Comparative study of generalized Born models: protein dynamics

In silico vaccine design for Yersinia enterocolitica: A comprehensive approach to enhanced immunogenicity, efficacy and protection

Yersinia enterocolitica, a foodborne pathogen, has emerged as a significant public health concern due to its increased prevalence and multidrug resistance. This study employed reverse vaccinology to identify novel vaccine candidates against Y. enterocolitica through comprehensive in silico analyses. The core genome's conserved protein translocase subunit SecY was selected as the target, and potential B-cell, MHC class I, and MHC class II epitopes were mapped. 3B-cell epitopes, 3 MHCI and 11 MHCII epitopes were acquired. A multi-epitope vaccine construct was designed by incorporating the identified epitopes, TLR4 Agonist was used as adjuvants to enhance the immunogenic response. EAAAK, CPGPG and AYY linkers were used to form a vaccine construct, followed by extensive computational evaluations. The vaccine exhibited desirable physicochemical properties, stable secondary and tertiary structures as evaluated by PDBSum and trRosetta. Moreover, favorable interactions with the human Toll-like receptor 4 (TLR4) was observed by ClusPro. Population coverage analysis estimated the vaccine's applicability across 99.74 % in diverse populations. In addition, molecular dynamics simulations and normal mode analysis confirmed the vaccine's structural stability and dynamics in a simulated biological environment. Furthermore, codon optimization and in silico cloning facilitated the evaluation of the vaccine's expression potential in E. coli and pET-28a was used a recombinant plasmid. This study provides a promising foundation for the development of an efficacious vaccine against Y. enterocolitica infections.

Systematic analysis and comparison of peptide specificity and selectivity between their cognate receptors and noncognate decoys

Protein-peptide interactions (PpIs) play an important role in cell signaling networks and have been exploited as new and attractive therapeutic targets. The affinity and specificity are two unity-of-opposite aspects of PpIs (and other biomolecular interactions); the former indicates the absolute binding strength between the peptide ligand and its cognate protein receptor in a PpI, while the latter represents the relative recognition selectivity of the peptide ligand for its cognate protein receptor in a PpI over those noncognate decoys that could be potentially encountered by the peptide in cell. Although the PpI binding affinity has been widely investigated over the past decades, the peptide recognition specificity (and selectivity) still remains largely unexplored to date. In this study, we classified PpI specificity into three types: (i) class-I specificity: peptide selectivity for its cognate wild-type protein receptor over the noncognate mutant decoys of this receptor, (ii) class-II specificity: peptide selectivity for its cognate protein receptor over other noncognate decoys that are homologous with this receptor, and (iii) class-III specificity: peptide selectivity for its cognate protein receptor over other noncognate decoys that are the cognate receptors of other peptides. We performed affinity and selectivity analysis for the three types of PpI specificity and revealed that the PpIs generally exhibit a moderate or modest specificity; peptide selectivity increases in the order: class-I < class-II < class-III. All the three types of PpI specificity were observed to have no statistically significant correlation with peptide length and hydrophobicity, but the class-I and class-II specificities can be influenced considerably by peptide secondary structures; the high specificity is preferentially associated with ordered structure types as compared to undefined structure types. In addition, the mutation distribution (for class-I specificity), sequence conservation (for class-II specificity), and structural similarity (for class-III specificity) seem also to address effects on peptide selectivity.

Conformations and Solvation of Synthetic Polymers in Water by Generalized Born Implicit-Solvent Molecular Dynamics Simulations: Stereoisomers of Poly(acrylic acid) and Poly(methacrylic acid)

We present the GB-OBC model as an approach for implicit-solvent MD simulations of a synthetic macromolecule in water. The model is tested and found to be successful in reproducing the chain dimensions and predicting the free energy of solvation of carboxylic acid vinyl polymers. The influence of stereochemistry and the hydrophobic nature of the polymer was investigated as a function of chain length (20 < N < 600) for poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMA). The dimensionless parameters of the GB-OBC model were parameterized to be applicable to PAA and PMA. Scaling relations for chain dimensions obtained using implicit-solvent MD simulations in this study are in good agreement with those from experiments, theory of solvated chains in good solvents, and all-atom MD simulations in explicit water. Results show that ⟨R_g²⟩/NL² is greater for the atactic chain as compared to the isotactic chain, for PAA as well as PMA. ⟨R_g²⟩/NL² values of chains attain constancy in water for N = 200, with the values being greater for PMA. The PMA chain is conformationally more perturbed than the PAA chain, for both isotactic and atactic stereochemistry. The solvation free energy ΔG_hyd of PAA and PMA in water is negative for all chain lengths (N = 20-600) and becomes more favorable with an increase in molecular weight. The ΔG_hyd values for isotactic and atactic chains are identical at lower values of N but differ slightly for N > 300. Irrespective of the hydrophobic nature of the polymer, the atactic chain is thermodynamically more soluble in water as compared to the isotactic chain. The isotactic chain is less hydrophilic as compared to the atactic chain due to the closer proximity of the COOH groups along the backbone. This implicit solvent method is an effective way to accurately simulate the configurational properties and solvation of synthetic polymers in water.

Applied Identification of Industry Data Science Using an Advanced Multi-Componential Discretization Model

Applied human large-scale data are collected from heterogeneous science or industry databases for the purposes of achieving data utilization in complex application environments, such as in financial applications. This has posed great opportunities and challenges to all kinds of scientific data researchers. Thus, finding an intelligent hybrid model that solves financial application problems of the stock market is an important issue for financial analysts. In practice, classification applications that focus on the earnings per share (EPS) with financial ratios from an industry database often demonstrate that the data meet the abovementioned standards and have particularly high application value. This study proposes several advanced multicomponential discretization models, named Models A–E, where each model identifies and presents a positive/negative diagnosis based on the experiences of the latest financial statements from six different industries. The varied components of the model test performance measurements comparatively by using data-preprocessing, data-discretization, feature-selection, two data split methods, machine learning, rule-based decision tree knowledge, time-lag effects, different times of running experiments, and two different class types. The experimental dataset had 24 condition features and a decision feature EPS that was used to classify the data into two and three classes for comparison. Empirically, the analytical results of this study showed that three main determinants were identified: total asset growth rate, operating income per share, and times interest earned. The core components of the following techniques are as follows: data-discretization and feature-selection, with some noted classifiers that had significantly better accuracy. Total solution results demonstrated the following key points: (1) The highest accuracy, 92.46%, occurred in Model C from the use of decision tree learning with a percentage-split method for two classes in one run; (2) the highest accuracy mean, 91.44%, occurred in Models D and E from the use of naïve Bayes learning for cross-validation and percentage-split methods for each class for 10 runs; (3) the highest average accuracy mean, 87.53%, occurred in Models D and E with a cross-validation method for each class; (4) the highest accuracy, 92.46%, occurred in Model C from the use of decision tree learning-C4.5 with the percentage-split method and no time-lag for each class. This study concludes that its contribution is regarded as managerial implication and technical direction for practical finance in which a multicomponential discretization model has limited use and is rarely seen as applied by scientific industry data due to various restrictions.

Improvements in GROMACS plugin for PyMOL including implicit solvent simulations and displaying results of PCA analysis

In order to get the dynamic molecule model from the static one, the molecular dynamics (MD) simulation needs to be performed. Some software sets such as GROMACS are used for that purpose. Unfortunately they lack GUI. The Dynamics PyMOL plugin allows researcher to perform MD simulations directly from the PyMOL software by GUI-based interface of GROMACS tools. This paper describes many improvements introduced into the Dynamics PyMOL plugin 2.0 including: an integration with ProDy library, possibility to use the implicit solvents, an ability to interpret the MD simulations, and implementation of some more GROMACS functionality.

Characterizing a histidine switch controlling pH-dependent conformational changes of the influenza virus hemagglutinin

During the fusion of the influenza virus to the host cell, bending of the HA2 chain of hemagglutinin into a hairpin-shaped structure in a pH-dependent manner facilitates the fusion of the viral envelope and the endosomal membrane. To characterize the structural and dynamical responses of the hinge region of HA2 to pH changes and examine the role of a conserved histidine in this region (the hinge histidine), we have performed an extensive set of molecular dynamics (MD) simulations of 26-residue peptides encompassing the hinge regions of several hemagglutinin subtypes under both neutral and low pH conditions, modeled by the change of the protonation state of the hinge histidine. More than 70 sets of MD simulations (collectively amounting to 25.1 μs) were performed in both implicit and explicit solvents to study the effect of histidine protonation on structural dynamics of the hinge region. In both explicit and implicit solvent simulations, hinge bending was consistently observed upon the protonation of the histidine in all the simulations starting with an initial straight helical conformation, whereas the systems with a neutral histidine retained their primarily straight conformation throughout the simulations. Conversely, the MD simulations starting from an initially bent conformation resulted in the formation of a straight helical structure upon the neutralization of the hinge histidine, whereas the bent structure was maintained when the hinge histidine remained protonated. Finally, mutation of the hinge histidine to alanine abolishes the bending response of the peptide altogether. A molecular mechanism based on the interaction of the hinge histidine with neighboring acidic residues is proposed to be responsible for its role in controlling the conformation of the hinge. We propose that this might present a common mechanism for pH-controlled structural changes in helical structures when histidines act as the pH sensor.

Hydrophobic organic linkers in the self-assembly of small molecule-DNA hybrid dimers: a computational-experimental study of the role of linkage direction in product distributions and stabilities

Detailed computational and experimental studies reveal the crucial role that hydrophobic interactions play in the self-assembly of small molecule-DNA hybrids (SMDHs) into cyclic nanostructures. In aqueous environments, the distribution of the cyclic structures (dimers or higher-order structures) greatly depends on how well the hydrophobic surfaces of the organic cores in these nanostructures are minimized. Specifically, when the cores are attached to the 3'-ends of the DNA component strands, they can insert into the minor groove of the duplex that forms upon self-assembly, favoring the formation of cyclic dimers. However, when the cores are attached to the 5'-ends of the DNA component strands, such insertion is hindered, leading to the formation of higher-order cyclic structures. These computational insights are supported by experimental results that show clear differences in product distributions and stabilities for a broad range of organic core-linked DNA hybrids with different linkage directions and flexibilities.

PowerBorn: A Barnes-Hut Tree Implementation for Accurate and Efficient Born Radii Computation

Implicit solvent models are one of the standard tools in computational biophysics. While Poisson-Boltzmann methods offer highly accurate results within this framework, generalized Born models have been used due to their higher computational efficiency in many (bio)molecular simulations, where computational power is a limiting factor. In recent years, there have been remarkable advances to reduce some deficiencies in the generalized Born models. On the other hand, these advances come at an increased computational cost that contrasts the reasons for choosing generalized Born models over Poisson-Boltzmann methods. To address this performance issue, we present a new algorithm for Born radii computation, one performance critical part in the evaluation of generalized Born models, which is based on a Barnes-Hut tree code scheme. We show that an implementation of this algorithm provides accurate Born radii and polar solvation free energies in comparison to Poisson-Boltzmann computations, while delivering up to an order of magnitude better performance over existing, similarly accurate methods. The C++ implementation of this algorithm will be available at http://www.int.kit.edu/nanosim/ .

Evaluation of DNA Force Fields in Implicit Solvation

DNA structural deformations and dynamics are crucial to its interactions in the cell. Theoretical simulations are essential tools to explore the structure, dynamics, and thermodynamics of biomolecules in a systematic way. Molecular mechanics force fields for DNA have benefited from constant improvements during the last decades. Several studies have evaluated and compared available force fields when the solvent is modeled by explicit molecules. On the other hand, few systematic studies have assessed the quality of duplex DNA models when implicit solvation is employed. The interest of an implicit modeling of the solvent consists in the important gain in the simulation performance and conformational sampling speed. In this study, respective influences of the force field and the implicit solvation model choice on DNA simulation quality are evaluated. To this end, extensive implicit solvent duplex DNA simulations are performed, attempting to reach both conformational and sequence diversity convergence. Structural parameters are extracted from simulations and statistically compared to available experimental and explicit solvation simulation data. Our results quantitatively expose the respective strengths and weaknesses of the different DNA force fields and implicit solvation models studied. This work can lead to the suggestion of improvements to current DNA theoretical models.

The VSGB 2.0 model: a next generation energy model for high resolution protein structure modeling

A novel energy model (VSGB 2.0) for high resolution protein structure modeling is described, which features an optimized implicit solvent model as well as physics-based corrections for hydrogen bonding, π-π interactions, self-contact interactions, and hydrophobic interactions. Parameters of the VSGB 2.0 model were fit to a crystallographic database of 2239 single side chain and 100 11-13 residue loop predictions. Combined with an advanced method of sampling and a robust algorithm for protonation state assignment, the VSGB 2.0 model was validated by predicting 115 super long loops up to 20 residues. Despite the dramatically increasing difficulty in reconstructing longer loops, a high accuracy was achieved: all of the lowest energy conformations have global backbone RMSDs better than 2.0 Å from the native conformations. Average global backbone RMSDs of the predictions are 0.51, 0.63, 0.70, 0.62, 0.80, 1.41, and 1.59 Å for 14, 15, 16, 17, 18, 19, and 20 residue loop predictions, respectively. When these results are corrected for possible statistical bias as explained in the text, the average global backbone RMSDs are 0.61, 0.71, 0.86, 0.62, 1.06, 1.67, and 1.59 Å. Given the precision and robustness of the calculations, we believe that the VSGB 2.0 model is suitable to tackle "real" problems, such as biological function modeling and structure-based drug discovery.

Electrostatics in proteins and protein-ligand complexes

Accurate computational methods for predicting electrostatic energies are of major importance for our understanding of protein energetics in general for computer-aided drug design as well as for the design of novel biocatalysts and protein therapeutics. Electrostatic energies are of particular importance in such applications as virtual screening, drug design and protein-protein docking due to the high charge density of protein ligands and small-molecule drugs, and the frequent protonation state changes observed when drugs bind to their protein targets. Therefore, the development of a reliable and fast algorithm for the evaluation of electrostatic free energies, as an important contributor to the overall protein energy function, has been the focus for many scientists over the past three decades. In this review we describe the current state-of-the-art in modeling electrostatic effects in proteins and protein-ligand complexes. We focus mainly on the merits and drawbacks of the continuum methodology, and speculate on future directions in refining algorithms for calculating electrostatic energies in proteins using experimental data.

On the role of electrostatics in protein-protein interactions

The role of electrostatics in protein-protein interactions and binding is reviewed in this paper. A brief outline of the computational modeling, in the framework of continuum electrostatics, is presented and the basic electrostatic effects occurring upon the formation of the complex are discussed. The effect of the salt concentration and pH of the water phase on protein-protein binding free energy is demonstrated which indicates that the increase of the salt concentration tends to weaken the binding, an observation that is attributed to the optimization of the charge-charge interactions across the interface. It is pointed out that the pH-optimum (pH of optimal binding affinity) varies among the protein-protein complexes, and perhaps is a result of their adaptation to particular subcellular compartments. The similarities and differences between hetero- and homo-complexes are outlined and discussed with respect to the binding mode and charge complementarity.

A high-performance parallel-generalized Born implementation enabled by tabulated interaction rescaling

Implicit solvent representations, in general, and generalized Born models, in particular, provide an attractive way to reduce the number of interactions and degrees of freedom in a system. The instantaneous relaxation of the dielectric shielding provided by an implicit solvent model can be extremely efficient for high-throughput and Monte Carlo studies, and a reduced system size can also remove a lot of statistical noise. Despite these advantages, it has been difficult for generalized Born implementations to significantly outperform optimized explicit-water simulations due to more complex functional forms and the two extra interaction stages necessary to calculate Born radii and the derivative chain rule terms contributing to the force. Here, we present a method that uses a rescaling transformation to make the standard generalized Born expression a function of a single variable, which enables an efficient tabulated implementation on any modern CPU hardware. The total performance is within a factor 2 of simulations in vacuo. The algorithm has been implemented in Gromacs, including single-instruction multiple-data acceleration, for three different Born radius models and corresponding chain rule terms. We have also adapted the model to work with the virtual interaction sites commonly used for hydrogens to enable long-time steps, which makes it possible to achieve a simulation performance of 0.86 micros/day for BBA5 with 1-nm cutoff on a single quad-core desktop processor. Finally, we have also implemented a set of streaming kernels without neighborlists to accelerate the non-cutoff setup occasionally used for implicit solvent simulations of small systems.

Structure-independent analysis of the breadth of the positional distribution of disordered groups in macromolecules from order parameters for long, variable-length vectors using NMR paramagnetic relaxation enhancement

Quantitative information regarding structurally disordered groups is crucial for a complete understanding of the relationship between structure, dynamics, and function in biological macromolecules. Experimental analysis, however, of the positional distribution of disordered groups in the macromolecular frame is extremely difficult. While NMR order parameters, S(2), for fixed-length bond vectors such as N-H and C-H are commonly used for investigations of conformational dynamics of macromolecules, these order parameters provide only angular information about internal motions and are totally insensitive to translational motions. Although analysis of S(2) for bond vectors permits identification of disordered groups in macromolecules, this type of order parameter cannot provide any information about the distribution radii of disordered groups. Here we describe an NMR approach to directly determine the distribution radius of a disordered group independent of any structural knowledge. This approach makes use of order parameters for long, variable-length vectors (including proton-paramagnetic center and proton-proton vectors) between a disordered group and a rigid portion of the macromolecule. We demonstrate the application of this formalism to paramagnetic relaxation enhancement vectors. In addition, the potential utility of the same formalism to (1)H-(1)H cross-relaxation rates is considered as an alternative approach for analyzing the breadth of the positional distribution of disordered groups.

Emerging methods for ensemble-based virtual screening

Ensemble based virtual screening refers to the use of conformational ensembles from crystal structures, NMR studies or molecular dynamics simulations. It has gained greater acceptance as advances in the theoretical framework, computational algorithms, and software packages enable simulations at longer time scales. Here we focus on the use of computationally generated conformational ensembles and emerging methods that use these ensembles for discovery, such as the Relaxed Complex Scheme or Dynamic Pharmacophore Model. We also discuss the more rigorous physics-based computational techniques such as accelerated molecular dynamics and thermodynamic integration and their applications in improving conformational sampling or the ranking of virtual screening hits. Finally, technological advances that will help make virtual screening tools more accessible to a wider audience in computer aided drug design are discussed.

DynaDock: A new molecular dynamics-based algorithm for protein-peptide docking including receptor flexibility

Molecular docking programs play an important role in drug development and many well-established methods exist. However, there are two situations for which the performance of most approaches is still not satisfactory, namely inclusion of receptor flexibility and docking of large, flexible ligands like peptides. In this publication a new approach is presented for docking peptides into flexible receptors. For this purpose a two step procedure was developed: first, the protein-peptide conformational space is scanned and approximate ligand poses are identified and second, the identified ligand poses are refined by a new molecular dynamics-based method, optimized potential molecular dynamics (OPMD). The OPMD approach uses soft-core potentials for the protein-peptide interactions and applies a new optimization scheme to the soft-core potential. Comparison with refinement results obtained by conventional molecular dynamics and a soft-core scaling approach shows significant improvements in the sampling capability for the OPMD method. Thus, the number of starting poses needed for successful refinement is much lower than for the other methods. The algorithm was evaluated on 15 protein-peptide complexes with 2-16mer peptides. Docking poses with peptide RMSD values <2.10 A from the equilibrated experimental structures were obtained in all cases. For four systems docking into the unbound receptor structures was performed, leading to peptide RMSD values <2.12 A. Using a specifically fitted scoring function in 11 of 15 cases the best scoring poses featured a peptide RMSD < or = 2.10 A.

Structure and dynamics of end-to-end loop formation of the penta-peptide Cys-Ala-Gly-Gln-Trp in implicit solvents

To investigate the effects of implicit solvents on peptide structure and dynamics, we performed extensive molecular dynamics simulations on the penta-peptide Cys-Ala-Gly-Gln-Trp. Two different implicit solvent models based on the CHARMM22 all-atom force field were used. Structural properties of the peptide such as distributions of end-to-end distances and dihedral angles obtained from molecular dynamics simulations with implicit solvent models were in a good agreement with those obtained from a previous explicit solvent simulation using the same force field. Representative structures observed in explicit solvent were sampled by implicit solvent models but with different relative probabilities. However, we observed significant differences in dynamical properties in explicit and implicit solvent models when we used traditional methods for the temperature control, such as Nose-Hoover or Berendsen thermostats. The explicitly solvated peptide displayed the slowest dynamics in both end-to-end contact formation and intrinsic diffusive motion of end-to-end distances. A closer agreement between implicit and explicit solvated peptide dynamics was observed when Langevin dynamics with a friction coefficient of 10 ps(-1) was used to maintain the temperature of the systems.

The AGBNP2 Implicit Solvation Model

The AGBNP2 implicit solvent model, an evolution of the Analytical Generalized Born plus Non-Polar (AGBNP) model we have previously reported, is presented with the aim of modeling hydration effects beyond those described by conventional continuum dielectric representations. A new empirical hydration free energy component based on a procedure to locate and score hydration sites on the solute surface is introduced to model first solvation shell effects, such as hydrogen bonding, which are poorly described by continuum dielectric models. This new component is added to the Generalized Born and non-polar AGBNP terms. Also newly introduced is an analytical Solvent Excluded Volume (SEV) model which improves the solute volume description by reducing the effect of spurious high-dielectric interstitial spaces present in conventional van der Waals representations. The AGBNP2 model is parametrized and tested with respect to experimental hydration free energies of small molecules and the results of explicit solvent simulations. Modeling the granularity of water is one of the main design principles employed for the the first shell solvation function and the SEV model, by requiring that water locations have a minimum available volume based on the size of a water molecule. It is shown that the new volumetric model produces Born radii and surface areas in good agreement with accurate numerical evaluations of these quantities. The results of molecular dynamics simulations of a series of mini-proteins show that the new model produces conformational ensembles in substantially better agreement with reference explicit solvent ensembles than the original AGBNP model with respect to both structural and energetics measures.

Interface analysis of the complex between ERK2 and PTP-SL

The activity of ERK2, an essential component of MAP-kinase pathway, is under the strict control of various effector proteins. Despite numerous efforts, no crystal structure of ERK2 complexed with such partners has been obtained so far. PTP-SL is a major regulator of ERK2 activity. To investigate the ERK2–PTP-SL complex we used a combined method based on cross-linking, MALDI-TOF analysis, isothermal titration calorimetry, molecular modeling and docking. Hence, new insights into the stoichiometry, thermodynamics and interacting regions of the complex are obtained and a structural model of ERK2-PTP-SL complex in a state consistent with PTP-SL phosphatase activity is developed incorporating all the experimental constraints available at hand to date. According to this model, part of the N-terminal region of PTP-SL has propensity for intrinsic disorder and becomes structured within the complex with ERK2. The proposed model accounts for the structural basis of several experimental findings such as the complex-dissociating effect of ATP, or PTP-SL blocking effect on the ERK2 export to the nucleus. A general observation emerging from this model is that regions involved in substrate binding in PTP-SL and ERK2, respectively are interacting within the interface of the complex.

Calculation of protein heat capacity from replica-exchange molecular dynamics simulations with different implicit solvent models

The heat capacity has played a major role in relating microscopic and macroscopic properties of proteins and their disorder-order phase transition of folding. Its calculation by atomistic simulation methods remains a significant challenge due to the complex and dynamic nature of protein structures, their solvent environment, and configurational averaging. To better understand these factors on calculating a protein heat capacity, we provide a comparative analysis of simulation models that differ in their implicit solvent description and force-field resolution. Our model protein system is the src Homology 3 (SH3) domain of alpha-spectrin, and we report a series of 10 ns replica-exchange molecular dynamics simulations performed at temperatures ranging from 298 to 550 K, starting from the SH3 native structure. We apply the all-atom CHARMM22 force field with different modified analytical generalized Born solvent models (GBSW and GBMV2) and compare these simulation models with the distance-dependent dielectric screening of charge-charge interactions. A further comparison is provided with the united-atom CHARMM19 plus a pairwise GB model. Unfolding-folding transition temperatures of SH3 were estimated from the temperature-dependent profiles of the heat capacity, root-mean-square distance from the native structure, and the fraction of native contacts, each calculated from the density of states by using the weighted histogram analysis method. We observed that, for CHARMM22, the unfolding transition and energy probability density were quite sensitive to the implicit solvent description, in particular, the treatment of the protein-solvent dielectric boundary in GB models and their surface-area-based hydrophobic term. Among the solvent models tested, the calculated melting temperature varied in the range 353-438 K and was higher than the experimental value near 340 K. A reformulated GBMV2 model of employing a smoother molecular-volume dielectric interface was the most accurate in reproducing the native conformation and a two-state folding landscape, although the melting transition temperature did not show the smallest deviation from experiment. For the lower-resolution CHARMM19/GB model, the simulations failed to yield a bimodal energy distribution, yet the melting temperature was observed to be a good estimate of higher-resolution simulation models. We also demonstrate that a careful analysis of a relatively long simulation is necessary to avoid trapping in local minima and to find a true thermodynamic transition temperature.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics

We report a serious problem associated with a number of current implementations of Andersen and Langevin dynamics algorithms. When long simulations are run in many segments, it is sometimes possible to have a repeating sequence of pseudorandom numbers enter the calcuation. We show that, if the sequence repeats rapidly, the resulting artifacts can quickly denature biomolecules and are then easily detectable. However, if the sequence repeats less frequently, the artifacts become subtle and easily overlooked. We derive a formula for the underlying cause of artifacts in the case of the Langevin thermostat, and find it vanishes slowly as the inverse square root of the number of time steps per simulation segment. Numerous examples of simulation artifacts are presented, including dissociation of a tetrameric protein after 110 ns of dynamics, reductions in atomic fluctuations for a small protein in implicit solvent, altered thermodynamic properties of a box of water molecules, and changes in the transition free energies between dihedral angle conformations. Finally, in the case of strong thermocoupling, we link the observed artifacts to previous work in nonlinear dynamics and show that it is possible to drive a 20-residue, implicitly solvated protein into periodic trajectories if the thermostat is not used properly. Our findings should help other investigators re-evaluate simulations that may have been corrupted and obtain more accurate results.

Refining homology models by combining replica-exchange molecular dynamics and statistical potentials

A protocol is presented for the global refinement of homology models of proteins. It combines the advantages of temperature-based replica-exchange molecular dynamics (REMD) for conformational sampling and the use of statistical potentials for model selection. The protocol was tested using 21 models. Of these 14 were models of 10 small proteins for which high-resolution crystal structures were available, the remainder were targets of the recent CASPR exercise. It was found that REMD in combination with currently available force fields could sample near-native conformational states starting from high-quality homology models. Conformations in which the backbone RMSD of secondary structure elements (SSE-RMSD) was lower than the starting value by 0.5-1.0 A were found for 15 out of the 21 cases (average 0.82 A). Furthermore, when a simple scoring function consisting of two statistical potentials was used to rank the structures, one or more structures with SSE-RMSD of at least 0.2 A lower than the starting value was found among the five best ranked structures in 11 out of the 21 cases. The average improvement in SSE-RMSD for the best models was 0.42 A. However, none of the scoring functions tested identified the structures with the lowest SSE-RMSD as the best models although all identified the native conformation as the one with lowest energy. This suggests that while the proposed protocol proved effective for the refinement of high-quality models of small proteins scoring functions remain one of the major limiting factors in structure refinement. This and other aspects by which the methodology could be further improved are discussed.

Electrostatic funneling of substrate in mitochondrial inner membrane carriers

Exchange of ATP and ADP across mitochondrial membrane replenishes the cytoplasm with newly synthesized ATP and provides the mitochondria with the substrate ADP for oxidative phosphorylation. The sole means of this exchange is the mitochondrial ADP/ATP carrier (AAC), a membrane protein that is suggested to cycle between two conformationally distinct states, cytosolic-open (c-state) and matrix-open (m-state), thereby shuttling nucleotides across the inner mitochondrial membrane. However, the c-state is the only structurally resolved state, and the binding site of ADP remains elusive. Here, we present approximately 0.3 mus of all-atom MD simulations of the c-state revealing rapid, spontaneous binding of ADP to deeply positioned binding sites within the AAC lumen. To our knowledge, a complete ligand-binding event has heretofore not been described in full atomic detail in unbiased simulations. The identified ADP-bound state and additional simulations shed light on key structural elements and the initial steps involved in conversion to the m-state. Electrostatic analysis of trajectories reveals the presence of an unusually strong positive electrostatic potential in the lumen of AAC that appears to be the main driving force for the observed spontaneous binding of ADP. We provide evidence that the positive electrostatic potential is likely a common attribute among the entire family of mitochondrial carriers. In addition to playing a key role in substrate recruitment and translocation, the electropositivity of mitochondrial carriers might also be critical for their binding to the negatively charged environment of the inner mitochondrial membrane.

All-atom level direct folding simulation of a betabetaalpha miniprotein

We performed ab initio folding simulation for a betabetaalpha peptide BBA5 (PDB code 1T8J) with a modified param99 force field using the generalized Born solvation model (param99MOD5/GBSA). For efficient conformational sampling, we extended a previously developed novel Q-replica exchange molecular dynamics (Q-REMD) into a multiplexed Q-REMD. Starting from a fully extended conformation, we were able to locate the nativelike structure in the global free minimum region at 280 K. The current approach, which combines the more balanced force field with the efficient sampling scheme, demonstrates a clear advantage in direct folding simulation at all-atom level.

Recent advances in implicit solvent-based methods for biomolecular simulations

Implicit solvent-based methods play an increasingly important role in molecular modeling of biomolecular structure and dynamics. Recent methodological developments have mainly focused on the extension of the generalized Born (GB) formalism for variable dielectric environments and accurate treatment of nonpolar solvation. Extensive efforts in parameterization of GB models and implicit solvent force fields have enabled ab initio simulation of protein folding to native or near-native structures. Another exciting area that has benefited from the advances in implicit solvent models is the development of constant pH molecular dynamics methods, which have recently been applied to the calculations of protein pK(a) values and the studies of pH-dependent peptide and protein folding.

Implicit membrane models for membrane protein simulation

Implicit models of membrane environments offer computational advantages in simulations of membrane-interacting proteins and peptides. Such methods are especially useful for studies of long time scale processes, such as folding and aggregation, or very large complexes that are otherwise intractable with explicit lipid environments. Implicit models replace explicit solute-solvent interactions with a mean-field approach. In the most physical models, continuum dielectric electrostatics is combined with empirical formulations for the nonpolar components of the free energy of solvation. The practical use of a number of implicit membrane models ranging from the empirical IMM1 method to generalized Born-based methods with two-dielectric and multidielectric representations of biological membrane characteristics is presented.

Dehydration-driven solvent exposure of hydrophobic surfaces as a driving force in peptide folding

Recent work has shown that the nature of hydration of pure hydrophobic surfaces changes with the length scale considered: water hydrogen-bonding networks adapt to small exposed hydrophobic species, hydrating or "wetting" them at relatively high densities, whereas larger hydrophobic areas are "dewetted" [Chandler D (2005), Nature 29:640-647]. Here we determine whether this effect is also present in peptides by examining the folding of a beta-hairpin (the 14-residue amyloidogenic prion protein H1 peptide), using microsecond time-scale molecular dynamics simulations. Two simulation models are compared, one explicitly including the water molecules, which may thus adapt locally to peptide configurations, and the other using a popular continuum approximation, the generalized Born/surface area implicit solvent model. The results obtained show that, in explicit solvent, peptide conformers with high solvent-accessible hydrophobic surface area indeed also have low hydration density around hydrophobic residues, whereas a concomitant higher hydration density around hydrophilic residues is observed. This dewetting effect stabilizes the fully folded beta-hairpin state found experimentally. In contrast, the implicit solvent model destabilizes the fully folded hairpin, tending to cluster hydrophobic residues regardless of the size of the exposed hydrophobic surface. Furthermore, the rate of the conformational transitions in the implicit solvent simulation is almost doubled with respect to that of the explicit solvent. The results suggest that dehydration-driven solvent exposure of hydrophobic surfaces may be a significant factor determining peptide conformational equilibria.

Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations

Different integrator time steps in NVT and NVE simulations of protein and nucleic acid systems are tested with the GBMV (Generalized Born using Molecular Volume) and GBSW (Generalized Born with simple SWitching) methods. The simulation stability and energy conservation is investigated in relation to the agreement with the Poisson theory. It is found that very close agreement between generalized Born methods and the Poisson theory based on the commonly used sharp molecular surface definition results in energy drift and simulation artifacts in molecular dynamics simulation protocols with standard 2-fs time steps. New parameters are proposed for the GBMV method, which maintains very good agreement with the Poisson theory while providing energy conservation and stable simulations at time steps of 1 to 1.5 fs.

The use of a generalized born model for the analysis of protein conformational transitions: a comparative study with explicit solvent simulations for chemotaxis Y protein (CheY)

To investigate whether implicit solvent models are appropriate for mechanistic studies of conformational transition in proteins, a recently developed generalized Born model (GBSW) was applied to a small signaling protein, chemotaxis protein Y (CheY), with different combinations of the phosphorylation state and conformation of the system; the results were compared to explicit solvent simulations using a stochastic boundary condition. The subtle but distinct conformational transitions involved in CheY activation makes the system ideally suited for comparing implicit and explicit solvent models because these conformational transitions are potentially accessible in both types of simulations. The structural and dynamical properties analyzed include not only those localized to the active site region but also throughout the protein, such as sidechain methyl group order parameters, backbone hydrogen bonding lifetime and occupancy as well as principal components of the trajectories. Overall, many properties were well reproduced by the GBSW simulations when compared with the explicit solvent calculations, although a number of observations consistently point to the suggestion that the current parameterization of the GBSW model tends to overestimate hydrogen-bonding interactions involving both charged groups and (charge-neutral) backbone atoms. This deficiency led to overstabilization of certain secondary structural motifs and more importantly, qualitatively different behaviors for the active site groups (Thr 87, Ala 88, the beta4-alpha4 loop) in response to phosphorylation, when compared with explicit solvent simulations. The current study highlights the value of carrying out both explicit and implicit solvent simulations for complementary mechanistic insights in the analysis of conformational transition in biomolecules.

GBr6: A Parameterization-Free, Accurate, Analytical Generalized Born Method

The Poisson-Boltzmann (PB) equation is widely used for modeling electrostatic effects and solvation for macromolecules. The generalized Born (GB) model has been developed to mimic PB results at substantial lower computational cost. Here, we report an analytical GB method that reproduces PB results with high accuracy. The analytical approach builds on previous work of Gallicchio and Levy (J. Comput. Chem. 2004, 25, 479), and incorporates an improvement, proposed by Grycuk (J. Chem. Phys. 2003, 119, 4817), of the Coulomb-field approximation used in most GB methods. Tested against PB results, our GB method has an average unsigned relative error of only 0.6% for a representative set of 55 proteins and of 0.4% and 0.3%, respectively, for folded and unfolded conformations of cytochrome b562 sampled in molecular dynamics simulations. The dependencies of the electrostatic solvation free energy on solute and solvent dielectric constants and on salt concentration are fully accounted for in our method.

Structural refinement of protein segments containing secondary structure elements: Local sampling, knowledge-based potentials, and clustering

In this article, we present an iterative, modular optimization (IMO) protocol for the local structure refinement of protein segments containing secondary structure elements (SSEs). The protocol is based on three modules: a torsion-space local sampling algorithm, a knowledge-based potential, and a conformational clustering algorithm. Alternative methods are tested for each module in the protocol. For each segment, random initial conformations were constructed by perturbing the native dihedral angles of loops (and SSEs) of the segment to be refined while keeping the protein body fixed. Two refinement procedures based on molecular mechanics force fields - using either energy minimization or molecular dynamics - were also tested but were found to be less successful than the IMO protocol. We found that DFIRE is a particularly effective knowledge-based potential and that clustering algorithms that are biased by the DFIRE energies improve the overall results. Results were further improved by adding an energy minimization step to the conformations generated with the IMO procedure, suggesting that hybrid strategies that combine both knowledge-based and physical effective energy functions may prove to be particularly effective in future applications.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model

The heterogeneous dielectric generalized Born (HDGB) methodology is an the extension of the GBMV model for the simulation of integral membrane proteins with an implicit membrane environment. Three large integral membrane proteins, the bacteriorhodopsin monomer and trimer and the BtuCD protein, were simulated with the HDGB model in order to evaluate how well thermodynamic and dynamic properties are reproduced. Effects of the truncation of electrostatic interactions were examined. For all proteins, the HDGB model was able to generate stable trajectories that remained close to the starting experimental structures, in excellent agreement with explicit membrane simulations. Dynamic properties evaluated through a comparison of B-factors are also in good agreement with experiment and explicit membrane simulations. However, overall flexibility was slightly underestimated with the HDGB model unless a very large electrostatic cutoff is employed. Results with the HDGB model are further compared with equivalent simulations in implicit aqueous solvent, demonstrating that the membrane environment leads to more realistic simulations.

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.

Molecular dynamics simulations of the hydrophobin SC3 at a hydrophobic/hydrophilic interface

Hydrophobins are small ( approximately 100 aa) proteins that have an important role in the growth and development of mycelial fungi. They are surface active and, after secretion by the fungi, self-assemble into amphipathic membranes at hydrophobic/hydrophilic interfaces, reversing the hydrophobicity of the surface. In this study, molecular dynamics simulation techniques have been used to model the process by which a specific class I hydrophobin, SC3, binds to a range of hydrophobic/hydrophilic interfaces. The structure of SC3 used in this investigation was modeled based on the crystal structure of the class II hydrophobin HFBII using the assumption that the disulfide pairings of the eight conserved cysteine residues are maintained. The proposed model for SC3 in aqueous solution is compact and globular containing primarily beta-strand and coil structures. The behavior of this model of SC3 was investigated at an air/water, an oil/water, and a hydrophobic solid/water interface. It was found that SC3 preferentially binds to the interfaces via the loop region between the third and fourth cysteine residues and that binding is associated with an increase in alpha-helix formation in qualitative agreement with experiment. Based on a combination of the available experiment data and the current simulation studies, we propose a possible model for SC3 self-assembly on a hydrophobic solid/water interface.

Implicit versus explicit solvent in free energy calculations of enzyme catalysis: Methyl transfer catalyzed by catechol O-methyltransferase

We compare free energy calculations for the methyl transfer reaction catalyzed by catechol O-methyltransferase using the quantum mechanical/molecular mechanical free energy method with implicit and explicit solvents. An analogous methylation reaction in a solution is also studied. For the explicit solvent model, we use the three-point transferable intermolecular potential model, and for the implicit model, we use the generalized Born molecular volume model as implemented in CHARMM. We find that activation and reaction free energies calculated with the two models are very similar, despite some structural differences that exist. A significant change in the polarization of the environment occurs as the reaction proceeds. This is more pronounced for the reaction in a solution than for the enzymatic reaction. For the enzymatic reaction, most of the changes take place in the protein rather than in the solvent, and, hence, the benefit of having an instantaneous relaxation of the solvent degrees of freedom is less pronounced for the enzymatic reaction than for the reaction in a solution. This is a likely reason why energies of the enzyme reaction are less sensitive to the choice of atomic radii than are energies of the reaction in a solution.

Electrostatics calculations: latest methodological advances

Electrostatics plays a major role in the stabilization and function of biomolecules; as such, it remains a major focus of theoretical and computational studies of macromolecules. Electrostatic interactions are long range, and strongly dependent on the solvent and ions surrounding the biomolecule under study. During the past year, progress has been reported in the treatment of electrostatics in explicit and implicit solvent models. Interesting new developments of explicit solvent models include more efficient Ewald summation methods, as well as alternative approaches based on reaction field theory, periodic images and Euler summations. Implicit solvent models remain divided into those that solve the Poisson-Boltzmann equation numerically and those based on the generalized Born formalism. Both approaches are now included in molecular dynamics simulations and their accuracies may be assessed by direct comparison against experimental data. It is worth mentioning the recent development of web interfaces that facilitate access to and usage of existing tools for computing electrostatic interactions.