RESUMEN

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.

RESUMEN

Electrostatic features are fundamental to protein functions and protein-protein interactions. Studying highly charged biomolecules is challenging given the heterogeneous distribution of the ionic cloud around such biomolecules. Here we report a new computational method, Hybridizing Ions Treatment-2 (HIT-2), which is used to model biomolecule-bound ions using the implicit solvation model. By modeling ions, HIT-2 allows the user to calculate important electrostatic features of the biomolecules. HIT-2 applies an efficient algorithm to calculate the position of bound ions from molecular dynamics simulations. Modeling parameters were optimized by machine learning methods from thousands of datasets. The optimized parameters produced results with errors lower than 0.2 Å. The testing results on bound Ca2+ and Zn2+ in NAMD simulations also proved that HIT-2 can effectively identify bound ion types, numbers, and positions. Also, multiple tests performed on HIT-2 suggest the method can handle biomolecules that undergo remarkable conformational changes. HIT-2 can significantly improve electrostatic calculations for many problems in computational biophysics.

RESUMEN

Calculation of protein-ligand binding affinity is a cornerstone of drug discovery. Classic implicit solvent models, which have been widely used to accomplish this task, lack accuracy compared to experimental references. Emerging data-driven models, on the other hand, are often accurate yet not fully interpretable and also likely to be overfitted. In this research, we explore the application of Theory-Guided Data Science in studying protein-ligand binding. A hybrid model is introduced by integrating Graph Convolutional Network (data-driven model) with the GBNSR6 implicit solvent (physics-based model). The proposed physics-data model is tested on a dataset of 368 complexes from the PDBbind refined set and 72 host-guest systems. Results demonstrate that the proposed Physics-Guided Neural Network can successfully improve the "accuracy" of the pure data-driven model. In addition, the "interpretability" and "transferability" of our model have boosted compared to the purely data-driven model. Further analyses include evaluating model robustness and understanding relationships between the physical features.

Asunto(s)

RESUMEN

Computational design of antimicrobial peptides (AMPs) is a promising area of research for developing novel agents against drug-resistant bacteria. AMPs are present naturally in many organisms, from bacteria to humans, a time-tested mechanism that makes them attractive as effective antibiotics. Depending on the environment, AMPs can exhibit α-helical or ß-sheet conformations, a mix of both, or lack secondary structure; they can be linear or cyclic. Prediction of their structures is challenging but critical for rational design. Promising AMP leads can be developed using essentially two approaches: traditional modeling of the physicochemical mechanisms that determine peptide behavior in aqueous and membrane environments and knowledge-based, e.g., machine learning (ML) techniques, that exploit ever-growing AMP databases. Here, we explore the conformational landscapes of two recently ML-designed AMPs, characterize the dependence of these landscapes on the medium conditions, and identify features in peptide and membrane landscapes that mediate protein-membrane association. For both peptides, we observe greater conformational diversity in an aqueous solvent than in a less polar solvent, and one peptide is seen to alter its conformation more dramatically than the other upon the change of solvent. Our results support the view that structural rearrangement in response to environmental changes is central to the mechanism of membrane-structure disruption by linear peptides. We expect that the design of AMPs by ML will benefit from the incorporation of peptide conformational substates as quantified here with molecular simulations.

Asunto(s)

RESUMEN

The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by the mesh, and the point charges are accounted for explicitly. In fact, there are several well-known boundary integral formulations available in the literature. This work presents a generalized expression of the boundary integral representation of the implicit solvent model, giving rise to new forms to compute the electrostatic potential. Moreover, it proposes a strategy to build efficient preconditioners for any of the resulting systems, improving the convergence of the linear solver. We perform systematic benchmarking of a set of formulations and preconditioners, focusing on the time to solution, matrix conditioning, and eigenvalue spectrum. We see that the eigenvalue clustering is a good indicator of the matrix conditioning, and show that they can be easily manipulated by scaling the preconditioner. Our results suggest that the optimal choice is problem-size dependent, where a simpler direct formulation is the fastest for small molecules, but more involved second-kind equations are better for larger problems. We also present a fast Calderón preconditioner for first-kind formulations, which shows promising behavior for future analysis. This work sets the basis towards choosing the most convenient boundary integral formulation of the Poisson-Boltzmann equation for a given problem.

Asunto(s)

RESUMEN

Fast and accurate calculations of the electrostatic features of highly charged biomolecules such as DNA, RNA, and highly charged proteins are crucial and challenging tasks. Traditional implicit solvent methods calculate the electrostatic features quickly, but these methods are not able to balance the high net biomolecular charges effectively. Explicit solvent methods add unbalanced ions to neutralize the highly charged biomolecules in molecular dynamic simulations, which require more expensive computing resources. Here we report developing a novel method, Hybridizing Ions Treatment (HIT), which hybridizes the implicit solvent method with an explicit method to realistically calculate the electrostatic potential for highly charged biomolecules. HIT utilizes the ionic distribution from an explicit method to predict the bound ions. The bound ions are then added in the implicit solvent method to perform the electrostatic potential calculations. In this study, two training sets were developed to optimize parameters for HIT. The performance on the testing set demonstrates that HIT significantly improves the electrostatic calculations. Results on molecular motors myosin and kinesin reveal some mechanisms and explain some previous experimental findings. HIT can be widely used to study highly charged biomolecules, including DNA, RNA, molecular motors, and other highly charged biomolecules. The HIT package is available at http://compbio.utep.edu/static/downloads/download_hit.zip.

RESUMEN

Coulomb interactions play a major role in determining the thermodynamics, structure, and dynamics of condensed-phase systems, but often present significant challenges. Computer simulations usually use periodic boundary conditions to minimize corrections from finite cell boundaries but the long range of the Coulomb interactions generates significant contributions from distant periodic images of the simulation cell, usually calculated by Ewald sum techniques. This can add significant overhead to computer simulations and hampers the development of intuitive local pictures and simple analytic theory. In this paper, we present a general framework based on local molecular field theory to accurately determine the contributions from long-ranged Coulomb interactions to the potential of mean force between ionic or apolar hydrophobic solutes in dilute aqueous solutions described by standard classical point charge water models. The simplest approximation leads to a short solvent (SS) model, with truncated solvent-solvent and solute-solvent Coulomb interactions and long-ranged but screened Coulomb interactions only between charged solutes. The SS model accurately describes the interplay between strong short-ranged solute core interactions, local hydrogen-bond configurations, and long-ranged dielectric screening of distant charges, competing effects that are difficult to capture in standard implicit solvent models.

RESUMEN

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ("dry" and "wet") hydration states. The resulting dry-wet transition rates are then used in a spatially dependent multistate continuous-time Markov chain Brownian dynamics simulation and the related Fokker-Planck equation calculations of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semiquantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of nonequilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding vs. unbinding. Our study thus provides a significant step forward toward efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

Asunto(s)

RESUMEN

Many natural products target mammalian tubulin but only a few can form a covalent bond and hence irreversibly affect microtubule function. Among them, zampanolide (ZMP) and taccalonolide AJ (TAJ) stand out, not only because they are very potent antitumor agents but also because the adducts they form with ß-tubulin have been structurally characterized in atomic detail. By applying model building techniques, molecular orbital calculations, molecular dynamics simulations and hybrid QM/MM methods, we have gained insight into the 1,2- and 1,4-addition reactions of His229 and Asp226 to ZMP and TAJ, respectively, in the taxane-binding site of ß-tubulin. The experimentally inaccessible precovalent complexes strongly suggest a water-mediated proton shuttle mechanism for ZMP adduct formation and a direct nucleophilic attack by the carboxylate of Asp226 on C22 of the C22R,C23R epoxide in TAJ. The M-loop, which is crucially important for interprotofilament interactions, is structured into a short helix in both types of complexes, mostly as a consequence of the fixation of the phenol ring of Tyr283 and the guanidinium of Arg284. As a side benefit, we obtained evidence supporting the existence of a commonly neglected intramolecular disulfide bond between Cys241 and Cys356 in ß-tubulin that contributes to protein compactness and is absent in the ßIII isotype associated with resistance to taxanes and other drugs.

Asunto(s)

RESUMEN

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Asunto(s)

RESUMEN

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson-Boltzmann/solvent-accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self-consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well-experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas-phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute-solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non-polar solvation effects. © 2018 Wiley Periodicals, Inc.

Asunto(s)

RESUMEN

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature-function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson-Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave-one-out test gives an optimal root-mean-square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.

RESUMEN

At least four classes of structurally distinct natural products with potent antiproliferative activities target the translation elongation factor eEF1A1, which is best known as the G-protein that delivers amino acyl transfer RNAs (aa-tRNAs) to ribosomes during mRNA translation. We present molecular models in atomic detail that provide a common structural basis for the high-affinity binding of didemnin B, ternatin, ansatrienin B and nannocystin A to eEF1A1, as well as a rationale based on molecular dynamics results that accounts for the deleterious effect of replacing alanine 399 with valine. The proposed binding site, at the interface between domains I and III, is eminently hydrophobic and exists only in the GTP-bound conformation. Drug binding at this site is expected to disrupt neither loading of aa-tRNAs nor GTP hydrolysis but would give rise to stabilization of this particular conformational state, in consonance with reported experimental findings. The experimental solution of the three-dimensional structure of mammalian eEF1A1 has proved elusive so far and the highly homologous eEF1A2 from rabbit muscle has been crystallized and solved only as a homodimer in a GDP-bound conformation. Interestingly, in this dimeric structure the large interdomain cavity where the drugs studied are proposed to bind is occupied by a mostly hydrophobic α-helix from domain I of the same monomer. Since binding of this α-helix and any of these drugs to domain III of eEF1A(1/2) is, therefore, mutually exclusive and involves two distinct protein conformations, one intriguing possibility that emerges from our study is that the potent antiproliferative effect of these natural products may arise not only from inhibition of protein synthesis, which is the current dogma, but also from interference with some other non-canonical functions. From this standpoint, this type of drugs could be considered antagonists of eEF1A1/2 oligomerization, a hypothesis that opens up novel areas of research.

Asunto(s)

RESUMEN

Density functional theory (DFT) calculations were performed to examine exothermic surface chemistry between alumina and four fluorinated, fragmented molecules representing species from decomposing fluoropolymers: F-, HF, CH3F, and CF4. The analysis has strong implications for the reactivity of aluminum (Al) particles passivated by an alumina shell. It was hypothesized that the alumina surface structure could be transformed due to hydrogen bonding effects from the environment that promote surface reactions with fluorinated species. In this study, the alumina surface was analyzed using model clusters as isolated systems embedded in a polar environment (i.e., acetone). The conductor-like screening model (COSMO) was used to mimic environmental effects on the alumina surface. Four defect models for specific active -OH sites were investigated including two terminal hydroxyl groups and two hydroxyl bridge groups. Reactions involving terminal bonds produce more energy than bridge bonds. Also, surface exothermic reactions between terminal -OH bonds and fluorinated species produce energy in decreasing order with the following reactant species: CF4 > HF > CH3F. Additionally, experiments were performed on aluminum powders using thermal equilibrium analysis techniques that complement the calculations. Consistently, the experimental results show a linear relationship between surface exothermic reactions and the main fluorination reaction for Al powders. These results connect molecular level reaction kinetics to macroscopic measurements of surface energy and show that optimizing energy available in surface reactions linearly correlates to maximizing energy in the main reaction.

RESUMEN

Intrinsically disordered proteins that populate the so-called "Dark Proteome" offer challenging benchmarks of atomistic simulation methods to accurately model conformational transitions on a multidimensional energy landscape. This work explores the application of parallel tempering with implicit solvent models as a computational framework to capture the conformational ensemble of an intrinsically disordered peptide derived from the Ebola virus protein VP35. A recent X-ray crystallographic study reported a protein-peptide interface where the VP35 peptide underwent a folding transition from a disordered form to a helix-ß-turn-helix topological fold upon molecular association with the Ebola protein NP. An assessment is provided of the accuracy of two generalized Born solvent models (GBMV2 and GBSW2) using the CHARMM force field and applied with temperature-based replica exchange dynamics to calculate the disorder propensity of the peptide and its probability density of states in a continuum solvent. A further comparison is presented of applying an explicit/implicit solvent hybrid replica exchange simulation of the peptide to determine the effect of modeling water interactions at the all-atom resolution.

RESUMEN

This article explores the impact of surface area, volume, curvature, and Lennard-Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent-solute interfaces, and define a generalized Poisson-Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature-based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.

Asunto(s)

RESUMEN

Density functional theory (DFT) calculations were performed to understand molecular variations on an alumina surface due to exposure to a polar environment. The analysis has strong implications for the reactivity of aluminum (Al) particles passivated by an alumina shell. Recent studies have shown a link between the carrier fluid used for Al powder intermixing and the reactivity of Al with fluorine containing reactive mixtures. Specifically, flame speeds show a threefold increase when polar liquids are used to intermix aluminum and fluoropolymer powder mixtures. It was hypothesized that the alumina lattice structure could be transformed due to hydrogen bonding forces exerted by the environment that induce modified bond distances and charges and influence reactivity. In this study, the alumina surface was analyzed using DFT calculations and model clusters as isolated systems embedded in polar environments (acetone and water). The conductor-like screening model (COSMO) was used to mimic environmental effects on the alumina surface. Five defect models for specific active -OH sites were investigated in terms of structures and vibrational -OH stretching frequencies. The observed changes of the surface OH sites invoked by the polar environment were compared to the bare surface. The calculations revealed a strong connection between the impact of carrier fluid polarity on the hydrogen bonding forces between the surface OH sites and surrounding species. Changes were observed in the OH characteristic properties such as OH distances (increase), atomic charges (increase), and OH stretching frequencies (decrease); these consequently improve OH surface reactivity. The difference between medium (acetone) and strong (water) polar environments was minimal in the COSMO approximation.

RESUMEN

Orientations of proteins in the membranes are crucial to their function and stability. Unfortunately the exact positions of these proteins in the lipid bilayer are mostly undetermined. Here, the spatial orientation of membrane proteins within the lipid membrane was evaluated using a Poisson-Boltzmann solvent continuum approach to calculate the electrostatic free energy of the protein solvation at various orientations in an implicit bilayer. The solvation energy was obtained by computing the difference in electrostatic energies of the protein in water and in lipid/water environments, treating each as an implicit solvent model. The optimal position of transmembrane proteins (TMP) in a lipid bilayer is identified by the minimum in the "downhill" pathway of the solvation energy landscape. The energy landscape pattern was considerably conserved in various TMP classes. Evaluation of the position of 1060 membrane proteins from the orientations of proteins in membranes (OPM) database revealed that most of the polytopic and ß-barrel proteins were in good agreement with those of the OPM database. The study provides a useful scheme for estimating the membrane solvation energy made by lipid-exposed amino acids in membrane proteins. In addition, our results tested with the bacterial potassium channel model demonstrated the potential usefulness of the approach in assessing the quality of membrane protein models. The present approach should be applicable for constructing transmembrane proteins-lipid configuration suitable for membrane protein simulations and will have utility for the structural modeling of membrane proteins.

Asunto(s)

RESUMEN

A method is proposed to study protein-ligand binding in a system governed by specific and nonspecific interactions. Strong associations lead to narrow distributions in the proteins configuration space; weak and ultraweak associations lead instead to broader distributions, a manifestation of nonspecific, sparsely populated binding modes with multiple interfaces. The method is based on the notion that a discrete set of preferential first-encounter modes are metastable states from which stable (prerelaxation) complexes at equilibrium evolve. The method can be used to explore alternative pathways of complexation with statistical significance and can be integrated into a general algorithm to study protein interaction networks. The method is applied to a peptide-protein complex. The peptide adopts several low-population conformers and binds in a variety of modes with a broad range of affinities. The system is thus well suited to analyze general features of binding, including conformational selection, multiplicity of binding modes, and nonspecific interactions, and to illustrate how the method can be applied to study these problems systematically. The equilibrium distributions can be used to generate biasing functions for simulations of multiprotein systems from which bulk thermodynamic quantities can be calculated.

Asunto(s)