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.     

MOLS sampling and its applications in structural biophysics

This review describes the MOLS method and its applications. This computational method has been developed in our laboratory primarily to explore the conformational space of small peptides and identify features of interest, particularly the minima, i.e., the low energy conformations. A systematic “brute-force” search through the vast conformational space for such features faces the insurmountable problem of combinatorial explosion, whilst other techniques, e.g., Monte Carlo searches, are somewhat limited in their region of exploration and may be considered inexhaustive. The MOLS method, on the other hand, uses a sampling technique commonly employed in experimental design theory to identify a small sample of the conformational space that nevertheless retains information about the entire space. The information is extracted using a technique that is a variant of the self-consistent mean field technique, which has been used to identify, for example, the optimal set of side-chain conformations in a protein. Applications of the MOLS method to understand peptide structure, predict the structures of loops in proteins, predict three-dimensional structures of small proteins, and arrive at the best conformation, orientation, and positions of a small molecule ligand in a protein receptor site have all yielded satisfactory results.     

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     

Conformational ensemble of an intrinsically flexible loop in mitochondrial import protein Tim21 studied by modeling and molecular dynamics simulations

BackgroundTim21, a subunit of a highly dynamic translocase of the inner mitochondrial membrane (TIM23) complex, translocates proteins by interacting with subunits in the translocase of the outer membrane (TOM) complex and Tim23 channel in the TIM23 complex. A loop segment in Tim21, which is in close proximity of the binding site of Tim23, has different conformations in X-ray, NMR and new crystal contact-free space (CCFS) structures. MD simulations can provide information on the structure and dynamics of the loop in solution.MethodsThe conformational ensemble of the loop was characterized using loop modeling and molecular dynamics (MD) simulations.ResultsMD simulations confirmed mobility of the loop. Multidimensional scaling and clustering were used to characterize the dynamic conformational ensemble of the loop. Free energy landscape showed that the CCFS crystal structure occupied a low energy region as compared to the conventional X-ray crystal structure. Analysis of crystal packing indicates that the CCFS provides larger conformational space for the motions of the loop.ConclusionsOur work reported the conformational ensemble of the loop in solution, which is in agreement with the structure obtained from CCFS approach. The combination of the experimental techniques and computational methods is beneficial for studying highly flexible regions of proteins.General significanceComputational methods, such as loop modeling and MD simulations, have proved to be useful for studying conformational flexibility of proteins. These methods in integration with experimental techniques such as CCFS has the potential to transform the studies on flexible regions of proteins.     

Backbone conformational flexibility of the lipid modified membrane anchor of the human N-Ras protein investigated by solid-state NMR and molecular dynamics simulation

The lipid modified human N-Ras protein, implicated in human cancer development, is of particular interest due to its membrane anchor that determines the activity and subcellular location of the protein. Previous solid-state NMR investigations indicated that this membrane anchor is highly dynamic, which may be indicative of backbone conformational flexibility. This article aims to address if a dynamic exchange between three structural models exist that had been determined previously. We applied a combination of solid-state nuclear magnetic resonance (NMR) methods and replica exchange molecular dynamics (MD) simulations using a Ras peptide that represents the terminal seven amino acids of the human N-Ras protein. Analysis of correlations between the conformations of individual amino acids revealed that Cys 181 and Met 182 undergo collective conformational exchange. Two major structures constituting about 60% of all conformations could be identified. The two conformations found in the simulation are in rapid exchange, which gives rise to low backbone order parameters and nuclear spin relaxation as measured by experimental NMR methods. These parameters were also determined from two 300 ns conventional MD simulations, providing very good agreement with the experimental data.     

Determination of conformational equilibrium of peptides in solution by NMR spectroscopy and theoretical conformational analysis: application to the calibration of mean-field solvation models.

Peptides occur in solution as ensembles of conformations rather than in a fixed conformation. The existing energy functions are usually inadequate to predict the conformational equilibrium in solution, because of failure to account properly for solvation, if the solvent is not considered explicitly (which is usually prohibitively expensive). NMR data are therefore widely incorporated into theoretical conformational analysis. Because of conformational flexibility, restrained molecular dynamics (with restraints derived from NMR data), which is usually applied to determine protein conformation is of limited use in the case of peptides. Instead, (a) the restraints are averaged within predefined time windows during molecular dynamics (MD) simulations (time averaging), (b) multiple-copy MD simulations are carried out and the restraints are averaged over the copies (ensemble averaging), or (c) a representative ensemble of sterically feasible conformations is generated and the weights of the conformations are then fitted so that the computed average observables match the experimental data (weight fitting). All these approaches are briefly discussed in this article. If an adequate force field is used, conformations with large statistical weights obtained from the weight-fitting procedure should also have low energies, which can be implemented in force field calibration. Such a procedure is particularly attractive regarding the parameterization of the solvation energy in nonaqueous solvents, e.g., dimethyl sulfoxide, for which thermodynamic solvation data are scarce. A method for calibration of solvation parameters in dimethyl sulfoxide, which is based on this principle was recently proposed by C. Baysal and H. Meirovitch (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800--812), in which the energy gap between the conformations compatible with NMR data and the alternative conformations is maximized. In this work we propose an alternative method based on the principle that the best-fitting statistical weights of conformations should match the Boltzmann weights computed with the force field applied. Preliminary results obtained using three test peptides of varying conformational mobility: H-Ser(1)-Pro(2)-Lys(3)-Leu(4)-OH, Ac-Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)-NH(2), and cyclo(Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)) are presented.     

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.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

A new Hybrid Monte Carlo algorithm for protein potential function test and structure refinement

A new Hybrid Monte Carlo (HMC) algorithm has been developed to test protein potential functions and, ultimately, refine protein structures. The main principle of this algorithm is, in each cycle, a new trial conformation is generated by carrying out a short period of molecular dynamics (MD) iterations with a set of random parameters (including the MD time step, the number of MD steps, the MD temperature, and the seed for initial MD velocity assignment); then to accept or reject the new conformation on the basis of the Metropolis criterion. The novelty in this paper is that the potential in MD iterations is different from that in the MC step. In the former, it is a molecular mechanics potential, in the latter it is a knowledge-based potential (KBP). Directed by the KBP, the MD iteration is used to search conformational space for realistic conformations with low KBP energy. It circumvents the difficulty in using KBP functions directly in MD simulation, as KBP functions are typically incomplete, and do not always have continuous derivatives required for the calculation of the forces. The new algorithm has been tested in explorations of conformational space. In these test calculations the KBP energy was found to drop below the value for the native conformation, and the correlation between the root mean square deviation (RMSD) and the KBP energy was shown to be different from the test results in other references. At the present time, the algorithm is useful for testing new KBP functions. Furthermore, if a KBP function can be found for which the native conformation has the lowest energy and the energy/RMSD correlation is good, then this new algorithm also will be a tool for refinement of the theory-based structural models.     

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.     

Are time-averaged restraints necessary for nuclear magnetic resonance refinement? A model study for DNA.

A recently suggested method for refinement of structural data obtained from two-dimensional nuclear magnetic resonance experiments using molecular dynamics (MD) is explored. In this method, the time-averaged values of the appropriate internal co-ordinates of the molecule, calculated from the MD trajectory, are driven by restraints towards the experimental target values. This contrasts with most refinement procedures currently in use, where restraints are applied based on the instantaneous values of the appropriate co-ordinates. Both refinement methods are applied to the EcoRI restriction site DNA hexamer d(GAATTC)2, using target nuclear Overhauser enhancement distances derived from a one nanosecond unrestrained MD simulation of this structure. The resulting refined structures are compared to the results of the unrestrained MD trajectory, which serves as our "experimental" data. We show that although both methods can yield an average structure with the correct gross morphology, the new method allows both a much more realistic picture of inherent flexibility, and reproduces fine conformational detail better, such as sequence dependency. We also analyze the very long MD trajectory generated here (longer than any previously reported for a DNA oligomer), and find that significantly shorter simulations, typical of those frequently performed, may not yield acceptably reliable values for certain structural parameters.     

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.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

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.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

Computational sampling of a cryptic drug binding site in a protein receptor: explicit solvent molecular dynamics and inhibitor docking to p38 MAP kinase

An increasing number of structural studies reveal alternative binding sites in protein receptors that become apparent only when an inhibitor binds, and correct prediction of these situations presents a significant challenge to computer-aided drug design efforts. A striking example is provided by recent crystal structures of the p38 MAP kinase, where a 10A movement of the Phe169 side-chain creates a new binding site adjacent to the ATP binding site that is exploited by the diaryl urea inhibitor BIRB796. Here, we show that this binding site can be successfully and repeatedly identified in explicit-solvent molecular dynamics (MD) simulations of the protein that begin from an unliganded p38 crystal structure. Ligand-docking calculations performed on 5000 different structural snapshots generated during MD indicate that the conformations sampled are often surprisingly competent to bind the inhibitor BIRB796 in the crystallographically correct position and with docked energies that are generally more favorable than those of other positions. Similar docking studies with an ATP-binding site-directed inhibitor suggest that it may be possible to develop hybrid inhibitors that target both the ATP and cryptic binding sites simultaneously. Intriguingly, both inhibitors are occasionally found to dock correctly even with p38's "DFG" motif in the "wrong" conformation and BIRB796 can successfully dock, albeit infrequently, without significant displacement of the Phe169 side-chain; this suggests that the inhibitor might facilitate the latter's conformational change. Finally, two quite different conformations of p38's DFG motif are also sampled for extended periods of time during the simulations; these may provide new opportunities for inhibitor development. The MD simulations reported here, which total 390 ns in length, therefore demonstrate that existing computational methods may be of surprising utility in predicting cryptic binding sites in protein receptors prior to their experimental discovery.     

Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular Dynamics

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.     

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.