Generalized Born Research Articles

Implicit Solvent with Explicit Ions Generalized Born Model in Molecular Dynamics: Application to DNA.

The ion atmosphere surrounding highly charged biomolecules, such as nucleic acids, is crucial for their dynamics, structure, and interactions. Here, we develop an approach for the explicit treatment of ions within an implicit solvent framework suitable for atomistic simulations of biomolecules. The proposed implicit solvent/explicit ions model, GBION, is based on a modified generalized Born (GB) model; it includes separate, modified GB terms for solute-ion and ion-ion interactions. The model is implemented in the AMBER package (version 24), and its performance is thoroughly investigated in atomistic molecular dynamics (MD) simulations of double-stranded DNA on a microsecond time scale. The aggregate characteristics of monovalent (Na+ and K+) and trivalent (Cobalt Hexammine, CoHex3+) counterion distributions around double-stranded DNA predicted by the model are in reasonable agreement with the experiment (where available), all-atom explicit water MD simulations, and the expectation from the Manning condensation theory. The radial distributions of monovalent cations around DNA are reasonably close to the ones obtained using the explicit water model: expressed in units of energy, the maximum deviations of local ion concentrations from the explicit solvent reference are within 1 kBT, comparable to the corresponding deviations expected between different established explicit water models. The proposed GBION model is able to simulate DNA fragments in a large volume of solvent with explicit ions with little additional computational overhead compared with the fully implicit GB treatment of ions. Ions simulated using the developed model explore conformational space at least 2 orders of magnitude faster than in the explicit solvent. These advantages allowed us to observe and explore an unexpected "stacking" mode of DNA condensation in the presence of trivalent counterions (CoHex3+) that was revealed by recent experiments.

Inclusion of Water Multipoles into the Implicit Solvation Framework Leads to Accuracy Gains.

The current practical "workhorses" of the atomistic implicit solvation─the Poisson-Boltzmann (PB) and generalized Born (GB) models─face fundamental accuracy limitations. Here, we propose a computationally efficient implicit solvation framework, the Implicit Water Multipole GB (IWM-GB) model, that systematically incorporates the effects of multipole moments of water molecules in the first hydration shell of a solute, beyond the dipole water polarization already present at the PB/GB level. The framework explicitly accounts for coupling between polar and nonpolar contributions to the total solvation energy, which is missing from many implicit solvation models. An implementation of the framework, utilizing the GAFF force field and AM1-BCC atomic partial charges model, is parametrized and tested against the experimental hydration free energies of small molecules from the FreeSolv database. The resulting accuracy on the test set (RMSE ∼ 0.9 kcal/mol) is 12% better than that of the explicit solvation (TIP3P) treatment, which is orders of magnitude slower. We also find that the coupling between polar and nonpolar parts of the solvation free energy is essential to ensuring that several features of the IWM-GB model are physically meaningful, including the sign of the nonpolar contributions.

Discovery of novel inhibitor via molecular dynamics simulations against D-alanyl-D-alanine carboxypeptidase of Enterobacter cloacae

Antibiotics resistance by bacterial pathogens is a major concern to public health worldwide resulting in high health care costs and rising mortality. Subtractive proteomics prioritized D-alanyl-D-alanine carboxypeptidas (DacB) enzyme from Enterobacter cloacae ATCC 13047 as a potential candidate for drugs designing to block pathogen cell wall biosynthesis. Virtual screening of an antibacterial library against the target unraveled a hit compound (2-[(1-methylsulfonylpiperidin-3-yl)methyl]-6-(1H-pyrazol-4-yl) pyrazine) showing high affinity and stability with the target. The N-methyl-N-propyl-methanesulfonamide of the compound is seen as a closed affinity towards domain involving strong hydrogen bonds with Ser41, Lys44, Ser285, and Asn287. The 4-methyl-1H-pyrazole is posed towards the open cavity of domain I and II and formed hydrophobic and hydrophilic contacts. The system is highly stable with average carbon-alpha deviations of 1.69 Å over trajectories of 400-ns. Three vital residues projected: Arg437, Arg438 and Leu400 from enzyme pocket via Radial distribution function (RDF) assay, which actively engaged the inhibitor. Further confirmation is done by estimating binding free energies, which confirms the very low delta energy of −7.24 kcal/mol in Generalized Born (GB) method and −7.4363 kcal/mol in Poisson-Boltzmann (PB) method. WaterSwap calculations were performed that revealed the energies highly converged, an agreement on good system stability. Lastly, three DacB mutants were created to investigate the role of functional active residues and a decline in binding affinity of the residues was noticed. These computational results provide a gateway for experimentalists to further confirm their efficacy both in-vitro and in-vivo. Communicated by Ramaswamy H. Sarma

Bending of Light by Magnetars within Generalized Born–Infeld Electrodynamics: Insights from the Gauss–Bonnet Theorem

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields.

On the absence of shock waves and vacuum birefringence in Born–Infeld electrodynamics

We study the interaction of two counter–propagating electromagnetic waves in vacuum in the Born–Infeld electrodynamics. First we investigate the Born case for linearly polarized beams, E · B = 0, i.e., G2=0 (crossed field configuration), which is identical for Born–Infeld and Born electrodynamics; subsequently we study the general Born–Infeld case for beams which are nonlinearly polarized, G2≠0. In both cases, we show that the nonlinear field equations decouple using self-similar solutions and investigate the shock wave formation. We show that the only nonlinear solutions are exceptional traveling wave solutions which propagate with constant speed and which do not turn into shocks for our approximation. We obtain two types of exceptional wave solutions, then we numerically analyze which phase velocities correspond to the counter- or co-propagating beams and subsequently we determine the direction of propagation of the exceptional waves.

Improving the Accuracy of Physics-Based Hydration-Free Energy Predictions by Machine Learning the Remaining Error Relative to the Experiment.

The accuracy of computational models of water is key to atomistic simulations of biomolecules. We propose a computationally efficient way to improve the accuracy of the prediction of hydration-free energies (HFEs) of small molecules: the remaining errors of the physics-based models relative to the experiment are predicted and mitigated by machine learning (ML) as a postprocessing step. Specifically, the trained graph convolutional neural network attempts to identify the "blind spots" in the physics-based model predictions, where the complex physics of aqueous solvation is poorly accounted for, and partially corrects for them. The strategy is explored for five classical solvent models representing various accuracy/speed trade-offs, from the fast analytical generalized Born (GB) to the popular TIP3P explicit solvent model; experimental HFEs of small neutral molecules from the FreeSolv set are used for the training and testing. For all of the models, the ML correction reduces the resulting root-mean-square error relative to the experiment for HFEs of small molecules, without significant overfitting and with negligible computational overhead. For example, on the test set, the relative accuracy improvement is 47% for the fast analytical GB, making it, after the ML correction, almost as accurate as uncorrected TIP3P. For the TIP3P model, the accuracy improvement is about 39%, bringing the ML-corrected model's accuracy below the 1 kcal/mol threshold. In general, the relative benefit of the ML corrections is smaller for more accurate physics-based models, reaching the lower limit of about 20% relative accuracy gain compared with that of the physics-based treatment alone. The proposed strategy of using ML to learn the remaining error of physics-based models offers a distinct advantage over training ML alone directly on reference HFEs: it preserves the correct overall trend, even well outside of the training set.

Tuning Potential Functions to Host-Guest Binding Data.

Software to more rapidly and accurately predict protein-ligand binding affinities is of high interest for early-stage drug discovery, and physics-based methods are among the most widely used technologies for this purpose. The accuracy of these methods depends critically on the accuracy of the potential functions that they use. Potential functions are typically trained against a combination of quantum chemical and experimental data. However, although binding affinities are among the most important quantities to predict, experimental binding affinities have not to date been integrated into the experimental data set used to train potential functions. In recent years, the use of host-guest complexes as simple and tractable models of binding thermodynamics has gained popularity due to their small size and simplicity, relative to protein-ligand systems. Host-guest complexes can also avoid ambiguities that arise in protein-ligand systems such as uncertain protonation states. Thus, experimental host-guest binding data are an appealing additional data type to integrate into the experimental data set used to optimize potential functions. Here, we report the extension of the Open Force Field Evaluator framework to enable the systematic calculation of host-guest binding free energies and their gradients with respect to force field parameters, coupled with the curation of 126 host-guest complexes with available experimental binding free energies. As an initial application of this novel infrastructure, we optimized generalized Born (GB) cavity radii for the OBC2 GB implicit solvent model against experimental data for 36 host-guest systems. This refitting led to a dramatic improvement in accuracy for both the training set and a separate test set with 90 additional host-guest systems. The optimized radii also showed encouraging transferability from host-guest systems to 59 protein-ligand systems. However, the new radii are significantly smaller than the baseline radii and lead to excessively favorable hydration free energies (HFEs). Thus, users of the OBC2 GB model currently may choose between GB cavity radii that yield more accurate binding affinities and GB cavity radii that yield more accurate HFEs. We suspect that achieving good accuracy on both will require more far-reaching adjustments to the GB model. We note that binding free-energy calculations using the OBC2 model in OpenMM gain about a 10× speedup relative to corresponding explicit solvent calculations, suggesting a future role for implicit solvent absolute binding free-energy (ABFE) calculations in virtual compound screening. This study proves the principle of using host-guest systems to train potential functions that are transferrable to protein-ligand systems and provides an infrastructure that enables a range of applications.

The Intrinsic Radius as a Key Parameter in the Generalized Born Model to Adjust Protein-Protein Electrostatic Interaction.

The generalized Born (GB) model is an extension of the continuum dielectric theory of Born solvation energy and is a powerful method for accelerating the molecular dynamic (MD) simulations of charged biological molecules in water. While the effective dielectric constant of water that varies as a function of the separation distance between solute molecules is incorporated into the GB model, adjustment of the parameters is indispensable for accurate calculation of the Coulomb (electrostatic) energy. One of the key parameters is the lower limit of the spatial integral of the energy density of the electric field around a charged atom, known as the intrinsic radius ρ. Although ad hoc adjustment of ρ has been conducted to improve the Coulombic (ionic) bond stability, the physical mechanism by which ρ affects the Coulomb energy remains unclear. Via energetic analysis of three differently sized systems, here, we clarify that the Coulomb bond stability increases with increasing ρ and that the increased stability is caused by the interaction energy term, not by the self-energy (desolvation energy) term, as was supposed previously. Our results suggest that the use of larger values for the intrinsic radii of hydrogen and oxygen atoms, together with the use of a relatively small value for the spatial integration cutoff in the GB model, can better reproduce the Coulombic attraction between protein molecules.

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 solvationfreeenergy 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.

Investigation of The Potential Inhibitor Effects Of Lycorine On Sars-Cov-2 Main Protease (Mpro) Using Molecular Dynamics Simulations and MMPBSA

The main protease (Mpro or 3CLpro) plays important roles in viral replication and is one of attractive targets for drug development for SARS-CoV-2. In this study, we investigated the potential inhibitory effect of lycorine molecule as a ligand on SARS-CoV-2 using computational approaches. For this purpose, we conducted molecular docking and molecular dynamics simulations MM-PB(GB)SA analyses. The findings showed that the lycorine ligand was successfully docked with catalytic dyad (Cys145 and His41) of SARS-CoV-2 Mpro with binding affinity changing between -6.71 and -7.03 kcal mol-1. MMPB(GB)SA calculations resulted according to GB (Generalized Born) approach in a Gibbs free energy changing between -24.925-+01152 kcal/mol between lycorine and SARS-CoV-2 which is promising. PB (Poisson Boltzmann) approach gave less favorable energy (-2.610±0.2611 kcal mol-1). Thus, Entropy calculations from the normal mode analysis (ΔS) were performed and it supported GB approach and conducted -23.100±6.4635 kcal mol-1. These results showed lycorine has a druggable potential but the drug effect of lycorine on COVID-19 is limited and experimental studies should be done with pharmacokinetic modifications that increase the drug effect of lycorine.

CHARMM-GUI Implicit Solvent Modeler for Various Generalized Born Models in Different Simulation Programs

Implicit solvent models are widely used because they are advantageous to speed up simulations by drastically decreasing the number of solvent degrees of freedom, which allows one to achieve long simulation time scales for large system sizes. CHARMM-GUI, a web-based platform, has been developed to support the setup of complex multicomponent molecular systems and prepare input files. This study describes an Implicit Solvent Modeler (ISM) in CHARMM-GUI for various generalized Born (GB) implicit solvent simulations in different molecular dynamics programs such as AMBER, CHARMM, GENESIS, NAMD, OpenMM, and Tinker. The GB models available in ISM include GB-HCT, GB-OBC, GB-neck, GBMV, and GBSW with the CHARMM and Amber force fields for protein, DNA, RNA, glycan, and ligand systems. Using the system and input files generated by ISM, implicit solvent simulations of protein, DNA, and RNA systems produce similar results for different simulation packages with the same input information. Protein-ligand systems are also considered to further validate the systems and input files generated by ISM. Simple ligand root-mean-square deviation (RMSD) and molecular mechanics generalized Born surface area (MM/GBSA) calculations show that the performance of implicit simulations is better than docking and can be used for early stage ligand screening. These reasonable results indicate that ISM is a useful and reliable tool to provide various implicit solvent simulation applications.

Generalized Born Implicit Solvent Models Do Not Reproduce Secondary Structures of De Novo Designed Glu/Lys Peptides.

We test a range of standard generalized Born (GB) models and protein force fields for a set of five experimentally characterized, designed peptides comprising alternating blocks of glutamate and lysine, which have been shown to differ significantly in α-helical content. Sixty-five combinations of force fields and GB models are evaluated in >800 μs of molecular dynamics simulations. GB models generally do not reproduce the experimentally observed α-helical content, and none perform well for all five peptides. These results illustrate that these models are not usefully predictive in this context. These peptides provide a useful test set for simulation methods.

Protein-Protein Binding Free Energy Predictions with the MM/PBSA Approach Complemented with the Gaussian-Based Method for Entropy Estimation.

Here, we present a Gaussian-based method for estimation of protein–protein binding entropy to augment the molecular mechanics Poisson–Boltzmann surface area (MM/PBSA) method for computational prediction of binding free energy (ΔG). The method is termed f5-MM/PBSA/E, where “E” stands for entropy and f5 for five adjustable parameters. The enthalpy components of ΔG (molecular mechanics, polar and non-polar solvation energies) are computed from a single implicit solvent generalized Born (GB) energy minimized structure of a protein–protein complex, while the binding entropy is computed using independently GB energy minimized unbound and bound structures. It should be emphasized that the f5-MM/PBSA/E method does not use snapshots, just energy minimized structures, and is thus very fast and computationally efficient. The method is trained and benchmarked in 5-fold validation test over a data set consisting of 46 protein–protein binding cases with experimentally determined dissociation constant Kd values. This data set has been used for benchmarking in recently published protein–protein binding studies that apply conventional MM/PBSA and MM/PBSA with an enhanced sampling method. The f5-MM/PBSA/E tested on the same data set achieves similar or better performance than these computationally demanding approaches, making it an excellent choice for high throughput protein–protein binding affinity prediction studies.

Structural and energetic features of the dimerization of the main proteinase of SARS-CoV-2 using molecular dynamic simulations.

The COVID-19 pandemic caused by SARS-CoV-2 has been declared a global health crisis. The development of anti-SARS-CoV-2 drugs heavily depends on the systematic study of the critical biological processes of key proteins of coronavirus among which the main proteinase (Mpro) dimerization is a key step for virus maturation. Because inhibiting the Mpro dimerization can efficiently suppress virus maturation, the key residues that mediate dimerization can be treated as targets of drug and antibody developments. In this work, the structure and energy features of the Mpro dimer of SARS-CoV-2 and SARS-CoV were studied using molecular dynamics (MD) simulations. The free energy calculations using the Generalized Born (GB) model showed that the dimerization free energy of the SARS-CoV-2 Mpro dimer (-107.5 ± 10.89 kcal mol-1) is larger than that of the SARS-CoV Mpro dimer (-92.83 ± 9.81 kcal mol-1), indicating a more stable and possibly a quicker formation of the Mpro dimer of SARS-CoV-2. In addition, the energy decomposition of each residue revealed 11 key attractive residues. Furthermore, Thr285Ala weakens the steric hindrance between the two protomers of SARS-CoV-2 that can form more intimate interactions. It is interesting to find 11 repulsive residues which effectively inhibit the dimerization process. At the interface of the Mpro dimer, we detected three regions that are rich in interfacial water which stabilize the SARS-CoV-2 Mpro dimer by forming hydrogen bonds with two protomers. The key residues and rich water regions provide important targets for the future design of anti-SARS-CoV-2 drugs through inhibiting Mpro dimerization.

Binding of Inhibitors to BACE1 Affected by pH-Dependent Protonation: An Exploration from Multiple Replica Gaussian Accelerated Molecular Dynamics and MM-GBSA Calculations.

To date, inhibiting the activity of β-amyloid cleaving enzyme 1 (BACE1) has been considered an efficient approach for treating Alzheimer's disease (AD). In the current work, multiple replica Gaussian accelerated molecular dynamics (MR-GaMD) simulations and the molecular mechanics general Born surface area (MM-GBSA) method were combined to investigate the effect of pH-dependent protonation on the binding of the inhibitors CS9, C6U, and 6WE to BACE1. Dynamic analyses based on the MR-GaMD trajectory show that pH-dependent protonation strongly affects the structural flexibility, correlated motions, and dynamic behavior of inhibitor-bound BACE1. According to the constructed free energy profiles, in the protonated state at low pH, inhibitor-bound BACE1 tends to populate at more conformations than in high pH. The binding free energies calculated by MM-GBSA suggest that inhibitors possess stronger binding abilities under the protonation conditions at high pH than under the protonation conditions at low pH. Moreover, pH-dependent protonation exerts a significant effect on the hydrogen bonding interactions of CS9, C6U, and 6WE to BACE1, which correspondingly alters the binding abilities of the three inhibitors to BACE1. Furthermore, in different protonated environments, three inhibitors share common interaction clusters and similar binding sites in BACE1, which are reliably used as efficient targets for the design of potent inhibitors of BACE1.

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.

Screening of natural compounds for identification of novel inhibitors against β-lactamase CTX-M-152 reported among Kluyvera georgiana isolates: An in vitro and in silico study

Multidrug resistance due to the expression of extended spectrum β-lactamases (ESBLs) by bacterial pathogens is an alarming health concern with huge socio-economic burden. Here, 102 bacterial isolates from Wastewater treatment plants (WTPs) were screened for resistance to different antibiotics. Kirby-Bauer method and phenotypic disc confirmatory test confirmed the prevalence of 20 ESBLs. Polymerase chain reaction-based detection confirmed 11 blaCTX-M positive bacterial isolates. Genotyping of bacterial isolates by 16S rRNA gene sequencing showed the dissemination of blaCTX-M in Escherichia fergusonii, Escherichia coli, Shigella sp., Kluyvera georgiana and Enterobacter sp. Amongst Kluyvera georgiana isolates, two were harboring blaCTX-M-152. The 3D model of CTX-M-152 protein was generated using SwissProt and characterized by Ramachandran plot and SAVES. A library of natural compounds was screened to identify novel CTX-M-152 inhibitor(s). High-throughput virtual screening (HTVS), standard precision (SP) and extra precision (XP) docking led to the identification of five natural compounds (Naringin dihydrochalcone, Salvianolic acid B, Inositol, Guanosine and Ellagic acid) capable of binding to active site of CTX-M-152. Futher, characterization by MM-GBSA (Molecular Mechanism General Born Surface Area), and ADMET (Adsorption, Distribution, Metabolism, Excretion and Toxicity) showed that Ellagic acid was the most potent inhibitor of CTX-M-152. Molecular dynamics simulation also confirmed that Ellagic acid form a stable complex with CTX-M-152. The ability of Ellagic acid to inhibit growth of bacteria harboring CTX-M-152 was confirmed by MIC (Minimum Inhibitory Concentration; broth dilution method) and Zone of Inhibition (ZOI) studies with respect to Cefotaxime. The identification of a novel inhibitor of CTX-M-152 from a natural source holds promise for employment in the control of bacterial infections.

A Critique of Nigerian Federalism and Need for Restructuring Towards Achieving Vision 2030

This paper underscores a critique of Nigeria’s choice of a federal option, the current state of which has led to the incessant clamour, across the nation for restructuring. Federalism in Nigeria since 1960 was adopted to accommodate the nation’s heterogeneous culture with the sole aim of maintaining unity in diversity. The dysfunctional system has been observed to be the main bane of Nigeria underdevelopment, instability, and absence of good governance all of which can negatively affect the achievement of a sustainable national development plan like the Vision 2030. This paper argues that Nigeria is yet to evolve a truly federal system capable of taking care of its numerous challenges. Writing from a historical perspective, the paper uncovers that there are logical inconsistencies in Nigeria’s practice of federalism. What gets here is a hidden unitary framework. The call for restructuring is in a general sense borne out of some apparent degrees of foul play and disparity presently perceived by the part units emerging from defective federalism. Understood in the above is that the necessary ingredients of sustainable democracy and governance are completely lacking in Nigeria. Thus, if the proposed Vision 2030 or any other national development plan is to be accomplished, there has to be a restructuring of the dysfunctional political system; a restructuring that devolves power to the federating units leaving the federal government with vital aspects like defence, foreign affairs among others; a return to the regional arrangement of the past.

Polarizable charges in a generalized Born reaction potential.

The generalized Born (GB) model is a fast implicit solvent model that is used as an approximation to the Poisson equation for solutes described by point charges. Due to the simple analytical form, GB models are widely used in molecular dynamics simulations to account for (implicit) solvation effects. In this work, we extend the application of the GB model to polarizable charges by coupling it to the bond capacity (BC) model. The resulting BC-GB model is a non-variational polarization model where the reaction potential is calculated from a GB expression and included in the polarization equation to account for solvation effects. Being non-variational, the BC-GB makes use of a Lagrange formulation for an efficient evaluation of energy gradients. The stability of the algorithm in molecular dynamics simulations is tested in the microcanonical ensemble, and the results show energy conservation as well as small fluctuations. The inclusion of implicit solvation increases the computational cost by only 15% compared to vacuum. Combined with a significant reduction in system size by describing the solvent as a continuum makes the BC-GB model an interesting model for applications requiring the combination of solute polarization and extensive conformational space sampling.

“Big Data” Fast Chemoinformatics Model to Predict Generalized Born Radius and Solvent Accessibility as a Function of Geometry

The Generalized Born (GB) solvent model is offering the best accuracy/computing effort ratio yet requires drastic simplifications to estimate of the Effective Born Radii (EBR) in bypassing a too expensive volume integration step. EBRs are a measure of the degree of burial of an atom and not very sensitive to small changes of geometry: in molecular dynamics, the costly EBR update procedure is not mandatory at every step. This work however aims at implementing a GB model into the Sampler for Multiple Protein-Ligand Entities (S4MPLE) evolutionary algorithm with mandatory EBR updates at each step triggering arbitrarily large geometric changes. Therefore, a quantitative structure-property relationship has been developed in order to express the EBRs as a linear function of both the topological neighborhood and geometric occupancy of the space around atoms. A training set of 810 molecular systems, starting from fragment-like to drug-like compounds, proteins, host-guest systems, and ligand-protein complexes, has been compiled. For each species, S4MPLE generated several hundreds of random conformers. For each atom in each geometry of each species, its "standard" EBR was calculated by numeric integration and associated to topological and geometric descriptors of the atom neighborhood. This training set (EBR, atom descriptors) involving >5 M entries was subjected to a boot-strapping multilinear regression process with descriptor selection. In parallel, the strategy was repurposed to also learn atomic solvent-accessible areas (SA) based on the same descriptors. Resulting linear equations were challenged to predict EBR and SA values for a similarly compiled external set of >2000 new molecular systems. Solvation energies calculated with estimated EBR and SA match "standard" energies within the typical error of a force-field-based approach (a few kilocalories per mole). Given the extreme diversity of molecular systems covered by the model, this simple EBR/SA estimator covers a vast applicability domain.