementarity in the assembly of two-dimensional virus arrays

A highly ordered assembly of biological molecules provides a powerful means to study the organizational principles of objects at the nanoscale. Two-dimensional cowpea mosaic virus arrays were assembled in an ordered manner on mica using osmotic depletion effects and a drop-and-dry method. The packing of the virus array was controlled systematically from rhombic packing to hexagonal packing by modulating the concentrations of poly(ethylene glycol) surfactant in the virus solutions. The orientation and packing symmetry of the virus arrays were found to be tuned by the concentrations of surfactants in the sample solutions. A phenomenological model for the present system is proposed to explain the assembly array morphology under the influence of the surfactant. Steric and electrostatic complementarity of neighboring virus capsids is found to be the key factors in controlling the symmetry of packing.

Docking flexible ligands in proteins with a solvent exposure- and distance-dependent dielectric function

Physics-based force fields for ligand-protein docking usually determine electrostatic energy with distance-dependent dielectric (DDD) functions, which do not fully account for the dielectric permittivity variance between approximately 2 in the protein core and approximately 80 in bulk water. Here we propose an atom-atom solvent exposure- and distance-dependent dielectric (SEDDD) function, which accounts for both electrostatic and dehydration energy components. Docking was performed using the ZMM program, the AMBER force field, and precomputed libraries of ligand conformers. At the seeding stage, hundreds of thousands of positions and orientations of conformers from the libraries were sampled within the rigid protein. At the refinement stage, the ten lowest-energy structures from the seeding stage were Monte Carlo-minimized with the flexible ligand and flexible protein. A search was considered a success if the root mean square deviation (RMSD) of the ligand atoms in the apparent global minimum from the x-ray structure was <2 A. Calculations on an examining set of 60 ligand-protein complexes with different DDD functions and solvent-exclusion energy revealed outliers in most of which the ligand-binding site was located at the protein surface. Using a training set of 16 ligand-protein complexes, which did not overlap with the examining set, we parameterized the SEDDD function to minimize the RMSD of the apparent global minima from the x-ray structures. Recalculation of the examining set with the SEDDD function demonstrated a 20% increase in the success rate versus the best-performing DDD function.

Understanding dynamics of myoglobin in heterogeneous aqueous environments using coupled water fractions

This work presents an analysis of near environment of myoglobin (Mb) in different aqueous solutions (in the presence of NaCl, sucrose, trehalose, urea, and glycerol) using the coupled water fractions measured using a quartz crystal microbalance (QCM). The secondary structural features of the protein from circular dichroic (CD) spectroscopy and the coupled water fractions give important clues to the overall dynamics of the protein. Using time resolved fluorescence, these leads have been applied to understand the observed lifetime relaxations of Mb. Though the time scales of observation of coupled water and the lifetimes are very different, our study suggests that the trends in coupled water fraction seem to be good indicators for regulation of the relaxation dynamics of the protein. The relaxations generally show a triphasic distribution of time scales. The initial relaxation in the picoseconds time scale represents the local motions of coupled water followed by a slightly slower decay in hundreds of picoseconds attributable to coupled water-'quasi free' water interactions. The third nanosecond lifetime is due to changes in transitions in isomers of hydrated protein. The dynamics of coupled water in Mb with NaCl is the fastest (around 21 ps) and is slowest in glycerol (250 ps). The results strongly indicate that it is the resident times of water molecules that play a dominant role in the overall stability of protein in a particular hydrated isomer and not just always the number of such water molecules in the hydrated protein.