Electrostatic Free Energy Research Articles

Nonlocal statistical field theory of dipolar particles forming chain-like clusters

We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the ’head-to-tail’ mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the point-like test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.

Wettability of Amphoteric Surfaces: The Effect of pH and Ionic Strength on Surface Ionization and Wetting.

We present a novel theory to predict the contact angle of water on amphoteric surfaces, as a function of pH and ionic strength. To validate our theory, experiments were performed on two commonly used amphoteric materials, alumina (Al2O3) and titania (TiO2). We find good agreement at all pH values, and at different salt concentrations. With increasing salt concentration, the theory predicts the contact angle-pH curve to get steeper, while keeping the same contact angle at pH = PZC (point of zero charge), in agreement with data. Our model is based on the amphoteric 1-pK model and includes the electrostatic free energy of an aqueous system as well as the surface energy of a droplet in contact with the surface. In addition, we show how our theory suggests the possibility of a novel responsive membrane design, based on amphoteric groups. At pH ∼ PZC, this membrane resists flow of water but at slightly more acidic or basic conditions the wettability of the membrane pores may change sufficiently to allow passage of water and solutes. Moreover, these membranes could act as active sensors that only allow solutions of high ionic strength to flow through in wastewater treatment.

Phase field modeling of grain boundary migration and preferential grain growth driven by electric current stressing

A phase field model incorporating the electrostatic free energy and the grain orientation effect is developed and employed to study the grain boundary migration and preferential grain growth in widely used beta-tin (β-Sn) under electric current stressing. The directional migration of grain boundaries and the preferential growth of the grain with its orientation having low electrical resistivity along the electric current direction are theoretically clarified. In a bicrystal system containing a circular grain, the shrinkage velocity and morphology changes of grains are dominated by the competition effect between the grain boundary energy and the electrostatic free energy; in particular, the high-density electric current can induce the instability of grain morphology evolution. Moreover, grain morphology evolution leads to the change of the voltage across the β-Sn system; it is found that the voltage decreases over time in a tricrystal system, while the variation of the voltage across the bicrystal system is related to the above-mentioned competition effect. The proposed model and results provide insights into the orientation-related microstructure evolution under electric current stressing.

TKSA-MC: A web server for rational mutation through the optimization of protein charge interactions.

The TKSAMC is a web server which calculates protein charge-charge interactions via the Tanford-Kirkwood Surface Accessibility model with the Monte Carlo method for sampling different protein protonation states. The optimization of charge-charge interactions via directed mutations has successfully enhanced the thermal stability of different proteins and could be a key to protein engineering improvement. The server presents the electrostatic free energy contribution of each polar-charged residue to the protein native state stability. Specific residues are suggested to be mutated for improving thermal stability. The choice of a residue is based on its fraction of side chain exposed to solvent and its positive free energy contribution, which tends to destabilize the protein native state. Any residue energy contribution can be shown as a function of pH condition. The web server is freely available at UNESP (São Paulo State University - DF/IBILCE): http://tksamc.df.ibilce.unesp.br and also on GitHub https://github.com/contessoto/tksamc.

Parameterization of a coarse-grained model of cholesterol with point-dipole electrostatics.

We present a new coarse-grained (CG) model of cholesterol (CHOL) for the electrostatic-based ELBA force field. A distinguishing feature of our CHOL model is that the electrostatics is modeled by an explicit point dipole which interacts through an ideal vacuum permittivity. The CHOL model parameters were optimized in a systematic fashion, reproducing the electrostatic and nonpolar partitioning free energies of CHOL in lipid/water mixtures predicted by full-detailed atomistic molecular dynamics simulations. The CHOL model has been validated by comparison to structural, dynamic and thermodynamic properties with experimental and atomistic simulation reference data. The simulation of binary DPPC/cholesterol mixtures covering the relevant biological content of CHOL in mammalian membranes is shown to correctly predict the main lipid behavior as observed experimentally.

Role of electrostatic correlations in polyelectrolyte charge association.

Reversible ion binding equilibria in polyelectrolyte solutions are strongly affected by interactions between dissociated ionic species. We examine how the structural correlations between ionic groups on polyelectrolytes impact the counterion binding. Treating the electrostatic correlation free energy using the classical Debye-Hückel expression leads to complete counterion dissociation in the concentrated regime. This unphysical behavior is shown to stem from improper regularization of the self-energy of dissociated ions and polyions and is mitigated by smearing point-like charges across a finite width. The influence of the self-energy on counterion binding is elaborated on by generalizing the Debye-Hückel free energy to polyelectrolytes with variable fractal dimension and stiffness. In the dilute regime, a greater propensity for binding is found for chains with more compact architectures, which in turn reduces the harsh self-repulsions of tightly packed arrangements of charge. In the concentrated regime, the effects of electrostatic correlations weaken due to screening and the extent of binding is governed by a balance of short-ranged interactions and the translational entropy of ions.

An accelerated nonlocal Poisson‐Boltzmann equation solver for electrostatics of biomolecule

The nonlocal modified Poisson-Boltzmann equation (NMPBE) is one important variant of a commonly used dielectric continuum model, the Poisson-Boltzmann equation (PBE), for computing electrostatics of biomolecules. In this paper, an accelerated NMPBE solver is constructed by finite element and finite difference hybrid techniques. It is then programmed as a software package for computing electrostatic solvation and binding free energies for a protein in a symmetric 1:1 ionic solvent. Numerical results validate the new solver and its numerical stability. They also demonstrate that the new solver has much better performance than the corresponding finite element solver in terms of computer CPU time. Furthermore, they show that the binding free energies produced by NMPBE can match chemical experiment data better than those by PBE.

Molecular Interaction Studies of Phosphatidylcholine As Drug Delivery Substrate For Asenapine Maleate

Phospholipid complexes have become promising delivery systems for delivery of drugs with poor bioavailability like asenapine maleate. To improve the bioavailability of asenapine maleate, phospholipid complex was chosen for the drug with Phospholipon 90 G (phosphatidylcholine). The automated molecular docking calculation for asenapine and maleate individually with phospholipid was performed by AutoGrid 4.2.6, a docking program. The van der Waals hydrogen bond, electrostatic potential energy and desolvation free energy grid maps were calculated by AutoDock parameter set- and distance-dependent dielectric functions respectively. The change in free energy was specifically seen for the complex between asenapine and phospholipid which exhibited least binding docking energy of –3.86 kcal/mol among the summary of 25 poses. Finally, molecular docking studies confirmed that the asenapine is able to make a complex with phosphatidylcholine, plausibly on account of its structural similarity with phospholipid in its physiochemical properties.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard–Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson–Boltzmann–Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the ‘Yukawa’-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

SCFT Study of Diblock Copolymer Melts in Electric Fields: Selective Stabilization of Orthorhombic Fddd Network Phase

Using self-consistent field theory (SCFT), we explore the phase behavior of a diblock copolymer (BCP) melt in an applied electric field, with different dielectric constants assigned to each monomer type. The electric field penalizes the interfaces between species domains that are not parallel to the field. Under the present mean-field approximation, lamellar and cylindrical structures reorient to align their interfaces with the electric field, such that these mesophases will have the same electrostatic free energy contribution as the mixed (disordered) state, and their relative stability will remain unchanged. In contrast, sphere and network phases do not have an axis of dielectric uniformity; consequently, the preferred orientation and morphological response of these phases must be determined numerically. We compute the phase diagram for a BCP melt in the presence of an applied electric field by comparing the free energy of each phase at its thermodynamically preferred orientation relative to the electri...

Electron Transfer Pathway Analysis from Cytochrome C to Cytochrome C Oxidase Under Turnover Conditions

The electron transfer (ET) reactions in mitochondrial and bacterial respiratory chains are essential processes for energy transduction in cells. A series of ET reactions is terminated at cytochrome c oxidase (CcO), where molecular oxygen is reduced to water. Associated with the reduction of molecular oxygen, CcO functions as a proton pump across the membrane, and the proton gradient is the primary driving force for the generation of ATP. In the respiratory chain of mitochondria, the electrons to reduce molecular oxygen at CcO are donated from a small hemoprotein, cytochrome c (Cyt c), and Cyt c forms an ET complex with CcO to promote the ET reaction. While the reduction of molecular oxygen to water molecules requires four electrons, Cyt c can carry only one electron, implying that Cyt c repetitively associates with and dissociates from CcO and suggesting that the specific interprotein interactions between Cyt c and CcO to form the ET pathway from Cyt c to CcO. To identify the specific interactions for the complex formation between Cyt c and CcO and estimate the ET pathway, we have determined the interaction site of Cyt c for CcO using NMR spectroscopy1. However, the NMR measurements can be applied only for ET complexes such as oxidized Cyt c – fully oxidized CcO or reduced Cyt c – fully reduced CcO complexes, where the ET reaction does not occur. In addition, our previous NMR analysis1 identified the CcO interaction site on Cyt c, while no information about the Cyt c interaction site on CcO has been obtained. A detailed analysis of the interactions essential for the formation of the ET pathway in the ET complexes under turnover conditions, where the ET reaction from Cyt c to CcO is induced, has not yet been conducted. Based on the mutational effects on the steady state kinetics of the ET reaction and our NMR analysis of the interaction site, we examined the structure of the ET complex between Cyt c and CcO under turnover conditions using protein docking simulation2, and energetically characterized the interactions essential for complex formation and estimated the ET pathway from Cyt c to CcO. The complex structures predicted by the protein docking simulation were computationally selected and validated by the experimental kinetic data for mutant Cyt c in the ET reaction to CcO. The interaction analysis using the selected Cyt c – CcO complex structure revealed the electrostatic and hydrophobic contributions of each amino acid residue to the free energy required for complex formation. Several charged residues showed large unfavorable (desolvation) electrostatic interactions which were almost cancelled out by large favorable (Columbic) electrostatic interactions, but resulting in the destabilization of the complex. The residual destabilizing free energy is compensated by the van der Waals interactions mediated by hydrophobic amino acid residues to give the stabilized complex. Thus, hydrophobic interactions are the primary factors that promote complex formation between Cyt c and CcO under turnover conditions, while the change in the electrostatic destabilization free energy provides the variance of the binding free energy in the mutants. The distribution of favorable and unfavorable electrostatic interactions in the interaction site determines the orientation of the binding of Cyt c on CcO. To determine the ET pathway from Cyt c to CcO, the pathway analysis3 was applied to the predicted ET complex between Cyt c and CcO under turnover conditions. The estimated ET pathway was found to be constructed by many hydrophobic amino acid residues, including Trp104 of the subunit II of CcO, which is supposed to be the electron entry site for CcO from Cyt c. The contribution of many hydrophobic amino acid residues to formation of the ET pathway also supports the crucial role of the dehydration from hydrophobic amino acid residues associated with the complex formation between Cyt c and CcO, and suggests formation of a structure blocking water access from the bulk water phase (a “molecular breakwater”) surrounding the ET pathway across the Cyt c - CcO interface to avoid formation of hydrogen-bond mediated non-specific ET pathways. Sakamoto, K.; Kamiya, M.; Imai, M.; Shinzawa-Itoh, K.; Uchida, T.; Kawano, K.; Yoshikawa, S.; Ishimori, K., Proc. Natl. Acad. Sci. USA 2011, 108, 12271-12276.Sato, W.; Hitaoka, S.; Inoue, K.; Imai, M.; Saio, T.; Uchida, T.; Shinzawa-Itoh, K.; Yoshikawa, S.; Yoshizawa, K.; Ishimori, K., J. Biol. Chem. 2016, 291, 15320-15331.Onuchic, J. N.; Beratan, D. N.; Winkler, J. R.; Gray, H. B., Ann. Rev. Biophys. Biomol. Struct. 1992, 21, 349-377.

Effects of dielectric inhomogeneity on electrostatic twist rigidity of a helical biomolecule in Debye-Hückel regime.

The electrostatic interactions play a crucial role in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Hückel regime using the analytical Green function that is calculated in the paper. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as a DNA and an actin filament. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters, and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.

Effects of pH and Salt Concentration on Stability of a Protein G Variant Using Coarse-Grained Models

The importance of charge-charge interactions in the thermal stability of proteins is widely known. pH and ionic strength play a crucial role in these electrostatic interactions, as well as in the arrangement of ionizable residues in each protein-folding stage. In this study, two coarse-grained models were used to evaluate the effect of pH and salt concentration on the thermal stability of a protein G variant (1PGB-QDD), which was chosen due to the quantity of experimental data exploring these effects on its stability. One of these coarse-grained models, the TKSA, calculates the electrostatic free energy of the protein in the native state via the Tanford-Kirkwood approach for each residue. The other one, CpHMD-SBM, uses a Coulomb screening potential in addition to the structure-based model Cα. Both models simulate the system in constant pH. The comparison between the experimental stability analysis and the computational results obtained by these simple models showed a good agreement. Through the TKSA method, the role of each charged residue in the protein’s thermal stability was inferred. Using CpHMD-SBM, it was possible to evaluate salt and pH effects throughout the folding process. Finally, the computational pKa values were calculated by both methods and presented a good level of agreement with the experiments. This study provides, to our knowledge, new information and a comprehensive description of the electrostatic contribution to protein G stability.

Theory Meets Experiment: Metal Ion Effects in HCV Genomic RNA Kissing Complex Formation.

The long-range base pairing between the 5BSL3. 2 and 3′X domains in hepatitis C virus (HCV) genomic RNA is essential for viral replication. Experimental evidence points to the critical role of metal ions, especially Mg2+ ions, in the formation of the 5BSL3.2:3′X kissing complex. Furthermore, NMR studies suggested an important ion-dependent conformational switch in the kissing process. However, for a long time, mechanistic understanding of the ion effects for the process has been unclear. Recently, computational modeling based on the Vfold RNA folding model and the partial charge-based tightly bound ion (PCTBI) model, in combination with the NMR data, revealed novel physical insights into the role of metal ions in the 5BSL3.2-3′X system. The use of the PCTBI model, which accounts for the ion correlation and fluctuation, gives reliable predictions for the ion-dependent electrostatic free energy landscape and ion-induced population shift of the 5BSL3.2:3′X kissing complex. Furthermore, the predicted ion binding sites offer insights about how ion-RNA interactions shift the conformational equilibrium. The integrated theory-experiment study shows that Mg2+ ions may be essential for HCV viral replication. Moreover, the observed Mg2+-dependent conformational equilibrium may be an adaptive property of the HCV genomic RNA such that the equilibrium is optimized to the intracellular Mg2+ concentration in liver cells for efficient viral replication.

Driving Force for Spontaneous Perforation of Bilayers Formed by Ionic Amphiphiles in Aqueous Salt.

Spontaneous perforation of amphiphilic membranes is important in both living matter and technology because of an impact on functions of biological membranes and shape transitions of self-assembling structures. Nevertheless, no definite molecular mechanism has been established so far even for simple ionic surfactant systems. We show that spontaneous perforation of a bilayer formed by an ionic amphiphile is driven by electrostatics. Creation of large pores with a concave-convex geometry of the rim is promoted by lower electrostatic free energy than that for a flat nonperforated bilayer. The opposite effect comes from the elasticity of the hydrocarbon tails of the amphiphile that prefer flat geometry of a nonperforated bilayer. The balance between electrostatics and tail deformation controls the appearance of pores; this balance is modulated by added salt that screens the electrostatic interactions. We illustrate the proposed mechanism with the aid of classical aggregation model that has been extended by including an analytical description of the electrostatic contribution for the toroidal rim of a pore. Numerical solution of the linearized Poisson-Boltzmann equation confirms the role of electrostatic forces in formation of pores. For the ionic surfactants of CnTAB family, we predict shape transitions including bilayer perforations and formation of branched micellar networks induced by changing salinity or temperature and demonstrate the effect of surfactant's molecular parameters on these transitions.

Grid-Based Surface Generalized Born Model for Calculation of Electrostatic Binding Free Energies

Fast and accurate calculation of solvation free energies is central to many applications, such as rational drug design. In this study, we present a grid-based molecular surface implementation of "R6" flavor of the generalized Born (GB) implicit solvent model, named GBNSR6. The speed, accuracy relative to numerical Poisson-Boltzmann treatment, and sensitivity to grid surface parameters are tested on a set of 15 small protein-ligand complexes and a set of biomolecules in the range of 268 to 25099 atoms. Our results demonstrate that the proposed model provides a relatively successful compromise between the speed and accuracy of computing polar components of the solvation free energies (ΔGpol) and binding free energies (ΔΔGpol). The model tolerates a relatively coarse grid size h = 0.5 Å, where the grid artifact error in computing ΔΔGpol remains in the range of kBT ∼ 0.6 kcal/mol. The estimated ΔΔGpols are well correlated (r2 = 0.97) with the numerical Poisson-Boltzmann reference, while showing virtually no systematic bias and RMSE = 1.43 kcal/mol. The grid-based GBNSR6 model is available in Amber (AmberTools) package of molecular simulation programs.

A hybrid solver of size modified Poisson–Boltzmann equation by domain decomposition, finite element, and finite difference

Abstract The size-modified Poisson–Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson–Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, Schwartz’s overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C , Fortran , and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug complex.

Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals--Cahn--Hilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the Poisson--Boltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics---its potential, free energy, and dielectric boundary force---with respect to the perturbation of dielectric boundary. We also prove the $\Gamma$-convergence of the phase-field free-energy functionals to their sharp-interface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals--Cahn--Hilliard functionals with minimal assumptions.

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions.

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

Levitated Plasmonic Nanoantennas in an Aqueous Environment.

We report on the manipulation of a plasmonic nanoantenna in an aqueous solution using an electrostatic trap created between a glass nanopipette and a substrate. By scanning a trapped gold nanosphere in the near field of a single colloidal quantum dot embedded under the substrate surface, we demonstrate about 8-fold fluorescence enhancement over a lateral full width at half-maximum of about 45 nm. We analyze our results with the predictions of numerical electromagnetic simulations under consideration of the electrostatic free energy in the trap. Our approach could find applications in a number of experiments, where plasmonic effects are employed at liquid-solid interfaces.