The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology

Influence of an Intrinsically Disordered Region on Protein Domains Revealed by NMR-Based Electrostatic Potential Measurements

Many human proteins possess intrinsically disordered regions containing consecutive aspartate or glutamate residues ("D/E repeats"). Approximately half of them are DNA/RNA-binding proteins. In this study, using nuclear magnetic resonance (NMR) spectroscopy, we investigated the electrostatic properties of D/E repeats and their influence on folded domains within the same protein. Local electrostatic potentials were directly measured for the HMGB1 protein, its isolated D/E repeats, and DNA-binding domains by NMR. The data provide quantitative information about the electrostatic interactions between distinct segments of HMGB1. Due to the interactions between the D/E repeats and the DNA-binding domains, local electrostatic potentials of the DNA-binding domains within the full-length HMGB1 protein were largely negative despite the presence of many positively charged residues. Our NMR data on counterions and electrostatic potentials show that the D/E repeats and DNA have similar electrostatic properties and compete for the DNA-binding domains. The competition promotes dissociation of the protein-DNA complex and influences the molecular behavior of the HMGB1 protein. These effects may be general among the DNA/RNA-binding proteins with D/E repeats.

Sorption properties of pristine and functionalized magnetic carbon nanotubes in relation to double-stranded DNA

BACKGROUND

Owing to improvement of the molecular diagnostic methods using purified preparations of nucleic acids (NAs), the development of effective methods providing the isolation of DNA is still relevant. The sorption properties of magnetic multi-walled carbon nanotubes (MWCNTs), oxidized MWCNTs and MWCNTs (pristine and oxidized) modified with polydiallyldimethylammonium chloride (pDADMAC) with respect to double strained DNA have been studied.

RESULTS

It was shown that in the presence of MWCNTs/pDADMAC particles the DNA molecules were reversibly retained by the particle's surface. The optimal conditions for each step of DNA extraction from model solutions using the obtained material were selected. A comparative evaluation of the effectiveness of the proposed method for DNA isolation based on the results of spectrophotometry and real-time PCR was carried out. It was shown that the desorbed DNA was efficiently amplified in PCR, inhibition of polymerase did not occurred. Probable mechanisms of DNA retention due to the influence of residual impurities of catalysts in the MWCNT composition, as well as the surface charge of nanotubes are proposed.

CONCLUSION

Sequentially oxidized and coated with pDADMAC magnetically susceptible CNTs are seemed to be a promising material for development of low-cost systems proving an easy isolation, storage, and subsequent use of dsDNA in molecular diagnostics. The sorption properties of such systems are determined with highly developed specific surface area and their chemical composition.

The Three-Dimensional Reference Interaction Site Model Approach as a Promising Tool for Studying Hydrated Viruses and Their Complexes with Ligands

Viruses are the most numerous biological form living in any ecosystem. Viral diseases affect not only people but also representatives of fauna and flora. The latest pandemic has shown how important it is for the scientific community to respond quickly to the challenge, including critically assessing the viral threat and developing appropriate measures to counter this threat. Scientists around the world are making enormous efforts to solve these problems. In silico methods, which allow quite rapid obtention of, in many cases, accurate information in this field, are effective tools for the description of various aspects of virus activity, including virus-host cell interactions, and, thus, can provide a molecular insight into the mechanism of virus functioning. The three-dimensional reference interaction site model (3D-RISM) seems to be one of the most effective and inexpensive methods to compute hydrated viruses, since the method allows us to provide efficient calculations of hydrated viruses, remaining all molecular details of the liquid environment and virus structure. The pandemic challenge has resulted in a fast increase in the number of 3D-RISM calculations devoted to hydrated viruses. To provide readers with a summary of this literature, we present a systematic overview of the 3D-RISM calculations, covering the period since 2010. We discuss various biophysical aspects of the 3D-RISM results and demonstrate capabilities, limitations, achievements, and prospects of the method using examples of viruses such as influenza, hepatitis, and SARS-CoV-2 viruses.

Observation of Electrostatically Driven Surface Adsorption in Mixed Surfactant Systems

We employed heterodyne-detected vibrational sum-frequency generation (HD-VSFG) spectroscopy to obtain a molecular-level understanding of the interaction between the anionic surfactant sodium dodecyl ammonium sulfate (SDS) and the cationic surfactant dodecyltrimethylammonium bromide (DTAB). We observed that these surfactants show a strong cooperative effect on their adsorption to the water-air interface. Even at bulk concentrations 1000 times lower than the critical micelle concentrations of SDS and DTAB, a nearly complete surface surfactant layer is observed when both surfactants are present. This strong enhancement of the surface concentrations of DS- and DTA+ can be quantitatively explained from the favorable Coulomb interaction of the oppositely charged headgroups of DS- and DTA+ and the electrostatic interactions with their counterions. The HD-VSFG results are complemented by a modified Langmuir adsorption model in which we include the free energy associated with the electrostatic interactions of the surfactant ions and their counterions.

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.

Computational insights into overcoming resistance mechanisms in targeted therapies for advanced breast cancer: focus on EGFR and HER2 co-inhibition

In the present study, the formation of a heterodimer involving both epidermal growth factor receptor (EGFR) and human epidermal growth factor receptor 2 (HER2) has been explored as a potential therapeutic mechanism to inhibit the progression of breast cancer. Virtual screening using molecular docking resulted in the three hit compounds (ZINC08382411, ZINC08382438, and ZINC08382292) with minimum binding scores and commonly binding to both receptors. Further, MD simulation analysis of these complexes illustrated the high stability of these compounds with EGFR and HER2. RMSD showed that ZINC08382411 displayed the most stable RMSD of 2 - 3 Å when bound to both receptors, suggesting to have strong compatibility with the active site of the receptor. Hydrogen bond analysis showed that ZINC08382411 forms the maximum number of H-bonds (2 to 3) in both EGFR and HER2 bound complexes, with the highest occupancy of 62% and 79%, respectively. Binding free energy calculation showed that ZINC08382411 possesses maximum affinity towards both the receptors with ΔGbind = -129.628 and -164.063 kJ/mol, respectively. This approach recognizes the significance of EGFR and HER2 in breast cancer development and aims to disrupt their collaborative signaling, which is known to promote the antagonistic behavior of cancer cells. By focusing on this EGFR/HER2 heterodimer, the study offers a promising avenue for identifying a potential candidate (ZINC08382411) that may inhibit breast cancer cell growth and potentially improve patient outcomes. The study's findings may contribute to the ongoing efforts to advance breast cancer treatment strategies.Communicated by Ramaswamy H. Sarma.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Underlying features for the enhanced electrostatic strength of the extremophilic malate dehydrogenase interface salt-bridge compared to the mesophilic one

Malate dehydrogenase (MDH) exists in multimeric form in normal and extreme solvent conditions where residues of the interface are involved in specific interactions. The interface salt-bridge (ISB) and its microenvironment (ME) residues may have a crucial role in the stability and specificity of the interface. To gain insight into this, we have analyzed 218 ISBs from 42 interfaces of 15 crystal structures along with their sequences. Comparative analyses demonstrate that the ISB strength is ∼30 times greater in extremophilic cases than that of the normal one. To this end, the interface residue propensity, ISB design and pair selection, and ME-residue's types, i.e., type-I and type-II, are seen to be intrinsically involved. Although Type-I is a common type, Type-II appears to be extremophile-specific, where the net ME-residue count is much lower with an excessive net ME-energy contribution, which seems to be a novel interface compaction strategy. Furthermore, the interface strength can be enhanced by selecting the desired mutant from the net-energy profile of all possible mutations of an unfavorable ME-residue. The study that applies to other similar systems finds applications in protein-protein interaction and protein engineering.Communicated by Ramaswamy H. Sarma.

Ensemble-based virtual screening of African natural products to target human thymidylate synthase

Human thymidylate synthase (hTS) is a validated drug target for chemotherapy. A virtual screening experiment was used to prioritize a list of compounds from African Natural Products Databases docked against the orthosteric binding pocket of hTS. Consensus scores of binding affinities from ensemble-based virtual screening, hydrated docking and MM-PBSA calculations ranked compounds NEA4433 and NEA4434 as the best candidates owing to binding affinity scores in the picomolar order, their excellent ADMET profiles and the good stability of the protein-ligand complexes formed. The current study demonstrates the role of water in small molecule binding to hTS in mediating protein-ligand interactions. Similarly, the robust ensemble docking (relaxed scheme complex) ranked NEA4433 and NEA4434 as the best candidates. Furthermore, the best candidates prioritized were shown to strongly interact with the same residues that interacted with hTS substrate and cofactor.

Numerical Study of the Time-Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel

Electroosmotic flow (EOF) is of utmost significance due to its numerous practical uses in controlling flow at micro/nanoscales. In the present study, the time-periodic EOF of a viscoelastic fluid is statistically analyzed using a short 10:1 constriction microfluidic channel joining two reservoirs on either side. The flow is modeled using the Oldroyd-B (OB) model and the Poisson-Boltzmann model. The EOF of a highly concentrated polyacrylamide (PAA) aqueous solution is investigated under the combined effects of an alternating current (AC) electric field and a direct current (DC) electric field. Power-law degradation is visible in the energy spectra of the velocity fluctuations over a wide frequency range, pointing to the presence of elastic instabilities in the EOF. The energy-spectra curves of the velocity fluctuations under a DC electric field exhibit peaks primarily beneath 20 Hz, with the greatest peak being observed close to 6 Hz. When under both DC and AC electric fields, the energy spectra of the velocity fluctuations exhibit a peak at the same frequency as the AC electric field, and the highest peak is obtained when the frequency of the AC electric field is near 6 Hz. Additionally, the frequency of the AC electric field affects how quickly the viscoelastic EOF flows. Higher flow rates are obtained at relatively low frequencies compared to under the DC electric field, and the greatest flow rate is found close to 6 Hz. But as the frequency rises further, the flow rate falls. The flow rate falls to a level below the DC electric field when the frequency is sufficiently high.

Observation of a Two-Dimensional Hydrophobic Collapse at the Surface of Water Using Heterodyne-Detected Surface Sum-Frequency Generation

We study the effect of sodium chloride (NaCl) on the properties of the interface of water and the surfactant dodecyl sulfate (DS-) using heterodyne-detected vibrational sum-frequency generation spectroscopy. We find that the signal of the O-H stretch vibrations of oriented water molecules at the interface is highly nonlinearly dependent on the NaCl concentration. This nonlinear dependence is explained by a combination of screening of the electric field of surface-bound DS- ions pointing into the bulk and screening of the Coulomb repulsion between the headgroups of the DS- ions in the surface plane. The latter effect strongly increases the oriented water signal within a limited NaCl concentration range of 10-100 mM, indicating a two-dimensional hydrophobic collapse of the surfactant layer. The occurrence of collapse is supported by model calculations of the surface potential and surface surfactant density.

Computational Study on the Enzyme-Ligand Relationship between Cannabis Phytochemicals and Human Acetylcholinesterase: Implications in Alzheimer's Disease

Cannabis has shown promise in treating various neurological disorders, including Alzheimer's disease (AD). AD is a devastating neurodegenerative disorder that affects millions of people worldwide. Current treatments for AD are limited and are not very effective. This study investigated the enzyme-ligand relationship between nine active components of cannabis and human acetylcholinesterase (HuAChE) enzyme, which is significant in AD. Specifically, computational methods such as quantum mechanics, molecular docking, molecular dynamics, and free energy calculations were used to identify the cannabis phytochemicals with the highest HuAChE affinity and to understand the specific binding mechanisms involved. Our results showed that cannabichromene and cannabigerol were the cannabis phytochemicals with the highest affinity for HuAChE, with cannabichromene exhibiting the greatest binding energy. However, both substances showed lower affinity than that of the pharmaceutical drug donepezil. This study suggests that cannabichromene has a specific affinity for the peripheral anionic site (PAS) and acyl-binding pocket (ABP), while cannabigerol predominantly binds to PAS. Also, it was found that cannabichromene has a specific affinity for PAS and ABP, while cannabigerol predominantly binds to PAS. Our findings suggest that cannabichromene and cannabigerol are potential therapeutic agents, but further research is needed to validate their effectiveness. The specific binding mechanisms identified may also provide helpful information for the design of more effective cannabis-based drugs. Overall, this study provides valuable insights into the potential of cannabis-based drugs for treating neurological diseases.

Binding of Mammea A/AA (MA) to calf thymus DNA revealed by the ratiometric absorbance of MA in the UV-visible range molecular dynamic simulations and TD-DFT calculations

The in vitro anti-proliferative activity of MA (5,7-dihydroxy-8-(3-methylbut-2-enyl)-6-(3-methyl-1-oxobutyl)-4-phenyl[1]2H-[1]benzopyran-2-one)on a variety of cancer cells was previously demonstrated. This work strives to understand the mechanisms by which MA exerts this biological activity. Thereafter, the binding of MA to calf thymus DNA was studied by monitoring the change in the UV-visible absorbance of MA. It was found that, the response of MA to binding with calf thymus DNA is characterised by an increase in the AS/AL ratio of the absorbance of the longest wavelength absorption band to the shortest one, and the appearance of a new band at about 377 nm assigned to S0→S1 transition, which is red shifted as compared to free MA. From the bands ratio, the binding constant is found to be 4.3x105 M-1, indicating strong binding. The deduced binding free energy, enthalpy and entropy are -7.7 kcal/mol, -10.89 ± 0.28 kcal/mol and -54.46 ± 4 J/K, respectively, indicating that MA binds to DNA by a non-bonding Van der Waals type interactions and hydrogen bonds. Further study with classical molecular dynamics shows that MA binds to DNA by intercalation, where it is positioned between two AT base pairs. Unlike isolated MA, TDDFT calculations on ten images extracted from the MD trajectory show that, the frontier molecular orbitals of the complex are distributed over the DNA and MA. This indicates a strong stacking interaction and then explains the hypochromism and the red shift of the S0→S1 transition. The present work demonstrates the potency of MA as antitumor compound and as absorbance-based molecular probe.Communicated by Ramaswamy H. Sarma.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Practical considerations for the measurement of near-surface electrostatics based on solvent paramagnetic relaxation enhancements

Electrostatic interactions can play important roles in regulating various biological processes. Quantifying surface electrostatics of biomolecules is, therefore, of significant interest. Recent advances in solution NMR spectroscopy have enabled site-specific measurements of de novo near-surface electrostatic potentials (ϕ_ENS) based on a comparison of solvent paramagnetic relaxation enhancements generated from differently charged paramagnetic co-solutes with similar structures. Although the NMR-derived near-surface electrostatic potentials have been shown to agree with theoretical calculations in the context of folded proteins and nucleic acids, such benchmark comparisons may not always be possible, particularly in cases where high-resolution structural models are lacking, such as in the study of intrinsically disordered proteins. Cross-validation of ϕ_ENS potentials can be achieved by comparing values obtained using three pairs of paramagnetic co-solutes, each with a different net charge. Notably we have found cases where agreement of ϕ_ENS potentials between the three pairs is poor and herein we investigate the source of this discrepancy in some detail. We show that for the systems considered here ϕ_ENS potentials obtained from cationic and anionic co-solutes are accurate and that the use of paramagnetic co-solutes with different structures can be a viable option for validation, although the optimal choice of paramagnetic compounds depends on the system of interest.

Linear scaling computation of forces for the domain-decomposition linear Poisson-Boltzmann method

The Linearized Poisson-Boltzmann (LPB) equation is a popular and widely accepted model for accounting solvent effects in computational (bio-) chemistry. In the present article, we derive the analytical forces using the domain-decomposition-based LPB-method with a van-der Waals or solvent-accessible surface. We present an efficient strategy to compute the forces and its implementation, allowing linear scaling of the method with respect to the number of atoms using the fast multipole method. Numerical tests illustrate the accuracy of the computation of the analytical forces and compare the efficiency with other available methods.

Structural Insight into the Working Mechanism of the FAD Synthetase from the Human Pathogen Streptococcus pneumoniae: A Molecular Docking Simulation Study

Flavin adenine dinucleotide synthetases (FADSs) catalyze FAD biosynthesis through two consecutive catalytic reactions, riboflavin (RF) phosphorylation and flavin mononucleotide (FMN) adenylylation. Bacterial FADSs have RF kinase (RFK) and FMN adenylyltransferase (FMNAT) domains, whereas the two domains are separated into two independent enzymes in human FADSs. Bacterial FADSs have attracted considerable attention as drug targets due to the fact that they differ from human FADSs in structure and domain combinations. In this study, we analyzed the putative FADS structure from the human pathogen Streptococcus pneumoniae (SpFADS) determined by Kim et al., including conformational changes of key loops in the RFK domain upon substrate binding. Structural analysis and comparisons with a homologous FADS structure revealed that SpFADS corresponds to a hybrid between open and closed conformations of the key loops. Surface analysis of SpFADS further revealed its unique biophysical properties for substrate attraction. In addition, our molecular docking simulations predicted possible substrate-binding modes at the active sites of the RFK and FMNAT domains. Our results provide a structural basis to understand the catalytic mechanism of SpFADS and develop novel SpFADS inhibitors.

Electrostatic Surface Potential as a Key Parameter in Virus Transmission and Evolution: How to Manage Future Virus Pandemics in the Post-COVID-19 Era

Virus-cell interactions involve fundamental parameters that need to be considered in strategies implemented to control viral outbreaks. Among these, the surface electrostatic potential can give valuable information to deal with new epidemics. In this article, we describe the role of this key parameter in the hemagglutination of red blood cells and in the co-evolution of synaptic receptors and neurotransmitters. We then establish the functional link between lipid rafts and the electrostatic potential of viruses, with special emphasis on gangliosides, which are sialic-acid-containing, electronegatively charged plasma membrane components. We describe the common features of ganglioside binding domains, which include a wide variety of structures with little sequence homology but that possess key amino acids controlling ganglioside recognition. We analyze the role of the electrostatic potential in the transmission and intra-individual evolution of HIV-1 infections, including gatekeeper and co-receptor switch mechanisms. We show how to organize the epidemic surveillance of influenza viruses by focusing on mutations affecting the hemagglutinin surface potential. We demonstrate that the electrostatic surface potential, by modulating spike-ganglioside interactions, controls the hemagglutination properties of coronaviruses (SARS-CoV-1, MERS-CoV, and SARS-CoV-2) as well as the structural dynamics of SARS-CoV-2 evolution. We relate the broad-spectrum antiviral activity of repositioned molecules to their ability to disrupt virus-raft interactions, challenging the old concept that an antibiotic or anti-parasitic cannot also be an antiviral. We propose a new concept based on the analysis of the electrostatic surface potential to develop, in real time, therapeutic and vaccine strategies adapted to each new viral epidemic.

Surface electrostatics dictate RNA-binding protein CAPRIN1 condensate concentration and hydrodynamic properties

Biomolecular condensates concentrate proteins, nucleic acids, and small molecules and play an essential role in many biological processes. Their formation is tuned by a balance between energetically favorable and unfavorable contacts, with charge-charge interactions playing a central role in some systems. The positively charged intrinsically disordered carboxy-terminal region of the RNA-binding protein CAPRIN1 is one such example, phase separating upon addition of negatively charged ATP or high concentrations of sodium chloride (NaCl). Using solution NMR spectroscopy, we measured residue-specific near-surface electrostatic potentials (ϕENS) of CAPRIN1 along its NaCl-induced phase separation trajectory to compare with those obtained using ATP. In both cases, electrostatic shielding decreases ϕENS values, yet surface potentials of CAPRIN1 in the two condensates can be different, depending on the amount of NaCl or ATP added. Our results establish that even small differences in ϕENS can significantly affect the level of protein enrichment and the mechanical properties of the condensed phase, leading, potentially, to the regulation of biological processes.

Molecular design and rational optimization of synergistic effect between the two wings of a roughly orthogonal cation-π-π stacking system at nasopharyngeal carcinoma YAP1-TEAD4 parallel Helix-Helix interaction interface

The Yes-associated protein-1 (YAP1) is an essential regulator of human Hippo signaling pathway and functions through interaction with TEA domain-4 (TEAD4) transcription factor involved in the tumorigenesis of nasopharyngeal cancer. Previously, a parallel helix-helix interaction (PHHI) was identified as the key hotspot at YAP1-TEAD4 complex interface and has been exploited as an attractive druggable target to disrupt the complex. In this study, we investigated a roughly orthogonal cation-π-π stacking system across the crystal PHHI packing interface by integrating computational modeling and binding assay, which forms between one YAP1 helical residue Phe69 and two TEAD4 helical residues Phe373/Lys376. A synergistic effect between cation-π and π-π interactions was observed; they separately represent two wings of the stacking system. The π-electron is primarily responsible for the synergistic effect. Combination between diverse aromatic/charged amino acids. as well as neutral alanine on the cation-π-π stacking, revealed that the presence of aromatic tryptophan and charged arginine at, respectively, the residues 373 and 376 of TEAD4 helix can considerably improve PHHI binding affinity by ~6-fold, whereas neutral alanine substitution on each residue and on both would reduce the affinity significantly, confirming a strong synergistic effect involved in the roughly orthogonal cation-π-π stacking system at YAP1-TEAD4 PHHI interface.

Computational Study of the pH-Dependent Ionic Environment around β-Lactoglobulin

Ions are involved in multiple biological processes and may exist bound to biomolecules or may be associated with their surface. Although the presence of ions in nucleic acids has traditionally gained more interest, ion-protein interactions, often with a marked dependency on pH, are beginning to gather attention. Here we present a detailed analysis on the binding and distribution of ions around β-lactoglobulin using a constant-pH MD (CpHMD) method, at a pH range 3-8, and compare it with the more traditional Poisson-Boltzmann (PB) model and the existing experimental data. Most analyses used ion concentration maps built around the protein, obtained from either the CpHMD simulations or PB calculations. The requirements of approximate charge neutrality and ionic strength equal to bulk, imposed on the MD box, imply that the absolute value of the ion excess should be half the protein charge, which is in agreement with experimental observation on other proteins ( Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2015879118) and lends support to this protocol. In addition, the protein total charge (including territorially bound ions) estimated with MD is in excellent agreement with electrophoretic measurements. Overall, the CpHMD simulations show good agreement with the nonlinear form of the PB (NLPB) model but not with its linear form, which involves a theoretical inconsistency in the calculation of the concentration maps. In several analyses, the observed pH-dependent trends for the counterions and co-ions are those generally expected, and the ion concentration maps correctly converge to the bulk ionic strength as one moves away from the protein. Despite the overall similarity, the CpHMD and NLPB approaches show some discrepancies when analyzed in more detail, which may be related to an apparent overestimation of counterion excess and underestimation of co-ion exclusion by the NLPB model, particularly at short distances from the protein.

Modeling of the Electrostatic Interaction and Catalytic Activity of [NiFe] Hydrogenases on a Planar Electrode

Hydrogenases are a group of enzymes that have caught the interest of researchers in renewable energies, due to their ability to catalyze the redox reaction of hydrogen. The exploitation of hydrogenases in electrochemical devices requires their immobilization on the surface of suitable electrodes, such as graphite. The orientation of the enzyme on the electrode is important to ensure a good flux of electrons to the catalytic center, through an array of iron-sulfur clusters. Here we present a computational approach to determine the possible orientations of a [NiFe] hydrogenase (PDB 1e3d) on a planar electrode, as a function of pH, salinity, and electrode potential. The calculations are based on the solution of the linearized Poisson-Boltzmann equation, using the PyGBe software. The results reveal that electrostatic interactions do not truly immobilize the enzyme on the surface of the electrode, but there is instead a dynamic equilibrium between different orientations. Nonetheless, after averaging over all thermally accessible orientations, we find significant differences related to the solution's salinity and pH, while the effect of the electrode potential is relatively weak. We also combine models for the protein adsoption-desorption equilibria and for the electron transfer between the proteins and the electrode to arrive at a prediction of the electrode's activity as a function of the enzyme concentration.

Monovalent ion-mediated charge-charge interactions drive aggregation of surface-functionalized gold nanoparticles

Monolayer-protected metal nanoparticles (NPs) are not only promising materials with a wide range of potential industrial and biological applications, but they are also a powerful tool to investigate the behaviour of matter at nanoscopic scales, including the stability of dispersions and colloidal systems. This stability is dependent on a delicate balance between attractive and repulsive interactions that occur in the solution, and it is described in quantitative terms by the classic Derjaguin-Landau-Vewey-Overbeek (DLVO) theory, that posits that aggregation between NPs is driven by van der Waals interactions and opposed by electrostatic interactions. To investigate the limits of this theory at the nanoscale, where the continuum assumptions required by the DLVO theory break down, here we investigate NP dimerization by computing the Potential of Mean Force (PMF) of this process using fully atomistic MD simulations. Serendipitously, we find that electrostatic interactions can lead to the formation of metastable NP dimers at physiological ion concentrations. These dimers are stabilized by complexes formed by negatively charged ligands belonging to distinct NPs that are bridged by positively charged monovalent ions present in solution. We validate our findings by collecting tomographic EM images of NPs in solution and by quantifying their radial distribution function, that shows a marked peak at interparticle distance comparable with that of MD simulations. Taken together, our results suggest that not only van der Waals interactions, but also electrostatic interactions mediated by monovalent ions at physiological concentrations, contribute to attraction between nano-sized charged objects at very short length scales.

AMOEBA Force Field Trajectories Improve Predictions of Accurate pKa Values of the GFP Fluorophore: The Importance of Polarizability and Water Interactions

Precisely quantifying the magnitude, direction, and biological functions of electric fields in proteins has long been an outstanding challenge in the field. The most widely implemented experimental method to measure such electric fields at a particular residue in a protein has been through changes in pKa of titratable residues. While many computational strategies exist to predict these values, it has been difficult to do this accurately or connect predicted results to key structural or mechanistic features of the molecule. Here, we used experimentally determined pKa values of the fluorophore in superfolder green fluorescent protein (GFP) with amino acid mutations made at position Thr 203 to evaluate the pKa prediction ability of molecular dynamics (MD) simulations using a polarizable force field, AMOEBA. Structure ensembles from AMOEBA were used to calculate pKa values of the GFP fluorophore. The calculated pKa values were then compared to trajectories using a conventional fixed charge force field (Amber03 ff). We found that the position of water molecules included in the pKa calculation had opposite effects on the pKa values between the trajectories from AMOEBA and Amber03 force fields. In AMOEBA trajectories, the inclusion of water molecules within 35 Å of the fluorophore decreased the difference between the predicted and experimental values, resulting in calculated pKa values that were within an average of 0.8 pKa unit from the experimental results. On the other hand, in Amber03 trajectories, including water molecules that were more than 5 Å from the fluorophore increased the differences between the calculated and experimental pKa values. The inaccuracy of pKa predictions determined from Amber03 trajectories was caused by a significant stabilization of the deprotonated chromophore's free energy compared to the result in AMOEBA. We rationalize the cutoffs for explicit water molecules when calculating pKa to better predict the electrostatic environment surrounding the fluorophore buried in GFP. We discuss how the results from this work will assist the prospective prediction of pKa values or other electrostatic effects in a wide variety of folded proteins.

Solvent paramagnetic relaxation enhancement as a versatile method for studying structure and dynamics of biomolecular systems

Solvent paramagnetic relaxation enhancement (sPRE) is a versatile nuclear magnetic resonance (NMR)-based method that allows characterization of the structure and dynamics of biomolecular systems through providing quantitative experimental information on solvent accessibility of NMR-active nuclei. Addition of soluble paramagnetic probes to the solution of a biomolecule leads to paramagnetic relaxation enhancement in a concentration-dependent manner. Here we review recent progress in the sPRE-based characterization of structural and dynamic properties of biomolecules and their complexes, and aim to deliver a comprehensive illustration of a growing number of applications of the method to various biological systems. We discuss the physical principles of sPRE measurements and provide an overview of available co-solute paramagnetic probes. We then explore how sPRE, in combination with complementary biophysical techniques, can further advance biomolecular structure determination, identification of interaction surfaces within protein complexes, and probing of conformational changes and low-population transient states, as well as deliver insights into weak, nonspecific, and transient interactions between proteins and co-solutes. In addition, we present examples of how the incorporation of solvent paramagnetic probes can improve the sensitivity of NMR experiments and discuss the prospects of applying sPRE to NMR metabolomics, drug discovery, and the study of intrinsically disordered proteins.

Mapping the per-residue surface electrostatic potential of CAPRIN1 along its phase-separation trajectory

Electrostatic interactions and charge balance are important for the formation of biomolecular condensates involving proteins and nucleic acids. However, a detailed, atomistic picture of the charge distribution around proteins during the phase-separation process is lacking. Here, we use solution NMR spectroscopy to measure residue-specific near-surface electrostatic potentials (ϕ_ENS) of the positively charged carboxyl-terminal intrinsically disordered 103 residues of CAPRIN1, an RNA-binding protein localized to membraneless organelles playing an important role in messenger RNA (mRNA) storage and translation. Measured ϕ_ENS values have been mapped along the adenosine triphosphate (ATP)-induced phase-separation trajectory. In the absence of ATP, ϕ_ENS values for the mixed state of CAPRIN1 are positive and large and progressively decrease as ATP is added. This is coupled to increasing interchain interactions, particularly between aromatic-rich and arginine-rich regions of the protein. Upon phase separation, CAPRIN1 molecules in the condensed phase are neutral (ϕ_ENS [Formula: see text] 0 mV), with ∼five molecules of ATP associated with each CAPRIN1 chain. Increasing the ATP concentration further inverts the CAPRIN1 electrostatic potential, so that molecules become negatively charged, especially in aromatic-rich regions, leading to re-entrance into a mixed phase. Our results collectively show that a subtle balance between electrostatic repulsion and interchain attractive interactions regulates CAPRIN1 phase separation and provides insight into how nucleotides, such as ATP, can induce formation of and subsequently dissolve protein condensates.

Ab initio machine learning of phase space averages

Equilibrium structures determine material properties and biochemical functions. We here propose to machine learn phase space averages, conventionally obtained by ab initio or force-field-based molecular dynamics (MD) or Monte Carlo (MC) simulations. In analogy to ab initio MD, our ab initio machine learning (AIML) model does not require bond topologies and, therefore, enables a general machine learning pathway to obtain ensemble properties throughout the chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. The AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data and to reach competitive prediction errors (mean absolute error ∼ 0.8 kcal/mol) for out-of-sample molecules-within milliseconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns of Boltzmann averages throughout the chemical compound space at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

Methodology-Centered Review of Molecular Modeling, Simulation, and Prediction of SARS-CoV-2

Despite tremendous efforts in the past two years, our understanding of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), virus-host interactions, immune response, virulence, transmission, and evolution is still very limited. This limitation calls for further in-depth investigation. Computational studies have become an indispensable component in combating coronavirus disease 2019 (COVID-19) due to their low cost, their efficiency, and the fact that they are free from safety and ethical constraints. Additionally, the mechanism that governs the global evolution and transmission of SARS-CoV-2 cannot be revealed from individual experiments and was discovered by integrating genotyping of massive viral sequences, biophysical modeling of protein-protein interactions, deep mutational data, deep learning, and advanced mathematics. There exists a tsunami of literature on the molecular modeling, simulations, and predictions of SARS-CoV-2 and related developments of drugs, vaccines, antibodies, and diagnostics. To provide readers with a quick update about this literature, we present a comprehensive and systematic methodology-centered review. Aspects such as molecular biophysics, bioinformatics, cheminformatics, machine learning, and mathematics are discussed. This review will be beneficial to researchers who are looking for ways to contribute to SARS-CoV-2 studies and those who are interested in the status of the field.

Predicting the Orientation of Adsorbed Proteins Steered with Electric Fields Using a Simple Electrostatic Model

Under the most common experimental conditions, the adsorption of proteins to solid surfaces is a spontaneous process that leads to a rather compact layer of randomly oriented molecules. However, controlling such orientation is critically important for the development of catalytic surfaces. In this regard, the use of electric fields is one of the most promising alternatives. Our work is motivated by experimental observations that show important differences in catalytic activity of a trypsin-covered surface, which depended on the applied potential during the adsorption. Even though adsorption results from the combination of several processes, we were able to determine that (under the selected conditions) mean-field electrostatics play a dominant role, determining the orientation and yielding a difference in catalytic activity. We simulated the electrostatic potential numerically, using an implicit-solvent model based on the linearized Poisson-Boltzmann equation. This was implemented in an extension of the code PyGBe that included an external electric field, and rendered the electrostatic component of the solvation free energy. Our model (extensions available at the Github repository) allowed estimating the overall affinity of the protein with the surface, and their most likely orientation as a function of the potential applied. Our results show that the active sites of trypsin are, on average, more exposed when the electric field is negative, which agrees with the experimental results of catalytic activity, and confirm the premise that electrostatic interactions can be used to control the orientation of adsorbed proteins.

Counterion condensation theory for finite polyelectrolyte and salt concentrations

In the present work we analyze the physical fundamentals of Manning's counterion condensation using his charged line model in a simple salt solution. We extend the theory for the cases of finite saline concentration and polymeric concentration tending to zero and the case of both finite concentrations. To find the equilibrium between the phases of free and condensed counterions, besides minimizing the free energy, we deduce an auxiliary equation to determine the two characteristic parameters of the theory, the fraction of condensed counterions and the volume of condensation. We compare the obtained results in the present work for only one infinite charged line with the ones of counterion condensation theory by Schurr and Fujimoto. We find that the linear density of critical charge depends on the concentration of added salt and takes values higher than one, instead of the unitary value predicted by Manning. We obtain the equations by the activity and osmotic coefficients in function of the critical charge density. We compare them with the corresponding equations by Manning for these parameters. We extend the counterion condensation theory to solutions of linear polyelectrolytes for finite saline and polymeric concentrations using a cell model. We modify the electrostatic contribution to the Gibbs energy adding, to the traditional one calculated by Manning, the energy excess due to the macroion present in a cylindrical cell. We apply the theory to obtain the osmotic coefficient and we compare our results with experimental data of DNA osmotic coefficient and with theoretical adjustment using the Poisson-Boltzmann equation.

Assessment of the Components of the Electrostatic Potential of Proteins in Solution: Comparing Experiment and Theory

In this work, the components of the protein electrostatic potentials in solution are analyzed with NMR paramagnetic relaxation enhancement experiments and compared with continuum solution theory, and multiscale simulations. To determine the contributions of the solution components, we analyze them at different ionic strengths from 0 to 745 mM. A theoretical approximation allows the determination of the electrostatic potential at a given proton without reference to the protein structure given the ratio of paramagnetic relaxation enhancements rates between a cationic and an anionic probe. The results derived from simulations show good agreement with experiment and simple continuum solvent theory for many of the residues. A discrepancy including a switch of sign of the electrostatic potential was observed for particular residues. By considering the components of the potential, we found the discrepancy is mainly caused by angular correlations of the probe molecules with these residues. The correction for the correlations allows a more accurate analysis of the experiments determining the electrostatic potential of proteins in solution.

A fast-slow method to treat solute dynamics in explicit solvent

Aiming to reduce the computational cost in the current explicit solvent molecular dynamics (MD) simulation, this paper proposes a fast-slow method for the fast MD simulation of biomolecules in explicit solvent. This fast-slow method divides the entire system into two parts: a core layer (typically solute or biomolecule) and a peripheral layer (typically solvent molecules). The core layer is treated using standard MD method but the peripheral layer is treated by a slower dynamics method to reduce the computational cost. We compared four different simulation models in testing calculations for several small proteins. These include gas-phase, implicit solvent, fast-slow explicit solvent and standard explicit solvent MD simulations. Our study shows that gas-phase and implicit solvent models do not provide a realistic solvent environment and fail to correctly produce reliable dynamic structures of proteins. On the other hand, the fast-slow method can essentially reproduce the same solvent effect as the standard explicit solvent model while gaining an order of magnitude in efficiency. This fast-slow method thus provides an efficient approach for accelerating the MD simulation of biomolecules in explicit solvent.

Evaluation of Neurotropic Activity and Molecular Docking Study of New Derivatives of pyrano[4″,3″:4',5']pyrido[3',2':4,5]thieno[3,2-d]pyrimidines on the Basis of pyrano[3,4-c]pyridines

Background: Heterocyclic compounds and their fused analogs, which contain pharmacophore fragments such as pyridine, thiophene and pyrimidine rings, are of great interest due to their broad spectrum of biological activity. Chemical compounds containing two or more pharmacophore groups due to additional interactions with active receptor centers usually enhance biological activity and can even lead to a new type of activity. The search for new effective neurotropic drugs in the series of derivatives of heterocycles containing pharmacophore groups in organic, bioorganic and medical chemistry is a serious problem. Methods: Modern methodology of drugs involves synthesis, physicochemical study, molecular modeling and selection of active compounds through virtual screening and experimental evaluation of the biological activity of new chimeric compounds with pharmacophore fragments. For the synthesis of new compounds, classical organic methods were used and developed. For the evaluation of neurotropic activity of new synthesized compounds, some biological methods were used according to indicators characterizing anticonvulsant, sedative and antianxiety activity as well as side effects. For docking analysis, various soft ware packages and methods were used. Results: As a result of multistep reactions, 11 new, tri- and tetracyclic heterocyclic systems were obtained. The studied compounds exhibit protection against pentylenetetrazole (PTZ) seizures as well as some psychotropic effects. The biological assays evidenced that nine of the eleven studied compounds showed a high anticonvulsant activity by antagonism with pentylenetetrazole. The toxicity of the compounds is low, and they do not induce muscle relaxation in the studied doses. According to the study of psychotropic activity, it was found that the selected compounds have an activating behavior and anxiolytic effects on the “open field” and “elevated plus maze” (EPM) models. The data obtained indicate the anxiolytic (antianxiety) activity of the derivatives of tricyclic thieno[2,3-b]pyridines and tetracyclic pyridothieno[3,2-d]pyrimidin-8-ones, especially pronounced in compounds 3b–f and 4e. The studied compounds increase the latent time of first immobilization on the “forced swimming” (FS) model and exhibit antidepressant effects; compounds 3e and 3f especially exhibit these effects, similarly to diazepam. Docking studies revealed that compounds 3c and 4b bound tightly in the active site of γ-aminobutyric acid type A (GABA_A) receptors with a value of the scoring function that estimates free energy of binding (∆G) at −10.0 ± 5 kcal/mol. Compound 4e showed the best affinity ((∆G) at −11.0 ± 0.54 kcal/mol) and seems to be an inhibitor of serotonin (SERT) transporter. Compounds 3c–f and 4e practically bound with the groove of T4L of 5HT_1A and blocked it completely, while the best affinity observed was in compound 3f ((∆G) at −9.3 ± 0.46 kcal/mol). Conclusions: The selected compounds have an anticonvulsant, activating behavior and anxiolytic effects and at the same time exhibit antidepressant effects.

Electrostatic free energies carry structural information on nucleic acid molecules in solution

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters—the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ET e) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Protein Electrostatics Investigated through Paramagnetic NMR for Nonpolar Groups

Experimental validation of theoretical models for protein electrostatics remains rare. Recently, we have developed a paramagnetic NMR-based method for de novo determination of effective near-surface electrostatic potentials, which allows for straightforward examination of electrostatic models for biomolecules. In the current work, we expand this method and demonstrate that effective near-surface electrostatic potentials can readily be determined from ¹H paramagnetic relaxation enhancement (PRE) data for protein C_αH and CH₃ groups. The experimental data were compared with those predicted from the Poisson-Boltzmann theory. The impact of structural dynamics on the effective near-surface electrostatic potentials was also assessed. The agreement between the experimental and theoretical data was particularly good for methyl ¹H nuclei. Compared to the conventional pK_a-based validation, our paramagnetic NMR-based approach can provide a far larger number of experimental data that can directly be used to examine the validity of theoretical electrostatic models for proteins.

Direct Measurement of Interhelical DNA Repulsion and Attraction by Quantitative Cross-Linking

To better understand the forces that mediate nucleic acid compaction in biology, we developed the disulfide cross-linking approach xHEED (X-linking of Helices to measure Electrostatic Effects at Distance) to measure the distance-dependent encounter frequency of two DNA helices in solution. Using xHEED, we determined the distance that the electrostatic potential extends from DNA helices, the dependence of this distance on ionic conditions, and the magnitude of repulsion when two helices approach one another. Across all conditions tested, the potential falls to that of the bulk solution within 15 Å of the major groove surface. For separations of ∼30 Å, we measured a repulsion of 1.8 kcal/mol in low monovalent ion concentration (30 mM Na+), with higher Na+ concentrations ameliorating this repulsion, and 2 M Na+ or 100 mM Mg2+ eliminating it. Strikingly, we found full screening at very low Co3+ concentrations and net attraction at higher concentrations, without the higher-order DNA condensation that typically complicates studies of helical attraction. Our measurements define the relevant distances for electrostatic interactions of nucleic-acid helices in biology and introduce a new method to propel further understanding of how these forces impact biological processes.

Mycobactin Analogues with Excellent Pharmacokinetic Profile Demonstrate Potent Antitubercular Specific Activity and Exceptional Efflux Pump Inhibition

In this study, we have designed and synthesized pyrazoline analogues that partially mimic the structure of mycobactin, to address the requirement of novel therapeutics to tackle the emerging global challenge of antimicrobial resistance (AMR). Our investigation resulted in the identification of novel lead compounds 44 and 49 as potential mycobactin biosynthesis inhibitors against mycobacteria. Moreover, candidates efficiently eradicated intracellularly surviving mycobacteria. Thermofluorimetric analysis and molecular dynamics simulations suggested that compounds 44 and 49 bind to salicyl-AMP ligase (MbtA), a key enzyme in the mycobactin biosynthetic pathway. To the best of our knowledge, these are the first rationally designed mycobactin inhibitors to demonstrate an excellent in vivo pharmacokinetic profile. In addition, these compounds also exhibited more potent whole-cell efflux pump inhibition than known efflux pump inhibitors verapamil and chlorpromazine. Results from this study pave the way for the development of 3-(2-hydroxyphenyl)-5-(aryl)-pyrazolines as a new weapon against superbug-associated AMR challenges.

Scanning the RBD-ACE2 molecular interactions in Omicron variant

The emergence of new SARS-CoV-2 variants poses a threat to the human population where it is difficult to assess the severity of a particular variant of the virus. Spike protein and specifically its receptor binding domain (RBD) which makes direct interaction with the ACE2 receptor of the human has shown prominent amino acid substitutions in most of the Variants of Concern. Here, by using all-atom molecular dynamics simulations we compare the interaction of Wild-type RBD/ACE2 receptor complex with that of the latest Omicron variant of the virus. We observed a very interesting diversification of the charge, dynamics and energetics of the protein complex formed upon mutations. These results would help us in understanding the molecular basis of binding of the Omicron variant with that of SARS-CoV-2 Wild-type.

Analytical solution of a linear nonlocal Poisson-Boltzmann equation with multiple charges in a spherical solute region surrounded by a water spherical shell

In this paper, an analytical solution of a linear nonlocal Poisson-Boltzmann equation (NPBE) test model with multiple charges in a spherical solute region surrounded by a water spherical shell is derived as a single series of Legendre polynomials and modified spherical Bessel functions. The classic Kirkwood ball model is then shown to be a special case of the NPBE test model so that its analytical solution is regained from a double series of associated Legendre polynomials (derived by Kirkwood in 1934) to a new single series of Legendre polynomials, sharply reducing its computational cost. As an application of these series solutions, a comparison study is done to demonstrate the differences between the Kirkwood and NPBE test models.

MLIMC: Machine Learning-Based Implicit-Solvent Monte Carlo

Monte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule. The two most popular implicit-solvent models are the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way such that the GB model is an approximation to the PB model but is much faster in simulation time. In this work, we develop a machine learning-based implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both implicit solvent models in accuracy and efficiency. Specifically, the MLIMC method uses a fast and accurate PB-based machine learning (PBML) scheme to compute the electrostatic solvation free energy at each step. We validate our MLIMC method by using a benzene-water system and a protein-water system. We show that the proposed MLIMC method has great advantages in speed and accuracy for molecular structure optimization and prediction.

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg2+) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg2+ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg2+ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg2+-excess concentrations and comparison with fluorescence titration measurements shows that on average 20-30% of the Mg2+ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.

The mutual interactions of RNA, counterions and water - quantifying the electrostatics at the phosphate-water interface

The structure and dynamics of polyanionic biomolecules, like RNA, are decisively determined by their electric interactions with the water molecules and the counterions in the environment. The solvation dynamics of the biomolecules involves a subtle balance of non-covalent and many-body interactions with structural fluctuations due to thermal motion occurring in a femto- to subnanosecond time range. This complex fluctuating many particle scenario is crucial in defining the properties of biological interfaces with far reaching significance for the folding of RNA structures and for facilitating RNA-protein interactions. Given the inherent complexity, suited model systems, carefully calibrated and benchmarked by experiments, are required to quantify the relevant interactions of RNA with the aqueous environment. In this feature article we summarize our recent progress in the understanding of the electrostatics at the biological interface of double stranded RNA (dsRNA) and transfer RNA (tRNA). Dimethyl phosphate (DMP) is introduced as a viable and rigorously accessible model system allowing the interaction strength with water molecules and counterions, their relevant fluctuation timescales and the spatial reach of interactions to be established. We find strong (up to ≈90 MV cm-1) interfacial electric fields with fluctuations extending up to ≈20 THz and demonstrate how the asymmetric stretching vibration νAS(PO2)- of the polarizable phosphate group can serve as the most sensitive probe for interfacial interactions, establishing a rigorous link between simulations and experiment. The approach allows for the direct interfacial observation of interactions of biologically relevant Mg2+ counterions with phosphate groups in contact pair geometries via the rise of a new absorption band imposed by exchange repulsion interactions at short interatomic distances. The systematic extension to RNA provides microscopic insights into the changes of the hydration structure that accompany the temperature induced melting of the dsRNA double helix and quantify the ionic interactions in the folded tRNA. The results show that pairs of negatively charged phosphate groups and Mg2+ ions represent a key structural feature of RNA embedded in water. They highlight the importance of binding motifs made of contact pairs in the electrostatic stabilization of RNA structures that have a strong impact on the surface potential and enable the fine tuning of the local electrostatic properties which are expected to be relevant for mediating the interactions between biomolecules.

Generalizing Continuum Solvation in Crystal to Nonaqueous Solvents: Implementation, Parametrization, and Application to Molecules and Surfaces

We present an extension of a generalized finite-difference Poisson-Boltzmann (FDPB) continuum solvation model based on a self-consistent reaction field treatment to nonaqueous solvents. Implementation and reparametrization of the cavitation, dispersion, and structural (CDS) effects nonelectrostatic model are presented in CRYSTAL, with applications to both finite and infinite periodic systems. For neutral finite systems, computed errors with respect to available experimental data on free energies of solvation of 2523 solutes in 91 solvents, as well as 144 transfer energies from water to 14 organic solvents are on par with the reference SM12 solvation model for which the CDS parameters have been developed. Calculations performed on a TiO₂ anatase surface and compared to VASPsol data revealed an overall very good agreement of computed solvation energies, surface energies, as well as band structure changes upon solvation in three different solvents, validating the general applicability of the reparametrized FDPB approach to neutral nonperiodic and periodic solutes in aqueous and nonaqueous solvents. For ionic species, while the reparametrized CDS model led to large errors on free energies of solvation of anions, addition of a corrective term based on Abraham's acidity of the solvent significantly improved the accuracy of the proposed continuum solvation model, leading to errors on aqueous pK_a of a test set of 83 solutes divided by a factor of 4 compared to the reference solvation model based on density (SMD). Overall, therefore, these encouraging results demonstrate that the generalized FDPB continuum solvation model can be applied to a broad range of solutes in various solvents, ranging from finite neutral or charged solutes to extended periodic surfaces.

Reversible, Selective, Ultrawide-Range Variable Stiffness Control by Spatial Micro-Water Molecule Manipulation

Evolution has decided to gift an articular structure to vertebrates, but not to invertebrates, owing to their distinct survival strategies. An articular structure permits kinematic motion in creatures. However, it is inappropriate for creatures whose survival strategy depends on the high deformability of their body. Accordingly, a material in which the presence of the articular structure can be altered, allowing the use of two contradictory strategies, will be advantageous in diverse dynamic applications. Herein, spatial micro-water molecule manipulation, termed engineering on variable occupation of water (EVO), that is used to realize a material with dual mechanical modes that exhibit extreme differences in stiffness is introduced. A transparent and homogeneous soft material (110 kPa) reversibly converts to an opaque material embodying a mechanical gradient (ranging from 1 GPa to 1 MPa) by on-demand switching. Intensive theoretical analysis of EVO yields the design of spatial transformation scheme. The EVO gel accomplishes kinematic motion planning and shows great promise for multimodal kinematics. This approach paves the way for the development and application of smart functional materials.

Quantifying the Separation of Positive and Negative Areas in Electrostatic Potential for Predicting Feasibility of Ammonium Sulfate for Protein Crystallization

Ammonium sulfate (AS) and poly(ethylene glycol) (PEG) are the most popular precipitants in protein crystallization. Some proteins are preferably crystallized by AS, while some are by PEG. The electrostatic potential is related to the preference of the precipitant agents. The iso-surfaces of the electrostatic potentials for the AS-crystallized proteins display a common shape and a distinct separation between the positive and negative areas. In contrast, the PEG-crystallized proteins show unclear positive and negative separation. In this work, we propose schemes to quantitatively evaluate the separation for predicting which precipitant is favorable for crystal growth between AS or PEG. Three methods were attempted to quantify the amplitude of the separation, separation distance, dipole moment, and shape regularity. The positive and negative areas are approximated to the spherical potentials caused by point charges. The first method is a measurement of the distance between the positive and negative point charges. The second one is an assessment including the quantity of electric charge into the distance. The last one is an approach monitoring the clarity of the positive and negative separation. The average value for 25 kinds of AS-preferring proteins was higher than that for the PEG-preferring ones in all three methods. Therefore, every method can distinguish the proteins preferring AS for crystal growth from those preferring PEG. These methods require an iso-surface of the electrostatic potential depicted at a certain contouring value. The shape of the iso-surface depends on the contouring value. The dependency on contour was examined by depicting the iso-surfaces of electrostatic potential with three values at ±0.8, ±0.5, and ±0.2 kT/e. While reducing the contouring value leads to the increase in separation distance and the decrease in shape regularity, dipole moment is independent of the alteration of contouring value. While the AS-preferring proteins are distinguishable from the PEG-preferring ones in any contouring values, the iso-surface at ±0.5 kT/e seems adequate for regular use. The dipole moment assessment is feasible for the choice of potent precipitants for crystal growth in experiments.

The SARS-CoV-2 spike protein is vulnerable to moderate electric fields

Most of the ongoing projects aimed at the development of specific therapies and vaccines against COVID-19 use the SARS-CoV-2 spike (S) protein as the main target. The binding of the spike protein with the ACE2 receptor (ACE2) of the host cell constitutes the first and key step for virus entry. During this process, the receptor binding domain (RBD) of the S protein plays an essential role, since it contains the receptor binding motif (RBM), responsible for the docking to the receptor. So far, mostly biochemical methods are being tested in order to prevent binding of the virus to ACE2. Here we show, with the help of atomistic simulations, that external electric fields of easily achievable and moderate strengths can dramatically destabilise the S protein, inducing long-lasting structural damage. One striking field-induced conformational change occurs at the level of the recognition loop L3 of the RBD where two parallel beta sheets, believed to be responsible for a high affinity to ACE2, undergo a change into an unstructured coil, which exhibits almost no binding possibilities to the ACE2 receptor. We also show that these severe structural changes upon electric-field application also occur in the mutant RBDs corresponding to the variants of concern (VOC) B.1.1.7 (UK), B.1.351 (South Africa) and P.1 (Brazil). Remarkably, while the structural flexibility of S allows the virus to improve its probability of entering the cell, it is also the origin of the surprising vulnerability of S upon application of electric fields of strengths at least two orders of magnitude smaller than those required for damaging most proteins. Our findings suggest the existence of a clean physical method to weaken the SARS-CoV-2 virus without further biochemical processing. Moreover, the effect could be used for infection prevention purposes and also to develop technologies for in-vitro structural manipulation of S. Since the method is largely unspecific, it can be suitable for application to other mutations in S, to other proteins of SARS-CoV-2 and in general to membrane proteins of other virus types.

The SARS-CoV-2 Spike protein is essential for viral infectivity and binds to the host receptor ACE2. Here, the authors present MD simulations of the Spike protein and its variants of concern and observe that the Spike protein is destabilised by moderate static electric fields, and undergoes field-induced conformational changes that hinder binding to ACE2.

What Binds Cationic Photosensitizers Better: Brownian Dynamics Reveals Key Interaction Sites on Spike Proteins of SARS-CoV, MERS-CoV, and SARS-CoV-2

We compared the electrostatic properties of the spike proteins (S-proteins) of three coronaviruses, SARS-CoV, MERS-CoV, and SARS-CoV-2, and their interactions with photosensitizers (PSs), octacationic octakis(cholinyl)zinc phthalocyanine (Zn-PcChol₈₊) and monocationic methylene blue (MB). We found a major common PS binding site at the connection of the S-protein stalk and head. The molecules of Zn-PcChol₈₊ and MB also form electrostatic encounter complexes with large area of negative electrostatic potential at the head of the S-protein of SARS-CoV-2, between fusion protein and heptad repeat 1 domain. The top of the SARS-CoV spike head demonstrates a notable area of electrostatic contacts with Zn-PcChol₈₊ and MB that corresponds to the N-terminal domain. The S-protein protomers of SARS-CoV-2 in “open” and “closed” conformations demonstrate different ability to attract PS molecules. In contrast with Zn-PcChol₈₊, MB possesses the ability to penetrate inside the pocket formed as a result of SARS-CoV-2 receptor binding domain transition into the “open” state. The existence of binding site for cationic PSs common to the S-proteins of SARS-CoV, SARS-CoV-2, and MERS-CoV creates prospects for the wide use of this type of PSs to combat the spread of coronaviruses.

ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson-Boltzmann equation

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal-oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS-CoV-2 and the ACE2 receptor. All the calculations are repeated by using the well-known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.