Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Effect of protein dynamics upon reactions that occur in the heme pocket of horseradish peroxidase

Free base and Pd porphyrin derivatives of horseradish peroxidase show long-lived excited states that are quenched by the presence of the peroxidase inhibitor, benzhydroxamic acid. The relaxation times of the excited-state luminescence and the rates of the quenching reaction for these derivatives of peroxidase were monitored as a function of pH, temperature, and viscosity with the view of examining how protein dynamics affect the quenching reaction. As solvent viscosity increases, the rate decreases, but at the limit of very high viscosity (i.e., high glycerol or sugar glass) the quenching still occurs. A model is presented that is consistent with the known structure of the enzyme-inhibitor complex. It is considered that the inhibitor is held at an established position but that solvent-dependent and independent motions allow a limited diffusion of the two reactants. Since there is a steep dependence upon distance and orientation, the diffusion toward the favorable position for reaction enhances the reaction rate. The solvent viscosity dependent and independent effects were separated and analyzed. The importance of internal reaction dynamics is demonstrated in the observation that rigidity of solvent imposed by incorporating the protein into glass at room temperature allows the reaction to occur, while the reaction is inhibited at low temperature. The results emphasize that protein dynamics plays a role in determining reaction rates.     

Quantitative Characterization of Local Protein Solvation To Predict Solvent Effects on Protein Structure

Characterization of solvent preferences of proteins is essential to the understanding of solvent effects on protein structure and stability. Although it is generally believed that solvent preferences at distinct loci of a protein surface may differ, quantitative characterization of local protein solvation has remained elusive. In this study, we show that local solvation preferences can be quantified over the entire protein surface from extended molecular dynamics simulations. By subjecting microsecond trajectories of two proteins (lysozyme and antibody fragment D1.3) in 4 M glycerol to rigorous statistical analyses, solvent preferences of individual protein residues are quantified by local preferential interaction coefficients. Local solvent preferences for glycerol vary widely from residue to residue and may change as a result of protein side-chain motions that are slower than the longest intrinsic solvation timescale of ～10 ns. Differences of local solvent preferences between distinct protein side-chain conformations predict solvent effects on local protein structure in good agreement with experiment. This study extends the application scope of preferential interaction theory and enables molecular understanding of solvent effects on protein structure through comprehensive characterization of local protein solvation.     

Solvent effects on protein motion and protein effects on solvent motion. Dynamics of the active site region of lysozyme

The stochastic boundary molecular dynamics methodology is applied to the active site of the enzyme lysozyme. A comparison is made of in vacuo dynamics results from the stochastic boundary method and a full conventional molecular dynamics simulation of lysozyme. Excellent agreement between the two approaches is obtained. The influence of solvent on the residues in the active site region is explored and it is shown that both the structure and dynamics are affected. Of particular importance for the structure of the protein is the solvation of polar residues and the stabilization of like-charged ion pairs. The magnitude of the fluctuations is only slightly altered by the solvent; the overall increase in the root-mean-square fluctuations, relative to the vacuum run, is 11%. The solvent effect on dynamical properties is found not to be simply related to the solvent viscosity. Both the solvent exposure and dynamic aspects of protein-solvent interactions, including the relative time scales of the motions, are shown to play a role. The effects of the protein on solvent dynamics and structure are also observed to be significant. The solvent molecules around atoms in charged, polar and apolar side-chains show markedly different diffusion coefficients as well as exhibiting different solvation structures. One key example is the water around apolar groups, which is much less mobile than bulk water, or water solvating polar groups.     

Effect of solvent viscosity on the heme-pocket dynamics of photolyzed (carbonmonoxy)hemoglobin

The heme-pocket dynamics subsequent to carbon monoxide photolysis from human hemoglobin have been monitored as a function of glycerol-water solvent composition with time-resolved resonance Raman spectroscopy. Prompt (geminate) ligand recombination rates and the transient heme-pocket geometry established within 10 ns after photolysis appear to be largely independent of solvent composition. The rate of relaxation of the transient geometry to an equilibrium deoxy configuration is, however, quite sensitive to solvent composition. These observations suggest that the former processes result from local, internal motions of the protein, while the relaxation dynamics of the proximal heme pocket are predicated upon more global protein motions that are dependent upon solvent viscosity.     

Diffusional barrier crossing in a two-state protein folding reaction.

There has been some debate as to whether protein folding involves diffusive chain motions and thus depends on solvent viscosity. The interpretation of folding kinetics in viscous solvents has remained difficult and controversial, in that viscogenic agents affect folding rates not only by increasing solvent viscosity but also by increasing protein stability. By carefully choosing experimental conditions, we can now eliminate the effect on stability and show that the folding dynamics of the cold shock protein CspB are viscosity dependent. Thus Kramers' theory of reaction rates rather than transition state theory should be used to describe this folding reaction.     

NMR investigation of Tyr105 mutants in TEM-1 beta-lactamase: dynamics are correlated with function

The existence of coupled residue motions on various time scales in enzymes is now well accepted, and their detailed characterization has become an essential element in understanding the role of dynamics in catalysis. To this day, a handful of enzyme systems has been shown to rely on essential residue motions for catalysis, but the generality of such phenomena remains to be elucidated. Using NMR spectroscopy, we investigated the electronic and dynamic effects of several mutations at position 105 in TEM-1 beta-lactamase, an enzyme responsible for antibiotic resistance. Even in absence of substrate, our results show that the number and magnitude of short and long range effects on (1)H-(15)N chemical shifts are correlated with the catalytic efficiencies of the various Y105X mutants investigated. In addition, (15)N relaxation experiments on mutant Y105D show that several active-site residues of TEM-1 display significantly altered motions on both picosecond-nanosecond and microsecond-millisecond time scales despite many being far away from the site of mutation. The altered motions among various active-site residues in mutant Y105D may account for the observed decrease in catalytic efficiency, therefore suggesting that short and long range residue motions could play an important catalytic role in TEM-1 beta-lactamase. These results support previous observations suggesting that internal motions play a role in promoting protein function.     

A Direct Coupling between Global and Internal Motions in a Single Domain Protein? MD Investigation of Extreme Scenarios

Proteins are not rigid molecules, but exhibit internal motions on timescales ranging from femto- to milliseconds and beyond. In solution, proteins also experience global translational and rotational motions, sometimes on timescales comparable to those of the internal fluctuations. The possibility that internal and global motions may be directly coupled has intriguing implications, given that enzymes and cell signaling proteins typically associate with binding partners and cellular scaffolds. Such processes alter their global motion and may affect protein function. Here, we present molecular dynamics simulations of extreme case scenarios to examine whether a possible relationship exists. In our model protein, a ubiquitin-like RhoGTPase binding domain of plexin-B1, we removed either internal or global motions. Comparisons with unrestrained simulations show that internal and global motions are not appreciably coupled in this single-domain protein. This lack of coupling is consistent with the observation that the dynamics of water around the protein, which is thought to permit, if not stimulate, internal dynamics, is also largely independent of global motion. We discuss implications of these results for the structure and function of proteins.     

An analysis of the influence of protein intrinsic dynamical properties on its thermal unfolding behavior

The influence of the protein topology-encoded dynamical properties on its thermal unfolding motions was studied in the present work. The intrinsic dynamics of protein topology was obtained by the anisotropic network model (ANM). The ANM has been largely used to investigate protein collective functional motions, but it is not well elucidated if this model can also reveal the preferred large-scale motions during protein unfolding. A small protein barnase is used as a typical case study to explore the relationship between protein topology-encoded dynamics and its unfolding motions. Three thermal unfolding simulations at 500 K were performed for barnase and the entire unfolding trajectories were sampled and partitioned into several windows. For each window, the preferred unfolding motions were investigated by essential dynamics analysis, and then associated with the intrinsic dynamical properties of the starting conformation in this window, which is detected by ANM. The results show that only a few slow normal modes imposed by protein structure are sufficient to give a significant overlap with the preferred unfolding motions. Especially, the large amplitude unfolding movements, which imply that the protein jumps out of a local energy basin, can be well described by a single or several ANM slow modes. Besides the global motions, it is also found that the local residual fluctuations encoded in protein structure are highly correlated with those in the protein unfolding process. Furthermore, we also investigated the relationship between protein intrinsic flexibility and its unfolding events. The results show that the intrinsic flexible regions tend to unfold early. Several early unfolding events can be predicted by analysis of protein structural flexibility. These results imply that protein structure-encoded dynamical properties have significant influences on protein unfolding motions.     

Conformational dynamics of cytochrome c: correlation to hydrogen exchange.

We study the dynamical fluctuations of horse heart cytochrome c by molecular dynamics (MD) simulations in aqueous solution, at four temperatures: 300 K, 360 K, 430 K, and 550 K. Each simulation covers a production time of at least 1.5 nanoseconds (ns). The conformational dynamics of the system is analyzed in terms of collective motions that involve the whole protein, and local motions that involve the formation and breaking of intramolecular hydrogen bonds. The character of the MD trajectories can be described within the framework of rugged energy landscape dynamics. The MD trajectories sample multiple conformational minima, with basins in protein conformational space being sampled for a few hundred picoseconds. The trajectories of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. As a consequence of the hierarchical nature of the dynamics, the mean square displacement autocorrelation function, <|x(t) - x(0)|2>, exhibits a power law dependence on time, with an exponent of around 0.5 for times shorter than 100 ps, and an exponent of 1.75 for longer times. This power law behavior indicates that the system exhibits suppressed diffusion (sub-diffusion) in sampling of configurational space at time scales shorter than 100 ps, and enhanced (super-diffusion) at longer time scales. The multi-basin feature of the trajectories is present at all temperatures simulated. Structural changes associated with inter-basin displacements correspond to collective motions of the Omega loops and coiled regions and relative motions of the alpha-helices as rigid bodies. Similar motions may be involved in experimentally observed amide hydrogen exchange. However, some groups showing large correlated motions do not expose the amino hydrogens to the solvent. We show that large fluctuations are not necessarily correlated to hydrogen exchange. For example, regions of the proteins forming alpha helices and turns show significant fluctuations, but as rigid bodies, and the hydrogen bonds involved in the formation of these structures do not break in proportion to these fluctuations. Proteins 1999;36:175-191. Published 1999 Wiley-Liss, Inc.     

Protein dynamics in solution and in a crystalline environment: a molecular dynamics study

The effect of a solvent and a crystalline environment on the dynamics of proteins is investigated by the method of computer simulation. Three 25-ps molecular dynamics simulations at 300 K of the bovine pancreatic trypsin inhibitor (BPTI), consisting of 454 heavy atoms, are compared: one of BPTI in vacuo, one of BPTI in a box with 2647 spherical nonpolar solvent atoms, and one of BPTI surrounded by fixed crystal image atoms. Both average and time-dependent molecular properties are examined to determine the effect of the environment on the behavior of the protein. The dynamics of BPTI in solution or in the crystal environment are found to be very similar to that found in the vacuum calculation. The primary difference in the average properties is that the equilibrium structure in the presence of solvent or the crystal field is significantly closer to the X-ray structure than is the vacuum result; concomitantly, the more realistic environment leads to a number density closer to experiment. The presence of solvent has a negligible effect on the overall magnitude of the positional or dihedral angle fluctuations in the interior of the protein; however, there are changes in the decay times of the fluctuations of interior atoms. For surface residues, both the magnitude and the time course of the motions are significantly altered by the solvent. There tends to be an increase in the displacements of long side chains and the flexible parts of the main chain that protrude into the solvent. Further, these motions tend to have a more diffusive character with longer relaxation times than in vacuo. The crystal environment has a specific effect on a number of side chains which are held in relatively fixed positions through hydrogen-bond and electric interactions with the neighboring protein atoms. Most of the effects of the solution environment seem to be sufficiently nonspecific that it may be possible to model them by applying a mean field and stochastic dynamic methods.     

Solvating atomic level fine-grained proteins in supra-molecular level coarse-grained water for molecular dynamics simulations

Simulation of the dynamics of a protein in aqueous solution using an atomic model for both the protein and the many water molecules is still computationally extremely demanding considering the time scale of protein motions. The use of supra-atomic or supra-molecular coarse-grained (CG) models may enhance the computational efficiency, but inevitably at the cost of reduced accuracy. Coarse-graining solvent degrees of freedom is likely to yield a favourable balance between reduced accuracy and enhanced computational speed. Here, the use of a supra-molecular coarse-grained water model that largely preserves the thermodynamic and dielectric properties of atomic level fine-grained (FG) water in molecular dynamics simulations of an atomic model for four proteins is investigated. The results of using an FG, a CG, an implicit, or a vacuum solvent environment of the four proteins are compared, and for hen egg-white lysozyme a comparison to NMR data is made. The mixed-grained simulations do not show large differences compared to the FG atomic level simulations, apart from an increased tendency to form hydrogen bonds between long side chains, which is due to the reduced ability of the supra-molecular CG beads that represent five FG water molecules to make solvent-protein hydrogen bonds. But, the mixed-grained simulations are at least an order of magnitude faster than the atomic level ones.     

Protein dynamics and motions in relation to their functions: several case studies and the underlying mechanisms

Proteins are dynamic entities in cellular solution with functions governed essentially by their dynamic personalities. We review several dynamics studies on serine protease proteinase K and HIV-1 gp120 envelope glycoprotein to demonstrate the importance of investigating the dynamic behaviors and molecular motions for a complete understanding of their structure–function relationships. Using computer simulations and essential dynamic (ED) analysis approaches, the dynamics data obtained revealed that: (i) proteinase K has highly flexible substrate-binding site, thus supporting the induced-fit or conformational selection mechanism of substrate binding; (ii) Ca²⁺ removal from proteinase K increases the global conformational flexibility, decreases the local flexibility of substrate-binding region, and does not influence the thermal motion of catalytic triad, thus explaining the experimentally determined decreased thermal stability, reduced substrate affinity, and almost unchanged catalytic activity upon Ca²⁺ removal; (iii) substrate binding affects the large concerted motions of proteinase K, and the resulting dynamic pocket can be connected to substrate binding, orientation, and product release; (iv) amino acid mutations 375 S/W and 423 I/P of HIV-1 gp120 have distinct effects on molecular motions of gp120, facilitating 375 S/W mutant to assume the CD4-bound conformation, while 423 I/P mutant to prefer for CD4-unliganded state. The mechanisms underlying protein dynamics and protein–ligand binding, including the concept of the free energy landscape (FEL) of the protein–solvent system, how the ruggedness and variability of FEL determine protein’s dynamics, and how the three ligand-binding models, the lock-and-key, induced-fit, and conformational selection are rationalized based on the FEL theory are discussed in depth.     

Computational analysis of chain flexibility and fluctuations in Rhizomucor miehei lipase.

We have performed molecular dynamics simulation of Rhizomucor miehei lipase (Rml) with explicit water molecules present. The simulation was carried out in periodic boundary conditions and conducted for 1. 2 ns in order to determine the concerted protein dynamics and to examine how well the essential motions are preserved along the trajectory. Protein motions are extracted by means of the essential dynamics analysis method for different lengths of the trajectory. Motions described by eigenvector 1 converge after approximately 200 ps and only small changes are observed with increasing simulation time. Protein dynamics along eigenvectors with larger indices, however, change with simulation time and generally, with increasing eigenvector index, longer simulation times are required for observing similar protein motions (along a particular eigenvector). Several regions in the protein show relatively large fluctuations and in particular motions in the active site lid and the segments Thr57-Asn63 and the active site hinge region Pro101-Gly104 are seen along several eigenvectors. These motions are generally associated with glycine residues, while no direct correlations are observed between these fluctuations and the positioning of prolines in the protein structure. The partial opening/closing of the lid is an example of induced fit mechanisms seen in other enzymes and could be a general mechanism for the activation of Rml.     

Computational studies of essential dynamics of Pseudomonas cepacia lipase

In order to investigate the interfacial activation of a lipase from Pseudomonas cepacia (PcL), molecular dynamics (MD) simulations and essential dynamics (ED) analysis were performed in different solvent environments: vacuum and explicit water solvents. Starting from the active (open) structure of PcL, the essential dynamics analysis of the simulations revealed large correlated motions, which may be responsible for the activation of the enzyme. Fluctuations in the U1 (active-site lid) and U2 domains are found to be important in the activation of PcL. In contrast, the catalytic triad exhibits very little displacement. These results are consistent with the previous X-ray structural determination. A combined analysis of the trajectories showed some differences for the simulations in different solvent environments. It was found that the region around the helix alpha5 showed larger displacements in the water simulations. It can be concluded that the open structure of PcL becomes unstable in water solvents, leading to the closing of the so-called 'lid' region. The simulations and ED analysis on the closed structure of PgL provided additional information concerning the structural changes involved in the activation of the lipases. It was found that structural changes for PcL and PgL, which are responsible for the essential motions of the protein, showed contrasting behavior in the different solvent environments.     

Neutron frequency windows and the protein dynamical transition

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, , that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations---an "equilibrium" model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a "frequency window" model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.     

Operator recognition by the phage 434 cI repressor: MD simulations of free and bound 50-bp DNA reveal important differences between the OR1 and OR2 sites

Using molecular dynamics simulations in explicit solvent, we investigated the behavior of a 50-bp DNA sequence containing the 434 bacteriophage operators OR1 and OR2 separated by an 8-bp spacer. Two simulations of 1 ns each were carried out, with DNA alone and with DNA complexed to dimers of the R1-69 DNA binding domain of the phage 434 cI repressor protein at the OR1 and OR2 sites. Strong correlations among average structural parameters are observed between our simulations and available experimental data for the bound OR1/OR2 subsites. In the free state, some differences appear between the three relevant fragments (OR1, the spacer, and OR2). Unbound OR1 exhibits a large, shallow major groove into which the base atoms protrude and is also bent toward the major groove. This structure is maintained because structural fluctuations are weak. Unbound OR2 resembles canonical B-DNA although the structural parameters show greater fluctuations, essentially due to a malleable step (the innermost CpA/TpG), absent in OR1. Complexation with the proteins slightly alters the base positions but strongly modifies the sugar and backbone motions. The most crucial repressor effects are changes in the flexibility of the OR1/OR2 sites. Structural fluctuations are enhanced for OR1, conferring a favorable energetic contribution to the OR1 binding, whereas they are reduced for OR2. Therefore, both structural and dynamic properties of DNA suggest OR1 is the most attractive site for the repressor, which may explain the different binding association constants observed for the OR1 and OR2 sites. Finally, we also investigated the impact of the protein on the DNA backbone dynamics and find that direct or indirect interactions facilitate the DNA structural variations required for achieving complementarity with the protein.     

Molecular dynamics simulation of sperm whale myoglobin: effects of mutations and trapped CO on the structure and dynamics of cavities

The results of extended (80-ns) molecular dynamics simulations of wild-type and YQR triple mutant of sperm whale deoxy myoglobin in water are reported and compared with the results of the simulation of the intermediate(s) obtained by photodissociation of CO in the wild-type protein. The opening/closure of pathways between preexistent cavities is different in the three systems. For the photodissociated state, we previously reported a clear-cut correlation between the opening probability and the presence of the photolyzed CO in the proximity of the passage; here we show that in wild-type deoxy myoglobin, opening is almost random. In wild-type deoxy myoglobin, the passage between the distal pocket and the solvent is strictly correlated to the presence/absence of a water molecule that simultaneously interacts with the distal histidine side chain and the heme iron; conversely, in the photodissociated myoglobin, the connection with the bulk solvent is always open when CO is in the vicinity of the A pyrrole ring. In YQR deoxy myoglobin, the mutated Gln(E7)64 is stably H-bonded with the mutated Tyr(B10)29. The essential dynamics analysis unveils a different behavior for the three systems. The motion amplitude is progressively restricted in going from wild-type to YQR deoxy myoglobin and to wild-type myoglobin photoproduct. In all cases, the principal motions involve mainly the same regions, but their directions are different. Analysis of the dynamics of the preexisting cavities indicates large fluctuations and frequent connections with the solvent, in agreement with the earlier hypothesis that some of the ligand may escape from the protein through these pathways.     

Internal motions in B- and Z-form poly(dG-dC).poly(dG-dC): 1H NMR relaxation studies

Proton NMR relaxation measurements are used to compare the molecular dynamics of 60 base pair duplexes of B- and Z-form poly(dG-dC).poly(dG-dC). The relaxation rates of the exchangeable guanine imino protons (Gim) in H2O and in 90% D2O show that below 20 degrees C spin-lattice relaxation is exclusively from proton-proton magnetic dipolar interactions while proton-nitrogen interactions contribute about 30% to the spin-spin relaxation. The observation that the spin-lattice relaxation is nonexponential and that the initial spin-lattice relaxation rate of the Gim, G-H8 and C-H6 protons depends on the selectivity of the exciting pulse shows that spin-diffusion dominates the spin-lattice relaxation. The relaxation rates of the Gim, C-H5, and C-H6 in B- and Z-form poly(dG-dC).poly(dG-dC) cannot be explained by assuming the DNA behaves as a rigid rod. The data can be fit by assuming large-amplitude out of plane motions (+/- 30-40 degrees, tau = 1-100 ns) and fast, large-amplitude local torsional motions (+/- 25-90 degrees, tau = 0.1-1.5 ns) in addition to collective torsional motions. The results for the B and Z forms show that the rapid internal motions are similar and large in both conformations although backbone motions are slightly slower, or of lower amplitude, in Z DNA. At high temperatures (greater than 60 degrees C), imino proton exchange with solvent dominates the spin-lattice relaxation of B-form poly(dG-dC).poly(dG-dC), but in the Z form no exchange contribution (less than 2 s-1) is observed at temperatures as high as 85 degrees C. Conformational fluctuations that expose the imino protons to the solvent are strikingly different in the B and Z forms. The results obtained here are compared with those previously reported for poly(dA-dT).poly(dA-dT).