The essential dynamics of Cu, Zn superoxide dismutase: suggestion of intersubunit communication.

A 300-ps molecular dynamics simulation of the whole Cu, Zn superoxide dismutase dimer has been carried out in water, and the trajectory has been analyzed by the essential dynamics method. The results indicate that the motion is defined by few preferred directions identified by the first four to six eigenvectors and that the motion of the two monomers at each instant is not symmetrical. The vectors symmetrical to the eigenvectors are significantly sampled, suggesting that, on average, the motions of the two subunits will exchange. Large intra- and intersubunit motions involving different subdomains of the protein are observed. A mechanical coupling between the two subunits is also suggested, because displacements of the loops surrounding the active site in one monomer are correlated with the motion of parts of the second toward the intersubunit interface.     

Molecular dynamics simulations of protein-tyrosine phosphatase 1B. II. substrate-enzyme interactions and dynamics

Molecular dynamics simulations of protein tyrosine phosphatase 1B (PTP1B) complexed with the phosphorylated peptide substrate DADEpYL and the free substrate have been conducted to investigate 1) the physical forces involved in substrate-protein interactions, 2) the importance of enzyme and substrate flexibility for binding, 3) the electrostatic properties of the enzyme, and 4) the contribution from solvation. The simulations were performed for 1 ns, using explicit water molecules. The last 700 ps of the trajectories was used for analysis determining enthalpic and entropic contributions to substrate binding. Based on essential dynamics analysis of the PTP1B/DADEpYL trajectory, it is shown that internal motions in the binding pocket occur in a subspace of only a few degrees of freedom. In particular, relatively large flexibilities are observed along several eigenvectors in the segments: Arg(24)-Ser(28), Pro(38)-Arg(47), and Glu(115)-Gly(117). These motions are correlated to the C- and N-terminal motions of the substrate. Relatively small fluctuations are observed in the region of the consensus active site motif (H/V)CX(5)R(S/T) and in the region of the WPD loop, which contains the general acid for catalysis. Analysis of the individual enzyme-substrate interaction energies revealed that mainly electrostatic forces contribute to binding. Indeed, calculation of the electrostatic field of the enzyme reveals that only the field surrounding the binding pocket is positive, while the remaining protein surface is characterized by a predominantly negative electrostatic field. This positive electrostatic field attracts negatively charged substrates and could explain the experimentally observed preference of PTP1B for negatively charged substrates like the DADEpYL peptide.     

Analysis of the dynamics of rhizomucor miehei lipase at different temperatures.

The dynamics of Rhizomucor miehei lipase has been studied by molecular dynamics simulations at temperatures ranging from 200-500K. Simulations carried out in periodic boundary conditions and using explicit water molecules were performed for 400 ps at each temperature. Our results indicate that conformational changes and internal motions in the protein are significantly influenced by the temperature increase. With increasing temperature, the number of internal hydrogen bonds decreases, while surface accessibility, radius of gyration and the number of residues in random coil conformation increase. In the temperature range studied, the motions can be described in a low dimensional subspace, whose dimensionality decreases with increasing temperature. Approximately 80% of the total motion is described by the first (i) 80 eigenvectors at T=200K, (ii) 30 eigenvectors at T=300K and (iii) 10 eigenvectors at T=400K. At high temperature, the alpha-helix covering the active site in the native Rhizomucor miehei lipase, the helix at which end the active site is located, and in particular, the loop (Gly35-Lys50) show extensive flexibility.     

Engineered control of enzyme structural dynamics and function

Enzymes undergo a range of internal motions from local, active site fluctuations to large‐scale, global conformational changes. These motions are often important for enzyme function, including in ligand binding and dissociation and even preparing the active site for chemical catalysis. Protein engineering efforts have been directed towards manipulating enzyme structural dynamics and conformational changes, including targeting specific amino acid interactions and creation of chimeric enzymes with new regulatory functions. Post‐translational covalent modification can provide an additional level of enzyme control. These studies have not only provided insights into the functional role of protein motions, but they offer opportunities to create stimulus‐responsive enzymes. These enzymes can be engineered to respond to a number of external stimuli, including light, pH, and the presence of novel allosteric modulators. Altogether, the ability to engineer and control enzyme structural dynamics can provide new tools for biotechnology and medicine.     

Conformational change in the activation of lipase: an analysis in terms of low-frequency normal modes.

The interfacial activation of Rhizomucor miehei lipase (RmL) involves the motion of an alpha-helical region (residues 82-96) which acts as a "lid" over the active site of the enzyme, undergoing a displacement from a "closed" to an "open" conformation upon binding of substrate. Normal mode analyses performed in both low and high dielectric media reveal that low-frequency vibrational modes contribute significantly to the conformational transition between the closed and open conformations. In these modes, the lid displacement is coupled to local motions of active site loops as well as global breathing motions. Atomic fluctuations of the first hinge of the lid (residues 83-84) are substantially larger in the low dielectric medium than in the high dielectric medium. Our results also suggest that electrostatic interactions of Arg86 play an important role in terms of both the intrinsic stability of the lid and its displacement, through enhancement of hinge mobility in a high dielectric medium. Additional calculations demonstrate that the observed patterns of atomic fluctuations are an intrinsic feature of the protein structure and not dependent on the nature of specific energy minima.     

Filtering molecular dynamics trajectories to reveal low-frequency collective motions: phospholipase A2

A novel method for analysing molecular dynamics trajectories has been developed, which filters out high frequencies using digital signal processing techniques and facilitates focusing on the low-frequency collective motions of proteins. These motions involve low energy slow motions, which lead to important biological phenomena such as domain closure and allosteric effects in enzymes. The filtering method treats each of the atomic trajectories obtained from the molecular dynamics simulation as a "signal". The trajectories of each of the atoms in the system (or any subset of interest) are Fourier transformed to the frequency domain, a filtering function is applied and then an inverse transformation back to the time domain yields the filtered trajectory. The filtering method has been used to study the dynamics of the enzyme phospholipase A2. In the filtered trajectory, all the high frequency bond and valence angle vibrations were eliminated, leaving only low-frequency motion, mainly fluctuations in torsions and conformational transitions. Analysis of this trajectory revealed interesting motions of the protein, including concerted movements of helices, and changes in shape of the active site cavity. Unlike normal mode analysis, which has been used to study the motion of proteins, this method does not require converged minimizations or diagonalization of a matrix of second derivatives. In addition, anharmonicity, multiple minima and conformational transitions are treated explicitly. Thus, the filtering method avoids most of the approximations implicit in other investigations of the dynamic behaviour of large systems.     

Local feature analysis: a statistical theory for reproducible essential dynamics of large macromolecules

Multivariate statistical methods are widely used to extract functional collective motions from macromolecular molecular dynamics (MD) simulations. In principal component analysis (PCA), a covariance matrix of positional fluctuations is diagonalized to obtain orthogonal eigenvectors and corresponding eigenvalues. The first few eigenvectors usually correspond to collective modes that approximate the functional motions in the protein. However, PCA representations are globally coherent by definition and, for a large biomolecular system, do not converge on the time scales accessible to MD. Also, the forced orthogonalization of modes leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. Here, we describe for the first time the application of local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low dimensional, and like PCA provide a reduced basis set for collective motions, but they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows. Also, the intrinsic dynamics of local domains is more extensively sampled than that of globally coherent PCA modes.     

Extended molecular dynamics simulation of the carbon monoxide migration in sperm whale myoglobin

We report the results of an extended molecular dynamics simulation on the migration of photodissociated carbon monoxide in wild-type sperm whale myoglobin. Our results allow following one possible ligand migration dynamics from the distal pocket to the Xe1 cavity via a path involving the other xenon binding cavities and momentarily two additional packing defects along the pathway. Comparison with recent time resolved structural data obtained by Laue crystallography with subnanosecond to millisecond resolution shows a more than satisfactory agreement. In fact, according to time resolved crystallography, CO, after photolysis, can occupy the Xe1 and Xe4 cavities. However, no information on the trajectory of the ligand from the distal pocket to the Xe1 is available. Our results clearly show one possible path within the protein. In addition, although our data refer to a single trajectory, the local dynamics of the ligand in each cavity is sufficiently equilibrated to obtain local structural and thermodynamic information not accessible to crystallography. In particular, we show that the CO motion and the protein fluctuations are strictly correlated: free energy calculations of the migration between adjacent cavities show that the migration is not a simple diffusion but is kinetically or thermodynamically driven by the collective motions of the protein; conversely, the protein fluctuations are influenced by the ligand in such a way that the opening/closure of the passage between adjacent cavities is strictly correlated to the presence of CO in its proximity. The compatibility between time resolved crystallographic experiments and molecular dynamics simulations paves the way to a deeper understanding of the role of internal dynamics and packing defects in the control of ligand binding in heme proteins.     

Structure and internal mobility of proteins: a molecular dynamics study of hen egg white lysozyme

The structure and internal motions of the protein hen egg white lysozyme are studied by analysis of simulation and experimental data. A molecular dynamics simulation and an energy minimization of the protein in vacuum have been made and the results compared with high-resolution structures and temperature factors of hen egg white lysozyme in two different crystal forms and of the homologous protein human lysozyme. The structures obtained from molecular dynamics and energy minimization have root-mean-square deviations for backbone atoms of 2.3 Å and 1.1–1.3 Å, respectively, relative to the crystal structures; the different crystal structures have root-mean-square deviations of 0.73–0.81 Å for the backbone atoms. In comparing the backbone dihedral angles, the difference between the dynamics and the crystal structure on which it is based is the same as that between any two crystal structures. The internal fluctuations of atomic positions calculated from the molecular dynamics trajectory agree well with the temperature factors from the three structures. Simulation and crystal results both show that there are large motions for residues involved in exposed turns of the backbone chain, relatively smaller motions for residues involved in the middle of helices or β-sheet structures, and relatively small motions of residues near disulfide bridges. Also, both the simulation and crystal data show that side-chain atoms have larger fluctuations than main-chain atoms. Moreover, the regions that have large deviations among the x-ray crystal structures, which indicates flexibility, are found to have large fluctuations in the simulation.     

Protein dynamics and enzyme catalysis: insights from simulations

The role of protein dynamics in enzyme catalysis is one of the most active and controversial areas in enzymology today. Some researchers claim that protein dynamics are at the heart of enzyme catalytic efficiency, while others state that dynamics make no significant contribution to catalysis. What is the biochemist - or student - to make of the ferocious arguments in this area? Protein dynamics are complex and fascinating, as molecular dynamics simulations and experiments have shown. The essential question is: do these complex motions have functional significance? In particular, how do they affect or relate to chemical reactions within enzymes, and how are chemical and conformational changes coupled together? Biomolecular simulations can analyse enzyme reactions and dynamics in atomic detail, beyond that achievable in experiments: accurate atomistic modelling has an essential part to play in clarifying these issues. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Outer membrane proteins: comparing X-ray and NMR structures by MD simulations in lipid bilayers

The structures of three bacterial outer membrane proteins (OmpA, OmpX and PagP) have been determined by both X-ray diffraction and NMR. We have used multiple (7 × 15 ns) MD simulations to compare the conformational dynamics resulting from the X-ray versus the NMR structures, each protein being simulated in a lipid (DMPC) bilayer. Conformational drift was assessed via calculation of the root mean square deviation as a function of time. On this basis the ‘quality’ of the starting structure seems mainly to influence the simulation stability of the transmembrane β-barrel domain. Root mean square fluctuations were used to compare simulation mobility as a function of residue number. The resultant residue mobility profiles were qualitatively similar for the corresponding X-ray and NMR structure-based simulations. However, all three proteins were generally more mobile in the NMR-based than in the X-ray simulations. Principal components analysis was used to identify the dominant motions within each simulation. The first two eigenvectors (which account for >50% of the protein motion) reveal that such motions are concentrated in the extracellular loops and, in the case of PagP, in the N-terminal α-helix. Residue profiles of the magnitude of motions corresponding to the first two eigenvectors are similar for the corresponding X-ray and NMR simulations, but the directions of these motions correlate poorly reflecting incomplete sampling on a ∼10 ns timescale.     

Large domain fluctuations on 50-ns timescale enable catalytic activity in phosphoglycerate kinase

Large-scale domain motions of enzymes are often essential for their biological function. Phosphoglycerate kinase has a wide open domain structure with a hinge near the active center between the two domains. Applying neutron spin echo spectroscopy and small-angle neutron scattering we have investigated the internal domain dynamics. Structural analysis reveals that the holoprotein in solution seems to be more compact compared to the crystal structure but would not allow the functionally important phosphoryl transfer between the substrates if the protein were static. Brownian large-scale domain fluctuation dynamics on a timescale of 50 ns was revealed by neutron spin echo spectroscopy. The dynamics observed was compared to the displacement patterns of low-frequency normal modes. The displacements along the normal-mode coordinates describe our experimental results reasonably well. In particular, the domain movements facilitate a close encounter of the key residues in the active center to build the active configuration. The observed dynamics shows that the protein has the flexibility to allow fluctuations and displacements that seem to enable the function of the protein. Moreover, the presence of the substrates increases the rigidity, which is deduced from a faster dynamics with smaller amplitude.     

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.     

Lid closure dynamics of porcine pancreatic lipase in aqueous solution

BackgroundPancreatic lipases hydrolyze fatty acids in dietary pathway. The activity of porcine pancreatic lipase (PPL) is controlled by lid domain along with a coenzyme, colipase. The active open-state conformation of the protein could be induced by detergents or bile salts which would be further stabilized by binding of colipase. In the absence of these interactions, the lid preferably attains a closed conformation in water.MethodsMolecular dynamic simulation was used to monitor the lid movement of PPL in open and closed conformations in water. Free energy surface was constructed from the simulation. Energy barriers and major structural changes during lid opening were evaluated.ResultsThe lid closure of PPL in water from its open conformation might be initiated by columbic interactions which initially move the lid away from domain 1. This is followed by major dihedral changes on the lid residues which alter the trajectory of motion. The lid then swirls back towards domain 1 to attain closed conformation. This is accompanied with conformational changes around β5- and β9-loops as well. However, PPL in closed conformation shows only the domain movements and the lid remains in its closed conformation.ConclusionsPPL in closed conformation is stable in water and the open conformation is driven towards closed state. The lid follows a swirling trajectory during the closure.General significanceConformational state of the lid regulates the activity and substrate specificity of PPL. Hence, it is essential to understand the lid dynamics and the role of specific amino acid residues involved.     

Concerted motions in copper plastocyanin and azurin: an essential dynamics study

Essential dynamics analysis of molecular dynamics simulation trajectories (1.1 ns) of two copper containing electron transfer proteins, plastocyanin and azurin, has been performed. The protein essential modes have been analysed in order to identify large concerted motions which could be relevant for the electron transfer function exerted by these proteins. The analysis, conducted for temporal windows of different lengths along the protein trajectories, shows a rapid convergence and indicates that for both the proteins the predominant internal motions occur in a subspace of only a few degrees of freedom. Moreover, it is found that for both the proteins the likely binding sites (i.e. the hydrophobic and negative patches) with the reaction partners move in a concerted fashion with a few structural regions far from the active site. Such results are discussed in connection with the possible involvement of large concerted motions in the recognition and binding interaction with physiological electron transfer partners.     

A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.     

Nonlinear optical studies of heme protein dynamics: implications for proteins as hybrid states of matter

Protein structure is fundamentally related to function. However, static structures alone are insufficient to understand how a protein works. Dynamics play an equally important role. Given that proteins are highly associated aperiodic systems, it may be expected that protein dynamics would follow glass-like dynamics. However, protein functions occur on time scales orders of magnitude faster than the time scales typically associated with glassy systems. It is becoming clear that the reaction forces driving functions do not sample entirely the large number of configurations available to a protein but are highly directed along an optimized pathway. Could there be any correlation between specific topological features in protein structures and dynamics that leads to strongly correlated atomic displacements in the dynamical response to a perturbation? This review will try to provide an answer by focusing upon recent nonlinear optical studies with the aim of directly observing functionally important protein motions over the entire dynamic range of the protein response function. The specific system chosen is photoinduced dynamics of ligand dissociation at the active site in heme proteins, with myoglobin serving as the simplest model system. The energetics and nuclear motions from the very earliest events involved in bond breaking on the femtosecond time scale all the way out to ligand escape and bimolecular rebinding on the microsecond and millisecond time scale have been mapped out. The picture that is emerging is that the system consists of strongly coupled motions from the very instant the bond breaks at the active site that cascade into low frequency collective modes specific to the protein structure. It is this coupling that imparts the ability of a protein to function on time scales more commensurate with liquids while simultaneously conserving structural integrity akin to solids.     

Analysis of active site motions from a 175 picosecond molecular dynamics simulation of camphor-bound cytochrome P450cam.

The structure and internal motions of the active site residues of camphor-bound cytochrome P450cam have been evaluated on the basis of a 175 psec molecular dynamics simulation. The active site residues generally show very small deviations away from their starting crystal positions. These residues also generally show much smaller fluctuations than for the enzyme as a whole. Phe 87 is dynamically very unusual and is suggested to play a role in substrate movement into and/or out of the active site. The average distance between the heme iron and atoms C5, C6, and C3 of camphor is 5.3, 6.0, and 7.0 A, respectively. This trend is consistent with the experimentally observed stereospecificity of the hydroxylation reaction. On the basis of distance and angle criteria, both 5-exo and 5-endo hydrogen abstraction are predicted to occur during the hydroxylation reaction; although the 5-exo pathway is expected to be 3-fold more likely.     

Molecular dynamics simulation and essential dynamics study of mutated plastocyanin: structural, dynamical and functional effects of a disulfide bridge insertion at the protein surface

A molecular dynamics simulation (1.1 ns) at 300 K, of fully hydrated Ile21Cys, Glu25Cys plastocyanin mutant has been performed to investigate the structural, dynamical and functional effects of a disulfide bridge insertion at the surface of the protein. A detailed analysis of the root mean square fluctuations, H-bonding pattern and dynamical cross-correlation map has been performed. An essential dynamics method has also been applied as complementary analysis to identify concerted motions (essential modes), that could be relevant to the electron transfer function. The results have been compared with those previously obtained for wild-type plastocyanin and have revealed that the mutant shows a different pattern of H-bonds, with several interactions lost and a higher flexibility, especially around the electron transfer copper site. The analysis of dynamical cross-correlation map and of essential modes, has shown that the mutant performs different functional concerted motions, which might be related to the binding recognition with its electron transfer partners in comparison with the wild-type protein.