Coarse-grained normal mode analysis in structural biology

The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained normal mode analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained normal mode analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

Normal-mode refinement of anisotropic thermal parameters for potassium channel KcsA at 3.2 A crystallographic resolution

We report a normal-mode method for anisotropic refinement of membrane-protein structures, based on a hypothesis that the global near-native-state disordering of membrane proteins in crystals follows low-frequency normal modes. Thus, a small set of modes is sufficient to represent the anisotropic thermal motions in X-ray crystallographic refinement. By applying the method to potassium channel KcsA at 3.2 A, we obtained a structural model with an improved fit with the diffraction data. Moreover, the improved electron density maps allowed for large structural adjustments for 12 residues in each subunit, including the rebuilding of 3 missing side chains. Overall, the anisotropic KcsA structure at 3.2 A was systematically closer to a 2.0 A KcsA structure, especially in the selectivity filter. Furthermore, the anisotropic thermal ellipsoids from the refinement revealed functionally relevant structural flexibility. We expect this method to be a valuable tool for structural refinement of many membrane proteins with moderate-resolution diffraction data.     

Effects of Disease Causing Mutations on the Essential Motions in Proteins

Abstract

This study embodies a detailed comparative analysis of the essential motions of the Wild type and the eight different disease mutant forms of the Human CYPlbl. The mutations considered in this study have been implicated in Primary Congenital Glaucoma, an in-born, genetic disorder associated with eye-abnormality. The principal component analysis for Wild type and the Mutants was carried out using the stabilized molecular dynamics trajectories, which ranged from 35 to 45 nanoseconds. Investigations revealed the nature of the collective motions that characterize functionally relevant ‘essential motions’. The essential motions in Wild type are characterized by the collective motions of the Substrate Access Channel including the β-rich domain and the loops in the region of p450-reductase interaction. Comparative analysis of the essential motions of the Wild type and Mutants, especially those involving the functionally important regions indicated distinct differences in their magnitudes as well as the residue-wise distribution. The Mutants in general are associated with higher root mean square fluctuations, and involve some of the relatively intact core regions of the protein, in large collective motions. This study sheds light on the possible effects of disease causing mutations on the large functionally important collective motions in proteins.     

Computer-based screening of functional conformers of proteins

A long-standing goal in biology is to establish the link between function, structure, and dynamics of proteins. Considering that protein function at the molecular level is understood by the ability of proteins to bind to other molecules, the limited structural data of proteins in association with other bio-molecules represents a major hurdle to understanding protein function at the structural level. Recent reports show that protein function can be linked to protein structure and dynamics through network centrality analysis, suggesting that the structures of proteins bound to natural ligands may be inferred computationally. In the present work, a new method is described to discriminate protein conformations relevant to the specific recognition of a ligand. The method relies on a scoring system that matches critical residues with central residues in different structures of a given protein. Central residues are the most traversed residues with the same frequency in networks derived from protein structures. We tested our method in a set of 24 different proteins and more than 260,000 structures of these in the absence of a ligand or bound to it. To illustrate the usefulness of our method in the study of the structure/dynamics/function relationship of proteins, we analyzed mutants of the yeast TATA-binding protein with impaired DNA binding. Our results indicate that critical residues for an interaction are preferentially found as central residues of protein structures in complex with a ligand. Thus, our scoring system effectively distinguishes protein conformations relevant to the function of interest.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.     

Elastic network models capture the motions apparent within ensembles of RNA structures

The role of structure and dynamics in mechanisms for RNA becomes increasingly important. Computational approaches using simple dynamics models have been successful at predicting the motions of proteins and are often applied to ribonucleo-protein complexes but have not been thoroughly tested for well-packed nucleic acid structures. In order to characterize a true set of motions, we investigate the apparent motions from 16 ensembles of experimentally determined RNA structures. These indicate a relatively limited set of motions that are captured by a small set of principal components (PCs). These limited motions closely resemble the motions computed from low frequency normal modes from elastic network models (ENMs), either at atomic or coarse-grained resolution. Various ENM model types, parameters, and structure representations are tested here against the experimental RNA structural ensembles, exposing differences between models for proteins and for folded RNAs. Differences in performance are seen, depending on the structure alignment algorithm used to generate PCs, modulating the apparent utility of ENMs but not significantly impacting their ability to generate functional motions. The loss of dynamical information upon coarse-graining is somewhat larger for RNAs than for globular proteins, indicating, perhaps, the lower cooperativity of the less densely packed RNA. However, the RNA structures show less sensitivity to the elastic network model parameters than do proteins. These findings further demonstrate the utility of ENMs and the appropriateness of their application to well-packed RNA-only structures, justifying their use for studying the dynamics of ribonucleo-proteins, such as the ribosome and regulatory RNAs.     

The change of protein intradomain mobility on ligand binding: is it a commonly observed phenomenon?

Analysis of changes in the dynamics of protein domains on ligand binding is important in several aspects: for the understanding of the hierarchical nature of protein folding and dynamics at equilibrium; for analysis of signal transduction mechanisms triggered by ligand binding, including allostery; for drug design; and for construction of biosensors reporting on the presence of target ligand in studied media. In this work we use the recently developed HCCP computational technique for the analysis of stabilities of dynamic domains in proteins, their intrinsic motions and of their changes on ligand binding. The work is based on comparative studies of 157 ligand binding proteins, for which several crystal structures (in ligand-free and ligand-bound forms) are available. We demonstrate that the domains of the proteins presented in the Protein DataBank are far more robust than it was thought before: in the majority of the studied proteins (152 out of 157), the ligand binding does not lead to significant change of domain stability. The exceptions from this rule are only four bacterial periplasmic transport proteins and calmodulin. Thus, as a rule, the pattern of correlated motions in dynamic domains, which determines their stability, is insensitive to ligand binding. This rule may be the general feature for a vast majority of proteins.     

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.     

Conformational changes and allosteric communications in human serum albumin due to ligand binding

It is well recognized that knowledge of structure alone is not sufficient to understand the fundamental mechanism of biomolecular recognition. Information of dynamics is necessary to describe motions involving relevant conformational states of functional importance. We carried out principal component analysis (PCA) of structural ensemble, derived from 84 crystal structures of human serum albumin (HSA) with different ligands and/or different conditions, to identify the functionally important collective motions, and compared with the motions along the low-frequency modes obtained from normal mode analysis of the elastic network model (ENM) of unliganded HSA. Significant overlap is observed in the collective motions derived from PCA and ENM. PCA and ENM analysis revealed that ligand selects the most favored conformation from accessible equilibrium structures of unliganded HSA. Further, we analyzed dynamic network obtained from molecular dynamics simulations of unliganded HSA and fatty acids- bound HSA. Our results show that fatty acids-bound HSA has more robust community network with several routes to communicate among different parts of the protein. Critical nodes (residues) identified from dynamic network analysis are in good agreement with allosteric residues obtained from sequence-based statistical coupling analysis method. This work underscores the importance of intrinsic structural dynamics of proteins in ligand recognition and can be utilized for the development of novel drugs with optimum activity.     

High-throughput modeling and analysis of protein structural dynamics

Protein function is a dynamic property closely related to the conformational mechanisms of protein structure in its physiological environment. To understand and control the function of target proteins, it becomes increasingly important to develop methods and tools for predicting collective motions at the molecular level. In this article, we review computational methods for predicting conformational dynamics and discuss software tools for data analysis. In particular, we discuss a high-throughput, web-based system called iGNM for protein structural dynamics. iGNM contains a database of protein motions for more than 20 000 PDB structures and supports online calculations for newly deposited PDB structures or user-modified structures. iGNM allows dynamics analysis of protein structures ranging from enzymes to large complexes and assemblies, and enables the exploration of protein sequence-structure-dynamics-function relations.     

Low-frequency vibrational modes and infrared absorbance of red, blue and green opsin

Vibrational excitations of low-frequency collective modes are essential for functionally important conformational transitions in proteins. We carried out an analysis of the low-frequency modes in the G protein coupled receptors (GPCR) family of cone opsins based on both normal-mode analysis and molecular dynamics (MD) simulations. Power spectra obtained by MD can be compared directly with normal modes. In agreement with existing experimental evidence related to transmembrane proteins, cone opsins have functionally important transitions that correspond to approximately 950 modes and are found below 80 cm⁻¹. This is in contrast to bacteriorhodopsin and rhodopsin, where the important low-frequency transition modes are below 50 cm⁻¹. We find that the density of states (DOS) profile of blue opsin in a solvent (e.g. water) has increased populations in the very lowest frequency modes (<15 cm⁻¹); this is indicative of the increased thermostability of blue opsin. From our work we found that, although light absorption behaves differently in blue, green and red opsins, their low-frequency vibrational motions are similar. The similarities and differences in the domain motions of blue, red and green opsins are discussed for several representative modes. In addition, the influence of the presence of a solvent is reported and compared with vacuum spectra. We thus demonstrate that terahertz spectroscopy of low-frequency modes might be relevant for identifying those vibrational degrees of freedom that correlate to known conformational changes in opsins. An erratum to this article can be found at     

Structure-based analysis of protein dynamics: comparison of theoretical results for hen lysozyme with X-ray diffraction and NMR relaxation data

An analytical approach based on Gaussian network model (GNM) is proposed for predicting the rotational dynamics of proteins. The method, previously shown to successfully reproduce X-ray crystallographic temperature factors for a series of proteins is extended here to predict bond torsional mobilities and reorientation of main chain amide groups probed by 15N-H nuclear magnetic resonance (NMR) relaxation. The dynamics of hen egg-white lysozyme (HEWL) in the folded state is investigated using the proposed approach. Excellent agreement is observed between theoretical results and experimental (X-ray diffraction and NMR relaxation) data. The analysis reveals the important role of coupled rotations, or cross-correlations between dihedral angle librations, in defining the relaxation mechanism on a local scale. The crystal and solution structures exhibit some differences in their local motions, but their global motions are identical. Hinge residues mediating the cooperative movements of the alpha- and beta-domains are identified, which comprise residues in helix C, Glu35 and Ser36 on the loop succeeding helix B, Ile55 and Leu56 at the turn between strands II and III. The central part of the beta-domain long loop and the turn between strands I and II display an enhanced mobility. Finally, kinetically hot residues and key interactions are identified, which point at helix B and beta-strand III as the structural elements underlying the stability of the tertiary structure.     

Water-protein interactions from high-resolution protein crystallography

To understand the role of water in life at molecular and atomic levels, structures and interactions at the protein-water interface have been investigated by cryogenic X-ray crystallography. The method enabled a much clearer visualization of definite hydration sites on the protein surface than at ambient temperature. Using the structural models of proteins, including several hydration water molecules, the characteristics in hydration structures were systematically analysed for the amount, the interaction geometries between water molecules and proteins, and the local and global distribution of water molecules on the surface of proteins. The tetrahedral hydrogen-bond geometry of water molecules in bulk solvent was retained at the interface and enabled the extension of a three-dimensional chain connection of a hydrogen-bond network among hydration water molecules and polar protein atoms over the entire surface of proteins. Networks of hydrogen bonds were quite flexible to accommodate and/or to regulate the conformational changes of proteins such as domain motions. The present experimental results may have profound implications in the understanding of the physico-chemical principles governing the dynamics of proteins in an aqueous environment and a discussion of why water is essential to life at a molecular level.     

Motions and structural variability within toxins: implication for their use as scaffolds for protein engineering

Animal toxins are small proteins built on the basis of a few disulfide bonded frameworks. Because of their high variability in sequence and biologic function, these proteins are now used as templates for protein engineering. Here we report the extensive characterization of the structure and dynamics of two toxin folds, the "three-finger" fold and the short alpha/beta scorpion fold found in snake and scorpion venoms, respectively. These two folds have a very different architecture; the short alpha/beta scorpion fold is highly compact, whereas the "three-finger" fold is a beta structure presenting large flexible loops. First, the crystal structure of the snake toxin alpha was solved at 1.8-A resolution. Then, long molecular dynamics simulations (10 ns) in water boxes of the snake toxin alpha and the scorpion charybdotoxin were performed, starting either from the crystal or the solution structure. For both proteins, the crystal structure is stabilized by more hydrogen bonds than the solution structure, and the trajectory starting from the X-ray structure is more stable than the trajectory started from the NMR structure. The trajectories started from the X-ray structure are in agreement with the experimental NMR and X-ray data about the protein dynamics. Both proteins exhibit fast motions with an amplitude correlated to their secondary structure. In contrast, slower motions are essentially only observed in toxin alpha. The regions submitted to rare motions during the simulations are those that exhibit millisecond time-scale motions. Lastly, the structural variations within each fold family are described. The localization and the amplitude of these variations suggest that the regions presenting large-scale motions should be those tolerant to large insertions or deletions.     

Functional motions can be extracted from on-lattice construction of protein structures

The three-dimensional structure of a 1509-residue protein-hemagglutinin is reconstructed on a simple cubic lattice by retaining all lattice sites that fall within close proximity of the X-ray coordinates. Coarse-grained normal modes analysis is performed using these lattice sites as the nodes of an elastic network. The collective deformations of the protein can still be extracted from such a structure that just mimics the overall shape of the protein but not its mass distribution. These results emphasize that the overall shape rather than the details of the protein fold determines the dynamical domains in proteins. Thus, low-resolution protein structures, even those constructed on a regularly spaced lattice, can provide insights about the functionally important global dynamics around the native state.     

Rings, bracelets, sleeves, and chevrons: new structures of kinetochore proteins

Electron microscopy has recently revealed striking structural orderliness in kinetochore proteins and protein complexes that associate with microtubules. In addition to their astonishing appearance and intrinsic beauty, the structures are functionally informative. The Dam1 and Ndc80 complexes bind to the microtubule lattice as rings and chevrons, respectively. These structures give insight into how the kinetochore couples to dynamic microtubules, a process crucial to the accurate segregation of chromosomes. HURP and kinesin-13 arrange tubulin into sleeves and bracelets surrounding the microtubule lattice. These structures might reflect the ability of these proteins to modulate microtubule dynamics by interacting with specialized tubulin configurations. In this review, we compare and contrast the structure of these proteins and their interactions with microtubules to illustrate how they attach to and modulate the dynamics of microtubules.     

Ribosomal antibiotics: structural basis for resistance, synergism and selectivity

Various antibiotics bind to ribosomes at functionally relevant locations such as the peptidyl-transferase center (PTC) and the exit tunnel for nascent proteins. High-resolution structures of antibiotics bound to ribosomal particles from a eubacterium that is similar to pathogens and an archaeon that shares properties with eukaryotes are deciphering subtle differences in these highly conserved locations that lead to drug selectivity and thereby facilitate clinical usage. These structures also show that members of antibiotic families with structural differences might bind to specific ribosomal pockets in different modes dominated by their chemical properties. Similarly, the chemical properties of drugs might govern variations in the nature of seemingly identical mechanisms of drug resistance. The observed variability in binding modes justifies expectations for structural design of improved antibiotic properties.