Mass-weighted molecular dynamics simulation of cyclic polypeptides.

A modified molecular dynamics (MD) method in which atomic masses are weighted was developed previously for studying the conformational flexibility of neuroregulating tetrapeptide Phe-Met-Arg-Phe-amide (FMRF-amide). The method has now been applied to longer and constrained molecules, namely a disulfide-linked cyclic hexapeptide, c[CYFQNC], and its linear and "pseudo-cyclic" analogues. The sampling of dehedral conformational space of teh linear hexapeptide in mass-weighted MD simulations was found to be improved significantly over conventional MD simulations, as in the case of the shorter FMRF-amide molecule studied previously. In the cyclic hexapeptide, the internal constraint of the molecule due to the intramolecular disulfide bond (hence the absence of free terminals in the molecule) does not adversely affect the significant improvement of conformational sampling in mass-weighted MD simulations over normal MD simulations. The pseudo-cyclic polypeptide is identical to the linear CYFQNC molecule in amino acid sequence (i.e., side chains of the cysteine residues are reduced), but the positions of its two terminal heavy atoms were held fixed in space such that the molecule has a nearly cyclic conformation. For this molecule, the mass-weighted MD simulation generated a wide range of polypeptide backbone conformations covering the internal dihedral degrees of freedom; moreover, the physical space of the pseudo-cyclic structure was also sampled in a complete revolution of the entire molecular fragment about the two fixed termini during the simulation. These characteristics suggest that mass-weighted MD can also be an extremely useful method for conformational analyses of constrained molecules and, in particular, for modeling loops on protein surfaces.     

Improved molecular dynamics simulations for the determination of peptide structures

In this article a few methods or modifications proven to be useful in the conformational examination of peptides and related molecules by molecular dynamics are illustrated. The first is the explicit use of organic solvents in the simulations. For many cases such solvents are appropriate since the nmr measurements (or other experimental observations) were carried out in the same solvent. Here, the use of dimethylsulfoxide and chloroform in molecular dynamics is described, with some advantages of the use of these solvents highlighted. A constant allowing for the scaling of the nonbonded interactions of the force field, an idea previously employed in distance geometry and simulated annealing, has been implemented. The usefulness of this method is that when the nonbonded term is turned to zero, atoms can pass through each other, while the connectivity of the molecule is maintained. It will be shown that such simulations, if a sufficient driving force is present (i.e., nuclear Overhauser effects restraints), can produce the correct stereoconfiguration (i.e., chiral center) as well as configurational isomer (i.e., cis/trans isomers). Lastly, a penalty term for coupling constants directly related to the Karplus curve has been plemented into the potential energy force field. The advantages of this method over the commonly used dihedral angle restraining are discussed. In particular, it is shown that with more than one coupling constant about a dihedral angle a great reduction of the allowed conformational space is obtained. © 1993 John Wiley & Sons, Inc.     

Temperature-induced conformational transition of a model elastin-like peptide GVG(VPGVG)(3) in water

The conformation of a single elastin-like peptide GVG(VPGVG)3 in liquid water is studied by computer simulations in the temperature interval between 280 and 440 K. Two main conformational states of the peptide can be distinguished: a rigid conformational state, dominating at low temperatures, and a flexible conformational state, dominating at high temperatures. A temperature-induced transition between these states occurs at about 310 K, rather close to a transition temperature seen in experiments. This transition is accompanied by the thermal breaking of the hydrogen-bonded spanning network of the hydration water via a percolation transition upon heating. This finding indicates that the H-bond clustering structure of the hydration water plays an important role in the conformational stability of biomolecules. A second important observation is the Gaussian distribution of the end-to-end distance in the high-temperature state, which supports the idea of a rubber-like elasticity of the studied elastin-like peptide. Finally our results challenge the idea of the folding of elastin-like peptides upon heating.     

The investigation of the secondary structure propensities and free-energy landscapes of peptide ligands by replica exchange molecular dynamics simulations

The conformational states of two peptide sequences that bind to staphylococcal enterotoxin B are sampled by replica exchange molecular dynamic (REMD) simulations in explicit water. REMD simulations were treated with 52 replicas in the range of 280–501 K for both peptides. The conformational ensembles of both peptides are dominated by random coil, bend and turn structures with a small amount of helical structures for each temperature. In addition, while an insignificant presence of β-bridge structures were observed for both peptides, the β-sheet structure was observed only for peptide 3. The results obtained from simulations at 300 K are consistent with the experimental results obtained from circular dichroism spectroscopy. From the analysis of REMD results, we also calculated hydrophobic and hydrophilic solvent accessible surface areas for both peptides, and it was observed that the hydrophobic segments of the peptides tend to form bend or turn structures. Moreover, the free-energy landscapes of both peptides were obtained by principal component analysis to understand how the secondary structural properties change according to their complex space. From the free-energy analysis, we have found several minima for both peptides at decreased temperature. For these obvious minima of both peptides, it was observed that the random coil, bend and turn structures are still dominant and the helix, β-bridge or β-sheet structures can appear or disappear with respect to minima. On the other hand, when we compare the results of REMD with conventional MD simulations for these peptides, the configurations of peptide 3 might be trapped in energy minima during the conventional MD simulations. Hence, it can be said that the REMD simulations have provided a sufficiently high sampling efficiency.     

Temperature dependence of the structure and dynamics of myoglobin. A simulation approach

The results of simulations of the structure and internal motions of carbonomonoxymyoglobin (MbCO) at two different temperatures (325 and 80 K) are presented and compared with experimental data. Properties calculated from the 120 ps trajectory at 325 K are used as a reference in the analysis of the motion of the protein at 80 K. Three separate 80 K molecular dynamics trajectories were calculated; they were started with different coordinate sets from the 325 K simulation and the lower temperature was achieved by scaling the velocities. The simulations yield results for the structural changes between 325 and 80 K that are in general accord with those from X-ray data. Both the experimental and calculated radii of gyration, distances from the center of mass and main-chain difference distance matrices show that there is a significant but inhomogeneous shrinkage with decreasing temperature. For the atomic fluctuations, by contrast, the calculated temperature dependence is very different from the X-ray results; i.e. the calculated root-mean-square backbone fluctuations decrease to 0.11 A at 80 K from 0.51 A at 325 K, while the fluctuations obtained from the X-ray B factors go from 0.56 A at 260 K to 0.47 A at 80 K. The smaller temperature dependence of the B factors suggests that there is significant conformational disorder in MbCO crystals at lower temperatures. This is in accord with the simulation results, which show that the protein is trapped in restricted regions of conformational space at 80 K, while at 325 K a much larger region is accessible to the protein. Analysis of the fluctuations at 325 K and 80 K shows that the room temperature flexibility of the protein is determined by the mobility of the loop regions and by side-chain torsional motions (in accord with earlier simulation results), while the low temperature fluctuations involve motion within a single well. Examination of the calculated iron atom fluctuations and comparison with Mossbauer data show good agreement. It is found that the dominant contribution to the iron motion arises from heme sliding; motion of the iron relative to the heme are much smaller.     

Simulation vs. reality: a comparison of in silico distance predictions with DEER and FRET measurements

Site specific incorporation of molecular probes such as fluorescent- and nitroxide spin-labels into biomolecules, and subsequent analysis by F?rster resonance energy transfer (FRET) and double electron-electron resonance (DEER) can elucidate the distance and distance-changes between the probes. However, the probes have an intrinsic conformational flexibility due to the linker by which they are conjugated to the biomolecule. This property minimizes the influence of the label side chain on the structure of the target molecule, but complicates the direct correlation of the experimental inter-label distances with the macromolecular structure or changes thereof. Simulation methods that account for the conformational flexibility and orientation of the probe(s) can be helpful in overcoming this problem. We performed distance measurements using FRET and DEER and explored different simulation techniques to predict inter-label distances using the Rpo4/7 stalk module of the M. jannaschii RNA polymerase. This is a suitable model system because it is rigid and a high-resolution X-ray structure is available. The conformations of the fluorescent labels and nitroxide spin labels on Rpo4/7 were modeled using in vacuo molecular dynamics simulations (MD) and a stochastic Monte Carlo sampling approach. For the nitroxide probes we also performed MD simulations with explicit water and carried out a rotamer library analysis. Our results show that the Monte Carlo simulations are in better agreement with experiments than the MD simulations and the rotamer library approach results in plausible distance predictions. Because the latter is the least computationally demanding of the methods we have explored, and is readily available to many researchers, it prevails as the method of choice for the interpretation of DEER distance distributions.     

Structure and energy landscape of a photoswitchable peptide: a replica exchange molecular dynamics study

A replica exchange molecular dynamics (REMD) simulation of a bicyclic azobenzene peptide in explicit dimethyl sulfoxide solution is presented in order to characterize the conformational structures and energy landscape of a photoswitchable peptide. It is shown that an enhanced-sampling technique such as the REMD method is essential to obtain a converged conformational sampling of the peptide at room temperature. This is because conventional MD simulations of less than approximately 100-ns length are either trapped in local minima (at 295 K) or-if run at high temperature-do not resemble the room-temperature REMD results. Calculating various nuclear Overhauser effects (NOEs) and (3)J-couplings, a good overall agreement between the REMD simulations and the NMR experiments of Renner et al. (Biopolymers 2000;54:501-514) is found. In particular, the REMD study confirms the general picture drawn by Renner et al. that the trans-isomer of the azobenzene peptide exhibits a well-defined structure, while the cis-isomer is a conformational heterogeneous system; that is, the trans-isomer occurs in 2 well-defined conformers, while the cis-isomer represents an energetically frustrated system that leads to an ensemble of conformational structures. Employing a principal component analysis of the REMD data, the free energy landscape of the systems is studied at various temperatures. The implications for the folding and unfolding pathways of the system are discussed.     

Application of the primary hydration shell approach to locally enhanced sampling simulated annealing: computer simulation of thyrotropin-releasing hormone in water

A unified model of simulated annealing with locally enhanced sampling (LES) in a primary hydration shell (PHS) aqueous environment is developed and tested by predicting the structure of the tripeptide thyrotropin-releasing hormone (TRH) in solution. The model extends the formulation of the restraining force in the PHS method as a function of temperature, number of copies in the LES method, and shell thickness. The dependence of the restraining force on temperature can be shown to follow the relationship c(1)T - c(2), which can be derived from the expression for kinetic energy in molecular dynamics simulations. The calibration of the restraining force for different simulation conditions reveals the dependence of c(1) and c(2) on the number of copies in the LES method and the thickness of the PHS. The predicted structure of TRH is in very good agreement with results from NMR experiments and from a 10-ns PHS simulation at 300 K. The method promises to be useful in predicting structure of peptides and proteins in an aqueous environment.     

Mass-weighted molecular dynamics simulation of the protein-ligand complex of rhizopuspepsin and inhibitor.

The mass-weighted molecular dynamics simulation method was developed previously for sampling the multidimensional conformational space of linear and cyclic polypeptides and studying their conformational flexibility. Herein results from molecular dynamics simulations of the protein-ligand complex of the aspartyl protease rhizopuspepsin and a polypeptide inhibitor are reported. The dihedral conformational space sampling for the linear peptide inhibitor in situ was found to be increased in the mass-weighted simulation as in other molecular systems previously studied. More significantly, the physical space of the enzyme binding pocket was also sampled efficiently in the simulations and multiple binding sites were identified for the inhibitor. These results suggest that it may be possible now to study, by computer simulations, the putative initial enzyme-inhibitor complex suggested experimentally from the time-dependent kinetics of enzyme inhibition by slow-binding inhibitors (Morrison, J. F., and C. T. Walsh. 1988. Adv. Enzymol. 61:201), and/or conformational substates in protein-ligand complexes suggested in the study of reassociation dynamics of myoglobin and carbon monoxide following photolysis (Austin, R. H., K. W. Beeson, L. Eisenstein, H. Frauenfelder, and I. C. Gunsalus. 1975. Biochemistry. 14:5355). Moreover, the intermediate binding steps and the molecular flexibility of the inhibitor shown in the MWMD simulation may have crucial roles in the ligand binding process.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

Computational studies of tryptophanyl-tRNA synthetase: activation of ATP by induced-fit

Catalysis of amino acid activation by Bacillus stearothermophilus tryptophanyl-tRNA synthetase involves three allosteric states: (1) Open; (2) closed pre-transition state (PreTS); and (3) closed products (Product). The interconversions of these states entail significant domain motions driven by ligand binding. We explore the application of molecular dynamics simulations to investigate ligand-linked conformational stability changes associated with this catalytic cycle. Multiple molecular dynamics trajectories (5 ns) for 11 distinct liganded and unliganded monomer configurations show that the PreTS conformation is unstable in the absence of ATP, reverting within approximately 600 ps nearly to the Open conformation. In contrast, Open and Product state trajectories were stable, even without ligands, confirming the previous suggestion that catalysis entails destabilization of the protein conformation, driven by ATP-binding energies developed as the PreTS state assembles during induced-fit. The simulations suggest novel mechanistic details associated with both induced-fit (Open-PreTS) and catalysis (PreTS-Product). Notably, Mg2+ -ATP interactions are coupled to interactions between ATP and active-site lysine side-chains via mechanisms that cannot be captured under the molecular mechanics approximations, and which therefore require restraining potentials for stable simulation. Simulations of Mg2+. ATP-bound PreTS complexes with restraining potentials and with a virtual K111A mutant confirm that these coupling interactions are necessary to sustain the PreTS conformation and, in turn, provide a new model for how the PreTS conformation activates ATP for catalysis. These results emphasize the central role of the PreTS state as a high-energy intermediate structure along the catalytic pathway and suggest that Mg2+ and the KMSKS loop function cooperatively during catalysis.     

The effect of motional averaging on the calculation of NMR-derived structural properties.

The effect of motional averaging when relating structural properties inferred from nuclear magnetic resonance (NMR) experiments to molecular dynamics simulations of peptides is considered. In particular, the effect of changing populations of conformations, the extent of sampling, and the sampling frequency on the estimation of nuclear Overhauser effect (NOE) inter-proton distances, vicinal (3)J-coupling constants, and chemical shifts are investigated. The analysis is based on 50-ns simulations of a beta-heptapeptide in methanol at 298 K, 340 K, 350 K, and 360 K. This peptide undergoes reversible folding and samples a significant proportion of the available conformational space during the simulations, with at 298 K being predominantly folded and at 360 K being predominantly unfolded. The work highlights the fact that when motional averaging is included, NMR data has only limited capacity to distinguish between a single fully folded peptide conformation and various mixtures of folded and unfolded conformations. Proteins 1999;36:542-555.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Molecular dynamics simulations of peptides and proteins with amplified collective motions

We present a novel method that uses the collective modes obtained with a coarse-grained model/anisotropic network model to guide the atomic-level simulations. Based on this model, local collective modes can be calculated according to a single configuration in the conformational space of the protein. In the molecular dynamics simulations, the motions along the slowest few modes are coupled to a higher temperature by the weak coupling method to amplify the collective motions. This amplified-collective-motion (ACM) method is applied to two test systems. One is an S-peptide analog. We realized the refolding of the denatured peptide in eight simulations out of 10 using the method. The other system is bacteriophage T4 lysozyme. Much more extensive domain motions between the N-terminal and C-terminal domain of T4 lysozyme are observed in the ACM simulation compared to a conventional simulation. The ACM method allows for extensive sampling in conformational space while still restricting the sampled configurations within low energy areas. The method can be applied in both explicit and implicit solvent simulations, and may be further applied to important biological problems, such as long timescale functional motions, protein folding/unfolding, and structure prediction.     

Conformational sampling using high-temperature molecular dynamics

High-temperature molecular dynamics as a method for conformational search was explored on the antigen combining site of McPC 603, a phosphorylcholine binding immunoglobulin. Simulations at temperatures of 500, 800, and 1500 K were run for 111.5, 101.7, and 76.3 ps, respectively. The effectiveness of the search was assessed using a variety of methods. For the shorter hypervariable loops, molecular dynamics explored an appreciable fraction of the conformational space as evidenced by a comparison to a simple theoretical model of the size of the conformational space. However, for the longer loops and the antigen combining site as a whole, the simulation times were too short for a complete search. The simulations at 500 and 800 K both generated conformations that minimized to energies 200 kcal/mole lower than the crystal structure. However, the 1500 K simulation produced higher energy structures, even after minimization; in addition, this highest temperature run had many cis-trans peptide isomerizations. This suggests that 1500 K is too high a temperature for unconstrained conformational sampling. Comparison of the results of high temperature molecular dynamics with a direct conformational search method, [R. E. Bruccoleri & M. Karplus (1987) Biopolymers 26, 137-168]. showed that the two methods did not overlap much in conformational space. Simple geometric measures of the conformational space indicated that the direct method covered more space than molecular dynamics at the lower temperature, but not at 1500 K. The results suggest that high-temperature molecular dynamics can aid in conformational searches.     

Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials

The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned "on" and "off." Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from approximately 25,000 to 2500. The computations are very efficient and the statistical error is small ( approximately 1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within approximately 2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining potentials can be computationally inexpensive and accurate.     

Enhanced sampling of molecular dynamics simulation of peptides and proteins by double coupling to thermal bath

Low sampling efficiency in conformational space is the well-known problem for conventional molecular dynamics. It greatly increases the difficulty for molecules to find the transition path to native state, and costs amount of CPU time. To accelerate the sampling, in this paper, we re-couple the critical degrees of freedom in the molecule to environment temperature, like dihedrals in generalized coordinates or nonhydrogen atoms in Cartesian coordinate. After applying to ALA dipeptide model, we find that this modified molecular dynamics greatly enhances the sampling behavior in the conformational space and provides more information about the state-to-state transition, while conventional molecular dynamics fails to do so. Moreover, from the results of 16 independent 100?ns simulations by the new method, it shows that trpzip2 has one-half chances to reach the naive state in all the trajectories, which is greatly higher than conventional molecular dynamics. Such an improvement would provide a potential way for searching the conformational space or predicting the most stable states of peptides and proteins.     

Protein flexibility: multiple molecular dynamics simulations of insulin chain B

Multiple molecular dynamics simulations totaling more than 100 ns were performed on chain B of insulin in explicit solvent at 300 K and 400 K. Despite some individual variations, a comparison of the protein dynamics of each simulation showed similar trends and most structures were consistent with NMR experimental values, even at the elevated temperature. The importance of packing interactions in determining the conformational transitions of the protein was observed, sometimes resulting in conformations induced by localized hydrophobic interactions. The high temperature simulation generated a more diverse range of structures with similar elements of secondary structure and populated conformations to the simulations at room temperature. A broad sampling of the conformational space of insulin chain B illustrated a wide range of conformational states with many transitions at room temperature in addition to the conformational states observed experimentally. The T-state conformation associated with insulin activity was consistently present and a possible mechanism of behavior was suggested.     

Thermal unfolding simulations of apo-calmodulin using leap-dynamics

The simulation method leap-dynamics (LD) has been applied to protein thermal unfolding simulations to investigate domain-specific unfolding behavior. Thermal unfolding simulations of the 148-residue protein apo-calmodulin with implicit solvent were performed at temperatures 290 K, 325 K, and 360 K and compared with the corresponding molecular dynamics trajectories in terms of a number of calculated conformational parameters. The main experimental results of unfolding are reproduced in showing the lower stability of the C-domain: at 290 K, both the N- and C-domains are essentially stable; at 325 K, the C-domain unfolds, whereas the N-domain remains folded; and at 360 K, both domains unfold extensively. This behavior could not be reproduced by molecular dynamics simulations alone under the same conditions. These results show an encouraging degree of convergence between experiment and LD simulation. The simulations are able to describe the overall plasticity of the apo-calmodulin structure and to reveal details such as reversible folding/unfolding events within single helices. The results show that by using the combined application of a fast and efficient sampling routine with a detailed molecular dynamics force field, unfolding simulations of proteins at atomic resolution are within the scope of current computational power.