Solute-solvent Interface Research Articles

Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

Accurate Boundary Integral Formulations for the Calculation of Electrostatic Forces with an Implicit-Solvent Model

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here we present a calculation of the electric field on the solute-solvent interface that is exact for piecewise linear variations of the potential and analyze four different alternatives to compute the force using a boundary element method. We performed a verification exercise for two cases: the isolated and two interacting molecules. Our results suggest that the boundary element method outperforms the finite difference method, as the latter needs a much finer mesh than in solvation energy calculations to get acceptable accuracy in the force, whereas the same surface mesh as in a standard energy calculation is appropriate for the boundary element method. Among the four evaluated alternatives of force calculation, we saw that the most accurate one is based on the Maxwell stress tensor. However, for a realistic application, like the barnase-barstar complex, the approach based on variations of the energy functional, which is less accurate, gives equivalent results. This analysis is useful toward using the Poisson-Boltzmann equation for force calculations in applications where high accuracy is key, for example, to feed molecular dynamics models or to enable the study of the interaction between large molecular structures, like viruses adsorbed onto substrates.

A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles

A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles

Advancing MM/PBSA calculations with machine learning and cuda GPUs

Poisson-Boltzmann equation (PBE)-based implicit solvent models have been widely used in computational studies of biomolecules. The main difficulty for these models is how to set up the discretized equation near the solute-solvent interface. We have studied and implemented several new methods to improve its performance, including the second-order harmonic averaging method and the -factor harmonic averaging method. We specifically designed these new algorithms to have uniform banded structure for their discretized equations, so they would be more suitable for parallel computing and thus gain a tremendous efficiency on Graphical Processing Units (GPUs).

A brief review on pharmaceutical dissolution - interlinking the aspects of science and regulation.

Dissolution is a multistep process between the affinity of the solute and the solvent by which a solid substance interacts among the heterogeneous phases of solute -solute, solvent-solvent and the solute-solvent interface to yield a solution. In pharmaceutical industry dissolution testing of solid dosage form gives a signal of the operability of the dosage form in biological system. The rate of absorption is partially or completely controlled by the dissolution of drug from its dosage forms in the gastrointestinal tract. This vital quality control aspects also ensures batch to batch uniformity in drug release, bioavailability, and to develop efficacious therapeutic dosage forms. It also ensures to evaluate critical biopharmaceutical parameters of the dosage forms. Hence the study of dissolution is an interplay between the science and the development of regulatory profile of a dosage form for quality control aspects. The present review focuses on the science, theories, factors relevant to in vitro dissolution, and therefore the role of it’s in the pharmaceutical regulation.

Coupling Monte Carlo, Variational Implicit Solvation, and Binary Level-Set for Simulations of Biomolecular Binding.

We develop a hybrid approach that combines the Monte Carlo (MC) method, a variational implicit-solvent model (VISM), and a binary level-set method for the simulation of biomolecular binding in an aqueous solvent. The solvation free energy for the biomolecular complex is estimated by minimizing the VISM free-energy functional of all possible solute-solvent interfaces that are used as dielectric boundaries. This functional consists of the solute volumetric, solute-solvent interfacial, solute-solvent van der Waals interaction, and electrostatic free energy. A technique of shifting the dielectric boundary is used to accurately predict the electrostatic part of the solvation free energy. Minimizing such a functional in each MC move is made possible by our new and fast binary level-set method. This method is based on the approximation of surface area by the convolution of an indicator function with a compactly supported kernel and is implemented by simple flips of numerical grid cells locally around the solute-solvent interface. We apply our approach to the p53-MDM2 system for which the two molecules are approximated by rigid bodies. Our efficient approach captures some of the poses before the final bound state. All-atom molecular dynamics simulations with most of such poses quickly reach the final bound state. Our work is a new step toward realistic simulations of biomolecular interactions. With further improvement of coarse graining and MC sampling, and combined with other models, our hybrid approach can be used to study the free-energy landscape and kinetic pathways of ligand binding to proteins.

Screening of Coulomb interactions in liquid dielectrics

The interaction of charges in dielectric materials is screened by the dielectric constant of the bulk dielectric. In dielectric theories, screening is assigned to surface charges appearing from preferential orientations of dipoles along the local field in the interface. For liquid dielectrics, such interfacial orientations are affected by the interfacial structure characterized by a separate interfacial dipolar susceptibility. We argue that dielectric properties of polar liquids should be characterized by two distinct susceptibilities responsible for local response (solvation) and long-range response (dielectric screening). A microscopic model for dipolar screening in polar liquids is developed here. It shows that the standard bulk dielectric constant is responsible for screening at large distances. The potential of mean force between ions in polar liquids becomes oscillatory at short distances. Oscillations arise from the coupling of collective longitudinal excitations (dipolarons) of the polar liquid with its interfacial density profile. Interfacial electrostatics demonstrates a crossover beyond the solute radius of ∼1 nm from the scaling laws roughly consistent with continuum expectations for small solutes to new scaling trends characterizing the much softer nano-scale solute–solvent interface. This crossover also marks the transition to a continuum-type electrostatic screening between ions, when short-distance oscillation of the potential of mean force become strongly damped. Screening oscillations are enhanced for more structured interfaces.

Recent Developments in Integral Equation Theory for Solvation to Treat Density Inhomogeneity at Solute–Solvent Interface

AbstractThe integration equation theory (IET) provides highly efficient tools for the calculation of structural and thermodynamic properties of molecular liquids. In recent years, the 3D reference interaction site model (3DRISM), the most developed IET for solvation, has been widely applied to study protein solvation, aggregation, and drug‐receptor binding. However, hydrophobic solutes with sufficient size (>nm) can induce water density depletion at the solute–solvent interface. This density depletion is not considered in the original 3DRISM theory. The authors here review the recent developments of 3DRISM at hydrophobic surfaces and related theories to address this challenge. At hydrophobic surfaces, an additional hydrophobicity‐induced density inhomogeneity equation is introduced to 3DRISM theory to consider this density depletion. Accordingly, several new closures equations including D2 closure and D2MSA closures are developed to enable stable numerical solutions of 3DRISM equations. These newly developed theories hold great promise for an accurate and rapid calculation of the solvation effect for complex molecular systems such as proteins. At the end of the report, the authors also provide a perspective on other challenges of the IETs as an efficient solvation model.

Numerical methods for solvent Stokes flow and solute-solvent interfacial dynamics of charged molecules

We develop a computational model for the solvation of charged molecules in an aqueous solvent. Such solvent is modeled as an incompressible fluid, and its dynamics is described by the Stokes equations. All the surface tension force, van der Waals dispersive force, electrostatic force, hydrostatic pressure, and viscous force are balanced on the solute-solvent interface, giving rise to the traction boundary conditions on such an interface. We use the level-set method for the solute-solvent interface motion. To describe the hydrophobic interaction that is characterized by the volume change of the solute region, we design special numerical boundary conditions for the Stokes equations. We then reformulate and discretize the Stokes equations with a second-order finite difference scheme using a MAC grid. At virtual nodes near the solute-solvent interface, we use interpolation to discretize the boundary conditions and formulate the difference equations at such nodes. The resulting linear system is reduced by the Schur complement and then solved by the least-squares method with various techniques of acceleration. Numerical tests show that our method has a second-order convergence in the maximum norm for both the velocity and pressure up to the boundary. We apply our methods to some model molecular systems. With the comparison of our approach with a well established, static solvation theory and method, our dynamic model and numerical techniques accurately reproduce the solvation free energies, and capture the dry and wet molecular states. Our work provides a possibility of describing solvent fluctuations through the solvent fluid flow.

Phonon Spectrometric Evaluation of the Solute–Solvent Interface in Solutions of Glycine and Its N-Methylated Derivatives

From the perspective of O:H-O bond cooperativity, we analyzed the solute capability of transiting the O:H-O bond from the mode of ordinary water to the hydration state and its consequence on the solution viscosity and surface stress. Phonon spectrometric results suggest that glycine and its N-methyl derivatives strongly affect the surrounding solvent molecules through H ↔ H repulsion and dipolar polarization. The H ↔ H interproton repulsion disrupts the surface stress, and the polarization enhances the solution viscosity.

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

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.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Hydrogen-bond transition from the vibration mode of ordinary water to the (H, Na)I hydration states: Molecular interactions and solution viscosity

With the aid of differential phonon spectrometrics (DPS) and surface stress detection, we show that HI and NaI solvation transforms different fractions of the HO stretching phonons from the mode of ordinary water centred at ∼3200 to the mode of hydration shell at ∼3500cm−1. Observations suggest that an addition of the H↔H anti-hydrogen-bond to the Zundel notion, [H(H2O)2]+, would be necessary as the HO bond due H3O+ has a 4.0eV energy, and the H↔H fragilization disrupts the solution network and the surface stress. The I− and Na+ ions form each a charge centre that aligns, stretches, and polarize the O:HO bond, resulting in shortening the HO bond and its phonon blue shift in the hydration shell or at the solute-solvent interface. The solute capabilities of bond-number-fraction transition follow: fH=0, fNa∝C, and fI∝1−exp(−C/C0) toward saturation, with C being the solute molar concentration and C0 the decay constant. The fH=0 evidences the non-polarizability of the H+ because of the H↔H formation. The linear fNa(C) suggests the invariance of the Na+ hydration shell size because of the fully-screened cationic potential by the H2O dipoles in the hydration shell but the nonlinear fI(C) fingerprints the I−↔I− interactions at higher concentrations. Concentration trend consistency between Jones–Dole’s viscosity and the fNaI(C) coefficient may evidence the same polarization origin of the solution viscosity and surface stress.

A Perspective on Water Site Prediction Methods for Structure Based Drug Design.

Over the last decade, a number of computational methods have been developed, which attempt to evaluate the thermodynamic properties of individual water molecules at the solute-solvent interface, in order to assess contributions to protein-ligand binding. In some cases, these tools tell us what we already know, e.g. that hydrophobic pockets prefer lipophilic substituents, and in other cases the methods only seem to add clarity when retrospectively applied. Hence we have grappled with how to utilize such approaches to understand non-intuitive results and to generate chemistry ideas that otherwise would not have been developed. Here we provide our perspective on these methods and describe how results have been interpreted and applied. We include examples from GSK and elsewhere that highlight how water methods have been (1) utilized retrospectively to explain non-intuitive structure- activity relationships and (2) applied prospectively for chemistry design. Finally, we discuss where this field of study could lead to maximal impact in drug discovery research.

Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvation-layer interface condition

We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics (Gibbs free energies, entropies, and heat capacities) in numerous polar solvents. We are also able to predict ion solvation free energies in water–co-solvent mixtures over available concentration series. The first modification to the classical dielectric Poisson model is a perturbation of the macroscopic dielectric-flux interface condition at the solute–solvent interface: we add a nonlinear function of the local electric field, giving what we have called a solvation-layer interface condition (SLIC). The second modification is including the microscopic interface potential (static potential) in our model. We show that the resulting model exhibits high accuracy without the need for fitting solute atom radii in a state-dependent fashion. Compared to experimental results in nine water–co-solvent mixtures, SLIC predicts transfer free energies to within 2.5 kJ/mol. The co-solvents include both protic and aprotic species, as well as biologically relevant denaturants such as urea and dimethylformamide. Furthermore, our results indicate that the interface potential is essential to reproduce entropies and heat capacities. These and previous tests of the SLIC model indicate that it is a promising dielectric continuum model for accurate predictions in a wide range of conditions.

Stable colloids in molten inorganic salts.

A colloidal solution is a homogeneous dispersion of particles or droplets of one phase (solute) in a second, typically liquid, phase (solvent). Colloids are ubiquitous in biological, chemical and technological processes, homogenizing highly dissimilar constituents. To stabilize a colloidal system against coalescence and aggregation, the surface of each solute particle is engineered to impose repulsive forces strong enough to overpower van der Waals attraction and keep the particles separated from each other. Electrostatic stabilization of charged solutes works well in solvents with high dielectric constants, such as water (dielectric constant of 80). In contrast, colloidal stabilization in solvents with low polarity, such as hexane (dielectric constant of about 2), can be achieved by decorating the surface of each particle of the solute with molecules (surfactants) containing flexible, brush-like chains. Here we report a class of colloidal systems in which solute particles (including metals, semiconductors and magnetic materials) form stable colloids in various molten inorganic salts. The stability of such colloids cannot be explained by traditional electrostatic and steric mechanisms. Screening of many solute-solvent combinations shows that colloidal stability can be traced to the strength of chemical bonding at the solute-solvent interface. Theoretical analysis and molecular dynamics modelling suggest that a layer of surface-bound solvent ions produces long-ranged charge-density oscillations in the molten salt around solute particles, preventing their aggregation. Colloids composed of inorganic particles in inorganic melts offer opportunities for introducing colloidal techniques to solid-state science and engineering applications.

Generalising the mean spherical approximation as a multiscale, nonlinear boundary condition at the solute–solvent interface

ABSTRACTIn this paper, we extend the familiar continuum electrostatic model to incorporate finite-size effects in the solvation layer, by perturbing the usual macroscopic interface condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale solvation-layer interface condition (SLIC/MSA). We show that SLIC/MSA reproduces MSA predictions for Born ions in a variety of polar solvents, including water as well as other protic and aprotic solvents. Importantly, the SLIC/MSA model predicts not only solvation free energies accurately but also solvation entropies, which standard continuum electrostatic models fail to predict. The SLIC/MSA model depends only on the normal electric field at the dielectric boundary, similar to our recent development of a SLIC model for charge-sign hydration asymmetry, and the reformulation of the MSA as an effective boundary condition enables its straightforward application to complex molecules such as proteins, whereas traditionally it is primarily a bulk theory. This work also opens the possibility for other electrolyte models to be incorporated into fast implicit-solvent models of biomolecular electrostatics.

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics.

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

On the microstructure of organic solutions of mono-carboxylic acids: Combined study by infrared spectroscopy, small-angle neutron scattering and molecular dynamics simulations

The data of infrared spectroscopy (IR), molecular dynamics (MD) simulations and small-angle neutron scattering (SANS) have been combined to conclude about the nanoscale structural organization of organic non-polar solutions of saturated mono-carboxylic acids with different alkyl chain lengths for diluted solutions of saturated myristic (C14) and stearic (C18) acids in benzene and decalin. In particular, the degree of dimerization was found from the IR spectra. The structural anisotropy of the acids and their dimers was used in the treatment of the data of MD simulations to describe the solute–solvent interface in a cylindrical approximation and show its rather strong influence on SANS. The corresponding scattering length density profiles were used to fit the experimental SANS data comprising the information about the acid molecule isomerization. The SANS data from concentrated solutions showed a partial self-assembling of the acids within the nematic transition is different for two solvents due to lyophobic peculiarities.