Nanosecond to microsecond protein dynamics probed by magnetic relaxation dispersion of buried water molecules

Large-scale protein conformational motions on nanosecond-microsecond time scales are important for many biological processes, but remain largely unexplored because of methodological limitations. NMR relaxation methods can access these time scales if protein tumbling is prevented, but the isotropy required for high-resolution solution NMR is then lost. However, if the immobilized protein molecules are randomly oriented, the water 2H and 17O spins relax as in a solution of freely tumbling protein molecules, with the crucial difference that they now sample motions on all time scales up to approximately 100 micros. In particular, the exchange rates of internal water molecules can be determined directly from the 2H or 17O magnetic relaxation dispersion (MRD) profile. This possibility opens up a new window for characterizing the motions of individual internal water molecules as well as the large-scale protein conformational fluctuations that govern the exchange rates of structural water molecules. We introduce and validate this new NMR method by presenting and analyzing an extensive set of 2H and 17O MRD data from cross-linked gels of two model proteins: bovine pancreatic trypsin inhibitor and ubiquitin. We determine residence times and order parameters of four internal water molecules in these proteins and show that they are quantitatively consistent with the information available from crystallography and solution MRD. We also show how slow motions of side-chains bearing labile hydrogens can be monitored by the same approach. Proteins of any size can be studied at physiological hydration levels with this method.     

Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Elastic network normal modes provide a basis for protein structure refinement

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.     

Pressure—A Gateway to Fundamental Insights into Protein Solvation,Dynamics, and Function

Now that the centennial anniversary of the first report on pressure denaturation of proteins by Nobel Laureate P. W. Bridgman can be celebrated, this Review on the application of high pressure as a key variable for studying the energetics and interactions of proteins appears. We demonstrate that combined temperature–pressure‐dependent studies help delineate the free‐energy landscape of proteins and elucidate which features are essential in determining their stability. Pressure perturbation also serves as an important tool to explore fluctuations in proteins and reveal their conformational substates. From shaping the free‐energy landscape of proteins themselves to that of their interactions, conformational fluctuations not only dictate a plethora of biological processes, but are also implicated in a number of debilitating diseases. Finally, the advantages of using pressure to explore biomolecular assemblies and modulate enzymatic reactions are discussed.     

Role of protein dynamics in reaction rate enhancement by enzymes

An integrated view of protein structure, dynamics, and function is emerging, where proteins are considered as dynamically active assemblies and internal motions are closely linked to function such as enzyme catalysis. Further, the motion of solvent bound to external regions of protein impacts internal motions and, therefore, protein function. Recently, we discovered a network of protein vibrations in enzyme cyclophilin A, coupled to its catalytic activity of peptidyl-prolyl cis-trans isomerization. Detailed studies suggest that this network, extending from surface regions to active site, is a conserved part of enzyme structure and has a role in promoting catalysis. In this report, theoretical investigations of concerted conformational fluctuations occurring on microsecond and longer time scales within the discovered network are presented. Using a new technique, kinetic energy was added to protein vibrational modes corresponding to conformational fluctuations in the network. The results reveal that protein dynamics promotes catalysis by altering transition state barrier crossing behavior of reaction trajectories. An increase in transmission coefficient and number of productive trajectories with increasing amounts of kinetic energy in vibrational modes is observed. Variations in active site enzyme-substrate interactions near transition state are found to be correlated with barrier recrossings. Simulations also showed that energy transferred from first solvation shell to surface residues impacts catalysis through network fluctuations. The detailed characterization of network presented here indicates that protein dynamics plays a role in rate enhancement by enzymes. Therefore, coupled networks in enzymes have wide implications in understanding allostericity and cooperative effects, as well as protein engineering and drug design.     

Identification of key residues for protein conformational transition using elastic network model

Proteins usually undergo conformational transitions between structurally disparate states to fulfill their functions. The large-scale allosteric conformational transitions are believed to involve some key residues that mediate the conformational movements between different regions of the protein. In the present work, a thermodynamic method based on the elastic network model is proposed to predict the key residues involved in protein conformational transitions. In our method, the key functional sites are identified as the residues whose perturbations largely influence the free energy difference between the protein states before and after transition. Two proteins, nucleotide binding domain of the heat shock protein 70 and human/rat DNA polymerase β, are used as case studies to identify the critical residues responsible for their open-closed conformational transitions. The results show that the functionally important residues mainly locate at the following regions for these two proteins: (1) the bridging point at the interface between the subdomains that control the opening and closure of the binding cleft; (2) the hinge region between different subdomains, which mediates the cooperative motions between the corresponding subdomains; and (3) the substrate binding sites. The similarity in the positions of the key residues for these two proteins may indicate a common mechanism in their conformational transitions.     

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.     

Time-resolved microscopy of chromatin in vitro and in vivo

In eukaryotic cell nuclei, double-stranded DNA is found in the form of chromatin, a large fiber made up of DNA complexed to histone proteins. In this article, recent studies using fluorescence techniques to look at the dynamics of chromatin, both in vivo and in vitro, are reviewed. Two-photon counterpropagating fluorescence recovery after patterned photobleaching is used to examine chromatin fluctuations on lengthscales ranging from less than 100 nm to microns. By combining in vivo studies with data on isolated nuclei and by measuring how these fluctuations depend on variables like ionic strength and photochemical cross-linking, it is demonstrated that the relatively large-scale motions of chromatin observed in vivo are consistent with smaller scale modifications of the histone-DNA interaction. This connection may provide a means to use conformational dynamics as an in vivo probe of the biochemical events involved in gene expression.     

Molecular dynamics of apo-adenylate kinase: a principal component analysis

Adenylate kinase from E. coli (AKE) is studied with molecular dynamics. AKE undergoes large-scale motions of its Lid and AMP-binding domains when its open form closes over its substrates, AMP and Mg2+-ATP. The third domain, the Core, is relatively stable during closing. The resulting trajectory is analyzed with a principal component analysis method that decomposes the atom motions into modes ordered by their decreasing contributions to the total protein fluctuation. Simulations at 303 K (normal T) and 500 K (high T) reveal that at both temperatures the first three modes account for 70% of the total fluctuation. The residues that contribute the most to these three modes are concentrated in the Lid and AMP-binding domains. Analysis of the normal T modes indicates that the Lid and AMP-binding domains sample a broad distribution of conformations indicating that AKE is designed to provide its substrates with a large set of conformations. The high T results show that the Lid initially closes toward the Core. Subsequently, the Lid rotates to a new stable conformation that is different from what is observed in the substrate-bound AKE. These results are discussed in the context of experimental data that indicate that adenylate kinases do sample more than one conformational state in solution and that each of these conformational states undergoes substantial fluctuations. A pair of residues is suggested for labeling that would be useful for monitoring distance fluctuations by energy transfer experiments.     

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 ?) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.     

Exploring multiple timescale motions in protein GB3 using accelerated molecular dynamics and NMR spectroscopy

Biological function relies on the complex spectrum of conformational dynamics occurring in biomolecules. We have combined Accelerated Molecular Dynamics (AMD) with experimental results derived from NMR to probe multiple time-scale motions in the third IgG-binding domain of Protein G (GB3). AMD is shown to accurately reproduce the amplitude and distribution of slow motional modes characterized using residual dipolar couplings, reporting on dynamics up to the millisecond timescale. In agreement with experiment, larger amplitude slower motions are localized in the beta-strand/loop motif spanning residues 14-24 and in loop 42-44. Principal component analysis shows these fluctuations participating in the primary mode, substantiating the existence of a correlated motion traversing the beta-sheet that culminates in maximum excursions at the active site of the molecule. Fast dynamics were simulated using extensive standard MD simulations and compared to order parameters extracted from 15N relaxation. Notably 60 2-ns fully solvated MD simulations exploring the different conformational substates sampled from AMD resulted in better reproduction of order parameters compared to the same number of simulations starting from the relaxed crystal structure. This illustrates the inherent dependence of protein dynamics on local conformational topology. The results provide rare insight into the complex hierarchy of dynamics present in GB3 and allow us to develop a model of the conformational landscape native to the protein, appearing as a steep sided potential well whose flat bottom comprises multiple similar but discrete conformational substates.     

An approximate method in using molecular mechanics simulations to study slow protein conformational changes

The broad range of characteristic motions in proteins has limited the applicability of molecular dynamics simulations in studying large-scale conformational transitions. We present an approximate method, making use of standard MD simulations and using a much larger integration time step, to obtain the structural changes for slow systematic motions of large complex systems. We show the applicability of this method by simulating the open to closed Calmodulin calcium binding domain conformational changes. Starting with the Ca2+-bound X-ray structure, and after the removal of the Ca2+ ions, our calculation yielded intermediate conformations during the rearrangement of helices in each Ca2+ binding pocket, leading to a structure with a lowest rmsd of 1.56 A compared to the NMR apo-calmodulin structure.     

Coarse-grained simulations of the conformational dynamics of proteins

The conformational dynamics of a set of proteins, cytochrome c, α-lactalbumin and barnase, is studied by an off-lattice Monte Carlo (MC)/Metropolis simulation technique. A low-resolution model (virtual bond model) for the protein structure is used with recently extracted knowledge-based potentials. The calculated root-mean-square fluctuations in the α-carbons are in good agreement with X-ray crystallographic temperature factors. The potentially yielding or non-yielding regions of the protein for unfolding, in the kinetic sense, are identified from the correlation analysis of the rotational motions of the backbone bonds. The bonds which display highly auto-correlated rotational motions, in general, belong to those regions which are experimentally identified to be highly resistant to unfolding.     

Conformational fluctuations and electronic properties in myoglobin

In this article we use the recently developed perturbed matrix method (PMM) to investigate the effect of conformational fluctuations on the electronic properties of heme in Myoglobin. This widely studied biomolecule has been chosen as a benchmark for evaluating the accuracy of PMM in a large and complex system. Using a long, 80-ns, molecular dynamics simulation and unperturbed Configuration Interaction (CISD) calculations in PMM, we reproduced the main spectroscopic features of deoxy-Myoglobin. Moreover, in line with our previous results on a photosensitive protein, this study reveals a clear dynamical coupling between electronic properties and conformational fluctuations, suggesting that this correlation could be a general feature of proteins.     

Protein structure along the order-disorder continuum

Thermal fluctuations cause proteins to adopt an ensemble of conformations wherein the relative stability of the different ensemble members is determined by the topography of the underlying energy landscape. "Folded" proteins have relatively homogeneous ensembles, while "unfolded" proteins have heterogeneous ensembles. Hence, the labels "folded" and "unfolded" represent attempts to provide a qualitative characterization of the extent of structural heterogeneity within the underlying ensemble. In this work, we introduce an information-theoretic order parameter to quantify this conformational heterogeneity. We demonstrate that this order parameter can be estimated in a straightforward manner from an ensemble and is applicable to both unfolded and folded proteins. In addition, a simple formula for approximating the order parameter directly from crystallographic B factors is presented. By applying these metrics to a large sample of proteins, we show that proteins span the full range of the order-disorder axis.     

Analytical Description of NMR Relaxation Highlights Correlated Dynamics in Intrinsically Disordered Proteins

The dynamic fluctuations of intrinsically disordered proteins (IDPs) define their function. Although experimental nuclear magnetic resonance (NMR) relaxation reveals the motional complexity of these highly flexible proteins, the absence of physical models describing IDP dynamics hinders their mechanistic interpretation. Combining molecular dynamics simulation and NMR, we introduce a framework in which distinct motions are attributed to local libration, backbone dihedral angle dynamics and longer‐range tumbling of one or more peptide planes. This model provides unique insight into segmental organization of dynamics in IDPs and allows us to investigate the presence and extent of the correlated motions that are essential for function.     

Protein dynamics in cytochrome P450 molecular recognition and substrate specificity using 2D IR vibrational echo spectroscopy

Cytochrome (cyt) P450s hydroxylate a variety of substrates that can differ widely in their chemical structure. The importance of these enzymes in drug metabolism and other biological processes has motivated the study of the factors that enable their activity on diverse classes of molecules. Protein dynamics have been implicated in cyt P450 substrate specificity. Here, 2D IR vibrational echo spectroscopy is employed to measure the dynamics of cyt P450(cam) from Pseudomonas putida on fast time scales using CO bound at the active site as a vibrational probe. The substrate-free enzyme and the enzyme bound to both its natural substrate, camphor, and a series of related substrates are investigated to explicate the role of dynamics in molecular recognition in cyt P450(cam) and to delineate how the motions may contribute to hydroxylation specificity. In substrate-free cyt P450(cam), three conformational states are populated, and the structural fluctuations within a conformational state are relatively slow. Substrate binding selectively stabilizes one conformational state, and the dynamics become faster. Correlations in the observed dynamics with the specificity of hydroxylation of the substrates, the binding affinity, and the substrates' molecular volume suggest that motions on the hundreds of picosecond time scale contribute to the variation in activity of cyt P450(cam) toward different substrates.     

Application of time series analysis on molecular dynamics simulations of proteins: a study of different conformational spaces by principal component analysis

Time series analysis is applied on the collective coordinates obtained from principal component analysis of independent molecular dynamics simulations of alpha-amylase inhibitor tendamistat and immunity protein of colicin E7 based on the Calpha coordinates history. Even though the principal component directions obtained for each run are considerably different, the dynamics information obtained from these runs are surprisingly similar in terms of time series models and parameters. There are two main differences in the dynamics of the two proteins: the higher density of low frequencies and the larger step sizes for the interminima motions of colicin E7 than those of alpha-amylase inhibitor, which may be attributed to the higher number of residues of colicin E7 and/or the structural differences of the two proteins. The cumulative density function of the low frequencies in each run conforms to the expectations from the normal mode analysis. When different runs of alpha-amylase inhibitor are projected on the same set of eigenvectors, it is found that principal components obtained from a certain conformational region of a protein has a moderate explanation power in other conformational regions and the local minima are similar to a certain extent, while the height of the energy barriers in between the minima significantly change. As a final remark, time series analysis tools are further exploited in this study with the motive of explaining the equilibrium fluctuations of proteins.     

Backbone motions of free and pheromone-bound major urinary protein I studied by molecular dynamics simulation

Molecular motions of free and pheromone-bound mouse major urinary protein I, previously investigated by NMR relaxation, were simulated in 30 ns molecular dynamics (MD) runs. The backbone flexibility was described in terms of order parameters and correlation times, commonly used in the NMR relaxation analysis. Special attention was paid to the effect of conformational changes on the nanosecond time scale. Time-dependent order parameters were determined in order to separate motions occurring on different time scales. As an alternative approach, slow conformational changes were identified from the backbone torsion angle variances, and "conformationally filtered" order parameters were calculated for well-defined conformation states. A comparison of the data obtained for the free and pheromone-bound protein showed that some residues are more rigid in the bound form, but a larger portion of the protein becomes more flexible upon the pheromone binding. This finding is in general agreement with the NMR results. The higher flexibility observed on the fast (fs-ps) time scale was typically observed for the residues exhibiting higher conformational freedom on the ns time scale. An inspection of the hydrogen bond network provided a structural explanation for the flexibility differences between the free and pheromone-bound proteins in the simulations.