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.     

Conformational properties of a cyclic peptide bradykinin B2 receptor antagonist using experimental and theoretical methods.

The solution conformation of the cyclic peptide J324 (cyclo0,6-[Lys0,Glu6,D-Phe7]BK), an antagonist targeted at the bradykinin (BK) B2 receptor, has been investigated using experimental and theoretical methods. In order to gain insight into the structural requirements essential for BK antagonism, we carried out molecular dynamics (MD) simulations using simulated annealing as the sampling protocol. Following a free MD simulation we performed simulations using nuclear Overhauser enhancement (NOE) distance constraints determined by NMR experiments. The low-energy structures obtained were compared with each other, grouped into families and analyzed with respect to the presence of secondary structural elements in their backbone. We also introduced new ways of plotting structural data for a more comprehensive analysis of large conformational sets. Finally, the relationship between characteristic backbone conformations and the spatial arrangement of specific pharmacophore centers was investigated.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

On the dependence of molecular conformation on the type of solvent environment: a molecular dynamics study of cyclosporin A

The dependence of the conformation of cyclosporin A (CPA), a cyclic undecapeptide with potent immunosuppressive activity, on the type of solvent environment is examined using the computer simulation method of molecular dynamics (MD). Conformational and dynamic properties of CPA in aqueous solution are obtained from MD simulations of a CPA molecule dissolved in a box with water molecules. Corresponding properties of CPA in apolar solution are obtained from MD simulations of CPA in a box with carbontetrachloride. The results of these simulations in H2O and in CCl4 are compared to each other and to those of previous simulations of crystalline CPA and of an isolated CPA molecule. The conformation of the backbone of the cyclic polypeptide is basically independent of the type of solvent. In aqueous solution the beta-pleated sheet is slightly weaker and the gamma-turn is a bit less pronounced than in apolar solution. Side chains may adopt different conformations in different solvents. In apolar solution the hydrophobic side chain of the MeBmt residue is in an extended conformation with its hydroxyl group hydrogen bonded to the backbone carbonyl group. In aqueous solution this hydrophobic side chain folds over the core of the molecule and the mentioned hydrogen bond is broken in favor of hydrogen bonding to water molecules. The conformation obtained from the MD simulation in CCl4 nicely agrees with experimental atom-atom distance data as obtained from nmr experiments in chloroform. In aqueous solution the relaxation of atomic motion tends to be slower than in apolar solution.     

Enhanced sampling of peptide and protein conformations using replica exchange simulations with a peptide backbone biasing-potential

During replica exchange molecular dynamics (RexMD) simulations, several replicas of a system are simulated at different temperatures in parallel allowing for exchange between replicas at frequent intervals. This technique allows significantly improved sampling of conformational space and is increasingly being used for structure prediction of peptides and proteins. A drawback of the standard temperature RexMD is the rapid increase of the replica number with increasing system size to cover a desired temperature range. In an effort to limit the number of replicas, a new Hamiltonian-RexMD method has been developed that is specifically designed to enhance the sampling of peptide and protein conformations by applying various levels of a backbone biasing potential for each replica run. The biasing potential lowers the barrier for backbone dihedral transitions and promotes enhanced peptide backbone transitions along the replica coordinate. The application on several peptide cases including in all cases explicit solvent indicates significantly improved conformational sampling when compared with standard MD simulations. This was achieved with a very modest number of 5-7 replicas for each simulation system making it ideally suited for peptide and protein folding simulations as well as refinement of protein model structures in the presence of explicit solvent.     

Low-mass molecular dynamics simulation: A simple and generic technique to enhance configurational sampling

CLN025 is one of the smallest fast-folding proteins. Until now it has not been reported that CLN025 can autonomously fold to its native conformation in a classical, all-atom, and isothermal–isobaric molecular dynamics (MD) simulation. This article reports the autonomous and repeated folding of CLN025 from a fully extended backbone conformation to its native conformation in explicit solvent in multiple 500-ns MD simulations at 277 K and 1 atm with the first folding event occurring as early as 66.1 ns. These simulations were accomplished by using AMBER forcefield derivatives with atomic masses reduced by 10-fold on Apple Mac Pros. By contrast, no folding event was observed when the simulations were repeated using the original AMBER forcefields of FF12SB and FF14SB. The results demonstrate that low-mass MD simulation is a simple and generic technique to enhance configurational sampling. This technique may propel autonomous folding of a wide range of miniature proteins in classical, all-atom, and isothermal–isobaric MD simulations performed on commodity computers—an important step forward in quantitative biology.     

Exploring the dynamic information content of a protein NMR structure: Comparison of a molecular dynamics simulation with the NMR and X‐ray structures of Escherichia coli ribonuclease HI

The multiconformer nature of solution nuclear magnetic resonance (NMR) structures of proteins results from the effects of intramolecular dynamics, spin diffusion and an uneven distribution of structural restraints throughout the molecule. A delineation of the former from the latter two contributions is attempted in this work for an ensemble of 15 NMR structures of the protein Escherichia coli ribonuclease HI (RNase HI). Exploration of the dynamic information content of the NMR ensemble is carried out through correlation with data from two crystal structures and a 1.7‐ns molecular dynamics (MD) trajectory of RNase HI in explicit solvent. Assessment of the consistency of the crystal and mean MD structures with nuclear Overhauser effect (NOE) data showed that the NMR ensemble is overall more compatible with the high‐resolution (1.48 Å) crystal structure than with either the lower‐resolution (2.05 Å) crystal structure or the MD simulation. Furthermore, the NMR ensemble is found to span more conformational space than the MD simulation for both the backbone and the sidechains of RNase HI. Nonetheless, the backbone conformational variability of both the NMR ensemble and the simulation is especially consistent with NMR relaxation measurements of two loop regions that are putative sites of substrate recognition. Plausible side‐chain dynamic information is extracted from the NMR ensemble on the basis of (i) rotamericity and syn‐pentane character of variable torsion angles, (ii) comparison of the magnitude of atomic mean‐square fluctuations (msf) with those deduced from crystallographic thermal factors, and (iii) comparison of torsion angle conformational behavior in the NMR ensemble and the simulation. Several heterogeneous torsion angles, while adopting non‐rotameric/syn‐pentane conformations in the NMR ensemble, exist in a unique conformation in the simulation and display low X‐ray thermal factors. These torsions are identified as sites whose variability is likely to be an artifact of the NMR structure determination procedure. A number of other torsions show a close correspondence between the conformations sampled in the NMR and MD ensembles, as well as significant correlations among crystallographic thermal factors and atomic msf calculated from the NMR ensemble and the simulation. These results indicate that a significant amount of dynamic information is contained in the NMR ensemble. The relevance of the present findings for the biological function of RNase HI, protein recognition studies, and previous investigations of the motional content of protein NMR structures are discussed. Proteins 1999;36:87–110. © 1999 Wiley‐Liss, Inc.     

Protein conformational dynamics of crambin in crystal, solution and in the trajectories of molecular dynamics simulations

Atomic displacement parameters — B factors of the eight crambin crystal structures obtained at 0.54–1.5 Å resolution and temperatures of 100–293 K have been analyzed. The comparable contributions to the B factor values are the intramolecular motions which are modeled by the harmonic vibration calculations and derived from the molecular dynamics simulation (MD) as well as rigid body changes in the position of a protein molecule as a whole. In solution for the average NMR structure of crambin the amplitudes of the backbone atomic fluctuations of the most residues of the segments with the regular backbone conformations are close to the amplitudes of the small scale harmonic vibrations. For the same residues the probability of the medium scale fluctuations fixed by the hydrogen exchange method is very low. The restricted conformational mobility of those segments is coupled with the depressed amplitudes of the fluctuation changes of the tertiary structure registered by the residue accessibility changes in an ensemble of NMR structures that forms the average NMR structure of crambin. The amplitudes of temperature fluctuations of backbone atoms and the tertiary structure raise in the segment with the irregular conformations, turn and loops. In the same segments the amplitudes of the calculated harmonic vibrations also increase, but to a lesser extent and especially in the interhelical loop with the most strong and complicated fluctuation changes of the backbone conformation. In solution for the NMR structure in this loop the conformational transitions occur between the conformational substates separated by the energy barriers, but they are not observed even in the long 100 ns trajectories from the MD simulation of crambin. These strong local fluctuation changes of the structure may play a key role in the protein functioning and modern performance improvements in the MD simulation techniques are oriented to increase the probability of protein appearance in the trajectories from the MD simulations.     

Application of biasing‐potential replica‐exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target‐template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP‐REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP‐REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T‐REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP‐REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

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 simulation by atomic mass weighting

A molecular dynamics-based simulation method in which atomic masses are weighted is described. Results from this method showed that the capability for conformation search in molecular dynamics simulation of a short peptide (FMRF-amide) is significantly increased by mass weighting.     

Asymmetric oscillations in cyclodextrin--a molecular dynamics study

A 30-ps molecular dynamics simulation of motions of cyclodextrin is completed on the free molecule and with two model substrates. Even with its cyclic constraint, the molecule traversed through large conformational space, showing high flexibility. The asymmetric oscillations of the free molecule are evident from the time course behavior of the ratio of the second moments (anisotropic ratio) of the atomic motions along the first two principal axes. The study also shows the stability of the molecule derived from specific substrate. The preference of chair conformation by glucose is also evident from these studies.     

Theoretical probes of conformational fluctuations in S-peptide and RNase A/3′–UMP enzyme product complex

The dynamic properties of the RNase A/3′–UMP enzyme/product complex and the S-peptide of RNase A have been investigated by molecular dynamics simulations using suitable generalization of ideas introduced to probe the energy landscape in structural glasses. We introduce two measures, namely, the kinetic energy fluctuation metric and the force metric, both of which are used to calculate the time needed for sampling the conformation space of the molecules. The calculation of the fluctuation metric requires a single trajectory whereas the force metric is computed using two independent trajectories. The vacuum MD simulations show that for both systems the time required for kinetic energy equipartitioning is surprisingly long even at high temperatures. We show that the force metric is a powerful means of probing the nature and relative importance of conformational substates which determine the dynamics at low temperatures. In particular the time dependence of the non-bonded force metric is used to demonstrate that at low temperatures the system is predominantly localized hi a single cluster of conformational substates. The force metric is used to show that relaxation of long range (in sequence space) interactions must be mediated by a sequence of local dihedral angle transitions. We also argue that the time needed for compact structure formation is intimately related to the time needed for the relaxation of the dihedral angle degrees of freedom. The tame for non-bonded interactions, which drive protein molecules to fold under appropriate conditions, to relax becomes extremely long as the temperature is lowered suggesting that the formation of maximally compact structure hi proteins must be a very slow process. © 1993 Wiley-Liss, Inc.     

Method of modeling protein structure by the two-dimensional nuclear magnetic resonance spectroscopy data; application to the proteinase inhibitor BUSI IIA from bull seminal plasma

A new approach is suggested to model the spatial structure of protein molecules in solution based on combined use of the methods of theoretical conformational analysis and NMR spectroscopy data. At the first stage, special means are used to convert d connectivity information into the most probable values of dihedral angles. This allows search for possible spatial structures in the limited regions of the conformational space at further stages using the methods of the theoretical conformational analysis. The suggested approach was verified in reconstructing the spatial backbone structure of the fragment 17-57 of the proteinase inhibitor BUSI IIA from the bull seminal plasma. The structural model parameters are compared with the corresponding characteristics obtained from the X-ray analysis data for the homologic proteinase inhibitor from the Japanese quail ovomucoid. The suggested approach is shown to correctly reproduce both the general molecule topology and the conformations of individual amino acid residues.     

MD simulations reveal alternate conformations of the oxyanion hole in the Zika virus NS2B/NS3 protease

Recent crystallography studies have shown that the binding site oxyanion hole plays an important role in inhibitor binding, but can exist in two conformations (active/inactive). We have undertaken molecular dynamics (MD) calculations to better understand oxyanion hole dynamics and thermodynamics. We find that the Zika virus (ZIKV) NS2B/NS3 protease maintains a stable closed conformation over multiple 100-ns conventional MD simulations in both the presence and absence of inhibitors. The S1, S2, and S3 pockets are stable as well. However, in two of eight simulations, the A132-G133 peptide bond in the binding pocket of S1' spontaneously flips to form a 3₁₀-helix that corresponds to the inactive conformation of the oxyanion hole, and then maintains this conformation until the end of the 100-ns conventional MD simulations without inversion of the flip. This conformational change affects the S1' pocket in ZIKV NS2B/NS3 protease active site, which is important for small molecule binding. The simulation results provide evidence at the atomic level that the inactive conformation of the oxyanion hole is more favored energetically when no specific interactions are formed between substrate/inhibitor and oxyanion hole residues. Interestingly, however, transition between the active and inactive conformation of the oxyanion hole can be observed by boosting the valley potential in accelerated MD simulations. This supports a proposed induced-fit mechanism of ZIKV NS2B/NS3 protease from computational methods and provides useful direction to enhance inhibitor binding predictions in structure-based drug design.     

Simulating nanoscale functional motions of biomolecules

We are describing efficient dynamics simulation methods for the characterization of functional motion of biomolecules on the nanometer scale. Multivariate statistical methods are widely used to extract and enhance functional collective motions from molecular dynamics (MD) simulations. A dimension reduction in MD is often realized through a principal component analysis (PCA) or a singular value decomposition (SVD) of the trajectory. Normal mode analysis (NMA) is a related collective coordinate space approach, which involves the decomposition of the motion into vibration modes based on an elastic model. Using the myosin motor protein as an example we describe a hybrid technique termed amplified collective motions (ACM) that enhances sampling of conformational space through a combination of normal modes with atomic level MD. Unfortunately, the forced orthogonalization of modes in collective coordinate space leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. In many biological molecules, such as HIV-1 protease, reflective or rotational symmetries are present that are broken using standard orthogonal basis functions. We present a method to compute the plane of reflective symmetry or the axis of rotational symmetry from the trajectory frames. Moreover, we develop an SVD that best approximates the given trajectory while respecting the symmetry. Finally, we describe a local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low-dimensional, and provide a reduced basis set for collective motions, but unlike global collective modes they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows.     

Influence of 8-Oxoguanosine on the Fine Structure of DNA Studied with Biasing-Potential Replica Exchange Simulations

Chemical modification or radiation can cause DNA damage, which plays a crucial role for mutagenesis of DNA, carcinogenesis, and aging. DNA damage can also alter the fine structure of DNA that may serve as a recognition signal for DNA repair enzymes. A new, advanced sampling replica-exchange method has been developed to specifically enhance the sampling of conformational substates in duplex DNA during molecular dynamics (MD) simulations. The approach employs specific biasing potentials acting on pairs of pseudodihedral angles of the nucleic acid backbone that are added in the replica simulations to promote transitions of the most common substates of the DNA backbone. The sampled states can exchange with a reference simulation under the control of the original force field. The application to 7,8-dihydro-8oxo-guanosine, one of the most common oxidative damage in DNA indicated better convergence of sampled states during 10 ns simulations compared to 20 times longer standard MD simulations. It is well suited to study systematically the fine structure and dynamics of large nucleic acids under realistic conditions, including explicit solvent and ions. The biasing potential-replica exchange MD simulations indicated significant differences in the population of nucleic acid backbone substates in the case of 7,8-dihydro-8oxo-guanosine compared to a regular guanosine in the same sequence context. This concerns both the ratio of the B-DNA substates B_I and B_II associated with the backbone dihedral angles ε and ζ but also coupled changes in the backbone dihedral angles α and γ. Such differences may play a crucial role in the initial recognition of damaged DNA by repair enzymes.     

Conformation and dynamics of an Fab'-bound peptide by isotope-edited NMR spectroscopy.

The dynamics and conformation of the peptide antigen MHKDFLEKIGGL bound to the Fab' fragment of the monoclonal antipeptide antibody B13A2, raised against a peptide from myohemerythrin, have been investigated by isotope-edited NMR techniques. The peptides were labeled with 15N (98%) or 13C (99%) at the backbone of individual amino acid residues. Well-resolved amide proton and nitrogen backbone resonances were obtained and assigned for eight of the 12 residues of this bound peptide. Significant resonance line width and chemical shift differences were observed. The 15N and 1H line width variations are attributed to differential backbone mobilities among the bound peptide residues which are consistent with the previously mapped epitope of this peptide antigen. Local structural information was obtained from isotope-directed NOE studies. The approximate distances associated with the experimental NOEs were estimated on the basis of a theoretical NOE analysis involving the relative integrated intensities of the NOE and source peaks. In this way, the sequential NH-NH NOEs obtained for seven of the Fab'-bound peptide residues were shown to correspond to interproton separations of approximately 3 A or less. Such short distances indicate that the backbone dihedral angles of these residues are in the alpha rather than the beta region of phi,psi conformational space; the peptide most likely adopts a helical conformation from F5 to G11 within the antibody combining site. The significance of these results with respect to the type and extent of conformational information obtainable from studies of high molecular weight systems is discussed.     

Conformational sampling by NMR solution structures calculated with the program DIANA evaluated by comparison with long-time molecular dynamics calculations in explicit water

The NMR solution structure of bovine pancreatic trypsin inhibitor (BPTI) obtained by distance geometry calculations with the program DIANA is compared with groups of conformers generated by molecular dynamics (MD) simulations in explicit water at ambient temperature and pressure. The MD simulations started from a single conformer and were free or restrained either by the experimental NOE distance restraints or by time-averaged restraints; the groups of conformers were collected either in 10 ps intervals during 200 ps periods of simulation, or in 50 ps intervals during a 1 ns period of simulation. Overall, these comparisons show that the standard protein structure determination protocol with the program DIANA provides a picture of the protein structure that is in agreement with MD simulations using “realistic” potential functions over a nanosecond timescale. For well-constrained molecular regions there is a trend in the free MD simulation of duration 1 ns that the sampling of the conformation space is slightly increased relative to the DIANA calculations. In contrast, for surface-exposed side-chains that are less extensively constrained by the NMR data, the DIANA conformers tend to sample larger regions of conformational space than conformers selected from any of the MD trajectories. Additional insights into the behavior of surface side-chains come from comparison of the MD runs of 200 ps or 1 ns duration. In this time range the sampling of conformation space by the protein surface depends strongly on the length of the simulation, which indicates that significant side-chain transitions occur on the nanosecond timescale and that much longer simulations will be needed to obtain statistically significant data on side-chain dynamics.