Conformational interconversion in compstatin probed with molecular dynamics simulations

Compstatin is a 13-residue cyclic peptide that has the potential to become a therapeutic agent against unregulated complement activation. In our effort to understand the structural and dynamic characteristics of compstatin that form the basis for rational and combinatorial optimization of structure and activity, we performed 1-ns molecular dynamics (MD) simulations. We used as input in the MD simulations the ensemble of 21 lowest energy NMR structures, the average minimized structure, and a global optimization structure. At the end of the MD simulations we identified five conformations, with populations ranging between 9% and 44%. These conformations are as follows: 1) coil with alphaR-alphaR beta-turn, as was the conformation of the initial ensemble of NMR structures; 2) beta-hairpin with epsilon-alphaR beta-turn; 3) beta-hairpin with alphaR-alphaR beta-turn; 4) beta-hairpin with alphaR-beta beta-turn; and 5) alpha-helical. Conformational switch was possible with small amplitude backbone motions of the order of 0.1-0.4 A and free energy barrier crossing of 2-11 kcal/mol. All of the 21 MD structures corresponding to the NMR ensemble possessed a beta-turn, with 14 structures retaining the alphaR-alphaR beta-turn type, but the average minimized structure and the global optimization structures were converted to alpha-helical conformations. Overall, the MD simulations have aided to gain insight into the conformational space sampled by compstatin and have provided a measure of conformational interconversion. The calculated conformers will be useful as structural and possibly dynamic templates for optimization in the design of compstatin using structure-activity relations (SAR) or dynamics-activity relations (DAR).     

Conformational landscapes of membrane proteins delineated by enhanced sampling molecular dynamics simulations

The expansion of computational power, better parameterization of force fields, and the development of novel algorithms to enhance the sampling of the free energy landscapes of proteins have allowed molecular dynamics (MD) simulations to become an indispensable tool to understand the function of biomolecules. The temporal and spatial resolution of MD simulations allows for the study of a vast number of processes of interest. Here, we review the computational efforts to uncover the conformational free energy landscapes of a subset of membrane proteins: ion channels, transporters and G-protein coupled receptors. We focus on the various enhanced sampling techniques used to study these questions, how the conclusions come together to build a coherent picture, and the relationship between simulation outcomes and experimental observables.     

Spontaneous conformational changes in the E. coli GroEL subunit from all-atom molecular dynamics simulations

The Escherichia coli chaperonin GroEL is a complex of identical subunit proteins (57 kDa each) arranged in a back-to-back stacking of two heptameric rings. Its hallmarks include nested positive intra-ring and negative inter-ring cooperativity in adenosine trisphosphate (ATP) binding and the ability to mediate the folding of newly transcribed and/or denatured substrate proteins. We performed unbiased molecular dynamics simulations of the GroEL subunit protein in explicit water both with and without the nucleotide KMgATP to understand better the details of the structural transitions that enable these behaviors. Placing KMgATP in the equatorial domain binding pocket of a t state subunit, which corresponds to a low ATP-affinity state, produced a short-lived (6 ns) state that spontaneously transitioned to the high ATP-affinity r state. The important feature of this transition is a large-scale rotation of the intermediate domain's helix M to close the ATP binding pocket. Pivoting of helix M is accompanied by counterclockwise rotation and slight deformation of the apical domain, important for lowering the affinity for substrate protein. Aligning simulation conformations into model heptamer rings demonstrates that the t-->r transition in one subunit is not sterically hindered by t state neighbors, but requires breakage of Arg(197)-Glu(386) intersubunit salt bridges, which are important for inter-ring positive cooperativity. Lowest-frequency quasi-harmonic modes of vibration computed pre- and post-transition clearly show that natural vibrations facilitate the transition. Finally, we propose a novel mechanism for inter-ring cooperativity in ATP binding inspired by the observation of spontaneous insertion of the side chain of Ala(480) into the empty nucleotide pocket.     

Misfolding pathways of the prion protein probed by molecular dynamics simulations

Although the cellular monomeric form of the benign prion protein is now well characterized, a model for the monomer of the misfolded conformation (PrP(Sc)) remains elusive. PrP(Sc) quickly aggregates into highly insoluble fibrils making experimental structural characterization very difficult. The tendency to aggregation of PrP(Sc) in aqueous solution implies that the monomer fold must be hydrophobic. Here, by using molecular dynamics simulations, we have studied the cellular mouse prion protein and its D178N pathogenic mutant immersed in a hydrophobic environment (solution of CCl4), to reveal conformational changes and/or local structural weaknesses of the prion protein fold in unfavorable structural and thermodynamic conditions. Simulations in water have been also performed. Although observing in general a rather limited conformation activity in the nanosecond timescale, we have detected a significant weakening of the antiparallel beta-sheet of the D178N mutant in CCl4 and to a less extent in water. No weakening is observed for the native prion protein. The increase of beta-structure in the monomer, recently claimed as evidence for misfolding to PrP(Sc), has been also observed in this study irrespective of the thermodynamic or structural conditions, showing that this behavior is very likely an intrinsic characteristic of the prion protein fold.     

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.     

Conformational analysis and molecular dynamics simulations of maltose

Constrained conformational energy minimizations have been used to calculate an adiabatic (Φ, ψ) potential energy surface for the disaccharide β-maltose. The inclusion of molecular flexibility in the conformational energy analysis of the disaccharide was found to significantly lower the barriers to conformational transitions, as has been observed previously for other systems. Several low energy wells were identified on the adiabatic surface which differ in energy by small amounts and with low absolute barriers separating them, indicating the possibility of a non-negligible equilibrium population distribution in each well. If such a distribution of conformations existed in the physical system, the conformation observed by NMR NOE measurements would thus be a “virtual” conformation. Molecular dynamics simulations of the motions of this molecule in vacuum were also conducted and indicate that the rate of relaxation of the molecule to the adiabatic surface may be slower than the typical timescale of conformational fluctuations. This effect is apparently due to an unphysical persistence of hydrogen bond patterns in vacuum which does not occur in aqueous solution. Trajectories undergoing transitions between wells were calculated and the effects of such conformational transitions upon the ensemble mean structure, such as might be observed in an NMR experiment, were demonstrated.     

Conformational properties of glucose-based disaccharides investigated using molecular dynamics simulations with local elevation umbrella sampling

Explicit-solvent molecular dynamics (MD) simulations of the 11 glucose-based disaccharides in water at 300 K and 1 bar are reported. The simulations were carried out with the GROMOS 45A4 force-field and the sampling along the glycosidic dihedral angles ? and ψ was artificially enhanced using the local elevation umbrella sampling (LEUS) method. The trajectories are analyzed in terms of free-energy maps, stable and metastable conformational states (relative free energies and estimated transition timescales), intramolecular H-bonds, single molecule configurational entropies, and agreement with experimental data. All disaccharides considered are found to be characterized either by a single stable (overwhelmingly populated) state ((1→n)-linked disaccharides with n = 1, 2, 3, or 4) or by two stable (comparably populated and differing in the third glycosidic dihedral angle ; gg or gt) states with a low interconversion barrier ((1→6)-linked disaccharides). Metastable (anti-? or anti-ψ) states are also identified with relative free energies in the range of 8-22 kJ mol⁻¹. The 11 compounds can be classified into four families: (i) the α(1→1)α-linked disaccharide trehalose (axial-axial linkage) presents no metastable state, the lowest configurational entropy, and no intramolecular H-bonds; (ii) the four α(1→n)-linked disaccharides (n = 1, 2, 3, or 4; axial-equatorial linkage) present one metastable (anti-ψ) state, an intermediate configurational entropy, and two alternative intramolecular H-bonds; (iii) the four β(1→n)-linked disaccharides (n = 1, 2, 3, or 4; equatorial-equatorial linkage) present two metastable (anti-? and anti-ψ) states, an intermediate configurational entropy, and one intramolecular H-bond; (iv) the two (1→6)-linked disaccharides (additional glycosidic dihedral angle) present no (isomaltose) or a pair of (gentiobiose) metastable (anti-?) states, the highest configurational entropy, and no intramolecular H-bonds. The observed conformational preferences appear to be dictated by four main driving forces (ring conformational preferences, exo-anomeric effect, steric constraints, and possible presence of a third glycosidic dihedral angle), leaving a secondary role to intramolecular H-bonding and specific solvation effects. In spite of the weak conformational driving force attributed to solvent-exposed H-bonds in water (highly polar protic solvent), intramolecular H-bonds may still have a significant influence on the physico-chemical properties of the disaccharide by decreasing its hydrophilicity. Along with previous work, the results also complete the suggestion of a spectrum of approximate transition timescales for carbohydrates up to the disaccharide level, namely: ∼30 ps (hydroxyl groups), ∼1 ns (free lactol group, free hydroxymethyl groups, glycosidic dihedral angle in (1→6)-linked disaccharides), ∼10 ns to 2 μs (ring conformation, glycosidic dihedral angles ? and ψ). The calculated average values of the glycosidic torsional angles agree well with the available experimental data, providing validation for the force-field and simulation methodology employed.     

Conformational transitions using molecular dynamics with minimum biasing

The molecular dynamics algorithm (MD), which simulates intramolecular motions on the subnanosecond timescale, has been modified to allow the investigation of slow conformational transitions that do not necessarily occur spontaneously in MD simulations. The method is designated CONTRA MD (CONformational TRAnsitions by Molecular Dynamics with minimum biasing). The method requires the prior definition of a single conformational variable that is required to vary monotonically from an initial conformation to a final target conformation. The simulation is broken up into a series of short free MD segments, and we determine, after each segment of MD, whether or not the system has evolved toward the final conformation. Those segments that do not move the system in that direction are deleted. Those that do move it toward the final conformation are patched together sequentially to generate a single representative trajectory along the transition pathway. The CONTRA MD method is demonstrated first by application to the simultaneous C2′-endo to C3′-endo repucker and anti to syn N-glycosidic torsion transitions in 2′-deoxyadenosine and then to the large-scale bending in phenylalanine transfer RNA. © 1993 John Wiley & Sons, Inc.     

Probing the "annealing" mechanism of GroEL minichaperone using molecular dynamics simulations

Although the intact chaperonin machinery is needed to rescue natural substrate proteins (SPs) under non-permissive conditions the "minichaperone" alone, containing only the isolated apical domain of GroEL, can assist folding of a certain class of proteins. To understand the annealing function of the minichaperone, we have carried out molecular dynamics simulations in the NPT ensemble totaling 300ns for four systems; namely, the isolated strongly binding peptide (SBP), the minichaperone, and the SBP and a weakly binding peptide (WBP) in complex with the minichaperone. The SBP, which is structureless in isolation, adopts a beta-hairpin conformation in complex with the minichaperone suggesting that favorable non-specific interactions of the SPs confined to helices H and I of the apical domains can induce local secondary structures. Comparison of the dynamical fluctuations of the apo and the liganded forms of the minichaperone shows that the stability (needed for SP capture) involves favorable hydrophobic interactions and hydrogen bond network formation between the SBP and WBP, and helices H and I. The release of the SP, which is required for the annealing action, involves water-mediated interactions of the charged residues at the ends of H and I helices. The simulation results are consistent with a transient binding release (TBR) model for the annealing action of the minichaperone. According to the TBR model, SP annealing occurs in two stages. In the first stage the SP is captured by the apical domain. This is followed by SP release (by thermal fluctuations) that places it in a different region of the energy landscape from which it can partition rapidly to the native state with probability Phi or be trapped in another misfolded state. The process of binding and release can result in enhancement of the native state yield. The TBR model suggests "that any cofactor that can repeatedly bind and release SPs can be effective in assisting protein folding." By comparing the structures of the non-chaperone alpha-casein (which has no sequence similarity with the apical domain) and the minichaperone and the hydrophobicity profiles we show that alpha-casein has a pair of helices that have similar sequence and structural profiles as H and I. Based on this comparison we identify residues that stabilize (destabilize) alpha-casein-protein complexes. This suggests that alpha-casein assists folding by the TBR mechanism.     

Conformation of prion protein repeat peptides probed by FRET measurements and molecular dynamics simulations

We report the combined use of steady-state fluorescence resonance energy transfer (FRET) experiments and molecular dynamics (MD) simulations to investigate conformational distributions of the prion protein (PrP) repeat system. FRET was used for the first time to probe the distance, as a function of temperature and pH, between a donor Trp residue and an acceptor dansyl group attached to the N-terminus in seven model peptides containing one to three repeats of the second decarepeat of PrP from marsupial possum (PHPGGSNWGQ)nG, and one and two human PrP consensus octarepeats (PHGGGWGQ)nG. In multirepeat peptides, single-Trp mutants were made by replacing other Trp(s) with Phe. As previous work has shown PrP repeats do not adopt a single preferred stable conformation, the FRET values are averages reflecting heterogeneity in the donor-acceptor distances. The T-dependence of the conformational distributions, and derived average dansyl-Trp distances, were obtained directly from MD simulation of the marsupial dansyl-PHPGGSNWGQG peptide. The results show excellent agreement between the FRET and MD T-dependent distances, and demonstrate the remarkable sensitivity and reproducibility of the FRET method in this first-time use for a set of disordered peptides. Based on the results, we propose a model involving cation-pi or pi-pi His-Trp interactions to explain the T- (5-85 degrees C) and pH- (6.0, 7.2) dependencies on distance, with HW i, i + 4 or WH i, i + 4 separations in sequence being more stable than HW i, i + 6 or WH i, i + 6 separations. The model has peptides adopting loosely folded conformations, with dansyl-Trp distances very much less than estimates for fully extended conformations, for example, approximately 16 vs. 33, approximately 21 vs. 69, and approximately 22 vs. 106 A for 1-3 decarepeats, and approximately 14 vs. 25 and approximately 19 vs. 54 A for 1-2 octarepeats, respectively. The study demonstrates the usefulness of combining FRET with MD, a combination reported only once previously. Initial "mapping" of the conformational distribution of flexible peptides by simulation can assist in designing and interpreting experiments using steady-state intensity methods, and indicating how time-resolved or anisotropy methods might be used.     

Conformational sampling and dynamics of membrane proteins from 10-nanosecond computer simulations

In the current report, we provide a quantitative analysis of the convergence of the sampling of conformational space accomplished in molecular dynamics simulations of membrane proteins of duration in the order of 10 nanoseconds. A set of proteins of diverse size and topology is considered, ranging from helical pores such as gramicidin and small beta-barrels such as OmpT, to larger and more complex structures such as rhodopsin and FepA. Principal component analysis of the C(alpha)-atom trajectories was employed to assess the convergence of the conformational sampling in both the transmembrane domains and the whole proteins, while the time-dependence of the average structure was analyzed to obtain single-domain information. The membrane-embedded regions, particularly those of small or structurally simple proteins, were found to achieve reasonable convergence. By contrast, extra-membranous domains lacking secondary structure are often markedly under-sampled, exhibiting a continuous structural drift. This drift results in a significant imprecision in the calculated B-factors, which detracts from any quantitative comparison to experimental data. In view of such limitations, we suggest that similar analyses may be valuable in simulation studies of membrane protein dynamics, in order to attach a level of confidence to any biologically relevant observations.     

Conformational model of the Holliday junction transition deduced from molecular dynamics simulations

Homologous recombination plays a key role in the restart of stalled replication forks and in the generation of genetic diversity. During this process, two homologous DNA molecules undergo strand exchange to form a four-way DNA (Holliday) junction. In the presence of metal ions, the Holliday junction folds into the stacked-X structure that has two alternative conformers. Experiments have revealed the spontaneous transitions between these conformers, but their detailed pathways are not known. Here, we report a series of molecular dynamics simulations of the Holliday junction at physiological and elevated (400 K) temperatures. The simulations reveal new tetrahedral intermediates and suggest a schematic framework for conformer transitions. The tetrahedral intermediates bear resemblance to the junction conformation in complex with a junction-resolving enzyme, T7 endonuclease I, and indeed, one intermediate forms a stable complex with the enzyme as demonstrated in one simulation. We also describe free energy minima for various states of the Holliday junction system, which arise during conformer transitions. The results show that magnesium ions stabilize the stacked-X form and destabilize the open and tetrahedral intermediates. Overall, our study provides a detailed dynamic model of the Holliday junction undergoing a conformer transition.     

Conformational states of the glucocorticoid receptor DNA-binding domain from molecular dynamics simulations

Molecular dynamics simulations (MD) have been performed on variant crystal and NMR-derived structures of the glucocorticoid receptor DNA-binding domain (GR DBD). A loop region five residues long, the so-called D-box, exhibits significant flexibility, and transient perturbations of the tetrahedral geometry of two structurally important Cys4 zinc finger are seen, coupled to conformational changes in the D-box. In some cases, one of the Cys ligands to zinc exchanges with water, although no global distortion of the protein structure is observed. Thus, from MD simulation, dynamics of the D-box could partly be explained by solvent effects in conjunction with structural reformation of the zinc finger.     

Unfolding stabilities of two structurally similar proteins as probed by temperature-induced and force-induced molecular dynamics simulations

Unfolding stabilities of two homologous proteins, cardiotoxin III and short-neurotoxin (SNTX) belonging to three-finger toxin (TFT) superfamily, have been probed by means of molecular dynamics (MD) simulations. Combined analysis of data obtained from steered MD and all-atom MD simulations at various temperatures in near physiological conditions on the proteins suggested that overall structural stabilities of the two proteins were different from each other and the MD results are consistent with experimental data of the proteins reported in the literature. Rationalization for the differential structural stabilities of the structurally similar proteins has been chiefly attributed to the differences in the structural contacts between C- and N-termini regions in their three-dimensional structures, and the findings endorse the ‘CN network’ hypothesis proposed to qualitatively analyse the thermodynamic stabilities of proteins belonging to TFT superfamily of snake venoms. Moreover, the ‘CN network’ hypothesis has been revisited and the present study suggested that ‘CN network’ should be accounted in terms of ‘structural contacts’ and ‘structural strengths’ in order to precisely describe order of structural stabilities of TFTs.     

Conformational studies of two bradykinin antagonists by using two-dimensional NMR techniques and molecular dynamics simulations

The solution conformations of two potent antagonists of bradykinin (Arg1-Pro2-Pro3-Gly4-Phe5-Ser6-Pro7-Phe8-Arg9), [Aca(-1),DArg0,Hyp3,Thi5,DPhe7,(N-Bzl)Gly8]BK (1) and [Aaa(-1),DArg0,Hyp3,Thi5,(2-DNal)7,Thi8]BK (2), were studied by using 2D NMR spectroscopy in DMSO-d6 and molecular dynamics simulations. The NMR spectra of peptide 1 reveals the existence of at least two isomers arising from isomerization across the DPhe7-(N-Bzl)Gly8 peptide bond. The more populated isomer possesses the cis peptide bond at this position. The ratio of cis/trans isomers amounted to 7:3. With both antagonists, the NMR data indicate a beta-turn structure for the Hyp3-Gly4 residues. In addition, for peptide 2, position 2,3 is likely to be occupied by turn-like structures. The cis peptide bond between DPhe7 and (N-Bzl)Gly8 in analogue 1 suggests type VI beta-turn at position 7,8. The molecular dynamics runs were performed on both peptides in DMSO solution. The results indicate that the structure of peptide 1 is characterized by type VIb beta-turn comprising residues Ser6-Arg9 and the betaI or betaII-turn involving the Pro2-Thi5 fragment, whereas peptide 2 shows the tendency towards the formation of type I beta-turn at position 2,3. The structures of both antagonists are stabilized by a salt bridge between the guanidine moiety of Arg1 and the carboxyl group of Arg9. Moreover, the side chain of DArg0 is apart of the rest of molecule and is not involved in structural elements except for a few calculated structures.     

Studies on the structural stability of rabbit prion probed by molecular dynamics simulations of its wild-type and mutants

Prion diseases are invariably fatal and highly infectious neurodegenerative diseases that affect humans and animals. Rabbits are the only mammalian species reported to be resistant to infection from prion diseases isolated from other species (Vorberg et al., 2003). Fortunately, the NMR structure of rabbit prion (124-228) (PDB entry 2FJ3), the NMR structure of rabbit prion protein mutation S173N (PDB entry 2JOH) and the NMR structure of rabbit prion protein mutation I214V (PDB entry 2JOM) were released recently. This paper studies these NMR structures by molecular dynamics simulations. Simulation results confirm the structural stability of wild-type rabbit prion, and show that the salt bridge between D177 and R163 greatly contributes to the structural stability of rabbit prion protein.     

Conformational changes of the p53-binding cleft of MDM2 revealed by molecular dynamics simulations

Two 35-ns molecular dynamics simulations of both ligated [mouse double minute protein 2 (MDM2(p53))] and unligated (MDM2(apo)) structures of human MDM2 bound to the N-terminal domain of the tumor suppressor p53 have been performed. Analysis of the dynamics revealed that the most flexible region of MDM2 was the p53-binding cleft. When MDM2 was bound to p53, a wider and more stable topology of the cleft was obtained, while unligated MDM2 showed a narrower and highly flexible cleft. It was also found that the dynamics involved in the opening/closing motions were due to the movement of different domains of the protein, which is in agreement with recent experimental data. Considering our results, a mechanism in which p53 might be recognized and attached to MDM2 is proposed, and some implications on future directions for in silico anticancer drug design efforts are discussed. In summary, the observations made here would be very useful not only for better understanding of the biological implications of the MDM2 dynamics, but also for future efforts in anticancer drug design and discovery.     

Mimicking the action of GroEL in molecular dynamics simulations: application to the refinement of protein structures

Bacterial chaperonin, GroEL, together with its co-chaperonin, GroES, facilitates the folding of a variety of polypeptides. Experiments suggest that GroEL stimulates protein folding by multiple cycles of binding and release. Misfolded proteins first bind to an exposed hydrophobic surface on GroEL. GroES then encapsulates the substrate and triggers its release into the central cavity of the GroEL/ES complex for folding. In this work, we investigate the possibility to facilitate protein folding in molecular dynamics simulations by mimicking the effects of GroEL/ES namely, repeated binding and release, together with spatial confinement. During the binding stage, the (metastable) partially folded proteins are allowed to attach spontaneously to a hydrophobic surface within the simulation box. This destabilizes the structures, which are then transferred into a spatially confined cavity for folding. The approach has been tested by attempting to refine protein structural models generated using the ROSETTA procedure for ab initio structure prediction. Dramatic improvements in regard to the deviation of protein models from the corresponding experimental structures were observed. The results suggest that the primary effects of the GroEL/ES system can be mimicked in a simple coarse-grained manner and be used to facilitate protein folding in molecular dynamics simulations. Furthermore, the results support the assumption that the spatial confinement in GroEL/ES assists the folding of encapsulated proteins.     

Conformational dynamics of chymotrypsin inhibitor 2 by coarse-grained simulations

A coarse-grained dynamic Monte Carlo (MC) simulation method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2). Each residue is represented therein by two interaction sites, one at the alpha-carbon and the other on the amino acid side-chain. The energy and geometry parameters extracted from databank structures are used. The calculated rms fluctuations of alpha-carbon atoms are in good agreement with crystallographic temperature factors. The two regions of the protein that pack against each other to form the main hydrophobic core exhibit negatively correlated fluctuations. The conformational dynamics could efficiently be probed by the time-delayed orientational and conformational correlation functions of the virtual bonds: the active site loop, excluding the active site bond, the turn region, and the N-terminal of the alpha-helix are relatively more mobile regions of the structure. A correlation is observed between the hydrogen/deuterium (H/D) exchange behavior and the long-time orientational and conformational autocorrelation function values for CI2. A cooperativity in the rotations of the bonds near in sequence is observed at all time windows, whereas the cooperative rotations of the bonds far along the sequence appear at long time windows; these correlations contribute to the stability of the secondary structures and the tertiary structure, respectively.     

Examination of structural stability and phase transitions in constant-pressure first-principles molecular dynamics simulations

Constant-pressure first-principles molecular dynamics (FPMD) simulation is a powerful tool for investigations of structures in crystals. However, it needs enourmous computations so that highly accurate calculations for electronic states cannot be employed at present. In this report, we examined the reliability and applicability of constant-pressure FPMD in the study of structural properties under this limitation. Crystalline silicon was employed as a benchmark to perform constant-pressure FPMD simulations (with a deformable simulation cell). It is found that, in high pressure (metallic) phases, crystalline symmetry is broken with the present simulation conditions. Several structural transformations were realized by compression and decompression, but they are not entirely consistent with experiment. We discuss this discrepancy and conclude that the number of k point sampling in the Brillouin zone is crucial. It is recommended that constant-pressure FPMD is employed to explore candidate structures for unknown solid phases at present computational resources.