A semi-implicit solvent model for the simulation of peptides and proteins

We present a new model of biomolecules hydration based on macroscopic electrostatic theory, that can both describe the microscopic details of solvent-solute interactions and allow for an efficient evaluation of the electrostatic hydration free energy. This semi-implicit model considers the solvent as an ensemble of polarizable pseudoparticles whose induced dipole describe both the electronic and orientational solvent polarization. In the presented version of the model, there is no mutual dipolar interaction between the particles, and they only interact through short-ranged Lennard-Jones interactions. The model has been integrated into a molecular dynamics code, and offers the possibility to simulate efficiently the conformational evolution of biomolecules. It is able to provide estimations of the electrostatic solvation free energy within short time windows during the simulation. It has been applied to the study of two small peptides, the octaalanine and the N-terminal helix of ribonuclease A, and two proteins, the bovine pancreatic trypsin inhibitor and the B1 immunoglobin-binding domain of streptococcal protein G. Molecular dynamics simulations of these biomolecules, using a slightly modified Amber force field, provide stable and meaningful trajectories in overall agreement with experiments and all-atom simulations. Correlations with respect to Poisson-Boltzmann electrostatic solvation free energies are also presented to discuss the parameterization of the model and its consequences.     

Monte Carlo simulations of antibody adsorption and orientation on charged surfaces

Monte Carlo simulations were performed to study the adsorption and orientation of antibodies on charged surfaces based on both colloidal and all-atom models. The colloidal model antibody consists of 12 connected beads representing the 12 domains of an antibody molecule. The structure of the all-atom antibody model was taken from the protein databank. The effects of the surface charge sign and density, the solution pH and ionic strength on the adsorption and orientation of different colloidal model antibodies with different dipole moments were examined. Simulation results show that both the 12-bead and the all-atom models of the antibody, for which the dipole moment points from the Fc to (Fab)2 fragments, tend to have the desired "end-on" orientation on positively charged surfaces and undesired "head-on" orientation on negatively charged surfaces at high surface charge density and low solution ionic strength where electrostatic interactions dominate. At low surface charge density and high solution ionic strength where van der Waals interactions dominate, 12-bead model antibodies tend to have "lying-flat" orientation on surfaces. The orientation of adsorbed antibodies results from the compromise between electrostatic and van der Waals interactions. The dipole moment of an antibody is an important factor for antibody orientation on charged surfaces when electrostatic interactions dominate. This charge-driven protein orientation hypothesis was verified by our simulations results in this work. It was further confirmed by surface plasmon resonance biosensor and time-of-flight secondary ion mass spectrometry experiments reported elsewhere.     

Misfolding of a polyalanine variant due to lack of electrostatic polarization effects

Folding of a polyalanine variant (A-AQ12 with the sequence Ac-[AAQAA]₂-GY-NH₂) in pure water is studied with molecular dynamics (MD) simulation using AMBER fixed charge model and AHBC charge variation model, respectively. The results show that AMBER ostensibly misfolds A-AQ12 into a well-defined α-helix, while A-AQ12 remains a random coil in AHBC agreeing better with the experimental predication of low fractional helical content. The difference is most likely due to the different backbone solvation with and without the incorporation of electrostatic polarization in the simulations, which highlights the importance of electrostatic polarization in H-bonds dynamics of α-helix in water.     

Solvation free energies and partition coefficients with the coarse-grained and hybrid all-atom/coarse-grained MARTINI models

We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.     

A coarse-grained protein-protein potential derived from an all-atom force field

In order to study protein-protein nonbonded interactions, we present the development of a new reduced protein model that represents each amino acid residue with one to three coarse grains, whose physical properties are derived in a consistent bottom-up procedure from the higher-resolution all-atom AMBER force field. The resulting potential energy function is pairwise additive and includes distinct van-der-Waals and Coulombic terms. The van-der-Waals effective interactions are deduced from preliminary molecular dynamics simulations of all possible amino acid homodimers. They are best represented by a soft 1/r6 repulsion and a Gaussian attraction, with parameters obeying Lorentz-Berthelot mixing rules. For the Coulombic interaction, coarse grain charges are optimized for each separate protein in order to best represent the all-atom electrostatic potential outside the protein core. This approach leaves the possibility of using any implicit solvent model to describe solvation effects and electrostatic screening. The coarse-grained force field is tested carefully for a small homodimeric complex, the magainin. It is shown to reproduce satisfactorily the specificity of the all-atom underlying potential, in particular within a PB/SA solvation model. The coarse-grained potential is applied to the redocking prediction of three different protein-protein complexes: the magainin dimer, the barnase-barstar, and the trypsin-BPTI complexes. It is shown to provide per se an efficient and discriminating scoring energy function for the protein-protein docking problem that remains pertinent at both the global and refinement stage.     

Implementation of a protein reduced point charge model toward molecular dynamics applications

A reduced point charge model was developed in a previous work from the study of extrema in smoothed charge density distribution functions generated from the Amber99 molecular electrostatic potential. In the present work, such a point charge distribution is coupled with the Amber99 force field and implemented in the program TINKER to allow molecular dynamics (MD) simulations of proteins. First applications to two polypeptides that involve α-helix and β-sheet motifs are analyzed and compared to all-atom MD simulations. Two types of coarse-grained (CG)-based trajectories are generated using, on one hand, harmonic bond stretching terms and, on the other hand, distance restraints. Results show that the use of the unrestrained CG conditions are sufficient to preserve most of the secondary structure characteristics but restraints lead to a better agreement between CG and all-atom simulation results such as rmsd, dipole moment, and time-dependent mean square deviation functions.     

Tryptophan side chain electrostatic interactions determine edge-to-face vs parallel-displaced tryptophan side chain geometries in the designed beta-hairpin "trpzip2"

The interaction geometries of the four tryptophan (Trp) side chains in the 12-residue designed beta-hairpin trpzip2 are investigated using all-atom explicit-solvent molecular dynamics simulations. The experimentally observed edge-to-face (EtF) pairwise interaction geometries are stable on a time scale of 10 ns. However, removing the electrostatic multipoles of the Trp side chains while retaining the dipoles of the side chains' NH moieties induces a conformational change to a geometry in which three of the four side chains interact in a parallel-displaced (PD) manner. Free energy simulations of the Etf to PD conformational change reveal that, with the side chain multipole moments intact (+MP), the EtF conformation is preferred by 5.79 kcal/mol. Conversely, with only the dipole moments of the side chain NH moieties intact (-MP), the PD conformation's free energy is more favorable by 1.71 kcal/mol. In contrast to energetic similarities for Trp side chain-water electrostatic and Trp side chain-Trp side chain and Trp side chain-water van der Waals, +MP Trp side chain-Trp side chain electrostatic interactions are more favorable by 4.21 kcal/mol in the EtF conformation, while in the -MP case the EtF and PD conformations' Trp side chain-Trp side chain electrostatic energies are nearly identical. The results highlight the importance of electrostatic multipole moments in determining aromatic-aromatic interaction geometries in aqueous biomolecular systems and argue for the inclusion of this physics in simplified models used for protein-ligand docking and protein structure prediction, possibly through a truncated Coulomb term between aromatic moieties.     

Prediction of Protein Loop Conformations using the AGBNP Implicit Solvent Model and Torsion Angle Sampling

The OPLS-AA all-atom force field and the Analytical Generalized Born plus Non-Polar (AGBNP) implicit solvent model, in conjunction with torsion angle conformational search protocols based on the Protein Local Optimization Program (PLOP), are shown to be effective in predicting the native conformations of 57 9-residue and 35 13-residue loops of a diverse series of proteins with low sequence identity. The novel nonpolar solvation free energy estimator implemented in AGBNP augmented by correction terms aimed at reducing the occurrence of ion pairing are important to achieve the best prediction accuracy. Extended versions of the previously developed PLOP-based conformational search schemes based on calculations in the crystal environment are reported that are suitable for application to loop homology modeling without the crystal environment. Our results suggest that in general the loop backbone conformation is not strongly influenced by crystal packing. The application of the temperature Replica Exchange Molecular Dynamics (T-REMD) sampling method for a few examples where PLOP sampling is insufficient are also reported. The results reported indicate that the OPLS-AA/AGBNP effective potential is suitable for high-resolution modeling of proteins in the final stages of homology modeling and/or protein crystallographic refinement.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.     

Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials

A coarse-grained residue-residue interaction potential derived from a statistical analysis of the Protein Data Bank is used to investigate the coil-to-helix transition for polyalanine. The interaction potentials depend on the radial distance between interaction sites, as well as the relative orientation of the sites. Two types of interaction sites are present in the model: a site representing the amino acid side chain, and a site representing a "virtual backbone," i.e., a site located in the peptide bond which accounts for backbone hydrogen bonding. Two chain lengths are studied and the results for the thermodynamics of the coil-to-helix transition are analyzed in terms of the Zimm-Bragg model. Results agree qualitatively and quantitatively with all-atom Monte Carlo simulations and other reduced-model Monte Carlo simulations.     

Structural Analysis of Host–Guest Systems. Methyl-substituted Phenols in beta;-Cyclodextrin

Complexation trajectories and the variation ofinduced circular dichroism are calculated for thedocking of phenol and 2,4,6-trimethyl-phenol with-cyclodextrin. The results are compared toexperimental chirality data to elucidate themechanism of nonspecific molecular recognitionprocesses in aqueous solution. Large geometricalchanges along nearly isoenergetic Dynamic Monte Carlotrajectories show the conformational flexibility ofsuch host–guest systems. This proves diffuseintermolecular interactions, van der Waals orelectrostatic in nature, as the main contributions to thebinding energy. The number and position of the methylsubstituents of the guest reduces the complexityof the conformational space as the guests positionbecomes fixed by steric constraints.The solvation free energy is calculated from thesolvent accessible surface area weighted byrespective atomic solvation parameters. Consideringthe solvation term in the dynamic simulationsrestricts the conformational flexibility of themacromolecular system. The relative importance ofvarious contributions to the solvation energy isdiscussed and it is shown that those terms arisingfrom the interaction of hydrophobic groups with theaqueous environment are essential for thedetermination of the complex structure. Consideringthese terms in the dynamic simulation model, the signand strength of the calculated rotatory strength isin perfect agreement with induced circular dichroismobtained from experimentally determined averagedspectra. The results demonstrate the accuracy of thegeometrical properties of host–guest systems obtainedfrom these simulations.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Secondary structure bias in generalized Born solvent models: comparison of conformational ensembles and free energy of solvent polarization from explicit and implicit solvation

The effects of the use of three generalized Born (GB) implicit solvent models on the thermodynamics of a simple polyalanine peptide are studied via comparing several hundred nanoseconds of well-converged replica exchange molecular dynamics (REMD) simulations using explicit TIP3P solvent to REMD simulations with the GB solvent models. It is found that when compared to REMD simulations using TIP3P the GB REMD simulations contain significant differences in secondary structure populations, most notably an overabundance of alpha-helical secondary structure. This discrepancy is explored via comparison of the differences in the electrostatic component of the free energy of solvation (DeltaDeltaG(pol)) between TIP3P (via thermodynamic Integration calculations), the GB models, and an implicit solvent model based on the Poisson equation (PE). The electrostatic components of the solvation free energies are calculated using each solvent model for four representative conformations of Ala10. Since the PE model is found to have the best performance with respect to reproducing TIP3P DeltaDeltaG(pol) values, effective Born radii from the GB models are compared to effective Born radii calculated with PE (so-called perfect radii), and significant and numerous deviations in GB radii from perfect radii are found in all GB models. The effect of these deviations on the solvation free energy is discussed, and it is shown that even when perfect radii are used the agreement of GB with TIP3P DeltaDeltaG(pol) values does not improve. This suggests a limit to the optimization of the effective Born radius calculation and that future efforts to improve the accuracy of GB models must extend beyond such optimizations.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.     

Aggregation Behavior of Trisiloxane-Tailed Surface Active Ionic Liquids in Aqueous Solution: Coarse-Grained Molecular Dynamics Study

The aggregation behaviors of two trisiloxane-tailed surface active ionic liquids in water have been investigated by coarse-grained (CG) molecular dynamics simulation on the basis of MARTINI force field. The new CG model is developed from the optimized molecule computed by using density functional theory. Direct comparison of angles and bonds obtained from all-atom (AA) simulations with those calculated from the CG model has been conducted to validate the latter model. Excellent agreement between AA and CG demonstrates that the potential of the new CG model can represent the complex system well. The long time CG simulation has been performed to understand the formation process of micelles when dissolving ionic liquids in water. Vesicles were observed at the final stage of the simulation and their partially truncated views and density profiles were obtained to describe the structure in detail.     

A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations

The development of coarse-grained (CG) models that correctly represent the important features of compounds is essential to overcome the limitations in time scale and system size currently encountered in atomistic molecular dynamics simulations. Most approaches reported in the literature model one or several molecules into a single uncharged CG bead. For water, this implicit treatment of the electrostatic interactions, however, fails to mimic important properties, e.g., the dielectric screening. Therefore, a coarse-grained model for water is proposed which treats the electrostatic interactions between clusters of water molecules explicitly. Five water molecules are embedded in a spherical CG bead consisting of two oppositely charged particles which represent a dipole. The bond connecting the two particles in a bead is unconstrained, which makes the model polarizable. Experimental and all-atom simulated data of liquid water at room temperature are used for parametrization of the model. The experimental density and the relative static dielectric permittivity were chosen as primary target properties. The model properties are compared with those obtained from experiment, from clusters of simple-point-charge water molecules of appropriate size in the liquid phase, and for other CG water models if available. The comparison shows that not all atomistic properties can be reproduced by a CG model, so properties of key importance have to be selected when coarse graining is applied. Yet, the CG model reproduces the key characteristics of liquid water while being computationally 1-2 orders of magnitude more efficient than standard fine-grained atomistic water models.     

Using simplified protein representation as a reference potential for all-atom calculations of folding free energy

An effective approach for evaluating folding free-energy surfaces of explicit all-atom models is developed and examined. This approach is based on using the potential of a simplified protein model as a reference potential for calculating the free energy of the corresponding explicit model. Preliminary results are presented for the folding free energy of a 12-residue helix. The potential of the method for studies of protein-folding processes is discussed, emphasizing the ability to determine the difference between the results of simplified and explicit models. This can help in establishing the validity of simplified folding models. Received: 30 December 1998 / Accepted: 27 January 1999 / Published online: 5 May 1999