Electrostatic Free Energy Research Articles

Charge regulation of nanoparticles in the presence of multivalent electrolytes.

We explore the charge regulation (CR) of spherical nanoparticles immersed in an asymmetric electrolyte of a specified pH. Using a recently developed reactive canonical Monte Carlo (MC) simulation method, titration isotherms are obtained for suspensions containing monovalent, divalent, and trivalent coions. A theory based on the modified Poisson-Boltzmann approximation, which incorporates the electrostatic ion solvation free energy and discrete surface charge effects, is used to compare with the simulation results. A remarkably good agreement is found without any fitting parameters, both for the ion distributions and titration curves, suggesting that ionic correlations between coions and hydronium ions at the nanoparticle surface play only a minor role in determining the association equilibrium between hydroniums and the functional sites on the nanoparticle surface. On the other hand, if suspension contains multivalent counterions, we observe a large deviation between theory and simulations, showing that the electrostatic correlations between counterions and hydronium ions at the nanoparticle surface are very significant and must be properly taken into account to correctly describe CR for such solutions.

Dielectric Boundary Force for the Minimization of the Mean-Field Electrostatic Free-Energy Functional Including the Ionic Size Effect

The generalized Poisson–Boltzmann equation with the uniform ionic size is investigated. In mean-field theory, the ionic size effect is added by modifying the entropy effect of solvent molecules in the electrostatic free-energy functional of ion concentrations. Taking minimization of the mean-field electrostatic free-energy functional including the ionic size effect with respect to the ion concentrations, the minimum free-energy is obtained (see (4.6) in Li [(2009a) “Continuum electrostatics for ionic solutions with non-uniform ionic sizes,” Nonlinearity 22(4), 811–833]. Maximizing the minimum free-energy with respect to the electrostatic potential determines the generalized Poisson–Boltzmann equation. By the definition of shape derivative, the first variation of this minimum free-energy with respect to variation of the dielectric boundary is derived. Thus, the dielectric boundary force of an ionic solution with multiple ionic species with the uniform ionic size is obtained.

The C-terminal activating domain promotes Panx1 channel opening.

Pannexin 1 (Panx1) constitutes a large pore channel responsible for the release of ATP from apoptotic cells. Strong evidence indicates that caspase-mediated cleavage of the C-terminus promotes the opening of the Panx1 channel by unplugging the pore. However, this simple pore-plugging mechanism alone cannot account for the observation that a Panx1 construct ending before the caspase cleavage site remains closed. Here, we show that a helical region located immediately before the caspase cleavage site, referred to as the "C-terminal activating domain (CAD)," plays a pivotal role in facilitating Panx1 activation. Electrophysiology and mutagenesis studies uncovered that two conserved leucine residues within the CAD plays a pivotal role. Cryo-EM analysis of the construct ending before reaching the CAD demonstrated that the N-terminus extends into an intracellular pocket. In contrast, the construct including the CAD revealed that this domain occupies the intracellular pocket, causing the N-terminus to flip upward within the pore. Analysis of electrostatic free energy landscape in the closed conformation indicated that the intracellular side of the ion permeation pore may be occupied by anions like ATP, creating an electrostatic barrier for anions attempting to permeate the pore. When the N-terminus flips up, it diminishes the positively charged surface, thereby reducing the drive to accumulate anions inside the pore. This dynamic change in the electrostatic landscape likely contributes to the selection of permeant ions. Collectively, these experiments put forth a novel mechanism in which C-terminal cleavage liberates the CAD, causing the repositioning of the N-terminus to promote Panx1 channel opening.

Poisson-Boltzmann-based machine learning model for electrostatic analysis

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity, and geometric complexity associated with the PB equation. The present work introduces a PB-based machine learning (PBML) model for biomolecular electrostatic analysis. Trained with the second-order accurate MIBPB solver, the proposed PBML model is found to be more accurate and faster than several eminent PB solvers in electrostatic analysis. The proposed PBML model can provide highly accurate PB electrostatic solvation free energy of new biomolecules or new conformations generated by molecular dynamics with much reduced computational cost.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions.

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

Alchemical approach performance in calculating the ligand-binding free energy.

Alchemical binding free energy calculations are one of the most accurate methods for estimating ligand-binding affinity. Assessing the accuracy of the approach over protein targets is one of the most interesting issues. The free energy difference of binding between a protein and a ligand was calculated via the alchemical approach. The alchemical approach exhibits satisfactory accuracy over four targets, including AmpC beta-lactamase (AmpC); glutamate receptor, ionotropic kainate 1 (GluK1); heat shock protein 90 (Hsp90); and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease (Mpro). In particular, the correlation coefficients between calculated binding free energies and the respective experiments over four targets range from 0.56 to 0.86. The affinity computed via free energy perturbation (FEP) simulations is overestimated over the experimental value. Particularly, the electrostatic interaction free energy rules the binding process of ligands to AmpC and GluK1. However, the van der Waals (vdW) interaction free energy plays an important role in the ligand-binding processes of HSP90 and SARS-CoV-2 Mpro. The obtained results associate with the hydrophilic or hydrophobic properties of the ligands. This observation may enhance computer-aided drug design.

Calculation of electrostatic free energy for the nonlinear Poisson-Boltzmann model based on the dimensionless potential

The Poisson-Boltzmann (PB) equation governing the electrostatic potential with a unit is often transformed to a normalized form for a dimensionless potential in numerical studies. To calculate the electrostatic free energy (EFE) of biological interests, a unit conversion has to be conducted, because the existing PB energy functionals are all described in terms of the original potential. To bypass this conversion, this paper proposes energy functionals in terms of the dimensionless potential for the first time in the literature, so that the normalized PB equation can be directly derived by using the Euler-Lagrange variational analysis. Moreover, alternative energy forms have been rigorously derived to avoid approximating the gradient of singular functions in the electrostatic stress term. A systematic study has been carried out to examine the surface integrals involved in alternative energy forms and their dependence on finite domain size and mesh step size, which leads to a recommendation on the EFE forms for efficient computation of protein systems. The calculation of the EFE in the regularization formulation, which is an analytical approach for treating singular charge sources of the PB equation, has also been studied. The proposed energy forms have been validated by considering smooth dielectric settings, such as diffuse interface and super-Gaussian, for which the EFE of the nonlinear PB model is found to be significantly different from that of the linearized PB model. All proposed energy functionals and EFE forms are designed such that the dimensionless potential can be simply plugged in to compute the EFE in the unit of kcal/mol, and they can also be applied in the classical sharp interface PB model.

Electrokinetic properties of healthy and β-thalassemia erythrocyte membranes under in vitro exposure to static magnetic field

Introduction: The current understanding of the biological impacts of a static magnetic field (SMF) is restricted to the direct interactions of the magnetic field with biological membranes. The electrokinetic (zeta) potential is an electrochemical property of erythrocyte surfaces which was negatively charged in physiological media after SMF exposure (0.1‒2.0 T).Methods: The novel data about electrokinetic parameters of the erythrocytes is determined by microelectrophoresis after SMF-exposure in norm and heterozygous β-thalassemia. The methods of light scattering, lipid peroxidation, fluorescence microscopy are used.Results: The electrokinetic potential of erythrocytes in norm is increased after SMF intensities due to enhanced negatively exposed charges on the outer surface of the membrane accompanied by an increase in light scattering where changes in cell morphology are observed. Conversely, a decrease in the zeta potential of β-thalassemia erythrocytes upon SMF-treatment was determined because of the reduction in the surface electrical charge of the membranes, where a significant decrease in light scattering at 1.5 T and 2.0 T was recorded. Exposure to SMF (0.5–2.0 T) was associated with an increase in the malondialdehyde content in erythrocytes. Biophysical studies regarding the influence of SMF on the electrostatic free energy of cells shows an increase in negative values in healthy erythrocytes, which corresponds to the implementation of a spontaneous process. This is also the process in β-thalassemia cells after SMF exposure with lower negative values of free electrostatic energy than erythrocytes in norm.Discussion: The effect of static magnetic field (SMF 0.1–2.0 T) on the electrokinetic and morphological characteristics of erythrocytes in norm and β-thalassemia is determined and correlated with the increase/reduction in surface charge and shrinkage/swelling of the cells, respectively. Lipid peroxidation of healthy and β-thalassemia erythrocytes caused an enhancement of lipid peroxidation because of the higher concentrations of TBARS products in cellular suspension. SMF (0.1‒2.0 T) altered the spontaneous chemical processes with negative values of electrostatic free energy of erythrocytes in norm and β-thalassemia accompanied by a lower FITC-Concanavalin A binding affinity to membrane receptors (SMF 2.0 T). The electrokinetic properties of human erythrocytes in norm and β-thalassemia upon SMF treatment and their interrelationship with the structural-functional state of the membrane were reported. The presented work would have future fundamental applications in biomedicine.

Measurement, correlation, and analysis of the solubility of triethylamine hydrochloride in ten pure solvents

In this work, the solubility of Triethylamine hydrochloride (TEA·HCl) in Ethylene carbonate (EC), Propylene carbonate (PC), Dimethyl carbonate (DMC), Vinylene carbonate (VC), Dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), Methyl isobutyl ketone (MIBK), Methanol, 2-Propanol, 1-Octanol were measured from 293.15 K to 348.15 K under ambient pressure via a static method. Subsequently, the solubility data were correlated with the modified Apelblat Equation, the Van't Hoff Equation, the λh Equation, and the NRTL model. The average relative deviation (ARD), and root-mean-square deviation (RMSD) were introduced to evaluate the correlated data. The findings indicated that, out of the four models, the modified Apelblat model offered the highest correlation. Moreover, using the Van't Hoff Equation, we determined the Gibbs energy, enthalpy, and entropy of TEA·HCl dissolution in each solvent examined, all of which point to a dissolving process that is endothermic and entropy-driven. In the temperature range studied, the solubility of TEA·HCl in selected solvents increased with the rising temperature, and the solubility sequence of TEA·HCl at 298.15 K was Methanol > VC > 2-Propanol > EC > 1-Octanol > DMSO > PC > DMF > MIBK > DMC. In order to understand how TEA·HCl dissolves, density functional theory (DFT) was used to calculate its molecular electrostatic potential (MEP) and solvation free energy. In the meantime, the KAT-LSER model for studying the solvent impact has been presented. This work will provide valuable data references for the purification of TEA·HCl by crystallization.

Photoelectron Spectroscopy of Oppositely Charged Molecular Switches in the Aqueous Phase: Theory and Experiment.

XUV photoelectron spectroscopy (XPS) is a powerful method for investigating the electronic structures of molecules. However, the correct interpretation of results in the condensed phase requires theoretical models that account for solvation. Here we present experimental aqueous-phase XPS of two organic biomimetic molecular switches, NAIP and p-HDIOP. These switches are structurally similar, but have opposite charges and thus present a stringent benchmark for solvation models which need to reproduce the observed ΔeBE = 1.1 eV difference in electron binding energy compared to the 8 eV difference predicted in the gas phase. We present calculations using implicit and explicit solvent models. The latter employs the average solvent electrostatic configuration and free energy gradient (ASEC-FEG) approach. Both nonequilibrium polarizable continuum models and ASEC-FEG calculations give vertical binding energies in good agreement with the experiment for three different computational protocols. Counterions, explicitly accounted for in ASEC-FEG, contribute to the stabilization of molecular states and reduction of ΔeBE upon solvation.

Identification of a novel risk factor for chronic wasting disease (CWD) in elk: S100G single nucleotide polymorphism (SNP) of the prion protein gene (PRNP)

Prion diseases are fatal and malignant infectious encephalopathies induced by the pathogenic form of prion protein (PrPSc) originating from benign prion protein (PrPC). A previous study reported that the M132L single nucleotide polymorphism (SNP) of the prion protein gene (PRNP) is associated with susceptibility to chronic wasting disease (CWD) in elk. However, a recent meta-analysis integrated previous studies that did not find an association between the M132L SNP and susceptibility to CWD. Thus, there is controversy about the effect of M132L SNP on susceptibility to CWD. In the present study, we investigated novel risk factors for CWD in elk. We investigated genetic polymorphisms of the PRNP gene by amplicon sequencing and compared genotype, allele, and haplotype frequencies between CWD-positive and CWD-negative elk. In addition, we performed a linkage disequilibrium (LD) analysis by the Haploview version 4.2 program. Furthermore, we evaluated the 3D structure and electrostatic potential of elk prion protein (PrP) according to the S100G SNP using AlphaFold and the Swiss-PdbViewer 4.1 program. Finally, we analyzed the free energy change of elk PrP according to the S100G SNP using I-mutant 3.0 and CUPSAT. We identified 23 novel SNP of the elk PRNP gene in 248 elk. We found a strong association between PRNP SNP and susceptibility to CWD in elk. Among those SNP, S100G is the only non-synonymous SNP. We identified that S100G is predicted to change the electrostatic potential and free energy of elk PrP. To the best of our knowledge, this was the first report of a novel risk factor, the S100G SNP, for CWD.

Upgrading nirmatrelvir to inhibit SARS-CoV-2 Mpro via DeepFrag and free energy calculations

The first oral drug for the treatment of COVID-19, Paxlovid, has been authorized; however, nirmatrelvir, a major component of the drug, is reported to be associated with some side effects. Moreover, the appearance of many novel variants raises concerns about drug resistance, and designing new potent inhibitors to prevent viral replication is thus urgent. In this context, using a hybrid approach combining machine learning (ML) and free energy simulations, 6 compounds obtained by modifying nirmatrelvir were proposed to bind strongly to SARS-CoV-2 Mpro. The structural modification of nirmatrelvir significantly enhances the electrostatic interaction free energy between the protein and ligand and slightly decreases the vdW term. However, the vdW term is the most important factor in controlling the ligand-binding affinity. In addition, the modified nirmatrelvir might be less toxic to the human body than the original inhibitor.

Beyond binding change: the molecular mechanism of ATP hydrolysis by F1-ATPase and its biochemical consequences.

F1-ATPase is a universal multisubunit enzyme and the smallest-known motor that, fueled by the process of ATP hydrolysis, rotates in 120o steps. A central question is how the elementary chemical steps occurring in the three catalytic sites are coupled to the mechanical rotation. Here, we performed cold chase promotion experiments and measured the rates and extents of hydrolysis of preloaded bound ATP and promoter ATP bound in the catalytic sites. We found that rotation was caused by the electrostatic free energy change associated with the ATP cleavage reaction followed by Pi release. The combination of these two processes occurs sequentially in two different catalytic sites on the enzyme, thereby driving the two rotational sub-steps of the 120o rotation. The mechanistic implications of this finding are discussed based on the overall energy balance of the system. General principles of free energy transduction are formulated, and their important physical and biochemical consequences are analyzed. In particular, how exactly ATP performs useful external work in biomolecular systems is discussed. A molecular mechanism of steady-state, trisite ATP hydrolysis by F1-ATPase, consistent with physical laws and principles and the consolidated body of available biochemical information, is developed. Taken together with previous results, this mechanism essentially completes the coupling scheme. Discrete snapshots seen in high-resolution X-ray structures are assigned to specific intermediate stages in the 120o hydrolysis cycle, and reasons for the necessity of these conformations are readily understood. The major roles played by the "minor" subunits of ATP synthase in enabling physiological energy coupling and catalysis, first predicted by Nath's torsional mechanism of energy transduction and ATP synthesis 25 years ago, are now revealed with great clarity. The working of nine-stepped (bMF1, hMF1), six-stepped (TF1, EF1), and three-stepped (PdF1) F1 motors and of the α3β3γ subcomplex of F1 is explained by the same unified mechanism without invoking additional assumptions or postulating different mechanochemical coupling schemes. Some novel predictions of the unified theory on the mode of action of F1 inhibitors, such as sodium azide, of great pharmaceutical importance, and on more exotic artificial or hybrid/chimera F1 motors have been made and analyzed mathematically. The detailed ATP hydrolysis cycle for the enzyme as a whole is shown to provide a biochemical basis for a theory of "unisite" and steady-state multisite catalysis by F1-ATPase that had remained elusive for a very long time. The theory is supported by a probability-based calculation of enzyme species distributions and analysis of catalytic site occupancies by Mg-nucleotides and the activity of F1-ATPase. A new concept of energy coupling in ATP synthesis/hydrolysis based on fundamental ligand substitution chemistry has been advanced, which offers a deeper understanding, elucidates enzyme activation and catalysis in a better way, and provides a unified molecular explanation of elementary chemical events occurring at enzyme catalytic sites. As such, these developments take us beyond binding change mechanisms of ATP synthesis/hydrolysis proposed for oxidative phosphorylation and photophosphorylation in bioenergetics.

Polyelectrolyte Brush Interacting with Ampholytic Nanoparticles as Coarse-Grained Models of Globular Proteins: Poisson-Boltzmann Theory.

The self-consistent field Poisson-Boltzmann framework is applied to analyze equilibrium partitioning of ampholytic nanoparticles (NPs) between buffer solution and polyelectrolyte (PE) polyanionic brush. We demonstrate that depending on pH and salt concentration in the buffer solution, interactions between ionizable (acidic and basic) groups on the NP surface and electrostatic field created by PE brush may either lead to the spontaneous uptake of NPs or create an electrostatic potential barrier, preventing the penetration of NPs inside PE brush. The capability of PE brush to absorb or repel NPs is determined by the shape of the insertion free energy that is calculated as a function of NP distance from the grafting surface. It is demonstrated that, at a pH value below or slightly above the isoelectric point (IEP), the electrostatic free energy of the particle is negative inside the brush and absorption is thermodynamically favorable. In the latter case, the insertion free energy exhibits a local maximum (potential barrier) at the entrance to the brush. An increase in pH leads to the shallowing of the free energy minimum inside the brush and a concomitant increase in the free energy maximum, which may result in kinetic hindering of NP uptake. Upon further increase in pH the insertion free energy becomes positive, making NP absorption thermodynamically unfavorable. An increase in salt concentration diminishes the depth of the free energy minimum inside the brush and eventually leads to its disappearance. Hence, in accordance with existing experimental data our theory predicts that an increase in salt concentration suppresses absorption of NPs (protein globules) by PE brush in the vicinity of IEP. The interplay between electrostatic driving force for NP absorption and osmotic repelling force (proportional to NP volume) indicates that for large NPs with relatively small number of ionizable groups osmotic repulsion overcomes electrostatic attraction preventing thereby absorption of NPs by PE brush.

Modeling of micellar‐catalyzed bimolecular ionic reactions by a nonlinear Poisson−Boltzmann equation and an electrostatic free energy model

AbstractThe hydrolysis reactions of crystal violet (CV) and p‐nitrophenyl acetate (PNPA) by sodium hydroxide in cetyltrimethylammonium bromide (CTAB) micellar solution were studied in this work. Combined with the Boltzmann probability of ionic species in an electrostatic potential field, a model with a numerical scheme was developed based on the nonlinear Poisson−Boltzmann equation in the micelle‐cell consisting of the reactants and the surfactant. The numerical solution gives the ionic species distribution in the micelle phase and the radius of the micelle‐phase. The dielectric constant of the micelle‐phase varies in the range of 39.8−54.4. The second‐order reaction rate constants in the micelle‐phase were determined using the electrostatic and dipolar free energy models. For the basic hydrolysis of CV and PNPA, the overall second‐order rate constants are three to five times and 1.4 times greater than the corresponding values in water, respectively. The rate enhancement occurs due to the distribution of the reactive ionic species in the cell region and the enhancement of the Coulombic and dipolar interactions among the ionic and polar reactants.

The Dielectric Boundary Force in Molecular Solvation of the Generalized Poisson–Boltzmann Equation with Ionic Sizes

In molecular solvation, the size-modified electrostatic free energy is investigated. With the uniform ionic and solvent molecular sizes, the generalized Poisson–Boltzmann (PB) equation is considered. The first variation of the size-modified electrostatic free energy with respect to the location variation of the interface is derived. The concept of shape derivative is used to define such variations. The explicit formula of the dielectric boundary force is derived.

Molecular electrostatics and pKa shifts calculations with the Generalized Born model. A tutorial through examples with Bluues2

Biomolecular electrostatics is of key importance for biological function and recognition. The continuum electrostatic model based on the Poisson-Boltzmann (PB) equation has been widely used to study biomolecular electrostatics. The solution of the PB equation gives the electrostatic potential over the space enclosing the molecule(s) of interest, typically obtained at points of a suitable grid.The Generalized Born (GB) model has been used to provide a useful approximation to the solution obtained by solving numerically the PB equation. The main advantage of the GB approach is to express the electrostatic energy of the system as the sum of pairwise interactions. The latter depend on geometric parameters (the GB radii) which depend on all atoms, and their radii, of the system. In this work we present a tutorial through examples for a more efficient and general version of the program Bluues which is able to compute:1) the generalized Born radius of each atom;2) the electrostatic potential at the surface of the molecule mapped to solvent accessible atoms;3) the solvent accessible surface in a PDB formatted file;4) the electrostatic potential in the volume surrounding the molecule;5) the electrostatic free energy and different contributions to it;6) the pH-dependent properties of proteins (total charge and pH-dependent free energy of folding) in the pH range −4 to 18;7) the pKa shifts due to molecular structure of all ionizable groups. Program summaryProgram Title: bluues2CPC Library link to program files:https://doi.org/10.17632/bx98gcrzbg.1Developer's repository link:https://github.com/federico-fogolari/bluues2Code Ocean capsule:https://codeocean.com/capsule/9338710Licensing provisions: GPLv3Programming language: CNature of problem: Biomolecular electrostatics is of key importance for biological function and recognition. Computation of electrostatic effects and their dissection in atomic contributions is a general problem in molecular modeling.Solution method: The GBR6 version of the Generalized Born (GB) model is implemented through surface integrals and all common molecular electrostatic analyses are performed by a single command line program.Additional comments including restrictions and unusual features: The program requires, as input, files in pqr format, which may be generated by independent software (e.g. babel, pdb2pqr). For the optional generation of the solvent excluded surface, the software msms must be installed and present in the path.

ES-Screen: A Novel Electrostatics-Driven Method for Drug Discovery Virtual Screening

Electrostatic interactions drive biomolecular interactions and associations. Computational modeling of electrostatics in biomolecular systems, such as protein-ligand, protein-protein, and protein-DNA, has provided atomistic insights into the binding process. In drug discovery, finding biologically plausible ligand-protein target interactions is challenging as current virtual screening and adjuvant techniques such as docking methods do not provide optimal treatment of electrostatic interactions. This study describes a novel electrostatics-driven virtual screening method called 'ES-Screen' that performs well across diverse protein target systems. ES-Screen provides a unique treatment of electrostatic interaction energies independent of total electrostatic free energy, typically employed by current software. Importantly, ES-Screen uses initial ligand pose input obtained from a receptor-based pharmacophore, thus independent of molecular docking. ES-Screen integrates individual polar and nonpolar replacement energies, which are the energy costs of replacing the cognate ligand for a target with a query ligand from the screening. This uniquely optimizes thermodynamic stability in electrostatic and nonpolar interactions relative to an experimentally determined stable binding state. ES-Screen also integrates chemometrics through shape and other physicochemical properties to prioritize query ligands with the greatest physicochemical similarities to the cognate ligand. The applicability of ES-Screen is demonstrated with in vitro experiments by identifying novel targets for many drugs. The present version includes a combination of many other descriptor components that, in a future version, will be purely based on electrostatics. Therefore, ES-Screen is a first-in-class unique electrostatics-driven virtual screening method with a unique implementation of replacement electrostatic interaction energies with broad applicability in drug discovery.

Convergence of a diffuse interface Poisson-Boltzmann (PB) model to the sharp interface PB model: A unified regularization formulation

Both the sharp interface and diffuse interface Poisson-Boltzmann (PB) models have been developed in the literature for studying electrostatic interaction between a solute molecule and its surrounding solvent environment. In the mathematical analysis and numerical computation for these PB models, a significant challenge is due to singular charge sources in terms of Dirac delta distributions. Recently, based on various regularization schemes for the sharp interface PB equation, the first regularization method for the diffuse interface PB model has been developed in [S. Wang, E. Alexov, and S. Zhao, Mathematical Biosciences and Engineering, 18, 1370–1405, (2021)] for analytically treating the singular charges. This work concerns with the convergence of a diffuse interface PB model to the sharp interface PB model, as the diffused Gaussian-convolution surface (GCS) approaches to the sharp solvent accessible surface (SAS). Due to the limitation in numerical algorithm and mesh resolution, such a convergence is impossible to be verified numerically. Through analyzing the weak solution for the regularized PB equations, the convergences for both the reaction-field potential and electrostatic free energy are rigorously proved in this work. Moreover, this study provides a unified regularization for both sharp interface and diffuse interface PB models, and clarifies the connection between this unified formulation and the existing regularizations. This lays a theoretical foundation to develop regularization for more complicated PB models.

Protein-Nucleic Acid Interactions for RNA Polymerase II Elongation Factors by Molecular Dynamics Simulations.

RNA polymerase II (Pol II) forms a complex with elongation factors to proceed to the elongation stage of the transcription process. In this work, we studied the elongation factor SPT5 and explored the protein-nucleic acid interactions for the isolated systems of KOW1 and KOW4 domains of SPT5 with DNA and RNA, respectively. We performed molecular dynamics (MD) simulations using three commonly used force fields that are CHARMM c36m, AMBER ff14sb, and ff19sb. Simulations showed strong protein-nucleic acid interactions and low electrostatic binding free energies for all force fields used. RNA was found to be highly dynamic with all force fields, while DNA had relatively more stable conformations with the AMBER force fields compared to that with CHARMM. Furthermore, we performed MD simulations of the complete elongation complex using CHARMM c36m and AMBER ff19sb force fields to compare the dynamics and interactions with the isolated systems. Similarly, strong KOW1 and DNA interactions were observed in the complete elongation complex simulations and DNA was further stabilized by a network of interactions involving SPT5-KOW1, SPT4, and rpb2 of Pol II. Overall, our study showed that the differences between CHARMM and AMBER force fields strongly affect the dynamics of the nucleic acids. CHARMM provides highly flexible DNA, while AMBER largely stabilizes the DNA structure. Although the presence of the entire interaction network stabilized the DNA and decreased the differences in the results from the two force fields, the discrepancies of the force fields for smaller systems may reflect their problems in generating accurate dynamics of nucleic acids.