Molecular dynamics simulations of a cyclic-beta-(1-->2) glucan containing an alpha-(1-->6) linkage as a 'molecular alleviator' for the macrocyclic conformational strain

The conformational preferences of a cyclic osmoregulated periplasmic glucan of Ralstonia solanacearum (OPGR), which is composed of 13 glucose units and linked entirely via beta-(1-->2) linkages excluding one alpha-(1-->6) linkage, were characterized by molecular dynamics simulations. Of the three force fields modified for carbohydrates that were applied to select a suitable one for the cyclic glucan, the carbohydrate solution force field (CSFF) was found to most accurately simulate the cyclic molecule. To determine the conformational characteristics of OPGR, we investigated the glycosidic dihedral angle distribution, fluctuation, and the potential energy of the glucan and constructed hypothetical cyclic (CYS13) and linear (LINEAR) glucans. All beta-(1-->2)-glycosidic linkages of OPGR adopted stable conformations, and the dihedral angles fluctuated in this energy region with some flexibility. However, despite the inherent flexibility of the alpha-(1-->6) linkage, the dihedral angles have no transition and are more rigid than that in a linear glucan. CYS13, which consists of only beta-(1-->2) linkages, is somewhat less flexible than other glycans, and one of its linkages adopts a higher energy conformation. In addition, the root-mean-square fluctuation of this linkage is lower than that of other linkages. Furthermore, the potential energy of glucans increases in the order of LINEAR, OPGR, and CYS13. These results provide evidence of the existence of conformational constraints in the cyclic glucan. The alpha-(1-->6)-glycosidic linkage can relieve this constraint more efficiently than the beta-(1-->2) linkage. The conformation of OPGR can reconcile the tendency for individual glycosidic bonds to adopt energetically favorable conformations with the requirement for closure of the macrocyclic ring by losing the inherent flexibility of the alpha-(1-->6)-glycosidic linkage.     

Starting‐structure dependence of nanosecond timescale intersubstate transitions and reproducibility of MD‐derived order parameters

Factors affecting the accuracy of molecular dynamics (MD) simulations are investigated by comparing generalized order parameters for backbone NH vectors of the B3 immunoglobulin‐binding domain of streptococcal protein G (GB3) derived from simulations with values obtained from NMR spin relaxation (Yao L, Grishaev A, Cornilescu G, Bax A, J Am Chem Soc 2010;132:4295‐4309.). Choices for many parameters of the simulations, such as buffer volume, water model, or salt concentration, have only minor influences on the resulting order parameters. In contrast, seemingly minor conformational differences in starting structures, such as orientations of sidechain hydroxyl groups, resulting from applying different protonation algorithms to the same structure, have major effects on backbone dynamics. Some, but not all, of these effects are mitigated by increased sampling in simulations. Most discrepancies between simulated and experimental results occur for residues located at the ends of secondary structures and involve large amplitude nanosecond timescale transitions between distinct conformational substates. These transitions result in autocorrelation functions for bond vector reorientation that do not converge when calculated over individual simulation blocks, typically of length similar to the overall rotational diffusion time. A test for convergence before averaging the order parameters from different blocks results in better agreement between order parameters calculated from different sets of simulations and with NMR‐derived order parameters. Thus, MD‐derived order parameters are more strongly affected by transitions between conformational substates than by fluctuations within individual substates themselves, while conformational differences in the starting structures affect the frequency and scale of such transitions. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

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.     

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed.     

A Physical Picture of Protein Dynamics and Conformational Changes

A physical model is reviewed which explains different aspects of protein dynamics consistently. At low temperatures, the molecules are frozen in conformational substates. Their average energy is 3/2RT. Solid-state vibrations occur on a time scale of femtoseconds to nanoseconds. Above a characteristic temperature, often called the dynamical transition temperature, slow modes of motions can be observed occurring on a time scale between about 140 and 1 ns. These motions are overdamped, quasidiffusive, and involve collective motions of segments of the size of an α-helix. Molecules performing these types of motion are in the “flexible state”. This state is reached by thermal activation. It is shown that these motions are essential for conformational relaxation. Based on this picture, a new approach is proposed to understand conformational changes. It connects structural fluctuations and conformational transitions.     

Hierarchical Conformational Analysis of Native Lysozyme Based on Sub-Millisecond Molecular Dynamics Simulations

Hierarchical organization of free energy landscape (FEL) for native globular proteins has been widely accepted by the biophysics community. However, FEL of native proteins is usually projected onto one or a few dimensions. Here we generated collectively 0.2 milli-second molecular dynamics simulation trajectories in explicit solvent for hen egg white lysozyme (HEWL), and carried out detailed conformational analysis based on backbone torsional degrees of freedom (DOF). Our results demonstrated that at micro-second and coarser temporal resolutions, FEL of HEWL exhibits hub-like topology with crystal structures occupying the dominant structural ensemble that serves as the hub of conformational transitions. However, at 100ns and finer temporal resolutions, conformational substates of HEWL exhibit network-like topology, crystal structures are associated with kinetic traps that are important but not dominant ensembles. Backbone torsional state transitions on time scales ranging from nanoseconds to beyond microseconds were found to be associated with various types of molecular interactions. Even at nanoseconds temporal resolution, the number of conformational substates that are of statistical significance is quite limited. These observations suggest that detailed analysis of conformational substates at multiple temporal resolutions is both important and feasible. Transition state ensembles among various conformational substates at microsecond temporal resolution were observed to be considerably disordered. Life times of these transition state ensembles are found to be nearly independent of the time scales of the participating torsional DOFs.     

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.     

Energy landscape of a native protein: Jumping-among-minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998. © 1998 Wiley-Liss, Inc.     

Phosphorylated Phospholamban Stabilizes a Compact Conformation of the Cardiac Calcium-ATPase

The sarcoendoplasmic reticulum calcium ATPase (SERCA) plays a key role in cardiac calcium handling and is considered a high-value target for the treatment of heart failure. SERCA undergoes conformational changes as it harnesses the chemical energy of ATP for active transport. X-ray crystallography has provided insight into SERCA structural substates, but it is not known how well these static snapshots describe in vivo conformational dynamics. The goals of this work were to quantify the direction and magnitude of SERCA motions as the pump performs work in live cardiac myocytes, and to identify structural determinants of SERCA regulation by phospholamban. We measured intramolecular fluorescence resonance energy transfer (FRET) between fluorescent proteins fused to SERCA cytoplasmic domains. We detected four discrete structural substates for SERCA expressed in cardiac muscle cells. The relative populations of these discrete states oscillated with electrical pacing. Low FRET states were most populated in low Ca (diastole), and were indicative of an open, disordered structure for SERCA in the E2 (Ca-free) enzymatic substate. High FRET states increased with Ca (systole), suggesting rigidly closed conformations for the E1 (Ca-bound) enzymatic substates. Notably, a special compact E1 state was observed after treatment with β-adrenergic agonist or with coexpression of phosphomimetic mutants of phospholamban. The data suggest that SERCA calcium binding induces the pump to undergo a transition from an open, dynamic conformation to a closed, ordered structure. Phosphorylated phospholamban stabilizes a unique conformation of SERCA that is characterized by a compact architecture.     

Backbone dynamics and energetics of a calmodulin domain mutant exchanging between closed and open conformations.

Previous studies have suggested that the Ca2+-saturated E140Q mutant of the C-terminal domain of calmodulin exhibits equilibrium exchange between "open" and "closed" conformations similar to those of the Ca2+-free and Ca2+-saturated states of wild-type calmodulin. The backbone dynamics of this mutant were studied using15N spin relaxation experiments at three different temperatures. Measurements at each temperature of the15N rate constants for longitudinal and transverse auto-relaxation, longitudinal and transverse cross-correlation relaxation, and the1H-15N cross-relaxation afforded unequivocal identification of conformational exchange processes on microsecond to millisecond time-scales, and characterization of fast fluctuations on picosecond to nanosecond time-scales using model-free approaches. The results show that essentially all residues of the protein are involved in conformational exchange. Generalized order parameters of the fast internal motions indicate that the conformational substates are well folded, and exclude the possibility that the exchange involves a significant population of unfolded or disordered species. The temperature dependence of the order parameters offers qualitative estimates of the contribution to the heat capacity from fast fluctuations of the protein backbone, revealing significant variation between the well-ordered secondary structure elements and the more flexible regions. The temperature dependence of the conformational exchange contributions to the transverse auto-relaxation rate constants directly demonstrates that the microscopic exchange rate constants are greater than 2.7x10(3)s-1at 291 K. The conformational exchange contributions correlate with the chemical shift differences between the Ca2+-free and Ca2+-saturated states of the wild-type protein, thereby substantiating that the conformational substates are similar to the open and closed states of wild-type calmodulin. Taking the wild-type chemical shifts to represent the conformational substates of the mutant and populations estimated previously, the microscopic exchange rate constants could be estimated as 2x10(4)to 3x10(4)s-1at 291 K for a subset of residues. The temperature depen dence of the exchange allows the characterization of apparent energy barriers of the conformational transition, with results suggesting a complex process that does not correspond to a single global transition between substates.     

Heterogeneity of Protein Substates Visualized by Spin-label EPR

The energy landscape of proteins is characterized by a hierarchy of substates, which give rise to conformational heterogeneity at low temperatures. In multiply spin-labeled membranous Na,K-ATPase, this heterogeneous population of conformations is manifest by strong inhomogeneous broadening of the electron paramagnetic resonance (EPR) line shapes and nonexponential spin-echo decays, which undergo a transition to homogeneous broadening and exponential relaxation at higher temperatures (previous study). In this study, we apply these EPR methods to small water-soluble proteins, of the type for which the existence of conformational substates is well established. Both α-helical and β-sheet aqueous proteins that are spin-labeled on a single cysteine residue display spin-echo decays with a single phase-memory time T_2M and conventional EPR line shapes with predominantly homogeneous broadening, over a broad range of temperatures from 77 K to ∼ 250 K or higher. Above ∼ 200 K, the residual inhomogeneous broadening is reduced almost to zero. In contrast, both the proteins and the spin label alone, when in a glycerol-water mixture below the glass transition, display heterogeneity in spin-echo phase-memory time and a stronger inhomogeneous broadening of the conventional line shapes, similar to multiply spin-labeled membranous Na,K-ATPase below 200 K. Above 200 K (or the glass transition), a single phase-memory time and predominantly homogeneous broadening are found in both spin-label systems. The results are discussed in terms of solvent-mediated protein transitions, the ability of single spin-label sites to detect conformational heterogeneity, and the desirability of exploring multiple sites for proteins with the size and complexity of the Na,K-ATPase.     

Heterogeneity of Protein Substates Visualized by Spin-label EPR

The energy landscape of proteins is characterized by a hierarchy of substates, which give rise to conformational heterogeneity at low temperatures. In multiply spin-labeled membranous Na,K-ATPase, this heterogeneous population of conformations is manifest by strong inhomogeneous broadening of the electron paramagnetic resonance (EPR) line shapes and nonexponential spin-echo decays, which undergo a transition to homogeneous broadening and exponential relaxation at higher temperatures (previous study). In this study, we apply these EPR methods to small water-soluble proteins, of the type for which the existence of conformational substates is well established. Both α-helical and β-sheet aqueous proteins that are spin-labeled on a single cysteine residue display spin-echo decays with a single phase-memory time T_2M and conventional EPR line shapes with predominantly homogeneous broadening, over a broad range of temperatures from 77 K to ∼ 250 K or higher. Above ∼ 200 K, the residual inhomogeneous broadening is reduced almost to zero. In contrast, both the proteins and the spin label alone, when in a glycerol-water mixture below the glass transition, display heterogeneity in spin-echo phase-memory time and a stronger inhomogeneous broadening of the conventional line shapes, similar to multiply spin-labeled membranous Na,K-ATPase below 200 K. Above 200 K (or the glass transition), a single phase-memory time and predominantly homogeneous broadening are found in both spin-label systems. The results are discussed in terms of solvent-mediated protein transitions, the ability of single spin-label sites to detect conformational heterogeneity, and the desirability of exploring multiple sites for proteins with the size and complexity of the Na,K-ATPase.     

Myoglobin-CO conformational substate dynamics: 2D vibrational echoes and MD simulations

Two-dimensional (2D) infrared vibrational echoes were performed on horse heart carbonmonoxymyoglobin (MbCO) in water over a range of temperatures. The A(1) and A(3) conformational substates of MbCO are found to have different dephasing rates with different temperature dependences. A frequency-frequency correlation function derived from molecular dynamics simulations on MbCO at 298 K is used to calculate the vibrational echo decay. The calculated decay shows substantial agreement with the experimentally measured decays. The 2D vibrational echo probes protein dynamics and provides an observable that can be used to test structural assignments for the MbCO conformational substates.     

Modeling mutations in protein structures

We describe an automated method for the modeling of point mutations in protein structures. The protein is represented by all non-hydrogen atoms. The scoring function consists of several types of physical potential energy terms and homology-derived restraints. The optimization method implements a combination of conjugate gradient minimization and molecular dynamics with simulated annealing. The testing set consists of 717 pairs of known protein structures differing by a single mutation. Twelve variations of the scoring function were tested in three different environments of the mutated residue. The best-performing protocol optimizes all the atoms of the mutated residue, with respect to a scoring function that includes molecular mechanics energy terms for bond distances, angles, dihedral angles, peptide bond planarity, and non-bonded atomic contacts represented by Lennard-Jones potential, dihedral angle restraints derived from the aligned homologous structure, and a statistical potential for non-bonded atomic interactions extracted from a large set of known protein structures. The current method compares favorably with other tested approaches, especially when predicting long and flexible side-chains. In addition to the thoroughness of the conformational search, sampled degrees of freedom, and the scoring function type, the accuracy of the method was also evaluated as a function of the flexibility of the mutated side-chain, the relative volume change of the mutated residue, and its residue type. The results suggest that further improvement is likely to be achieved by concentrating on the improvement of the scoring function, in addition to or instead of increasing the variety of sampled conformations.     

Protein conformational landscapes: Energy minimization and clustering of a long molecular dynamics trajectory

Using energy minimization and cluster analysis, we have analyzed a 1020 ps molecular dynamics trajectory of solvated bovine pancreatic trypsin inhibitor. Elucidation of conformational sub states in this way both illustrates the degree of conformational convergence in the simulation and reduces the structural data to a tractable subset. The relative movement of structures upon energy minimization was used to estimate the sizes of features on the protein potential energy surface. The structures were analyzed using their pairwise root-mean-square C_α deviations, which gave a global measure of conformational changes that would not be apparent by monitoring single degrees of freedom. At time scales of 0.1 ps, energy minimization detected sharp transitions between energy minima separated by 0.1 Å rms deviation. Larger conformational clusters containing these smaller minima and separated by 0.25 Å were seen at 1 ps time scales. Both of these small features of the conformational landscape were characterized by movements in loop regions associated with small, correlated backbone dihedral angle shifts. On a nanosecond time scale, the main features of the protein energy landscape were clusters separated by over 0.7 Å rms deviation, with only seven of these sub states visited over the 1 ns trajectory. These substates, discernible both before and after energy minimization, differ mainly in a monotonic pivot of the loop residues 11–18 over the course of the simulation. This loop contains lysine 17, which specifically binds to trypsin in the active site. The trajectory did not return to previously visited clusters, indicating that this trajectory has not been shown to have completely sampled the conformational substates available to it. Because the apparent convergence to a single region of conformation space depends on both the time scale of observation and the size of the conformational features examined, convergence must be operationally defined within the context of the simulation. © 1995 Wiley-Liss, Inc.     

Molecular dynamics simulations and the conformational mobility of blood group oligosaccharides

Molecular dynamics simulations were carried out without explicit consideration of solvent to explore the conformational mobility of blood group A and H oligosaccharides. The potential energy force field of Rasmussen and co-workers was used with the CHARMM program on a number of disaccharide and trisaccharide models composed of fucose, galactose, glucose, N-acetyl glucosamine, and N-acetyl galactosamine chosen to represent various fragments of blood group oligosaccharides. In agreement with results of earlier studies, stable chair conformations were found for each pyranoside from which no transitions were detected in simulations as long as 800 ps. Exocyclic dihedral angles, including that of C5-C6, generally show numerous transitions on a time scale of approximately 5-30 ps. The dihedral angles of some but not all glycosidic linkages of blood group oligosaccharides show transitions on the time scale of 30-50 ps, implying that the extent of internal motion in blood group oligosaccharides depends strongly on linkage stereochemistry. For certain blood group A and H oligosaccharides that show limited internal motion in these simulations, we argue that the calculations are consistent with our previous analysis of 1H nuclear Overhauser enhancement (NOE) data that imply single conformations over a wide range of temperature and solvent conditions. While the trajectories are consistent with 13C T1 values that have been interpreted as indicating rigid conformations, measurements of 13C-NOE and T1 as a function of magnetic field strength are proposed as an improved method for experimental detection of the internal motion that is suggested for certain oligosaccharides in these simulations. The results of these simulations differ substantially from those of peptides of a similar molecular weight in that the oligosaccharides show much less internal motion.     

Ionic channels with conformational substates.

Recent studies of protein dynamics suggest that ionic channels can assume many conformational substates. Long-lived substates have been directly observed in single-channel current records. In many cases, however, the lifetimes of conformational states will be far below the theoretical limit of time resolution of single-channel experiments. The existence of such hidden substates may strongly influence the observable (time-averaged) properties of a channel, such as the concentration dependence of conductance. A channel exhibiting fast, voltage-dependent transitions between different conductance states may behave as an intrinsic rectifier. In the presence of more than one permeable ion species, coupling between ionic fluxes may occur, even when the channel has only a single ion-binding site. In special situations the rate of ion translocation becomes limited by the rate of conformational transitions, meaning that the channel approaches the kinetic behavior of a carrier. As a result of the strong coulombic interaction between an ion in a binding site and polar groups of the protein, rate constants of conformational transitions may depend on the occupancy of the binding site. Under this condition a nonequilibrium distribution of conformational states is created when ions are driven through the channel by an external force. This may lead to an apparent violation of microscopic reversibility, i.e., to a situation in which the frequency of transitions from state A to state B is no longer equal to the transition frequency from state B to state A.     

Influence of non-bonded parameters on the quality of NMR structures: A new force field for NMR structure calculation

The effects of different non-bonded parameters of force fields for NMR structure calculation on the quality of the resulting NMR solution structures were investigated using Interleukin 4 as a model system. NMR structure ensembles were calculated with an ab initio protocol using torsion angle dynamics. The calculations were repeated with five different non-bonded energy functions and parameters. The resulting ensembles were compared with the available X-ray structures, and their quality was assessed with common structure validation programs. In addition, the impact of torsion angle restraints and dihedral energy terms for the sidechains and the backbone was studied. The further improvement of the quality by refinement in explicit solvent was demonstrated. The optimal parameters, including those necessary for water refinement, are available in the new version of the PARALLHDG force field.     

Dynamics of electron-conformational transitions in proteins and physical mechanisms of biomacromolecule function]

The proteins can be considered as a microheterogeneous structured media possessing memory and feedback properties. The conformational energy surface depends on the chemical states of protein groups. Conformational motions are local diffusion with relaxation times much longer than vibrational relaxation times in condensed media. Owing to the hierarchy of relaxation times chemical reaction rates depend on conformation parametrically. Regulation of functional activity by conformational mobility is accomplished via transmission of information in the form of changes in the distribution functions of separate groups along the conformational substates. The interpretation of drastic effects on conformational mobility needs super-stochastic approaches. A possible mechanism of sharp conformational change are discussed in terms of the catastrophe theory.