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.     

Backbone dynamics of TEM-1 determined by NMR: evidence for a highly ordered protein

Backbone dynamics of TEM-1 beta-lactamase (263 amino acids, 28.9 kDa) were studied by 15N nuclear magnetic resonance relaxation at 11.7, 14.1, and 18.8 T. The high quality of the spectra allowed us to measure the longitudinal relaxation rate (R1), the transverse relaxation rate (R2), and the {1H}-15N NOE for up to 227 of the 250 potentially observable backbone amide groups. The model-free formalism was used to determine internal motional parameters using an axially anisotropic model. TEM-1 exhibits a small prolate axial anisotropy (D(parallel)/D(perpendicular) = 1.23 +/- 0.01) and a global correlation time (tau(m)) of 12.41 +/- 0.01 ns. The unusually high average generalized order parameter (S2) of 0.90 +/- 0.02 indicates that TEM-1 is one of the most ordered proteins studied by liquid-state NMR to date. Although the omega-loop has a high degree of order in the picosecond-to-nanosecond time scale (mean S2 value of 0.90 +/- 0.02), we observed the presence of microsecond-to-millisecond time scale motions for this loop, as for the vicinity of the active site. These motions could be relevant for the catalytic function of TEM-1. Amide exchange experiments were also performed, and several amide groups were not exchanged after 12 days, an indication that global motions in TEM-1 are also very limited. Although detailed dynamics characterization by NMR cannot be readily applied to TEM-1 in the presence of relevant substrates, the unusual picosecond-to-nanosecond dynamics behavior of TEM-1 presented here will be essential to the validation and improvement of future molecular dynamics simulations of TEM-1 in the presence of functionally relevant substrates.     

Model-free Analysis of Protein Dynamics: Assessment of Accuracy and Model Selection Protocols Based on Molecular Dynamics Simulation

The popular model-free approach to analyze NMR relaxation measurements has been examined using artificial amide (15)N relaxation data sets generated from a 10 nanosecond molecular dynamics trajectory of a dihydrofolate reductase ternary complex in explicit water. With access to a detailed picture of the underlying internal motions, the efficacy of model-free analysis and impact of model selection protocols on the interpretation of NMR data can be studied. In the limit of uncorrelated global tumbling and internal motions, fitting the relaxation data to the model-free models can recover a significant amount of quantitative information on the internal dynamics. Despite a slight overestimation, the generalized order parameter is quite accurately determined. However, the model-free analysis appears to be insensitive to the presence of nanosecond time scale motions with relatively small magnitude. For such cases, the effective correlation time can be significantly underestimated. As a result, proteins appear to be more rigid than they really are. The model selection protocols have a major impact on the information one can reliably obtain. The commonly employed protocol based on step-up hypothesis testing has severe drawbacks of oversimplification and underfitting. The consequences are that the order parameter is more severely overestimated and the correlation time more severely underestimated. Instead, model selection based on Bayesian Information Criteria (BIC), recently introduced to the model-free analysis by d'Auvergne and Gooley (2003), provides a better balance between bias and variance. More appropriate models can be selected, leading to improved estimate of both the order parameter and correlation time. In addition, the computational cost is significantly reduced and subjective parameters such as the significance level are unnecessary.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

The effects of rigid motions on elastic network model force constants

Elastic network models provide an efficient way to quickly calculate protein global dynamics from experimentally determined structures. The model's single parameter, its force constant, determines the physical extent of equilibrium fluctuations. The values of force constants can be calculated by fitting to experimental data, but the results depend on the type of experimental data used. Here, we investigate the differences between calculated values of force constants and data from NMR and X-ray structures. We find that X-ray B factors carry the signature of rigid-body motions, to the extent that B factors can be almost entirely accounted for by rigid motions alone. When fitting to more refined anisotropic temperature factors, the contributions of rigid motions are significantly reduced, indicating that the large contribution of rigid motions to B factors is a result of over-fitting. No correlation is found between force constants fit to NMR data and those fit to X-ray data, possibly due to the inability of NMR data to accurately capture protein dynamics.     

Global Motions of the Nuclear Pore Complex: Insights from Elastic Network Models

The nuclear pore complex (NPC) is the gate to the nucleus. Recent determination of the configuration of proteins in the yeast NPC at ∼5 nm resolution permits us to study the NPC global dynamics using coarse-grained structural models. We investigate these large-scale motions by using an extended elastic network model (ENM) formalism applied to several coarse-grained representations of the NPC. Two types of collective motions (global modes) are predicted by the ENMs to be intrinsically favored by the NPC architecture: global bending and extension/contraction from circular to elliptical shapes. These motions are shown to be robust against tested variations in the representation of the NPC, and are largely captured by a simple model of a toroid with axially varying mass density. We demonstrate that spoke multiplicity significantly affects the accessible number of symmetric low-energy modes of motion; the NPC-like toroidal structures composed of 8 spokes have access to highly cooperative symmetric motions that are inaccessible to toroids composed of 7 or 9 spokes. The analysis reveals modes of motion that may facilitate macromolecular transport through the NPC, consistent with previous experimental observations.     

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.     

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.     

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.     

Modelling the dynamics of an antigenic peptide using NMR relaxation data.

The internal dynamics of a cyclic peptide which was designed to mimic an antigenic loop of the haemagglutinin, is studied through heteronuclear relaxation along the 13C alpha-1H alpha vectors and through homonuclear relaxation along the 1H alpha-1HN and 1H beta-1H beta' vectors. Order parameters are extracted from the longitudinal and cross-relaxation data. Molecular dynamics simulations are performed and the order parameters are calculated in different ways from the trajectories. The simulation, which is performed in vacuo, gives smaller order parameters (vector motions of larger amplitude) than the experimental results. However, the general features of the experimental order parameters are reproduced by the molecular dynamics simulation. The flexibility of the molecule can then be investigated from the results of the molecular dynamics. It shows that the mobility observed through the order parameters is due to motions in flanking regions, remote from the observed vectors.     

Adaptation to high temperatures through macromolecular dynamics by neutron scattering

Work on the relationship between hyperthermophile protein dynamics, stability and activity is reviewed. Neutron spectroscopy has been applied to measure and compare the macromolecular dynamics of various hyperthermophilic and mesophilic proteins, under different conditions. First, molecular dynamics have been analyzed for the hyperthermophile malate dehydrogenase from Methanococcus jannaschii and a mesophilic homologue, the lactate dehydrogenase from Oryctolagus cunniculus (rabbit) muscle. The neutron scattering approach has provided independent measurements of the global flexibility and structural resilience of each protein, and it has been demonstrated that macromolecular dynamics represents one of the molecular mechanisms of thermoadaptation. The resilience was found to be higher for the hyperthermophilic protein, thus ensuring similar flexibilities in both enzymes at their optimal activity temperature. Second, the neutron method has been developed to quantify the average macromolecular flexibility and resilience within the natural crowded environment of the cell, and mean macromolecular motions have been measured in vivo in psychrophile, mesophile, thermophile and hyperthermophile bacteria. The macromolecular resilience in bacteria was found to increase with adaptation to high temperatures, whereas flexibility was maintained within narrow limits, independent of physiological temperature for all cells in their active state. Third, macromolecular motions have been measured in free and immobilized dihydrofolate reductase from Escherichia coli. The immobilized mesophilic enzyme has increased stability and decreased activity, so that its properties are changed to resemble those of a thermophilic enzyme. Quasi-elastic neutron scattering measurements have also been performed to probe the protein motions. Compared to the free enzyme, the average height of the activation free energy barrier to local motions was found to be increased by 0.54 kcal.mol(-1) in the immobilized dihydrofolate reductase, a value that is of the same order as expected from the theoretical rate equation.     

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.     

Fundamental and biotechnological applications of neutron scattering measurements for macromolecular dynamics

To explore macromolecular dynamics on the picosecond timescale, we used neutron spectroscopy. First, molecular dynamics were analyzed for the hyperthermophile malate dehydrogenase from Methanococcus jannaschii and a mesophilic homologue, the lactate dehydrogenase from Oryctolagus cunniculus muscle. Hyperthermophiles have elaborate molecular mechanisms of adaptation to extremely high temperature. Using a novel elastic neutron scattering approach that provides independent measurements of the global flexibility and of the structural resilience (rigidity), we have demonstrated that macromolecular dynamics represents one of these molecular mechanisms of thermoadaptation. The flexibilities were found to be similar for both enzymes at their optimal activity temperature and the resilience is higher for the hyperthermophilic protein. Secondly, macromolecular motions were examined in a native and immobilized dihydrofolate reductase (DHFR) from Escherichia coli. The immobilized mesophilic enzyme has increased stability and decreased activity, so that its properties are changed to resemble those of the thermophilic enzyme. Are these changes reflected in dynamical behavior? For this study, we performed quasielastic neutron scattering measurements to probe the protein motions. The residence time is 7.95 ps for the native DHFR and 20.36 ps for the immobilized DHFR. The average height of the potential barrier to local motions is therefore increased in the immobilized DHFR, with a difference in activation energy equal to 0.54 kcal/mol, which is, using the theoretical rate equation, of the same order than expected from calculation.     

Brownian dynamics simulations of supercoiled DNA with bent sequences.

The recently presented Brownian dynamics model for superhelical DNA is extended to include local curvature of the DNA helix axis. Here we analyze the effect of a permanent bend on the structure and dynamics of an 1870-bp superhelix with delta Lk = -10. Furthermore, we define quantitative expressions for computing structural parameters such as loop positions, superhelix diameter, and plectonemic content for trajectories of superhelical DNA, and assess the convergence toward global equilibrium. The structural fluctuations in an interwound superhelix, as reflected in the change in end loop positions, seem to occur by destruction/creation of loops rather than by a sliding motion of the DNA around its contour. Their time scale is on the order of 30-100 microseconds. A permanent bend changes the structure and the internal motions of the DNA drastically. The position of the end loop is fixed at the permanent bend, and the local motions of the chain are enhanced near the loops. A displacement of the bend from the end loop to a position inside the plectonemic part of the superhelix results in the formation of a new loop and the disappearance of the old one; we estimate the time involved in this process to be about 0.5 ms.     

Dimerization affects collective dynamics of triosephosphate isomerase

Molecular dynamics simulations (30-60 ns runs) are performed on free/apo triosephosphate isomerase (TIM) to determine any correlation between collective motions and loop 6 dynamics. Native TIM is reported to be active only as a homodimer even though cooperativity has not been observed between the two identical subunits. Both dimeric and monomeric (isolated from dimer) forms of TIM are simulated in explicit water at 300 K and 1 bar to inspect any differences between the structures in terms of fluctuation dynamics and functionally important loop 6 dynamics/closure. Significant cross-correlations between residue fluctuations are observed in the dimer, which result from the global counter-rotations of the two identical subunits in the essential modes of the dimer. Specifically, the first essential mode contributing to 34% of overall motion of the dimer is strongly coupled to the loop 6's closure over the active site. In contrast, such significant correlations cannot be observed in the monomeric structure, which maintains relatively localized motions of the loops in the essential modes. Thus, the onset of collective motions at ns time scale due to dimerization has functional implications as to the coordination of loop 6 closure.     

Analysis of the relationship between enzyme activity and its internal motion using nuclear magnetic resonance: 15N relaxation studies of wild-type and mutant lysozyme

A mutant lysozyme where R14 and H15 are deleted together has higher activity and a similar binding ability to an inhibitor, trimer of N-acetylglucosamine ((NAG)3), compared with wild-type lysozyme. Since this has been attributed to intrinsic protein dynamic properties, we investigated the relationship between the activity and the internal motions of proteins. Backbone dynamics of the free and the complex forms with the (NAG)3 have been studied by measurement of the 15N T1 and T2 relaxation rates and NOE determinations at 600 MHz. Analysis of the data using the model-free formalism showed that the generalized order parameters (S2) were almost the same in wild-type and mutant lysozyme in unbound state, indicating that the mutation had little effect on the global internal motions. On the other hand, in the presence of (NAG)3, although some signals located around the active site were broadened or decreased in intensity because of strong perturbation by (NAG)3, there were several residues that showed increased or decreased backbone S2 in the complexed lysozymes. A comparison of the internal motions of the wild-type and mutant complexes showed a number of distinct dynamic differences between them. In particular, many residues located at or near active-site regions (turn 1, strand 2, turn 2 and long loop), displayed greater backbone dynamics reflecting the order parameter in mutant complex relative to mutant free. Furthermore, the Rex values at the loop C-D region, which was considered to be important for enzymatic activity, significantly increased. From these results, it was suggested that variations in the dynamics of these regions may play an important role in the enzyme activity.     

Solvent effects in the slow dynamics of proteins

The influence of solvent on the slow internal dynamics of proteins is studied by comparing molecular dynamics simulations of solvated and unsolvated lysozyme. The dynamical trajectories are projected onto the protein's normal modes in order to obtain a separate analysis for each of the associated time scales. The results show that solvent effects are important for the slowest motions (below approximately 1 ps(-1)) but negligible for faster motions. The damping effects seen in the latter show that the principal source of friction in protein dynamics is not the solvent, but the protein itself.