Implicit solvent models for flexible protein-protein docking by molecular dynamics simulation

The suitability of three implicit solvent models for flexible protein-protein docking by procedures using molecular dynamics simulation is investigated. The three models are (i) the generalized Born (GB) model implemented in the program AMBER6.0; (ii) a distance-dependent dielectric (DDD) model; and (iii) a surface area-dependent model that we have parameterized and call the NPSA model. This is a distance-dependent dielectric model modified by neutralizing the ionizable side-chains and adding a surface area-dependent solvation term. These solvent models were first tested in molecular dynamics simulations at 300 K of the native structures of barnase, barstar, segment B1 of protein G, and three WW domains. These protein structures display a range of secondary structure contents and stabilities. Then, to investigate the performance of the implicit solvent models in protein docking, molecular dynamics simulations of barnase/barstar complexation, as well as PIN1 WW domain/peptide complexation, were conducted, starting from separated unbound structures. The simulations show that the NPSA model has significant advantages over the DDD and GB models in maintaining the native structures of the proteins and providing more accurate docked complexes.     

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.     

Reversible scaling of dihedral angle barriers during molecular dynamics to improve structure prediction of cyclic peptides.

Peptide cyclization or chemical cross-linking has frequently been used to restrict the conformational freedom of a peptide, for example, to enhance its capacity for selective binding to a target receptor molecule. Structure prediction of cyclic peptides is important to evaluate possible conformations prior to synthesis. Because of the conformational constraints imposed by cyclization low energy conformations of cyclic peptides can be separated by large energy barriers. In order to improve the conformational search properties of molecular dynamics (MD) simulations a potential scaling method has been designed. The approach consists of several consecutive MD simulations with a specific lowering of dihedral energy barriers and reduced nonbonded interactions between atoms separated by three atoms followed by gradually scaling the potential until the original barriers are reached. Application to four cyclic penta- and hexa-peptide test cases and a protein loop of known structure indicates that the potential scaling method is more efficient and faster in locating low energy conformations than standard MD simulations. Combined with a generalized Born implicit solvation model the low energy cyclic peptide conformations and the loop structure are in good agreement with experiment. Applications in the presence of explicit water molecules during the simulations showed also improved convergence to structures close to experiment compared with regular MD.     

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Protein molecular dynamics with the generalized Born/ACE solvent model

Implicit solvent models are increasingly important for the study of proteins in aqueous solution. Here, the generalized Born (GB) solvent polarization model as implemented in the analytical ACE potential [Schaefer and Karplus (1996) J Phys Chem 100:1578] is used to perform molecular dynamics simulations of two small, homologous proteins: the immunoglobulin-binding domain of streptococcal protein G and the Ras binding domain of Raf. Several model parameterizations are compared through more than 60 ns of simulation. Results are compared with two simpler solvent models-an accessible surface area model and a distant-dependent dielectric model, with finite-difference Poisson calculations, with existing explicit solvent simulations, and with experimental data. The simpler models yield stable but distorted structures. The best GB/ACE implementation uses a set of atomic Voronoi volumes reported recently, obtained by averaging over a large database of crystallographic protein structures. A 20% reduction is applied to the volumes, compensating in an average sense for an excessive de-screening of individual charges inherent in the ACE self-energy and for an undersolvation of dipolar groups inherent in the GB screening function. This GB/ACE parameterization yields stable trajectories on the 0.5-1-ns time scale that deviate moderately (approximately 1.5-2.5 A) from the X-ray structure, reproduce approximately the surface distribution of charged, polar, and hydrophobic groups, and reproduce accurately backbone flexibility as measured by amide NMR-order parameters. Over longer time scales (1.5-3 ns), some of the protein G runs escape from the native energy basin and deviate strongly (3 A) from the native structure. The conformations sampled during the transition out of the native energy basin are overstabilized by the GB/ACE solvation model, as compared with a numerical treatment of the full dielectric continuum model.     

Conformational sampling with implicit solvent models: application to the PHF6 peptide in tau protein

Implicit solvent models approximate the effects of solvent through a potential of mean force and therefore make solvated simulations computationally efficient. Yet despite their computational efficiency, the inherent approximations made by implicit solvent models can sometimes lead to inaccurate results. To test the accuracy of a number of popular implicit solvent models, we determined whether implicit solvent simulations can reproduce the set of potential energy minima obtained from explicit solvent simulations. For these studies, we focus on a six-residue amino-acid sequence, referred to as the paired helical filament 6 (PHF6), which may play an important role in the formation of intracellular aggregates in patients with Alzheimer's disease. Several implicit solvent models form the basis of this work--two based on the generalized Born formalism, and one based on a Gaussian solvent-exclusion model. All three implicit solvent models generate minima that are in good agreement with minima obtained from simulations with explicit solvent. Moreover, free-energy profiles generated with each implicit solvent model agree with free-energy profiles obtained with explicit solvent. For the Gaussian solvent-exclusion model, we demonstrate that a straightforward ranking of the relative stability of each minimum suggests that the most stable structure is extended, a result in excellent agreement with the free-energy profiles. Overall, our data demonstrate that for some peptides like PHF6, implicit solvent can accurately reproduce the set of local energy minimum arising from quenched dynamics simulations with explicit solvent. More importantly, all solvent models predict that PHF6 forms extended beta-structures in solution, a finding consistent with the notion that PHF6 initiates neurofibrillary tangle formation in patients with Alzheimer's disease.     

Solvation Effects on the Conformational Behaviour of Gellan and Calcium Ion Binding to Gellan Double Helices

The contribution of the presence of solvent to the conformations adopted by disaccharide fragments within the repeat unit of gellan have been studied by molecular modelling techniques. Initial conformational energy searches, using a dielectric continuum to represent the solvent, provided starting geometries for a series of molecular dynamics simulations. The solution behaviour from these simulations was subsequently compared to fibre diffraction data of the potassium gellan salt. The present calculations indicate considerable flexibility of the glycosidic linkages, and this is discussed in relation to its effect on gel formation. One of the fragments was solvated with explicit water molecules. These calculations showed the same conformational behaviour as those simulations conducted in implicit solvent.Finally, a series of molecular dynamics (MD) simulations were performed to study the calcium binding to gellan. The results from this clearly showed a well defined binding site for this ion.Abbreviations MM molecular mechanics - MD molecular dynamics     

Elastic energy storage in an unmineralized collagen type I molecular model with explicit solvation and water infiltration

Collagen type I is a structural protein that provides tensile strength to tendons and ligaments. Type I collagen molecules form collagen fibers, which are viscoelastic and can therefore store energy elastically via molecular elongation and dissipate viscous energy through molecular rearrangement and fibrillar slippage. The ability to store elastic energy is important for the resiliency of tendons and ligaments, which must be able to deform and revert to their initial lengths with changes in load.In an earlier paper by one of the present authors, molecular modeling was used to investigate the role of mineralization upon elastic energy storage in collagen type I. Their collagen model showed a similar trend to their experimental data but with an over-estimation of elastic energy storage. Their simulations were conducted in vacuum and employed a distance-dependent dielectric function. In this study, we performed a re-evaluation of Freeman and Silver's model data incorporating the effects of explicit solvation and water infiltration, in order to determine whether the model data could be improved with a more accurate representation of the solvent and osmotic effects. We observed an average decrease in the model's elastic energy storage of 45.1%±6.9% in closer proximity to Freeman and Silver's experimental data. This suggests that although the distance-dependent dielectric implicit solvation approach was favored for its increased speed and decreased computational requirements, an explicit representation of water may be necessary to more accurately model solvent interactions in this particular system. In this paper, we discuss the collagen model described by Freeman and Silver, the present model building approach, the application of the present model to that of Freeman and Silver, and additional assumptions and limitations.     

Parameterization and Application of an Implicit Solvent Model for Macromolecules

Abstract

As the field of theoretical biophysics begins to recognize systems of longer timescales and larger magnitude, rapid approaches for investigating these systems are required. One promising simplification of the typical system of a solute surrounded by water is the use of implicit solvation models. The generalized Born implicit solvent offers a rapid approach for computing the electrostatic effects of bulk solvent without the explicit representation of water molecules. This report describes the parameterization of a generalized Born (GB) model for protein and nucleic acid structures. As a demonstration of the usefulness of this approach, the GB model is applied toward the discrimination of misfolded and properly folded protein structures. This study attempts to illustrate the potential of the GB model for molecular dynamics simulations over longer timescales as well as for screening large structural databases.     

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.     

Conformation in solution and dynamics of a structurally constrained linear insect kinin pentapeptide analogue

The preferred conformations of the active diuretic insect kinin pentapeptide analogue Phe-Phe-Aib-Trp-Gly-NH2 were studied using nmr spectroscopy and molecular modeling. Structure sets consistent with rotating frame nuclear Overhauser effect spectroscopy distance constraints obtained by restrained simulated annealing in vacuo indicate a predominant population of a type II beta-turn involving the Phe1-Trp4 region. An equilibrium between this type II and a type I beta-turn formed by residues Phe2 and Gly5 was observed in a 5 ns restrained molecular dynamics simulation using the implicit generalized Born solvent accessible surface area (GB/SA) solvation model. When subjected to 500 ps dynamics with explicit water both beta-turn folds were conserved throughout the simulations. The results obtained with implicit and explicit solvation models are compared, and their consistency with the nmr observations is discussed. The behavior of the linear pentapeptide in this study is in agreement with an earlier report on the consensus conformation of the insect kinin active core derived from analysis of cyclic active analogues.     

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.     

Unrestrained stochastic dynamics simulations of the UUCG tetraloop using an implicit solvation model.

Three unrestrained stochastic dynamics simulations have been carried out on the RNA hairpin GGAC[UUCG] GUCC, using the AMBER94 force field (Cornell et al., 1995. J. Am. Chem. Soc. 117:5179-5197) in MacroModel 5.5 (Mohamadi et al., 1990. J. Comp. Chem. 11:440-467) and either the GB/SA continuum solvation model (Still et al., 1990. J. Am. Chem. Soc. 112:6127-6129) or a linear distance-dependent dielectric (1/R) treatment. The linear distance-dependent treatment results in severe distortion of the nucleic acid structure, restriction of all hydroxyl dihedrals, and collapse of the counterion atmosphere over the course of a 5-ns simulation. An additional vacuum simulation without counterions shows somewhat improved behavior. In contrast, the two GB/SA simulations (1.149 and 3.060 ns in length) give average structures within 1.2 A of the initial NMR structure and in excellent agreement with results of an earlier explicit solvent simulation (Miller and Kollman, 1997. J. Mol. Biol. 270:436-450). In a 3-ns GB/SA simulation starting with the incorrect UUCG tetraloop structure (Cheong et al., 1990. Nature. 346:680-682), this loop conformation converts to the correct loop geometry (Allain and Varani, 1995. J. Mol. Biol. 250:333-353), suggesting enhanced sampling relative to the previous explicit solvent simulation. Thermodynamic effects of 2'-deoxyribose substitutions of loop nucleotides were experimentally determined and are found to correlate with the fraction of time the ribose 2'-OH is hydrogen bonded and the distribution of the hydroxyl dihedral is observed in the GB/SA simulations. The GB/SA simulations thus appear to faithfully represent structural features of the RNA without the computational expense of explicit solvent.     

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.     

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.     

Calculations of free-energy contributions to protein-RNA complex stabilization

The problem of calculating binding affinities of protein-RNA complexes is addressed by analyzing a computational strategy of modeling electrostatic free energies based on a nonlinear Poisson-Boltzmann (NLPB) model and linear response approximation (LRA). The underlying idea is to treat binding as a two-step process. Solutions to the NLPB equation calculate free energies arising from electronic polarizability and the LRA is constructed from molecular dynamics simulations to model reorganization free energies due to conformational transitions. By implementing a consistency condition of requiring the NLPB model to reproduce the solute-solvent free-energy transitions determined by the LRA, a "macromolecule dielectric constant" (epsilon(m)) for treating reorganization is obtained. The applicability of this hybrid approach was evaluated by calculating the absolute free energy of binding and free-energy changes for amino acid substitutions in the complex between the U1A spliceosomal protein and its cognate RNA hairpin. Depending on the residue substitution, epsilon(m) varied from 3 to 18, and reflected dipolar reorientation not included in the polarization modeled by epsilon(m) = 2. Although the changes in binding affinities from substitutions modeled strictly at the implicit level by the NLPB equation with epsilon(m) = 4 reproduced the experimental values with good overall agreement, substitutions problematic to this simple treatment showed significant improvement when solved by the NLPB-LRA approach.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

An evaluation of implicit and explicit solvent model systems for the molecular dynamics simulation of bacteriophage T4 lysozyme

In this report we examine several solvent models for use in molecular dynamics simulations of protein molecules with the Discover program from Biosym Technologies. Our goal was to find a solvent system which strikes a reasonable balance among theoretical rigor, computational efficiency, and experimental reality. We chose phage T4 lysozyme as our model protein and analyzed 14 simulations using different solvent models. We tested both implicit and explicit solvent models using either a linear distance-dependent dielectric or a constant dielectric. Use of a linear distance-dependent dielectric with implicit solvent significantly diminished atomic fluctuations in the protein and kept the protein close to the starting crystal structure. In systems using a constant dielectric and explicit solvent, atomic fluctuations were much greater and the protein was able to sample a larger portion of conformational space. A series of nonbonded cutoff distances (9.0, 11.5, 15.0, 20.0 Å) using both abrupt and smooth truncation of the nonbonded cutoff distances were tested. The method of dual cutoffs was also tested. We found that a minimum nonbonded cutoff distance of 15.0 Å was needed in order to properly couple solvent and solute. Distances shorter than 15.0 Å resulted in a significant temperature gradient between the solvent and solute. In all trajectories using the proprietary Discover switching function, we found significant denaturation in the protein backbone; we were able to run successful trajectories only in those simulations that used no switching function. We were able to significantly reduce the computational burden by using dual cutoffs and still calculate a quality trajectory. In this method, we found that an outer cutoff distance of 15.0 Å and an inner cutoff distance of 11.5 worked well. While a 10 Å shell of explicit water yielded the best results, a 6 A shell of water yielded satisfactory results with nearly a 40% reduction in computational cost. © 1994 John Wiley & Sons, Inc.