Correlation Times and Adiabatic Barriers for Methyl Rotation in SNase

The relation of rotational correlation times to adiabatic rotational barriers for alanine methyl groups in staphylococcal nuclease (SNase) is investigated. The hypothesis that methyl rotational barriers may be useful probes of local packing in proteins is supported by an analysis of ten X-ray crystal structures of SNase mutants. The barrier heights are consistent across a set of ten structures of a native SNase and mutants containing single-point mutations or single or double insertions, most in a ternary SNase complex. The barriers for different methyls have a range of 7.5 kcal/mol, which at 300 K would correspond to a five-order-of-magnitude range in correlation time. It is demonstrated that adiabatic rotational barriers can fluctuate significantly during an MD simulation of hydrated SNase, but that a Boltzmann weighted average is predictive of rotational correlation times determined from correlation functions. Even if a given methyl is on average quite sterically hindered, infrequently sampled low-barrier conformations may dominate the Boltzmann distribution. This result is consistent with the observed uniformity of NMR correlation times for (13)C-labeled methyls. The methyl barriers in simulation fluctuate on multiple time scales, which can make the precise relationship between methyl rotational correlation time and methyl rotation barriers complicated. The implications of these issues for the interpretation of correlation times determined from NMR and simulation are discussed.     

Theoretical studies of the structure and molecular dynamics of a peptide crystal

Energy minimizations and molecular dynamics simulations have been performed on the cyclic peptide cyclo-(Ala-Pro-D-Phe)2 in both the isolated and crystal states. The results of these calculations have been analyzed, both to investigate our ability to reproduce experimental data (structure and vibrational and NMR spectra) and to investigate the effects of environment on the energy, structure, and dynamics of peptides. Comparison of the minimized and time-averaged crystal systems with the experimental peptide structure shows that the calculations have closely reproduced the experimental structure. Molecular dynamics of the isolated molecule has led to a new conformation, which is approximately equal to 8.5 kcal/mol more stable than the conformation that exists in the crystal, the latter conformation being stabilized by intermolecular (packing) forces. This illustrates the considerable effect that environment can have on the conformation of peptides. The crystal environment has also been shown to significantly reduce the dynamic conformational fluctuations seen for the isolated molecule. The behavior of the peptide during the isolated simulation also supports the experimental NMR observation of a symmetric structure that differs from the asymmetric, instantaneous structures which characterize the molecule during the dynamics. Calculations of vibrational frequencies of the peptide in the crystal and isolated states show the expected shifts in bond-stretching frequencies due to intermolecular interactions. Finally, we have calculated NMR coupling constants from the dynamics simulation of the isolated peptide and have compared these with the experimental values. This has led to a possible reinterpretation of the experimental data.     

Force-based analysis of multidimensional energy landscapes: application of dynamic force spectroscopy and steered molecular dynamics simulations to an antibody fragment-peptide complex

Multidimensional energy landscapes are an intrinsic property of proteins and define their dynamic behavior as well as their response to external stimuli. In order to explore the energy landscape and its implications on the dynamic function of proteins dynamic force spectroscopy and steered molecular dynamics (SMD) simulations have proved to be important tools. In this study, these techniques have been employed to analyze the influence of the direction of the probing forces on the complex of an antibody fragment with its peptide antigen. Using an atomic force microscope, experiments were performed where the attachment points of the 12 amino acid long peptide antigen were varied. These measurements yielded clearly distinguishable basal dissociation rates and potential widths, proving that the direction of the applied force determines the unbinding pathway. Complementary atomistic SMD simulations were performed, which also show that the unbinding pathways of the system are dependent on the pulling direction. However, the main barrier to be crossed was independent of the pulling direction and is represented by a backbone hydrogen bond between Gly^H-H40 of the antibody fragment and Glu^Oε-6_peptide of the peptide. For each pulling direction, the observed barriers can be correlated with the rupture of specific interactions, which stabilize the bound complex. Furthermore, although the SMD simulations were performed at loading rates exceeding the experimental rates by orders of magnitude due to computational limitations, a detailed comparison of the barriers that were overcome in the SMD simulations with the data obtained from the atomic force microscope unbinding experiments show excellent agreement.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Multiscale simulations of protein folding: application to formation of secondary structures

A multiscale simulation method of protein folding is proposed, using atomic representation of protein and solvent, combing genetic algorithms to determine the key protein structures from a global view, with molecular dynamic simulations to reveal the local folding pathways, thus providing an integrated landscape of protein folding. The method is found to be superior to previously investigated global search algorithms or dynamic simulations alone. For secondary structure formation of a selected peptide, RN24, the structures and dynamics produced by this method agree well with corresponding experimental results. Three most populated conformations are observed, including hairpin, β-sheet and α-helix. The energetic barriers separating these three structures are comparable to the kinetic energy of the atoms of the peptide, implying that the transition between these states can be easily triggered by kinetic perturbations, mainly through electrostatic interactions between charged atoms. Transitions between α-helix and β-sheet should jump over at least two energy barriers and may stay in the energetic trap of hairpin. It is proposed that the structure of proteins should be jointly governed by thermodynamic and dynamic factors; free energy is not the exclusive dominant for stability of proteins.     

Molecular dynamics simulations of a guaiacyl beta-O-4 lignin model compound: examination of intramolecular hydrogen bonding and conformational flexibility

The dynamical conformational behavior of a guaiacyl beta-O-4 lignin model compound has been investigated by molecular simulations. The potential energy surface of the molecule in vacuum has been examined by means of an adiabatic map, showing a large accessible conformational space with multiple energy minima separated by low barriers. Molecular dynamics simulations have been performed in vacuum and with explicit solvent molecules for 10 and 2.1 ns, respectively. Molecular dynamics trajectories recorded in vacuum have shown the molecule to be flexible and to visit a large number of conformations. Many intramolecular H-bonds have been observed, existing for more than 90% of the total simulation time. The presence of explicit solvent molecules induces a significant broadening of some regions of the accessible conformational space and also largely reduces the statistical significance of intramolecular H-bonding. Intramolecular H-bonds observed in vacuum do not persist significantly and are preferentially exchanged with intermolecular H-bonds to the surrounding solvent molecules. The theoretical results are in good agreement with experimental NMR data that do not support the existence of strong and persistent intramolecular H-bonds in solution but instead indicate that H-bonds to solvent predominate. Finally, both molecular modeling and NMR approaches predict the guaiacyl beta-O-4 structure to be flexible and indicate that intramolecular H-bonds are not strong and persistent enough to confer rigidity to the molecule in solution.     

Steric and electronic influences on the torsional energy landscape of retinal

We have performed quantum mechanical calculations for retinal model compounds to establish the rotational energy barriers for the C5-, C9-, and C13-methyl groups known to play an essential role in rhodopsin activation. Intraretinal steric interactions as well as electronic effects lower the rotational barriers of both the C9- and C13-methyl groups, consistent with experimental ²H NMR data. Each retinal methyl group has a unique rotational behavior which must be treated individually. These results are highly relevant for the parameterization of molecular mechanics force fields which form the basis of molecular dynamics simulations of retinal proteins such as rhodopsin.     

Analysis of peptide rotational diffusion by homonuclear NMR

The analysis of the rotational diffusion of a molecule using homonuclear NMR is investigated. The homonuclear longitudinal and transverse cross-relaxation rates, which can be quantitatively measured using off-Resonance Rotating frame nuclear Overhauser Effect Spectroscopy (ROESY), are used to build a distribution, which exhibits a solid-state-like pattern characteristic of the diffusion tensor. The distributions of the antimicrobial peptide ranalexin in water and in 30% of trifluoracetic acid (TFE) are compared, and the peptide rotational diffusion is shown to be more isotropic in water than in 30% TFE. This difference is further supported by the analysis of NMR ranalexin conformers in 30% TFE, and by the analysis of a molecular dynamics simulation of peptide in water.     

Conformation and dynamic properties of a saturated hydrocarbon chain confined in a model membrane: a Brownian dynamics simulation

A Brownian dynamics simulation of a saturated hydrocarbon chain with simple mean-field potentials, namely anchorage, orientation and enclosing, reproducing a biological membrane environment is presented. The simulation was performed for a time equivalent to 1.4 micros thanks to the simplicity of our model. The results are compared with those obtained for a hydrocarbon chain simulated in the absence of the membrane potentials but with confinement. With the appropriate choice of parameters, equilibrium properties, such as deuterium order parameter, chain length, tilt angle and geometry, and dynamic properties, such as dihedral angle transition rate, rotational and translational diffusion, recovered from our simulations, correctly reproduced, are consistent with hydrocarbon-derived molecule experimental results and simulation results obtained from other more complex studies.     

Structural and dynamical studies of Humanin in water and TFE/water mixture: a molecular dynamics simulation

The structural and dynamical properties of Humanin, a small peptide with neuroprotective activity against the insults of the Alzheimer's disease-related genes and the neurotoxic amyloid peptide, are studied in two different environments by molecular dynamics simulation. In this study, we have performed comparative molecular dynamics simulations in the absence and in the presence of TFE. The resulting trajectories were analyzed in terms of structural and dynamical properties of peptide and compared to the available NMR data. In water humanin is observed to partly unfold. The peptide is readily stabilized in an ordered helical conformation in the TFE/water mixture. Our simulations show that the peptide is flexible with definite turn point in its structure in water environment. It is free to interact with receptors that mediate its action in polar environment. Humanin may also find an alpha helix structure necessary for passage through biomembranes and/or specific interactions.     

Conformational flexibility of the MHC class I alpha1-alpha2 domain in peptide bound and free states: a molecular dynamics simulation study

Major histocompatibility complex class I proteins play a key role in the recognition and presentation of peptide antigens to the host immune system. The structure of various major histocompatibility complex class I proteins has been determined experimentally in complex with several antigenic peptides. However, the structure in the unbound (empty) form is not known. To study the conformational dynamics of the empty major histocompatibility complex class I molecule comparative molecular dynamics simulations have been performed starting from the crystal structure of a peptide bound class I peptide-binding domain in the presence and absence of a peptide ligand. Simulations including the bound peptide stayed close to the experimental start structure at both simulation temperatures (300 and 355 K) during the entire simulation of 26 ns. Several independent simulations in the absence of peptide indicate that the empty domain may not adopt a single defined conformation but is conformationally significantly more heterogeneous in particular within the alpha-helices that flank the peptide binding cleft. The calculated conformational dynamics along the protein chain correlate well with available spectroscopic data and with the observed site-specific sensitivity of the empty class I protein to proteolytic digestion. During the simulations at 300 K the binding region for the peptide N-terminus stayed close to the conformation in the bound state, whereas the anchor region for the C-terminus showed significantly larger conformational fluctuations. This included a segment at the beginning of the second alpha-helix in the domain that is likely to be involved in the interaction with the chaperone protein tapasin during the peptide-loading process. The simulation studies further indicate that peptide binding at the C- and N-terminus may follow different mechanisms that involve different degrees of induced conformational changes in the peptide-binding domain. In particular binding of the peptide C-terminus may require conformational stabilization by chaperone proteins during peptide loading.     

Not only enthalpy: large entropy contribution to ion permeation barriers in single-file channels

The effect of channel length on the barrier for potassium ion permeation through single-file channels has been studied by means of all-atom molecular dynamics simulations. Using series of peptidic gramicidin-like and simplified ring-structured channels, both embedded in model membranes, we obtained two distinct types of behavior: saturation of the central free energy barriers for peptidic channels and a linear increase in simplified ring-structured channels with increasing channel length. The saturation of the central free energy barrier for the peptidic channels occurs at relatively short lengths, and it is correlated with the desolvation from the bulk water. Remarkably, decomposition of free energy barriers into enthalpic and entropic terms reveals an entropic cost for ion permeation. Furthermore, this entropic cost dominates the ion permeation free energy barrier, since the corresponding free energy contribution is higher than the enthalpic barrier. We conclude that the length dependence of the free energy is enthalpy-dominated, but the entropy is the major contribution to the permeation barrier. The decrease in rotational water motion and the reduction of channel mobility are putative origins for the overall entropic penalty.     

Molecular dynamics study of a calmodulin-like protein with an IQ peptide: spontaneous refolding of the protein around the peptide

The Calmodulin (CaM) is a small (16.7 kDa), highly acidic protein that is crucial to all eukaryotes by serving as a prototypical calcium sensor. In the present study, we investigated, through molecular dynamics simulations, the dynamics of a complex between the Mlc1p protein, which is a CaM-like protein, and the IQ4 peptide. This protein-peptide interaction is of high importance because IQ motifs are widely distributed among different kinds of CaM-binding proteins. The Mlc1p-IQ4 complex, which had been resolved by crystallography to 2.1 A, confers to a Ca(+2)-independent stable structure. During the simulations, the complex undergoes a complicated modulation process, which involves bending of the angles between the alpha-helices of the protein, breaking of the alpha-helical structure of the IQ4 peptide into two sections, and formation of new contact points between the protein and the peptide. The dynamics of the process consist of fast sub picosecond events and much slower ones that take a few nanoseconds to completion. Our study expands the information embedded in the crystal structure of the Mlc1p-IQ4 complex by describing its dynamic behavior as it evolves from the crystal structure to a form stable in solution. The article shows that careful application of molecular dynamics simulations can be used for extending the structural information presented by the crystal structure, thereby revealing the dynamic configuration of the protein in its physiological environment.     

Conformational dynamics of the F1-ATPase beta-subunit: a molecular dynamics study

According to the different nucleotide occupancies of the F(1)-ATPase beta-subunits and due to the asymmetry imposed through the central gamma-subunit, the beta-subunit adopts different conformations in the crystal structures. Recently, a spontaneous and nucleotide-independent closure of the open beta-subunit upon rotation of the gamma-subunit has been proposed. To address the question whether this closure is dictated by interactions to neighbored subunits or whether the open beta-subunit behaves like a prestressed "spring," we report multinanosecond molecular dynamics simulations of the isolated beta-subunit with different start conformations and different nucleotide occupancies. We have observed a fast, spontaneous closure motion of the open beta(E)-subunit, consistent with the available x-ray structures. The motions and kinetics are similar to those observed in simulations of the full (alpha beta)(3)gamma-complex, which support the view of a prestressed "spring," i.e., that forces internal to the beta(E)-subunit dominate possible interactions from adjacent alpha-subunits. Additionally, nucleotide removal is found to trigger conformational transitions of the closed beta(TP)-subunit; this provides evidence that the recently resolved half-closed beta-subunit conformation is an intermediate state before product release. The observed motions provide a plausible explanation why ADP and P(i) are required for the release of bound ATP and why gamma-depleted (alpha beta)(3) has a drastically reduced hydrolysis rate.     

Loop propensity of the sequence YKGQP from staphylococcal nuclease: implications for the folding of nuclease.

Recently we performed molecular dynamics (MD) simulations on the folding of the hairpin peptide DTVKLMYKGQPMTFR from staphylococcal nuclease in explicit water. We found that the peptide folds into a hairpin conformation with native and nonnative hydrogen-bonding patterns. In all the folding events observed in the folding of the hairpin peptide, loop formation involving the region YKGQP was an important event. In order to trace the origins of the loop propensity of the sequence YKGQP, we performed MD simulations on the sequence starting from extended, polyproline II and native type I' turn conformations for a total simulation length of 300 ns, using the GROMOS96 force field under constant volume and temperature (NVT) conditions. The free-energy landscape of the peptide YKGQP shows minima corresponding to loop conformation with Tyr and Pro side-chain association, turn and extended conformational forms, with modest free-energy barriers separating the minima. To elucidate the role of Gly in facilitating loop formation, we also performed MD simulations of the mutated peptide YKAQP (Gly --> Ala mutation) under similar conditions starting from polyproline II conformation for 100 ns. Two minima corresponding to bend/turn and extended conformations were observed in the free-energy landscape for the peptide YKAQP. The free-energy barrier between the minima in the free-energy landscape of the peptide YKAQP was also modest. Loop conformation is largely sampled by the YKGQP peptide, while extended conformation is largely sampled by the YKAQP peptide. We also explain why the YKGQP sequence samples type II turn conformation in these simulations, whereas the sequence as part of the hairpin peptide DTVKLMYKGQPMTFR samples type I' turn conformation both in the X-ray crystal structure and in our earlier simulations on the folding of the hairpin peptide. We discuss the implications of our results to the folding of the staphylococcal nuclease.     

Combined use of molecular dynamics simulations and NMR to explore peptide bond isomerization and multiple intramolecular hydrogen-bonding possibilities in a cyclic pentapeptide, cyclo(Gly-Pro-D-Phe-Gly-Val).

The conformational behavior of a model cyclic pentapeptide--cyclo(Gly-L-Pro-D-Phe-Gly-L-Val)--has been explored through the combined use of in vacuo molecular dynamics simulations and a range of nmr experiments (preceding paper). The molecular dynamics analysis suggests that, despite the conformational constraints imposed by formation of the pentapeptide cycle, this pentapeptide undergoes conformational transitions between various hydrogen-bonded conformations, characterized by low energy barriers. An inverse gamma turn with Pro in position i + 1 and a gamma turn with D-Phe in position i + 1 are two alternatives occurring frequently. Like other DLDDL cyclic pentapeptides, cyclo(Gly-Pro-D-Phe-Gly-Val) is also stabilized by an inverse gamma-turn structure with the beta-branched Val residue in position i + 1, and this hydrogen bond is retained in the different conformational families. The gamma-turn around D-Phe3 and the inverse gamma turn around Val5 are consistent with the nmr observations. 3JNH-CH alpha coupling constants of the all-trans forms were calculated from one of the molecular dynamics trajectories and are comparable to nmr experimental data, suggesting that the conformational states visited during the simulation are representative of the conformational distribution in solution. In addition to the equilibrium among various hydrogen-bonded all-trans conformers, the observation in nmr spectra of two sets of resonances for all peptide protons indicated a slow conformational interconversion of the Gly-Pro peptide bond between trans and cis isomers. The activation energy between these two conformers was determined experimentally by magnetization transfer and was calculated by high temperature constrained molecular dynamics simulation. Both methods yield a free energy of activation of ca. 20 kcal/mol. Furthermore, the free energy of activation is dependent on the direction of rotation of the Gly-Pro peptide bond.