Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions

PypKa server: online pKa predictions and biomolecular structure preparation with precomputed data from PDB and AlphaFold DB

When preparing biomolecular structures for molecular dynamics simulations, pKa calculations are required to provide at least a representative protonation state at a given pH value. Neglecting this step and adopting the reference protonation states of the amino acid residues in water, often leads to wrong electrostatics and nonphysical simulations. Fortunately, several methods have been developed to prepare structures considering the protonation preference of residues in their specific environments (pKa values), and some are even available for online usage. In this work, we present the PypKa server, which allows users to run physics-based, as well as ML-accelerated methods suitable for larger systems, to obtain pKa values, isoelectric points, titration curves, and structures with representative pH-dependent protonation states compatible with commonly used force fields (AMBER, CHARMM, GROMOS). The user may upload a custom structure or submit an identifier code from PBD or UniProtKB. The results for over 200k structures taken from the Protein Data Bank and the AlphaFold DB have been precomputed, and their data can be retrieved without extra calculations. All this information can also be obtained from an application programming interface (API) facilitating its usage and integration into existing pipelines as well as other web services. The web server is available at pypka.org.

Building polarization into protein-inhibitor binding dynamics in rational drug design for rheumatoid arthritis

Standard force field-based simulations to accomplish structure-based evaluations of lead molecules is a powerful tool. Combining protein fragmentation into tractable sub-systems with continuum solvation method is envisaged to enable quantum mechanics-based electronic structure calculations of macromolecules in their realistic environment. This along with incorporation of many-body polarization effect in molecular dynamics simulations may augment an accurate description of electrostatics of protein-inhibitor systems for effective drug design. Rheumatoid arthritis (RA) is a complex autoimmune disorder plagued by the ceiling effect of current targeted therapies, encouraging identification of new druggable targets and corresponding drug design to tackle the refractory form of disease. In this study, polarization-inclusive force field approach has been used to model protein solvation and ligand binding for 'Mitogen-activated protein kinase' (MAP3K8), a regulatory node of notable pharmacological relevance in RA synovial biology. For MAP3K8 inhibitors belonging to different scaffold series, the calculations illustrated differential electrostatic contribution to their relative binding affinities and successfully explained examples from available structure-activity relationship studies. Results from this study exemplified i) the advantage of this approach in reliably ranking inhibitors having close nanomolar range activities for the same target; and ii) its prospective application in lead molecule identification aiding drug discovery efforts in RA.Communicated by Ramaswamy H. Sarma.

Similarities and Differences in Ligand Binding to Protein and RNA Targets: The Case of Riboflavin

It is nowadays clear that RNA molecules can play active roles in several biological processes. As a result, an increasing number of RNAs are gradually being identified as potentially druggable targets. In particular, noncoding RNAs can adopt highly organized conformations that are suitable for drug binding. However, RNAs are still considered challenging targets due to their complex structural dynamics and high charge density. Thus, elucidating relevant features of drug-RNA binding is fundamental for advancing drug discovery. Here, by using Molecular Dynamics simulations, we compare key features of ligand binding to proteins with those observed in RNA. Specifically, we explore similarities and differences in terms of (i) conformational flexibility of the target, (ii) electrostatic contribution to binding free energy, and (iii) water and ligand dynamics. As a test case, we examine binding of the same ligand, namely riboflavin, to protein and RNA targets, specifically the riboflavin (RF) kinase and flavin mononucleotide (FMN) riboswitch. The FMN riboswitch exhibited enhanced fluctuations and explored a wider conformational space, compared to the protein target, underscoring the importance of RNA flexibility in ligand binding. Conversely, a similar electrostatic contribution to the binding free energy of riboflavin was found. Finally, greater stability of water molecules was observed in the FMN riboswitch compared to the RF kinase, possibly due to the different shape and polarity of the pockets.

Coupling finite and boundary element methods to solve the Poisson-Boltzmann equation for electrostatics in molecular solvation

The Poisson-Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the linearised Poisson-Boltzmann equation, where the finite element method is applied in a confined solute region and the boundary element method in the external solvent region. As a proof-of-concept exercise, we use the simplest methods available: Johnson-Nédélec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. As validation, we compare against well-established finite difference solvers for an extensive binding energy data set, and with the finite difference code APBS (to 0.5%) for Gaussian permittivities. We also show scaling results from protein G B1 (955 atoms) up to immunoglobulin G (20,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large-sized problems on a single workstation. The development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments that consider space-varying field parameters, and mixed linear-nonlinear schemes for molecular electrostatics with implicit solvent models.

High Charge Density in Peptide Dendrimers is Required to Destabilize Membranes: Insights into Endosome Evasion

Peptide dendrimers are a type of branched, symmetric, and topologically well-defined molecule that have already been used as delivery systems for nucleic acid transfection. Several of the most promising sequences showed high efficiency in many key steps of transfection, namely, binding siRNA, entering cells, and evading the endosome. However, small changes to the peptide dendrimers, such as in the hydrophobic core, the amino acid chirality, or the total available charges, led to significantly different experimental results with unclear mechanistic insights. In this work, we built a computational model of several of those peptide dendrimers (MH18, MH13, and MH47) and some of their variants to study the molecular details of the structure and function of these molecules. We performed CpHMD simulations in the aqueous phase and in interaction with a lipid bilayer to assess how conformation and protonation are affected by pH in different environments. We found that while the different peptide dendrimer sequences lead to no substantial structural differences in the aqueous phase, the total charge and, more importantly, the total charge density are key for the capacity of the dendrimer to interact and destabilize the membrane. These dendrimers become highly charged when the pH changes from 7.5 to 4.5, and the presence of a high charge density, which is decreased for MH47 that has four fewer titratable lysines, is essential to trigger membrane destabilization. These findings are in excellent agreement with the experimental data and help us to understand the high efficiency of some dendrimers and why the dendrimer MH47 is unable to complete the transfection process. This evidence provides further understanding of the mode of action of these peptide dendrimers and will be pivotal for the future design of new sequences with improved transfection capabilities.

Molecular Ballet: Investigating the Complex Interaction between Self-Assembling Dendrimers and Human Serum Albumin via Computational and Experimental Methods

Dendrimers, intricate macromolecules with highly branched nanostructures, offer unique attributes including precise control over size, shape, and functionality, making them promising candidates for a wide range of biomedical applications. The exploration of their interaction with biological environments, particularly human serum albumin (HSA), holds significant importance for biomedical utilization. In this study, the interaction between HSA and a recently developed self-assembling amphiphilic dendrimer (AD) was investigated using various experimental techniques. Fluorescence spectroscopy and isothermal titration calorimetry revealed moderate interactions between the protein and the AD nanomicelles (NMs), primarily attributed to favorable enthalpic contributions arising from electrostatic interactions and hydrogen bonding. Structural analysis indicated minimal changes in HSA upon complexation with the AD NMs, which was further supported by computational simulations demonstrating stable interactions at the atomistic level. These findings provide valuable insights into the binding mechanisms and thermodynamic parameters governing HSA/AD NM interactions, thereby contributing to the understanding of their potential biomedical applications.

Influence of ion and hydration atmospheres on RNA structure and dynamics: insights from advanced theoretical and computational methods

RNA, a highly charged biopolymer composed of negatively charged phosphate groups, defies electrostatic repulsion to adopt well-defined, compact structures. Hence, the presence of positively charged metal ions is crucial not only for RNA's charge neutralization, but they also coherently decorate the ion atmosphere of RNA to stabilize its compact fold. This feature article elucidates various modes of close RNA-ion interactions, with a special emphasis on Mg2+ as an outer-sphere and inner-sphere ion. Through examples, we highlight how inner-sphere chelated Mg2+ stabilizes RNA pseudoknots, while outer-sphere ions can also exert long-range electrostatic interactions, inducing groove narrowing, coaxial helical stacking, and RNA ring formation. In addition to investigating the RNA's ion environment, we note that the RNA's hydration environment is relatively underexplored. Our study delves into its profound interplay with the structural dynamics of RNA, employing state-of-the-art atomistic simulation techniques. Through examples, we illustrate how specific ions and water molecules are associated with RNA functions, leveraging atomistic simulations to identify preferential ion binding and hydration sites. However, understanding their impact(s) on the RNA structure remains challenging due to the involvement of large length and long time scales associated with RNA's dynamic nature. Nevertheless, our contributions and recent advances in coarse-grained simulation techniques offer insights into large-scale structural changes dynamically linked to the RNA ion atmosphere. In this connection, we also review how different cutting-edge computational simulation methods provide a microscopic lens into the influence of ions and hydration on RNA structure and dynamics, elucidating distinct ion atmospheric components and specific hydration layers and their individual and collective impacts.

Exciton interactions of chlorophyll tetramer in water-soluble chlorophyll-binding protein BoWSCP

The exciton interaction of four chlorophyll a (Chl a) molecules in a symmetrical tetrameric complex of the water-soluble chlorophyll-binding protein BoWSCP was analyzed in the pH range of 3-11. Exciton splitting ΔE = 232 ± 2 cm-1 of the Qy band of Chl a into two subcomponents with relative intensities of 78.1 ± 0.7 % and 21.9 ± 0.7 % was determined by a joint decomposition of the absorption and circular dichroism spectra into Gaussian functions. The exciton coupling parameters were calculated based on the BoWSCP atomic structure in three approximations: the point dipole model, the distributed atomic monopoles, and direct ab initio calculations in the TDDFT/PCM approximation. The Coulomb interactions of monomers were calculated within the continuum model using three values of optical permittivity. The models based on the properties of free Chl a in solution suffer from significant errors both in estimating the absolute value of the exciton interaction and in the relative intensity of exciton transitions. Calculations within the TDDFT/PCM approximation reproduce the experimentally determined parameters of the exciton splitting and the relative intensities of the exciton bands. The following factors of pigment-protein and pigment-pigment interactions were examined: deviation of the macrocycle geometry from the planar conformation of free Chl; the formation of hydrogen bonds between the macrocycle and water molecules; the overlap of wave functions of monomers at close distances. The most significant factor is the geometrical deformation of the porphyrin macrocycle, which leads to an increase in the dipole moment of Chl monomer from 5.5 to 6.9 D and to a rotation of the dipole moment by 15° towards the cyclopentane ring. The contributions of resonant charge-transfer states to the wave functions of the Chl dimer were determined and the transition dipole moments of the symmetric and antisymmetric charge-transfer states were estimated.

Molecular mechanisms and evolutionary robustness of a color switch in proteorhodopsins

Proteorhodopsins are widely distributed photoreceptors from marine bacteria. Their discovery revealed a high degree of evolutionary adaptation to ambient light, resulting in blue- and green-absorbing variants that correlate with a conserved glutamine/leucine at position 105. On the basis of an integrated approach combining sensitivity-enhanced solid-state nuclear magnetic resonance (ssNMR) spectroscopy and linear-scaling quantum mechanics/molecular mechanics (QM/MM) methods, this single residue is shown to be responsible for a variety of synergistically coupled structural and electrostatic changes along the retinal polyene chain, ionone ring, and within the binding pocket. They collectively explain the observed color shift. Furthermore, analysis of the differences in chemical shift between nuclei within the same residues in green and blue proteorhodopsins also reveals a correlation with the respective degree of conservation. Our data show that the highly conserved color change mainly affects other highly conserved residues, illustrating a high degree of robustness of the color phenotype to sequence variation.

Development and test of highly accurate endpoint free energy methods. 3: partition coefficient prediction using a Poisson-Boltzmann method combined with a solvent accessible surface area model for SAMPL challenges

Accurately predicting solvation free energy is the key to predict protein-ligand binding free energy. In addition, the partition coefficient (log P), which is an important physicochemical property that determines the distribution of a drug in vivo, can be derived directly from transfer free energies, i.e., the difference between solvation free energies (SFEs) in different solvents. Within the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL) 9 challenge, we applied the Poisson-Boltzmann (PB) surface area (SA) approach to predict the toluene/water transfer free energy and partition coefficient (log Ptoluene/water) from SFEs. For each solute, only a single conformation automatically generated by the free software Open Babel was used. The PB calculation directly adopts our previously optimized boundary definition - a set of general AMBER force field 2 (GAFF2) atom-type based sphere radii for solute atoms. For the non-polar SA model, we newly developed the solvent-related molecular surface tension parameters γ and offset b for toluene and cyclohexane targeting experimental SFEs. This approach yielded the highest predictive accuracy in terms of root mean square error (RMSE) of 1.52 kcal mol-1 in transfer free energy for 16 small drug molecules among all 18 submissions in the SAMPL9 blind prediction challenge. The re-evaluation of the challenge set using multi-conformation strategies based on molecular dynamics (MD) simulations further reduces the prediction RMSE to 1.33 kcal mol-1. At the same time, an additional evaluation of our PBSA method on the SAMPL5 cyclohexane/water distribution coefficient (log Dcyclohexane/water) prediction revealed that our model outperformed COSMO-RS, the best submission model with RMSEPBSA = 1.88 versus RMSECOSMO-RS = 2.11 log units. Two external log Ptoluene/water and log Pcyclohexane/water datasets that contain 110 and 87 data points, respectively, are collected for extra validation and provide an in-depth insight into the error source of the PBSA method.

In Silico Screening of Natural Flavonoids against 3-Chymotrypsin-like Protease of SARS-CoV-2 Using Machine Learning and Molecular Modeling

The "Long-COVID syndrome" has posed significant challenges due to a lack of validated therapeutic options. We developed a novel multi-step virtual screening strategy to reliably identify inhibitors against 3-chymotrypsin-like protease of SARS-CoV-2 from abundant flavonoids, which represents a promising source of antiviral and immune-boosting nutrients. We identified 57 interacting residues as contributors to the protein-ligand binding pocket. Their energy interaction profiles constituted the input features for Machine Learning (ML) models. The consensus of 25 classifiers trained using various ML algorithms attained 93.9% accuracy and a 6.4% false-positive-rate. The consensus of 10 regression models for binding energy prediction also achieved a low root-mean-square error of 1.18 kcal/mol. We screened out 120 flavonoid hits first and retained 50 drug-like hits after predefined ADMET filtering to ensure bioavailability and safety profiles. Furthermore, molecular dynamics simulations prioritized nine bioactive flavonoids as promising anti-SARS-CoV-2 agents exhibiting both high structural stability (root-mean-square deviation < 5 Å for 218 ns) and low MM/PBSA binding free energy (<-6 kcal/mol). Among them, KB-2 (PubChem-CID, 14630497) and 9-O-Methylglyceofuran (PubChem-CID, 44257401) displayed excellent binding affinity and desirable pharmacokinetic capabilities. These compounds have great potential to serve as oral nutraceuticals with therapeutic and prophylactic properties as care strategies for patients with long-COVID syndrome.

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Discovery of Potent and Selective CB2 Agonists Utilizing a Function-Based Computational Screening Protocol

Nowadays, the identification of agonists and antagonists represents a great challenge in computer-aided drug design. In this work, we developed a computational protocol enabling us to design/screen novel chemicals that are likely to serve as selective CB2 agonists. The principle of this protocol is that by calculating the ligand-residue interaction profile (LRIP) of a ligand binding to a specific target, the agonist-antagonist function of a compound is then able to be determined after statistical analysis and free energy calculations. This computational protocol was successfully applied in CB2 agonist development starting from a lead compound, and a success rate of 70% was achieved. The functions of the synthesized derivatives were determined by in vitro functional assays. Moreover, the identified potent CB2 agonists and antagonists strongly interact with the key residues identified using the already known potent CB2 agonists/antagonists. The analysis of the interaction profile of compound 6, a potent agonist, showed strong interactions with F2.61, I186, and F2.64, while compound 39, a potent antagonist, showed strong interactions with L17, W6.48, V6.51, and C7.42. Still, some residues including V3.32, T3.33, S7.39, F183, W5.43, and I3.29 are hotspots for both CB2 agonists and antagonists. More significantly, we identified three hotspot residues in the loop, including I186 for agonists, L17 for antagonists, and F183 for both. These hotspot residues are typically not considered in CB1/CB2 rational ligand design. In conclusion, LRIP is a useful concept in rationally designing a compound to possess a certain function.

DIAPH1-MFN2 interaction regulates mitochondria-SR/ER contact and modulates ischemic/hypoxic stress

Inter-organelle contact and communication between mitochondria and sarco/endoplasmic reticulum (SR/ER) maintain cellular homeostasis and are profoundly disturbed during tissue ischemia. We tested the hypothesis that the formin Diaphanous-1 (DIAPH1), which regulates actin dynamics, signal transduction and metabolic functions, contributes to these processes. We demonstrate that DIAPH1 interacts directly with Mitofusin-2 (MFN2) to shorten mitochondria-SR/ER distance, thereby enhancing mitochondria-ER contact in cells including cardiomyocytes, endothelial cells and macrophages. Solution structure studies affirm the interaction between the Diaphanous Inhibitory Domain and the cytosolic GTPase domain of MFN2. In male rodent and human cardiomyocytes, DIAPH1-MFN2 interaction regulates mitochondrial turnover, mitophagy, and oxidative stress. Introduction of synthetic linker construct, which shorten the mitochondria-SR/ER distance, mitigated the molecular and functional benefits of DIAPH1 silencing in ischemia. This work establishes fundamental roles for DIAPH1-MFN2 interaction in the regulation of mitochondria-SR/ER contact networks. We propose that targeting pathways that regulate DIAPH1-MFN2 interactions may facilitate recovery from tissue ischemia.

In silico structural and mechanical insights into bedaquiline resistance associated with high-grade non-synonymous mutations in atpE, mmpR5, and pepQ

Clinical resistance against bedaquiline (BDQ) remains intractable to anti-tuberculosis therapies since its introduction to the market over a decade ago. Herein, we investigated the structural and mechanical aspects of BDQ resistance in AtpE, MmpR5, and PepQ. The known target-specific resistant single non-synonymous mutations were refined to high-grade candidates. Thus, 7 (AtpE), 5 (MmpR5), and 1 (PepQ) single nucleotide polymorphisms (SNPs) and one insertion frameshift mutation in MmpR5 were recreated at the molecular level, and these phenotypic models were then directed to stringent dynamics to define time-scaled changes. The AtpE variants destabilized the structure; mainly, L59V, E61D, and I66M were detrimental to the complex fitness, while L74V and L114P boosted the BDQ binding to MmpR5. The first three and last two alterations gave rise to loss- and gain-of-function to AtpE and MmpR5, respectively. Hence, these five mutants are functionally relevant and therapeutically targetable hotspots of BDQ resistance. There were no noticeable changes in PepQ data analysis. The present study revealed that MmpR5 mutations confer BDQ resistance, whereas AtpE and PepQ SNPs display low susceptibility. These results were tallied with the published findings, which testified to the pursued method's reliability and accuracy. We hope these data and inferences could be helpful for the futuristic design of novel TB drugs.Communicated by Ramaswamy H. Sarma.

Development and test of highly accurate endpoint free energy methods. 2: Prediction of logarithm of n-octanol-water partition coefficient (logP) for druglike molecules using MM-PBSA method

The logarithm of n-octanol-water partition coefficient (logP) is frequently used as an indicator of lipophilicity in drug discovery, which has substantial impacts on the absorption, distribution, metabolism, excretion, and toxicity of a drug candidate. Considering that the experimental measurement of the property is costly and time-consuming, it is of great importance to develop reliable prediction models for logP. In this study, we developed a transfer free energy-based logP prediction model-FElogP. FElogP is based on the simple principle that logP is determined by the free energy change of transferring a molecule from water to n-octanol. The underlying physical method to calculate transfer free energy is the molecular mechanics-Poisson Boltzmann surface area (MM-PBSA), thus this method is named as free energy-based logP (FElogP). The superiority of FElogP model was validated by a large set of 707 structurally diverse molecules in the ZINC database for which the measurement was of high quality. Encouragingly, FElogP outperformed several commonly-used QSPR or machine learning-based logP models, as well as some continuum solvation model-based methods. The root-mean-square error (RMSE) and Pearson correlation coefficient (R) between the predicted and measured values are 0.91 log units and 0.71, respectively, while the runner-up, the logP model implemented in OpenBabel had an RMSE of 1.13 log units and R of 0.67. Given the fact that FElogP was not parameterized against experimental logP directly, its excellent performance is likely to be expanded to arbitrary organic molecules covered by the general AMBER force fields.

Benchmarking In Silico Tools for Cysteine pKa Prediction

Accurate estimation of the pK_a's of cysteine residues in proteins could inform targeted approaches in hit discovery. The pK_a of a targetable cysteine residue in a disease-related protein is an important physiochemical parameter in covalent drug discovery, as it influences the fraction of nucleophilic thiolate amenable to chemical protein modification. Traditional structure-based in silico tools are limited in their predictive accuracy of cysteine pK_a's relative to other titratable residues. Additionally, there are limited comprehensive benchmark assessments for cysteine pK_a predictive tools. This raises the need for extensive assessment and evaluation of methods for cysteine pK_a prediction. Here, we report the performance of several computational pK_a methods, including single-structure and ensemble-based approaches, on a diverse test set of experimental cysteine pK_a's retrieved from the PKAD database. The dataset consisted of 16 wildtype and 10 mutant proteins with experimentally measured cysteine pK_a values. Our results highlight that these methods are varied in their overall predictive accuracies. Among the test set of wildtype proteins evaluated, the best method (MOE) yielded a mean absolute error of 2.3 pK units, highlighting the need for improvement of existing pK_a methods for accurate cysteine pK_a estimation. Given the limited accuracy of these methods, further development is needed before these approaches can be routinely employed to drive design decisions in early drug discovery efforts.

Exploiting the co-crystal ligands shape, features and structure-based approaches for identification of SARS-CoV-2 Mpro inhibitors

SARS-CoV-2 enters the host cell through the ACE2 receptor and replicates its genome using an RNA-Dependent RNA Polymerase (RDRP). The functional RDRP is released from pro-protein pp1ab by the proteolytic activity of Main protease (Mpro) which is encoded within the viral genome. Due to its vital role in proteolysis of viral polyprotein chains, it has become an attractive potential drug target. We employed a hierarchical virtual screening approach to identify small synthetic protease inhibitors. Statistically optimized molecular shape and color-based features (various functional groups) from co-crystal ligands were used to screen different databases through various scoring schemes. Then, the electrostatic complementarity of screened compounds was matched with the most active molecule to further reduce the hit molecules' size. Finally, five hundred eighty-seven molecules were docked in Mpro catalytic binding site, out of which 29 common best hits were selected based on Glide and FRED scores. Five best-fitting compounds in complex with Mpro were subjected to MD simulations to analyze their structural stability and binding affinities with Mpro using MM/GB(PB)SA models. Modeling results suggest that identified hits can act as the lead compounds for designing better active Mpro inhibitors to enhance the chemical space to combat COVID-19.Communicated by Ramaswamy H. Sarma.

Development and test of highly accurate endpoint free energy methods. 1: Evaluation of ABCG2 charge model on solvation free energy prediction and optimization of atom radii suitable for more accurate solvation free energy prediction by the PBSA method

Accurate estimation of solvation free energy (SFE) lays the foundation for accurate prediction of binding free energy. The Poisson-Boltzmann (PB) or generalized Born (GB) combined with surface area (SA) continuum solvation method (PBSA and GBSA) have been widely used in SFE calculations because they can achieve good balance between accuracy and efficiency. However, the accuracy of these methods can be affected by several factors such as the charge models, polar and nonpolar SFE calculation methods and the atom radii used in the calculation. In this work, the performance of the ABCG2 (AM1-BCC-GAFF2) charge model as well as other two charge models, that is, RESP (Restrained Electrostatic Potential) and AM1-BCC (Austin Model 1-bond charge corrections), on the SFE prediction of 544 small molecules in water by PBSA/GBSA was evaluated. In order to improve the performance of the PBSA prediction based on the ABCG2 charge, we further explored the influence of atom radii on the prediction accuracy and yielded a set of atom radius parameters for more accurate SFE prediction using PBSA based on the ABCG2/GAFF2 by reproducing the thermodynamic integration (TI) calculation results. The PB radius parameters of carbon, oxygen, sulfur, phosphorus, chloride, bromide and iodine, were adjusted. New atom types, on, oi, hn1, hn2, hn3, were introduced to further improve the fitting performance. Then, we tuned the parameters in the nonpolar SFE model using the experimental SFE data and the PB calculation results. By adopting the new radius parameters and new nonpolar SFE model, the root mean square error (RMSE) of the SFE calculation for the 544 molecules decreased from 2.38 to 1.05 kcal/mol. Finally, the new radius parameters were applied in the prediction of protein-ligand binding free energies using the MM-PBSA method. For the eight systems tested, we could observe higher correlation between the experiment data and calculation results and smaller prediction errors for the absolute binding free energies, demonstrating that our new radius parameters can improve the free energy calculation using the MM-PBSA method.

Molecular Modeling Study of a Receptor-Orthosteric Ligand-Allosteric Modulator Signaling Complex

Allosteric modulators (AMs) are considered as a perpetual hotspot in research for their higher selectivity and various effects on orthosteric ligands (OL). They are classified in terms of their functionalities as positive, negative, or silent allosteric modulators (PAM, NAM, or SAM, respectively). In the present work, 11 pairs of three-dimensional (3D) structures of receptor-orthosteric ligand and receptor-orthosteric ligand-allosteric modulator complexes have been collected for the studies, including three different systems: GPCR, enzyme, and ion channel. Molecular dynamics (MD) simulations are applied to quantify the dynamic interactions in both the orthosteric and allosteric binding pockets and the structural fluctuation of the involved proteins. Our results showed that MD simulations of moderately large molecules or peptides undergo insignificant changes compared to crystal structure results. Furthermore, we also studied the conformational changes of receptors that bound with PAM and NAM, as well as the different allosteric binding sites in a receptor. There should be no preference for the position of the allosteric binding pocket after comparing the allosteric binding pockets of these three systems. Finally, we aligned four distinct β2 adrenoceptor structures and three N-methyl-d-aspartate receptor (NMDAR) structures to investigate conformational changes. In the β2 adrenoceptor systems, the aligned results revealed that transmembrane (TM) helices 1, 5, and 6 gradually increased outward movement from an enhanced inactive state to an improved active state. TM6 endured the most significant conformational changes (around 11 Å). For NMDAR, the bottom section of NMDAR's ligand-binding domain (LBD) experienced an upward and outward shift during the gradually activating process. In conclusion, our research provides insight into receptor-orthosteric ligand-allosteric modulator studies and the design and development of allosteric modulator drugs using MD simulation.

Overcoming pancreatic cancer immune resistance by codelivery of CCR2 antagonist using a STING-activating gemcitabine-based nanocarrier

STING agonist has recently gained much attention for cancer treatment, but the therapeutic potential of STING agonist is hampered by STING-associated tumor immune resistance. In this work, guided by both bioinformatics and computer modeling, we rationally designed a "one stone hits two birds" nanoparticle-based strategy to simultaneously activate STING innate immune response while eliminating STING-associated immune resistance for the treatment of pancreatic ductal adenocarcinoma (PDAC). We discovered that the ultra-small sized micellar system based on gemcitabine-conjugated polymer (PGEM), which showed superior capacity of penetration in pancreatic tumor spheroid model and orthotopic tumor model, could serve as a novel "STING agonist". The activation of STING signaling in dendritic cells (DCs) by PGEM increased both innate nature killer (NK) and adaptive anti-tumor T cell response. However, activation of STING signaling by PGEM in tumor cells also drove the induction of chemokines CCL2 and CCL7, resulting in immune resistance by recruiting tumor associated macrophage (TAM) and myeloid-derived suppressor cells (MDSCs). Through the combination of computer modeling and experimental screening, we developed a dual delivery modality by incorporating a CCR2 (the receptor shared by both CCL2 and CCL7) antagonist PF-6309 (PF) into PGEM micellar system. Our studies demonstrated that PGEM/PF formulation significantly reduced pancreatic tumor burden and induced potent anti-tumor immunity through reversing the CCL2/CCL7-mediated immunosuppression. Moreover, PGEM/PF sensitized PDAC tumors to anti-PD-1 therapy, leading to complete suppression/eradication of the tumors. Our work has shed light to the multi-faceted role of STING activation and provided a novel immunotherapy regimen to maximize the benefit of STING activation for PDAC treatment. In addition, this work paved a new way for bioinformatics and computer modeling-guided rational design of nanomedicine.

Investigation of the Fuzzy Complex between RSV Nucleoprotein and Phosphoprotein to Optimize an Inhibition Assay by Fluorescence Polarization

The interaction between Respiratory Syncytial Virus phosphoprotein P and nucleoprotein N is essential for the formation of the holo RSV polymerase that carries out replication. In vitro screening of antivirals targeting the N-P protein interaction requires a molecular interaction model, ideally consisting of a complex between N protein and a short peptide corresponding to the C-terminal tail of the P protein. However, the flexibility of C-terminal P peptides as well as their phosphorylation status play a role in binding and may bias the outcome of an inhibition assay. We therefore investigated binding affinities and dynamics of this interaction by testing two N protein constructs and P peptides of different lengths and composition, using nuclear magnetic resonance and fluorescence polarization (FP). We show that, although the last C-terminal Phe₂₄₁ residue is the main determinant for anchoring P to N, only longer peptides afford sub-micromolar affinity, despite increasing mobility towards the N-terminus. We investigated competitive binding by peptides and small compounds, including molecules used as fluorescent labels in FP. Based on these results, we draw optimized parameters for a robust RSV N-P inhibition assay and validated this assay with the M76 molecule, which displays antiviral properties, for further screening of chemical libraries.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Arf GTPase activates the WAVE regulatory complex through a distinct binding site

Cross-talk between Rho- and Arf-family guanosine triphosphatases (GTPases) plays an important role in linking the actin cytoskeleton to membrane protrusions, organelle morphology, and vesicle trafficking. The central actin regulator, WAVE regulatory complex (WRC), integrates Rac1 (a Rho-family GTPase) and Arf signaling to promote Arp2/3-mediated actin polymerization in many processes, but how WRC senses Arf signaling is unknown. Here, we have reconstituted a direct interaction between Arf and WRC. This interaction is greatly enhanced by Rac1 binding to the D site of WRC. Arf1 binds to a previously unidentified, conserved surface on the Sra1 subunit of WRC, which, in turn, drives WRC activation using a mechanism distinct from that of Rac1. Mutating the Arf binding site abolishes Arf1-WRC interaction, disrupts Arf1-mediated WRC activation, and impairs lamellipodia formation and cell migration. This work uncovers a new mechanism underlying WRC activation and provides a mechanistic foundation for studying how WRC-mediated actin polymerization links Arf and Rac signaling in cells.

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.

Analysis of Protein-Protein Interactions for Intermolecular Bond Prediction

Protein-protein interactions often involve a complex system of intermolecular interactions between residues and atoms at the binding site. A comprehensive exploration of these interactions can help reveal key residues involved in protein-protein recognition that are not obvious using other protein analysis techniques. This paper presents and extends DiffBond, a novel method for identifying and classifying intermolecular bonds while applying standard definitions of bonds in chemical literature to explain protein interactions. DiffBond predicted intermolecular bonds from four protein complexes: Barnase-Barstar, Rap1a-raf, SMAD2-SMAD4, and a subset of complexes formed from three-finger toxins and nAChRs. Based on validation through manual literature search and through comparison of two protein complexes from the SKEMPI dataset, DiffBond was able to identify intermolecular ionic bonds and hydrogen bonds with high precision and recall, and identify salt bridges with high precision. DiffBond predictions on bond existence were also strongly correlated with observations of Gibbs free energy change and electrostatic complementarity in mutational experiments. DiffBond can be a powerful tool for predicting and characterizing influential residues in protein-protein interactions, and its predictions can support research in mutational experiments and drug design.

A Closed-Form, Analytical Approximation for Apparent Surface Charge and Electric Field of Molecules

Closed-form, analytical approximations for electrostatic properties of molecules are of unique value as these can provide computational speed, versatility, and physical insight. Here, we have derived a simple, closed-form formula for the apparent surface charge (ASC) as well as for the electric field generated by a molecular charge distribution in aqueous solution. The approximation, with no fitted parameters, was tested against numerical solutions of the Poisson equation, where it has produced a significant speed-up. For neutral small molecules, the hydration free energies estimated from the closed-form ASC formula are within 0.8 kcal/mol RMSD from the numerical Poisson reference; the electric field at the surface is in quantitative agreement with the reference. Performance of the approximation was also tested on larger structures, including a protein, a DNA fragment, and a viral receptor-target complex. For all structures tested, a near-quantitative agreement with the numerical Poisson reference was achieved, except in regions of high negative curvature, where the new approximation is still qualitatively correct. A unique efficiency feature of the proposed "source-based″ closed-form approximation is that the ASC and electric field can be estimated individually at any point or surface patch, without the need to obtain the full global solution. An open-source software implementation of the method is available: https://people.cs.vt.edu/~onufriev/CODES/aasc.zip.

A Fast and Interpretable Deep Learning Approach for Accurate Electrostatics-Driven pKa Predictions in Proteins

Existing computational methods for estimating pK_a values in proteins rely on theoretical approximations and lengthy computations. In this work, we use a data set of 6 million theoretically determined pK_a shifts to train deep learning models, which are shown to rival the physics-based predictors. These neural networks managed to infer the electrostatic contributions of different chemical groups and learned the importance of solvent exposure and close interactions, including hydrogen bonds. Although trained only using theoretical data, our pKAI+ model displayed the best accuracy in a test set of ∼750 experimental values. Inference times allow speedups of more than 1000× compared to physics-based methods. By combining speed, accuracy, and a reasonable understanding of the underlying physics, our models provide a game-changing solution for fast estimations of macroscopic pK_a values from ensembles of microscopic values as well as for many downstream applications such as molecular docking and constant-pH molecular dynamics simulations.

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.

Electrostatic Complementarity in Structure-Based Drug Design

Optimization of electrostatic complementarity is an important strategy in structure-based drug discovery for improving the affinity of molecules against a specific protein target. In this Miniperspective we identify examples where deliberate optimization of protein-ligand electrostatic complementarity or intramolecular electrostatic interactions gave improvements in target affinity (up to 250-fold), physicochemical properties, in vitro properties, and off-target selectivity. We also look retrospectively at a series of factor Xa inhibitors that show an almost 8000-fold range in potency that can be correlated with the calculated electrostatic potential (ESP) surfaces. Recent developments using a graph-convolutional deep neural network to rapidly generate high quality ESP surfaces have the potential to make this useful tool more accessible for a wider audience within the field of medicinal chemistry.

Protein pKa Prediction by Tree-Based Machine Learning

Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.

Characterizing Protein Protonation Microstates Using Monte Carlo Sampling

Proteins are polyelectrolytes with acidic and basic amino acids Asp, Glu, Arg, Lys, and His, making up ≈25% of the residues. The protonation state of residues, cofactors, and ligands defines a "protonation microstate". In an ensemble of proteins some residues will be ionized and others neutral, leading to a mixture of protonation microstates rather than in a single one as is often assumed. The microstate distribution changes with pH. The protein environment also modifies residue proton affinity so microstate distributions change in different reaction intermediates or as ligands are bound. Particular protonation microstates may be required for function, while others exist simply because there are many states with similar energy. Here, the protonation microstates generated in Monte Carlo sampling in MCCE are characterized in HEW lysozyme as a function of pH and bacterial photosynthetic reaction centers (RCs) in different reaction intermediates. The lowest energy and highest probability microstates are compared. The ΔG, ΔH, and ΔS between the four protonation states of Glu35 and Asp52 in lysozyme are shown to be calculated with reasonable precision. At pH 7 the lysozyme charge ranges from 6 to 10, with 24 accepted protonation microstates, while RCs have ≈50,000. A weighted Pearson correlation analysis shows coupling between residue protonation states in RCs and how they change when the quinone in the Q_B site is reduced. Protonation microstates can be used to define input MD parameters and provide insight into the motion of protons coupled to reactions.

Computational Approach for Probing Redox Potential for Iron-Sulfur Clusters in Photosystem I

Photosystem I is a light-driven electron transfer device. Available X-ray crystal structure from Thermosynechococcus elongatus showed that electron transfer pathways consist of two nearly symmetric branches of cofactors converging at the first iron-sulfur cluster F_X, which is followed by two terminal iron-sulfur clusters F_A and F_B. Experiments have shown that F_X has lower oxidation potential than F_A and F_B, which facilitates the electron transfer reaction. Here, we use density functional theory and Multi-Conformer Continuum Electrostatics to explain the differences in the midpoint Em potentials of the F_X, F_A and F_B clusters. Our calculations show that F_X has the lowest oxidation potential compared to F_A and F_B due to strong pairwise electrostatic interactions with surrounding residues. These interactions are shown to be dominated by the bridging sulfurs and cysteine ligands, which may be attributed to the shorter average bond distances between the oxidized Fe ion and ligating sulfurs for F_X compared to F_A and F_B. Moreover, the electrostatic repulsion between the 4Fe-4S clusters and the positive potential of the backbone atoms is lowest for F_X compared to both F_A and F_B. These results agree with the experimental measurements from the redox titrations of low-temperature EPR signals and of room temperature recombination kinetics.

Prediction of protein pK a with representation learning

The behavior of proteins is closely related to the protonation states of the residues. Therefore, prediction and measurement of pK a are essential to understand the basic functions of proteins. In this work, we develop a new empirical scheme for protein pK a prediction that is based on deep representation learning. It combines machine learning with atomic environment vector (AEV) and learned quantum mechanical representation from ANI-2x neural network potential (J. Chem. Theory Comput. 2020, 16, 4192). The scheme requires only the coordinate information of a protein as the input and separately estimates the pK a for all five titratable amino acid types. The accuracy of the approach was analyzed with both cross-validation and an external test set of proteins. Obtained results were compared with the widely used empirical approach PROPKA. The new empirical model provides accuracy with MAEs below 0.5 for all amino acid types. It surpasses the accuracy of PROPKA and performs significantly better than the null model. Our model is also sensitive to the local conformational changes and molecular interactions.

Structure, dynamics, and function of SrnR, a transcription factor for nickel-dependent gene expression

Streptomyces griseus, a bacterium producing antibacterial drugs and featuring possible application in phytoremediation, expresses two metal-dependent superoxide dismutase (SOD) enzymes, containing either Fe(II) or Ni(II) in their active site. In particular, the alternative expression of the two proteins occurs in a metal-dependent mode, with the Fe(II)-enzyme gene (sodF) repressed at high intracellular Ni(II) concentrations by a two-component system (TCS). This complex involves two proteins, namely SgSrnR and SgSrnQ, which represent the transcriptional regulator and the Ni(II) sensor of the system, respectively. SgSrnR belongs to the ArsR/SmtB family of metal-dependent transcription factors; in the apo-form and in the absence of SgSrnQ, it can bind the DNA operator of sodF, upregulating gene transcription. According to a recently proposed hypothesis, Ni(II) binding to SgSrnQ would promote its interaction with SgSrnR, causing the release of the complex from DNA and the consequent downregulation of the sodF expression. SgSrnQ is predicted to be highly disordered, thus the understanding, at the molecular level, of how the SgSrnR/SgSrnQ TCS specifically responds to Ni(II) requires the knowledge of the structural, dynamic, and functional features of SgSrnR. These were investigated synergistically in this work using X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, atomistic molecular dynamics calculations, isothermal titration calorimetry, and in silico molecular docking. The results reveal that the homodimeric apo-SgSrnR binds to its operator in a two-step process that involves the more rigid globular portion of the protein and leaves its largely disordered regions available to possibly interact with the disordered SgSrnQ in a Ni-dependent process.

DiffBond: A Method for Predicting Intermolecular Bond Formation

Many tools that explore models of protein complexes are also able to analyze interactions between specific residues and atoms. A comprehensive exploration of these interactions can often uncover aspects of protein-protein recognition that are not obvious using other protein analysis techniques. This paper describes DiffBond, a novel method for searching for intermolecular interactions between protein complexes while differentiating between three different types of interaction: hydrogen bonds, ionic bonds, and salt bridges. DiffBond incorporates textbook definitions of these three interactions while contending with uncertainties that are inherent in computational models of interacting proteins. We used it to examine the barnase-barstar, Rap1a-raf, and Smad2-Smad4 complexes, as well as a subset of protein complexes formed between three-finger toxins and nAChRs. Based on electrostatic interactions established by previous experimental studies, DiffBond was able to identify ionic and hydrogen bonds with high precision and recall, and identify salt bridges with high precision. In combination with other electrostatic analysis methods, DiffBond can be a useful tool in helping predict influential amino acids in protein-protein interactions and characterizing the type of interaction.

Computational modeling of protein conformational changes - Application to the opening SARS-CoV-2 spike

We present a new approach to compute and analyze the dynamical electro-geometric properties of proteins undergoing conformational changes. The molecular trajectory is obtained from Markov state models, and the electrostatic potential is calculated using the continuum Poisson-Boltzmann equation. The numerical electric potential is constructed using a parallel sharp numerical solver implemented on adaptive Octree grids. We introduce novel a posteriori error estimates to quantify the solution's accuracy on the molecular surface. To illustrate the approach, we consider the opening of the SARS-CoV-2 spike protein using the recent molecular trajectory simulated through the Folding@home initiative. We analyze our results, focusing on the characteristics of the receptor-binding domain and its vicinity. This work lays the foundation for a new class of hybrid computational approaches, producing high-fidelity dynamical computational measurements serving as a basis for protein bio-mechanism investigations.

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.

Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson-Boltzmann equation model

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

A Structural and Dynamic Analysis of the Partially Disordered Polymerase-Binding Domain in RSV Phosphoprotein

The phosphoprotein P of Mononegavirales (MNV) is an essential co-factor of the viral RNA polymerase L. Its prime function is to recruit L to the ribonucleocapsid composed of the viral genome encapsidated by the nucleoprotein N. MNV phosphoproteins often contain a high degree of disorder. In Pneumoviridae phosphoproteins, the only domain with well-defined structure is a small oligomerization domain (P_OD). We previously characterized the differential disorder in respiratory syncytial virus (RSV) phosphoprotein by NMR. We showed that outside of RSV P_OD, the intrinsically disordered N-and C-terminal regions displayed a structural and dynamic diversity ranging from random coil to high helical propensity. Here we provide additional insight into the dynamic behavior of P_Cα, a domain that is C-terminal to P_OD and constitutes the RSV L-binding region together with P_OD. By using small phosphoprotein fragments centered on or adjacent to P_OD, we obtained a structural picture of the P_OD–P_Cα region in solution, at the single residue level by NMR and at lower resolution by complementary biophysical methods. We probed P_OD–P_Cα inter-domain contacts and showed that small molecules were able to modify the dynamics of P_Cα. These structural properties are fundamental to the peculiar binding mode of RSV phosphoprotein to L, where each of the four protomers binds to L in a different way.

pK a Calculations in Membrane Proteins from Molecular Dynamics Simulations

The conformational changes of membrane proteins are crucial to their function and usually lead to fluctuations in the electrostatic environment of the protein surface. A very effective way to quantify these changes is by calculating the pK _a values of the protein's titratable residues, which can be regarded as electrostatic probes. To achieve this, we need to take advantage of the fast and reliable pK _a calculators developed for globular proteins and adapt them to include the explicit effects of membranes. Here, we provide a detailed linear response approximation protocol that uses our own software (PypKa) to calculate reliable pK _a values from short MD simulations of membrane proteins.

The N-terminal Helix-Turn-Helix Motif of Transcription Factors MarA and Rob Drives DNA Recognition

DNA-binding proteins play an important role in gene regulation and cellular function. The transcription factors MarA and Rob are two homologous members of the AraC/XylS family that regulate multidrug resistance. They share a common DNA-binding domain, and Rob possesses an additional C-terminal domain that permits binding of low-molecular weight effectors. Both proteins possess two helix-turn-helix (HTH) motifs capable of binding DNA; however, while MarA interacts with its promoter through both HTH-motifs, prior studies indicate that Rob binding to DNA via a single HTH-motif is sufficient for tight binding. In the present work, we perform microsecond time scale all-atom simulations of the binding of both transcription factors to different DNA sequences to understand the determinants of DNA recognition and binding. Our simulations characterize sequence-dependent changes in dynamical behavior upon DNA binding, showcasing the role of Arg40 of the N-terminal HTH-motif in allowing for specific tight binding. Finally, our simulations demonstrate that an acidic C-terminal loop of Rob can control the DNA binding mode, facilitating interconversion between the distinct DNA binding modes observed in MarA and Rob. In doing so, we provide detailed molecular insight into DNA binding and recognition by these proteins, which in turn is an important step toward the efficient design of antivirulence agents that target these proteins.

Recent advances in user-friendly computational tools to engineer protein function

Progress in technology and algorithms throughout the past decade has transformed the field of protein design and engineering. Computational approaches have become well-engrained in the processes of tailoring proteins for various biotechnological applications. Many tools and methods are developed and upgraded each year to satisfy the increasing demands and challenges of protein engineering. To help protein engineers and bioinformaticians navigate this emerging wave of dedicated software, we have critically evaluated recent additions to the toolbox regarding their application for semi-rational and rational protein engineering. These newly developed tools identify and prioritize hotspots and analyze the effects of mutations for a variety of properties, comprising ligand binding, protein-protein and protein-nucleic acid interactions, and electrostatic potential. We also discuss notable progress to target elusive protein dynamics and associated properties like ligand-transport processes and allosteric communication. Finally, we discuss several challenges these tools face and provide our perspectives on the further development of readily applicable methods to guide protein engineering efforts.

In silico binding profile characterization of SARS-CoV-2 spike protein and its mutants bound to human ACE2 receptor

Severe acute respiratory syndrome coronavirus (SARS-CoV-2), a novel coronavirus, has brought an unprecedented pandemic to the world and affected over 64 million people. The virus infects human using its spike glycoprotein mediated by a crucial area, receptor-binding domain (RBD), to bind to the human ACE2 (hACE2) receptor. Mutations on RBD have been observed in different countries and classified into nine types: A435S, D364Y, G476S, N354D/D364Y, R408I, V341I, V367F, V483A and W436R. Employing molecular dynamics (MD) simulation, we investigated dynamics and structures of the complexes of the prototype and mutant types of SARS-CoV-2 spike RBDs and hACE2. We then probed binding free energies of the prototype and mutant types of RBD with hACE2 protein by using an end-point molecular mechanics Poisson Boltzmann surface area (MM-PBSA) method. According to the result of MM-PBSA binding free energy calculations, we found that V367F and N354D/D364Y mutant types showed enhanced binding affinities with hACE2 compared to the prototype. Our computational protocols were validated by the successful prediction of relative binding free energies between prototype and three mutants: N354D/D364Y, V367F and W436R. Thus, this study provides a reliable computational protocol to fast assess the existing and emerging RBD mutations. More importantly, the binding hotspots identified by using the molecular mechanics generalized Born surface area (MM-GBSA) free energy decomposition approach can guide the rational design of small molecule drugs or vaccines free of drug resistance, to interfere with or eradicate spike-hACE2 binding.

In silico studies on stilbenolignan analogues as SARS-CoV-2 Mpro inhibitors

COVID-19, a new strain of coronavirus family, was identified at the end of 2019 in China. The COVID-19 virus spread rapidly all over the world. Scientists strive to find virus-specific antivirals for the treatment of COVID-19. The present study reports a molecular docking study of the stilbenolignans and SARS-CoV-2 main protease (SARS-CoV-2 Mpro) inhibitors. The detailed interactions between the stilbenolignan analogues and SARS-CoV-2 Mpro inhibitors were determined as hydrophobic bonds, hydrogen bonds and electronic bonds, inhibition activity, ligand efficiency, bonding type and distance and etc. The binding energies of the stilbenolignan analogues were obtained from the molecular docking of SARS-CoV-2 Mpro. Lehmbachol D, Maackolin, Gnetucleistol, Gnetifolin F, Gnetofuran A and Aiphanol were found to be -7.7, -8.2, -7.3, -8.5, -8.0 and -7.3 kcal/mol, respectively. Osirus, Molinspiration and SwissADME chemoinformatic tools were used to examine ADMET properties, pharmacokinetic parameters and toxicological characteristics of the stilbenolignan analogues. All analogues obey the Lipinski's rule of five. Furthermore, stilbenolignan analogues were studied to predict their binding affinities against SARS-CoV-2 Mpro using molecular modeling and simulation techniques, and the binding free energy calculations of all complexes were calculated using the molecular mechanics/Poisson-Boltzmann surface area (MM-PBSA) method. With the data presented here it has been observed that these analogues may be a good candidate for SARS-CoV-2 Mpro in vivo studies, so more research can be done on stilbenolignan analogues.

Dielectric Behavior near a Spherical Ion

The dielectric response of a polar solvent to an ion is analyzed in terms of the bound charge, the net charge that accumulates near the ion as a consequence of the inhomogeneous polarization of the surrounding solvent. We demonstrate that the total bound charge arising in a full molecular treatment is identical to the total bound charge from standard continuum theory. In continuum theory, the bound charge resides in an infinitely thin layer, while in a molecular description the bound charge is spread over a region of finite width. Near simple atomic ions, the width of the bound charge distribution is roughly 1.3 nm. By simulating a sequence of ion charges from 0.1 to 2 e, where e is the magnitude of the electron charge, we analyze the applicability of linear response theory, which has been used by several authors. With increasing charge, the nonlinear response extends to an increasing distance from the ion. However, outside the region containing bound charge, the response is linear and in accord with continuum theory. Previous attempts to assign a dielectric constant to a solvent in the interfacial region are analyzed.

The Electrostatic Features of Dengue Virus Capsid Assembly

Dengue virus causes serious diseases and deaths in the world. Understanding the fundamental mechanisms of dengue virus is highly demanded to develop treatments for dengue virus caused diseases. Here, we present a computational work which focused on the stability of dengue viral capsid. The interactions among E proteins on the dengue viral capsid were studied using several computational approaches. It was found that the electrostatic distribution on a single E protein monomer is highly inhomogeneous, which makes an E protein strongly binding with another E protein. This is the reason why all the E proteins form homodimers as the basic units on the whole dengue viral capsids. The pKa calculations of E proteins demonstrated that the folding energy of an E protein is low and stable in the range of pH 6–10, which is different from many other proteins that are stable at certain pH. The pH dependence of binding energy of E protein homodimer shows that the binding energy is low and independent from pH when the pH is also in the range of 6–10. This finding implies that the dengue virus can survive in a wide range of pH, which can explain why the dengue virus is so widely distributed in the world and spreads fast.

On regularization of charge singularities in solving the Poisson-Boltzmann equation with a smooth solute-solvent boundary

Numerical treatment of singular charges is a grand challenge in solving the Poisson-Boltzmann (PB) equation for analyzing electrostatic interactions between the solute biomolecules and the surrounding solvent with ions. For diffuse interface PB models in which solute and solvent are separated by a smooth boundary, no effective algorithm for singular charges has been developed, because the fundamental solution with a space dependent dielectric function is intractable. In this work, a novel regularization formulation is proposed to capture the singularity analytically, which is the first of its kind for diffuse interface PB models. The success lies in a dual decomposition - besides decomposing the potential into Coulomb and reaction field components, the dielectric function is also split into a constant base plus space changing part. Using the constant dielectric base, the Coulomb potential is represented analytically via Green's functions. After removing the singularity, the reaction field potential satisfies a regularized PB equation with a smooth source. To validate the proposed regularization, a Gaussian convolution surface (GCS) is also introduced, which efficiently generates a diffuse interface for three-dimensional realistic biomolecules. The performance of the proposed regularization is examined by considering both analytical and GCS diffuse interfaces, and compared with the trilinear method. Moreover, the proposed GCS-regularization algorithm is validated by calculating electrostatic free energies for a set of proteins and by estimating salt affinities for seven protein complexes. The results are consistent with experimental data and estimates of sharp interface PB models.

Molecular mechanism study of EGFR allosteric inhibitors using molecular dynamics simulations and free energy calculations

ABTRACTThe epidermal growth factor receptor (EGFR) kinase inhibitors Gefitinib, Erlotinib, Afatinib and Osimertinib have been approved for the treatments of non-small cell lung cancer patients harboring sensitive EGFR mutations, but resistance arises rapidly. To date all approved EGFR inhibitors are ATP-competitive inhibitors, highlighting the need for therapeutic agents with alternative mechanisms of action. Allosteric kinase inhibitors offer a promising new therapeutic strategy to ATP-competitive inhibitors. The mutant-selective allosteric EGFR inhibitors EAI045 exhibited higher potency for EGFR^L858R&T790M compared to WT, which was also effective in EGFR-mutant models including those harboring the C797S mutation. However, it was not effective as a single-agent inhibitor, and require the co-administration of the anti-EGFR antibody Cetuximab. Further efforts produced a more potent analog JBJ-04-125-02, which can inhibit cell proliferation as a single-agent inhibitor. In the present study, molecular dynamics simulations and free energy calculations were performed and revealed the detailed inhibitory mechanism of JBJ-04-125-02 as more potent EGFR inhibitor. Moreover, the energy difference between HOMO and LUMO calculated by DFT implied the higher interaction of JBJ-04-125-02 than EAI045 in the active site of the EGFR. The identified key features obtained from the molecular modeling enabled us to design novel EGFR allosteric inhibitors.Communicated by Ramaswamy H. Sarma.