Cooperative fluctuations and subunit communication in tryptophan synthase

Allosteric regulation of substrate channeling: Salmonella typhimurium tryptophan synthase

The regulation of the synthesis of L-tryptophan (L-Trp) in enteric bacteria begins at the level of gene expression where the cellular concentration of L-Trp tightly controls expression of the five enzymes of the Trp operon responsible for the synthesis of L-Trp. Two of these enzymes, trpA and trpB, form an αββα bienzyme complex, designated as tryptophan synthase (TS). TS carries out the last two enzymatic processes comprising the synthesis of L-Trp. The TS α-subunits catalyze the cleavage of 3-indole D-glyceraldehyde 3′-phosphate to indole and D-glyceraldehyde 3-phosphate; the pyridoxal phosphate-requiring β-subunits catalyze a nine-step reaction sequence to replace the L-Ser hydroxyl by indole giving L-Trp and a water molecule. Within αβ dimeric units of the αββα bienzyme complex, the common intermediate indole is channeled from the α site to the β site via an interconnecting 25 Å-long tunnel. The TS system provides an unusual example of allosteric control wherein the structures of the nine different covalent intermediates along the β-reaction catalytic path and substrate binding to the α-site provide the allosteric triggers for switching the αββα system between the open (T) and closed (R) allosteric states. This triggering provides a linkage that couples the allosteric conformational coordinate to the covalent chemical reaction coordinates at the α- and β-sites. This coupling drives the α- and β-sites between T and R conformations to achieve regulation of substrate binding and/or product release, modulation of the α- and β-site catalytic activities, prevention of indole escape from the confines of the active sites and the interconnecting tunnel, and synchronization of the α- and β-site catalytic activities. Here we review recent advances in the understanding of the relationships between structure, function, and allosteric regulation of the complex found in Salmonella typhimurium.

Protein Fluctuations in Response to Random External Forces

Elastic network models (ENMs) have been widely used in the last decades to investigate protein motions and dynamics. There the intrinsic fluctuations based on the isolated structures are obtained from the normal modes of these elastic networks, and they generally show good agreement with the B-factors extracted from X-ray crystallographic experiments, which are commonly considered to be indicators of protein flexibility. In this paper, we propose a new approach to analyze protein fluctuations and flexibility, which has a more appropriate physical basis. It is based on the application of random forces to the protein ENM to simulate the effects of collisions of solvent on a protein structure. For this purpose, we consider both the Cα-atom coarse-grained anisotropic network model (ANM) and an elastic network augmented with points included for the crystallized waters. We apply random forces to these protein networks everywhere, as well as only on the protein surface alone. Despite the randomness of the directions of the applied perturbations, the computed average displacements of the protein network show a remarkably good agreement with the experimental B-factors. In particular, for our set of 919 protein structures, we find that the highest correlation with the B-factors is obtained when applying forces to the external surface of the water-augmented ANM (an overall gain of 3% in the Pearson’s coefficient for the entire dataset, with improvements up to 30% for individual proteins), rather than when evaluating the fluctuations obtained from the normal modes of a standard Cα-atom coarse-grained ANM. It follows that protein fluctuations should be considered not just as the intrinsic fluctuations of the internal dynamics, but also equally well as responses to external solvent forces, or as a combination of both.

Identifying the leading dynamics of ubiquitin: A comparison between the tICA and the LE4PD slow fluctuations in amino acids' position

Molecular Dynamics (MD) simulations of proteins implicitly contain the information connecting the atomistic molecular structure and proteins' biologically relevant motion, where large-scale fluctuations are deemed to guide folding and function. In the complex multiscale processes described by MD trajectories, it is difficult to identify, separate, and study those large-scale fluctuations. This problem can be formulated as the need to identify a small number of collective variables that guide the slow kinetic processes. The most promising method among the ones used to study the slow leading processes in proteins' dynamics is the time-structure based on time-lagged independent component analysis (tICA), which identifies the dominant components in a noisy signal. Recently, we developed an anisotropic Langevin approach for the dynamics of proteins, called the anisotropic Langevin Equation for Protein Dynamics or LE4PD-XYZ. This approach partitions the protein's MD dynamics into mostly uncorrelated, wavelength-dependent, diffusive modes. It associates with each mode a free-energy map, where one measures the spatial extension and the time evolution of the mode-dependent, slow dynamical fluctuations. Here, we compare the tICA modes' predictions with the collective LE4PD-XYZ modes. We observe that the two methods consistently identify the nature and extension of the slowest fluctuation processes. The tICA separates the leading processes in a smaller number of slow modes than the LE4PD does. The LE4PD provides time-dependent information at short times and a formal connection to the physics of the kinetic processes that are missing in the pure statistical analysis of tICA.

Low-Frequency Harmonic Perturbations Drive Protein Conformational Changes

Protein dynamics has been investigated since almost half a century, as it is believed to constitute the fundamental connection between structure and function. Elastic network models (ENMs) have been widely used to predict protein dynamics, flexibility and the biological mechanism, from which remarkable results have been found regarding the prediction of protein conformational changes. Starting from the knowledge of the reference structure only, these conformational changes have been usually predicted either by looking at the individual mode shapes of vibrations (i.e., by considering the free vibrations of the ENM) or by applying static perturbations to the protein network (i.e., by considering a linear response theory). In this paper, we put together the two previous approaches and evaluate the complete protein response under the application of dynamic perturbations. Harmonic forces with random directions are applied to the protein ENM, which are meant to simulate the single frequency-dependent components of the collisions of the surrounding particles, and the protein response is computed by solving the dynamic equations in the underdamped regime, where mass, viscous damping and elastic stiffness contributions are explicitly taken into account. The obtained motion is investigated both in the coordinate space and in the sub-space of principal components (PCs). The results show that the application of perturbations in the low-frequency range is able to drive the protein conformational change, leading to remarkably high values of direction similarity. Eventually, this suggests that protein conformational change might be triggered by external collisions and favored by the inherent low-frequency dynamics of the protein structure.

Comparison between slow anisotropic LE4PD fluctuations and the principal component analysis modes of ubiquitin

The biological function and folding mechanisms of proteins are often guided by large-scale slow motions, which involve crossing high energy barriers. In a simulation trajectory, these slow fluctuations are commonly identified using a principal component analysis (PCA). Despite the popularity of this method, a complete analysis of its predictions based on the physics of protein motion has been so far limited. This study formally connects the PCA to a Langevin model of protein dynamics and analyzes the contributions of energy barriers and hydrodynamic interactions to the slow PCA modes of motion. To do so, we introduce an anisotropic extension of the Langevin equation for protein dynamics, called the LE4PD-XYZ, which formally connects to the PCA "essential dynamics." The LE4PD-XYZ is an accurate coarse-grained diffusive method to model protein motion, which describes anisotropic fluctuations in the alpha carbons of the protein. The LE4PD accounts for hydrodynamic effects and mode-dependent free-energy barriers. This study compares large-scale anisotropic fluctuations identified by the LE4PD-XYZ to the mode-dependent PCA predictions, starting from a microsecond-long alpha carbon molecular dynamics atomistic trajectory of the protein ubiquitin. We observe that the inclusion of free-energy barriers and hydrodynamic interactions has important effects on the identification and timescales of ubiquitin's slow modes.

Resistance of Mycobacterium tuberculosis to indole 4-carboxamides occurs through alterations in drug metabolism and tryptophan biosynthesis

Tryptophan biosynthesis represents an important potential drug target for new anti-TB drugs. We identified a series of indole-4-carboxamides with potent antitubercular activity. In vitro, Mycobacterium tuberculosis (Mtb) acquired resistance to these compounds through three discrete mechanisms: (1) a decrease in drug metabolism via loss-of-function mutations in the amidase that hydrolyses these carboxamides, (2) an increased biosynthetic rate of tryptophan precursors via loss of allosteric feedback inhibition of anthranilate synthase (TrpE), and (3) mutation of tryptophan synthase (TrpAB) that decreased incorporation of 4-aminoindole into 4-aminotryptophan. Thus, these indole-4-carboxamides act as prodrugs of a tryptophan antimetabolite, 4-aminoindole.

Computational Ways to Enhance Protein Inhibitor Design

Two new computational approaches are described to aid in the design of new peptide-based drugs by evaluating ensembles of protein structures from their dynamics and through the assessing of structures using empirical contact potential. These approaches build on the concept that conformational variability can aid in the binding process and, for disordered proteins, can even facilitate the binding of more diverse ligands. This latter consideration indicates that such a design process should be less restrictive so that multiple inhibitors might be effective. The example chosen here focuses on proteins/peptides that bind to hemagglutinin (HA) to block the large-scale conformational change for activation. Variability in the conformations is considered from sets of experimental structures, or as an alternative, from their simple computed dynamics; the set of designe peptides/small proteins from the David Baker lab designed to bind to hemagglutinin, is the large set considered and is assessed with the new empirical contact potentials.

Computational Analysis of Dynamical Fluctuations of Oncoprotein E7 (HPV 16) for the Hot Spot Residue Identification Using Elastic Network Model

Aims:

To find out Potential Drug targets against HPV E7.

Background:

Oncoprotein E7 of Human Papilloma Virus (HPV-16), after invading human body alter host protein-protein interaction networks caused by the fluctuations of amino acid residues present in E7. E7 interacts with Rb protein of human host with variable residual fluctuations, leading towards the progression of cervical cancer.

Objective:

Our study was focused our computational analysis of the binding and competing interactions of the E7 protein of HPV with Rb protein.

Methods:

Our study is based on analysis of dynamic fluctuations of E7 in host cell and correlation analysis of specific residue found in motif of LxCxE, that is the key region in stabilizing interaction between E7 and Rb.

Results and Discussion:

Cysteine, Leucine and Glutamic acid have been identified as hot spot residues of E7 which can provide platform for drug designing and understanding of pathogenesis of cervical cancer, in future. Our study shows validation of the vitality of linear binding motifs LxCxE of E7 of HPV in interacting with Rb as an important event in propagation of HPV in human cells and transformation of infection into cervical cancer.

Conclusion:

Our study shows validation of the vitality of linear binding motifs LxCxE of E7 of HPV in interacting with Rb as an important event in propagation of HPV in human cells and transformation of infection into cervical cancer.

Other:

E7 interacts with Rb protein of human host with variable residual fluctuations, leading towards the progression of cervical cancer.

Kinetics analysis of ubiquitin local fluctuations with Markov state modeling of the LE4PD normal modes

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a selection mechanism of binding. Thus, an accurate characterization of local fluctuations may be important for modeling the kinetic mechanism that leads to the biological activity of a protein. In this paper, we study the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to model its fluctuations. A coarse-grained, diffusive, mode-dependent description of fluctuations is accomplished using the Langevin Equation for Protein Dynamics (LE4PD). This equation decomposes the dynamics of a protein, simulated by molecular dynamics, into dynamical pathways that explore mode-dependent free energy surfaces. We calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free energy surfaces using Markov state modeling. We find that the LE4PD predicts slow fluctuations in three important binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. These results suggest that the LE4PD can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin.

Dynamics fingerprints of active conformers of epidermal growth factor receptor kinase

Epidermal growth factor receptor (EGFR) is a prototypical cell-surface receptor that plays a key role in the regulation of cellular signaling, proliferation and differentiation. Mutations of its kinase domain have been associated with the development of a variety of cancers and, therefore, it has been the target of drug design. Single amino acid substitutions (SASs) in this domain have been proven to alter the equilibrium of pre-existing conformer populations. Despite the advances in structural descriptions of its so-called active and inactive conformations, the associated dynamics aspects that characterize them have not been thoroughly studied yet. As the dynamic behaviors and molecular motions of proteins are important for a complete understanding of their structure-function relationships we present a novel procedure, using (or based on) normal mode analysis, to identify the collective dynamics shared among different conformers in EGFR kinase. The method allows the comparison of patterns of low-frequency vibrational modes defining representative directions of motions. Our procedure is able to emphasize the main similarities and differences between the collective dynamics of different conformers. In the case of EGFR kinase, two representative directions of motions have been found as dynamics fingerprints of the active conformers. Protein motion along both directions reveals to have a significant impact on the cavity volume of the main pocket of the active site. Otherwise, the inactive conformers exhibit a more heterogeneous distribution of collective motions. © 2018 Wiley Periodicals, Inc.

Protein stability and dynamics influenced by ligands in extremophilic complexes - a molecular dynamics investigation

In this study, we explore the structural and dynamic adaptations of the Tryptophan synthase α-subunit in a ligand bound state in psychrophilic, mesophilic and hyperthermophilic organisms at different temperatures by MD simulations. We quantify the global and local fluctuations in the 40 ns time scale by analyzing the root mean square deviation/fluctuations. The distinct behavior of the active site and loop 6 is observed with the elevation of temperature. Protein stability relies more on electrostatic interactions, and these interactions might be responsible for the stability of varying temperature evolved proteins. The paper also focuses on the effect of temperature on protein dynamics and stability governed by the distinct behavior of the ligand associated with its retention, binding and dissociation over the course of time. The integration of principle component analysis and a free energy landscape was useful in identifying the conformational space accessible to ligand bound homologues and how the presence of the ligand alters the conformational and dynamic properties of the protein.

Structural and dynamics evidence for scaffold asymmetric flexibility of the human transthyretin tetramer

The molecular symmetry of multimeric proteins is generally determined by using X-ray diffraction techniques, so that the basic question as to whether this symmetry is perfectly preserved for the same protein in solution remains open. In this work, human transthyretin (TTR), a homotetrameric plasma transport protein with two binding sites for the thyroid hormone thyroxine (T4), is considered as a case study. Based on the crystal structure of the TTR tetramer, a hypothetical D2 symmetry is inferred for the protein in solution, whose functional behavior reveals the presence of two markedly different Kd values for the two T4 binding sites. The latter property has been ascribed to an as yet uncharacterized negative binding cooperativity. A triple mutant form of human TTR (F87M/L110M/S117E TTR), which is monomeric in solution, crystallizes as a tetrameric protein and its structure has been determined. The exam of this and several other crystal forms of human TTR suggests that the TTR scaffold possesses a significant structural flexibility. In addition, TTR tetramer dynamics simulated using normal modes analysis exposes asymmetric vibrational patterns on both dimers and thermal fluctuations reveal small differences in size and flexibility for ligand cavities at each dimer-dimer interface. Such small structural differences between monomers can lead to significant functional differences on the TTR tetramer dynamics, a feature that may explain the functional heterogeneity of the T4 binding sites, which is partially overshadowed by the crystal state.

Inhibiting mycobacterial tryptophan synthase by targeting the inter-subunit interface

Drug discovery efforts against the pathogen Mycobacterium tuberculosis (Mtb) have been advanced through phenotypic screens of extensive compound libraries. Such a screen revealed sulfolane 1 and indoline-5-sulfonamides 2 and 3 as potent inhibitors of mycobacterial growth. Optimization in the sulfolane series led to compound 4, which has proven activity in an in vivo murine model of Mtb infection. Here we identify the target and mode of inhibition of these compounds based on whole genome sequencing of spontaneous resistant mutants, which identified mutations locating to the essential α- and β-subunits of tryptophan synthase. Over-expression studies confirmed tryptophan synthase as the biological target. Biochemical techniques probed the mechanism of inhibition, revealing the mutant enzyme complex incurs a fitness cost but does not prevent inhibitor binding. Mapping of the resistance conferring mutations onto a low-resolution crystal structure of Mtb tryptophan synthase showed they locate to the interface between the α- and β-subunits. The discovery of anti-tubercular agents inhibiting tryptophan synthase highlights the therapeutic potential of this enzyme and draws attention to the prospect of other amino acid biosynthetic pathways as future Mtb drug targets.

Evaluating the effect of mutations and ligand binding on transthyretin homotetramer dynamics

Native transthyretin (TTR) homotetramer dissociation is the first step of the fibrils formation process in amyloid disease. A large number of specific point mutations that destabilize TTR quaternary structure have shown pro-amyloidogenic effects. Besides, several compounds have been proposed as drugs in the therapy of TTR amyloidosis due to their TTR tetramer binding affinities, and therefore, contribution to its integrity. In the present paper we have explored key positions sustaining TTR tetramer dynamical stability. We have identified positions whose mutations alter the most the TTR tetramer equilibrium dynamics based on normal mode analysis and their response to local perturbations. We have found that these positions are mostly localized at β-strands E and F and EF-loop. The monomer-monomer interface is pointed out as one of the most vulnerable regions to mutations that lead to significant changes in the TTR-tetramer equilibrium dynamics and, therefore, induces TTR amyloidosis. Besides, we have found that mutations on residues localized at the dimer-dimer interface and/or at the T4 hormone binding site destabilize the tetramer more than the average. Finally, we were able to compare several compounds according to their effect on vibrations associated to the ligand binding. Our ligand comparison is discussed and analyzed in terms of parameters and measurements associated to TTR-ligand binding affinities and the stabilization of its native state.

Bridging Enzymatic Structure Function via Mechanics: A Coarse-Grain Approach

Flexibility is a central aspect of protein function, and ligand binding in enzymes involves a wide range of structural changes, ranging from large-scale domain movements to small loop or side-chain rearrangements. In order to understand how the mechanical properties of enzymes, and the mechanical variations that are induced by ligand binding, relate to enzymatic activity, we carried out coarse-grain Brownian dynamics simulations on a set of enzymes whose structures in the unbound and ligand-bound forms are available in the Protein Data Bank. Our results show that enzymes are remarkably heterogeneous objects from a mechanical point of view and that the local rigidity of individual residues is tightly connected to their part in the protein's overall structure and function. The systematic comparison of the rigidity of enzymes in their unbound and bound forms highlights the fact that small conformational changes can induce large mechanical effects, leading to either more or less flexibility depending on the enzyme's architecture and the location of its ligand-biding site. These mechanical variations target a limited number of specific residues that occupy key locations for enzymatic activity, and our approach thus offers a mean to detect perturbation-sensitive sites in enzymes, where the addition or removal of a few interactions will lead to important changes in the proteins internal dynamics.

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.

Visualizing the tunnel in tryptophan synthase with crystallography: Insights into a selective filter for accommodating indole and rejecting water

Four new X-ray structures of tryptophan synthase (TS) crystallized with varying numbers of the amphipathic N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F6) molecule are presented. These structures show one of the F6 ligands threaded into the tunnel from the β-site and reveal a distinct hydrophobic region. Over this expanse, the interactions between F6 and the tunnel are primarily nonpolar, while the F6 phosphoryl group fits into a polar pocket of the β-subunit active site. Further examination of TS structures reveals that one portion of the tunnel (T1) binds clusters of water molecules, whereas waters are not observed in the nonpolar F6 binding region of the tunnel (T2). MD simulation of another TS structure with an unobstructed tunnel also indicates the T2 region of the tunnel excludes water, consistent with a dewetted state that presents a significant barrier to the transfer of water into the closed β-site. We conclude that hydrophobic molecules can freely diffuse between the α- and β-sites via the tunnel, while water does not. We propose that exclusion of water serves to inhibit reaction of water with the α-aminoacrylate intermediate to form ammonium ion and pyruvate, a deleterious side reaction in the αβ-catalytic cycle. Finally, while most TS structures show βPhe280 partially blocking the tunnel between the α- and β-sites, new structures show an open tunnel, suggesting the flexibility of the βPhe280 side chain. Flexible docking studies and MD simulations confirm that the dynamic behavior of βPhe280 allows unhindered transfer of indole through the tunnel, therefore excluding a gating role for this residue.

Computing the Amino Acid Specificity of Fluctuations in Biomolecular Systems

We developed a new amino acid specific method for the computation of spatial fluctuations of proteins around their native structures. We show the consistency with experimental values and the increased performance in comparison to an established model, based on statistical estimates for a set of test proteins. We apply the new method to HIV-1 protease in its wild-type form and to a V82F-I84V mutant that shows resistance to protease inhibitors. We further show how the method can be successfully used to explain the molecular biophysics of drug resistance of the mutant.

Protonation states and catalysis: Molecular dynamics studies of intermediates in tryptophan synthase

The importance of protonation states and proton transfer in pyridoxal 5'-phosphate (PLP)-chemistry can hardly be overstated. Although experimental approaches to investigate pKa values can provide general guidance for assigning proton locations, only static pictures of the chemical species are available. To obtain the overall protein dynamics for the interpretation of detailed enzyme catalysis in this study, guided by information from solid-state NMR, we performed molecular dynamics (MD) simulations for the PLP-dependent enzyme tryptophan synthase (TRPS), whose catalytic mechanism features multiple quasi-stable intermediates. The primary objective of this work is to elucidate how the position of a single proton on the reacting substrate affects local and global protein dynamics during the catalytic cycle. In general, proteins create a chemical environment and an ensemble of conformational motions to recognize different substrates with different protonations. The study of these interactions in TRPS shows that functional groups on the reacting substrate, such as the phosphoryl group, pyridine nitrogen, phenolic oxygen and carboxyl group, of each PLP-bound intermediate play a crucial role in constructing an appropriate molecular interface with TRPS. In particular, the protonation states of the ionizable groups on the PLP cofactor may enhance or weaken the attractions between the enzyme and substrate. In addition, remodulation of the charge distribution for the intermediates may help generate a suitable environment for chemical reactions. The results of our study enhance knowledge of protonation states for several PLP intermediates and help to elucidate their effects on protein dynamics in the function of TRPS and other PLP-dependent enzymes.

Switches of hydrogen bonds during ligand-protein association processes determine binding kinetics

Revealing the processes of ligand-protein associations deepens our understanding of molecular recognition and binding kinetics. Hydrogen bonds (H-bonds) play a crucial role in optimizing ligand-protein interactions and ligand specificity. In addition to the formation of stable H-bonds in the final bound state, the formation of transient H-bonds during binding processes contributes binding kinetics that define a ligand as a fast or slow binder, which also affects drug action. However, the effect of forming the transient H-bonds on the kinetic properties is little understood. Guided by results from coarse-grained Brownian dynamics simulations, we used classical molecular dynamics simulations in an implicit solvent model and accelerated molecular dynamics simulations in explicit waters to show that the position and distribution of the H-bond donor or acceptor of a drug result in switching intermolecular and intramolecular H-bond pairs during ligand recognition processes. We studied two major types of HIV-1 protease ligands: a fast binder, xk263, and a slow binder, ritonavir. The slow association rate in ritonavir can be attributed to increased flexibility of ritonavir, which yields multistep transitions and stepwise entering patterns and the formation and breaking of complex H-bond pairs during the binding process. This model suggests the importance of conversions of spatiotemporal H-bonds during the association of ligands and proteins, which helps in designing inhibitors with preferred binding kinetics.

Local packing modulates diversity of iron pathways and cooperative behavior in eukaryotic and prokaryotic ferritins

Ferritin-like molecules show a remarkable combination of the evolutionary conserved activity of iron uptake and release that engage different pores in the conserved ferritin shell. It was hypothesized that pore selection and iron traffic depend on dynamic allostery with no conformational changes in the backbone. In this study, we detect the allosteric networks in Pseudomonas aeruginosa bacterioferritin (BfrB), bacterial ferritin (FtnA), and bullfrog M and L ferritins (Ftns) by a network-weaving algorithm (NWA) that passes threads of an allosteric network through highly correlated residues using hierarchical clustering. The residue-residue correlations are calculated in the packing-on elastic network model that introduces atom packing into the common packing-off model. Applying NWA revealed that each of the molecules has an extended allosteric network mostly buried inside the ferritin shell. The structure of the networks is consistent with experimental observations of iron transport: The allosteric networks in BfrB and FtnA connect the ferroxidase center with the 4-fold pores and B-pores, leaving the 3-fold pores unengaged. In contrast, the allosteric network directly links the 3-fold pores with the 4-fold pores in M and L Ftns. The majority of the network residues are either on the inner surface or buried inside the subunit fold or at the subunit interfaces. We hypothesize that the ferritin structures evolved in a way to limit the influence of functionally unrelated events in the cytoplasm on the allosteric network to maintain stability of the translocation mechanisms. We showed that the residue-residue correlations and the resultant long-range cooperativity depend on the ferritin shell packing, which, in turn, depends on protein sequence composition. Switching from the packing-on to the packing-off model reduces correlations by 35%-38% so that no allosteric network can be found. The influence of the side-chain packing on the allosteric networks explains the diversity in mechanisms of iron traffic suggested by experimental approaches.

Nonlinear excitations match correlated motions unveiled by NMR in proteins: a new perspective on allosteric cross-talk

In this paper we propose a novel theoretical framework for interpreting long-range dynamical correlations unveiled in proteins through NMR measurements. The theoretical rationale relies on the hypothesis that correlated motions in proteins may be reconstructed as large-scale, collective modes sustained by long-lived nonlinear vibrations known as discrete breathers (DB) localized at key, hot-spot sites. DBs are spatially localized modes, whose nonlinear nature hinders resonant coupling with the normal modes, thus conferring them long lifetimes as compared to normal modes. DBs have been predicted to exist in proteins, localized at few hot-spot residues typically within the stiffest portions of the structure. We compute DB modes analytically in the framework of the nonlinear network model, showing that the displacement patterns of many DBs localized at key sites match to a remarkable extent the experimentally uncovered correlation blueprint. The computed dispersion relations prove that it is physically possible for some of these DBs to be excited out of thermal fluctuations at room temperature. Based on our calculations, we speculate that transient energy redistribution among the vibrational modes in a protein might favor the emergence of DB-like bursts of long-lived energy at hot-spot sites with lifetimes in the ns range, able to sustain critical, function-encoding correlated motions. More generally, our calculations provide a novel quantitative tool to predict fold-spanning dynamical pathways of correlated residues that may be central to allosteric cross-talk in proteins.

How does hemoglobin generate such diverse functionality of physiological relevance?

The absolute values of the O2-affinities (P50, Klow, and Khigh) of hemoglobin (Hb) are regulated neither by changes in the static T-/R-quaternary and associated tertiary structures nor the ligation states. They are pre-determined and regulated by the extrinsic environmental factors such as pH, buffers, and heterotropic effectors. The effect and role of O2 on Hb are reversibly to drive the structural allosteric equilibrium between the T(deoxy)- and R(oxy)-Hb toward R(oxy)-Hb (the structural allostery). R(oxy)-Hb has a higher O2-affinity (Khigh) relative to that (Klow) of the T(deoxy)-Hb (Khigh>Klow) under any fixed environmental conditions. The apparent O2-affinity of Hb is high, as the globin matrix interferes with the dissociation process of O2, forcing the dissociated O2 geminately to re-bind to the heme Fe. This artificially increases [oxy-Hb] and concomitantly decreases [deoxy-Hb], leading to the apparent increases of the O2-affinity of Hb. The effector-linked high-frequency thermal fluctuations of the globin matrix act as a gating mechanism to modulate such physical, energetic, and kinetic barriers to enhance the dissociation process of O2, resulted in increases in [deoxy-Hb] and concomitant decrease in [oxy-Hb], leading to apparent reductions of the O2-affinity of Hb (the entropic allostery). The heme in Hb is simply a low-affinity O2-trap, the coordination structure of which is not altered by static T-/R-quaternary and associated tertiary structural changes of Hb. Thus, heterotrophic effectors are the signal molecule, which acts as a functional link between these two allosteries and generates the diverse functionality of Hb of physiological relevance. This article is part of a Special Issue entitled: Oxygen Binding and Sensing Proteins.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

EVOLUTION OF A CATALYTICALLY EFFECTIVE MODEL ENZYME: THE IMPORTANCE OF TUNED CONFORMATIONAL FLUCTUATIONS

Possible causal connections between the dynamics of a thermally fluctuating model enzyme molecule and catalysis are explored. The model is motivated by observations from experiment and simulation that amino acid residues residing in different enzymatic domains may show markedly different degrees of conformational freedom. Consequently, we are interested in the catalytic efficacy of an enzyme as a function of long-range many-atom cooperative effects resulting from strong, moderate, and weak interactions between enzymatic residues. Here we show and quantify through molecular dynamics simulations how the number and distribution of these interactions affects an enzyme's conformational fluctuation dynamics and its effectiveness as a catalyst. For any given distribution of "stiff" and "loose" enzymatic domains, catalytic fitness is defined as the number of chemical events — specifically the number of times a catalytic residue and substrate surmount a chemical reaction barrier — during molecular dynamics simulation. Through mutation, recombination, and a selection procedure following the ideas of Darwinian evolution, a genetic algorithm drives a population of enzyme molecules to greater catalytic fitness by modifying the mix of stiff and loose interactions. Approximately 30,000 different enzyme molecules are generated by the genetic algorithm — each with a unique number and distribution of strong, moderate, and weak inter-residue interactions. While the catalytically least fit enzyme exhibits 16 chemical events, the fittest boasts 253. That point mutations far from the active-site chemistry in the fittest enzyme have a strong effect on the number of chemical events suggests that catalysis depends, in part, on long-range many-atom globally correlated dynamical fluctuations.

Exploring and exploiting allostery: Models, evolution, and drug targeting

The concept of allostery was elaborated almost 50years ago by Monod and coworkers to provide a framework for interpreting experimental studies on the regulation of protein function. In essence, binding of a ligand at an allosteric site affects the function at a distant site exploiting protein flexibility and reshaping protein energy landscape. Both monomeric and oligomeric proteins can be allosteric. In the past decades, the behavior of allosteric systems has been analyzed in many investigations while general theoretical models and variations thereof have been steadily proposed to interpret the experimental data. Allostery has been established as a fundamental mechanism of regulation in all organisms, governing a variety of processes that range from metabolic control to receptor function and from ligand transport to cell motility. A number of studies have shed light on how evolutionary pressures have favored and molded the development of allosteric features in specific macromolecular systems. The widespread occurrence of allostery has been recently exploited for the development and design of allosteric drugs that bind to either physiological or non-physiological allosteric sites leading to gain of function or loss of function. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Normal modes and phase transition of the protein chain based on the Hamiltonian formalism

We use the torsional angles of the protein chain as generalized coordinates in the canonical formalism, derive canonical equations of motion, and investigate the coordinate dependence of the kinetic energy expressed in terms of the canonical momenta. We use the formalism to compute the normal-frequency distributions of the α helix and the β sheet, under the assumption that they are stabilized purely through hydrogen bonding. In addition, we obtain the free-energy relations of the α helix, the β sheet, and the random coil of a 15-residue polyalanine. Interestingly, our results predict a phase transition from an α helix to a β sheet at a critical temperature.

Deregulation of allosteric response of Lactococcus lactis prolidase and its effects on enzyme activity

The allosteric behaviour of Lactococcus lactis prolidase (Xaa-Pro dipeptidase) of this proline-specific peptidase was investigated where it was hypothesized that intersubunit interactions between a loop structure and three residues near the active site contributed to this behaviour. Seven mutant prolidases were constructed, and it was observed that the loopless mutant and His303 substitution inactivated the enzyme. Ser307 substitution revealed that this residue influenced the substrate binding, as judged from its kinetic constants and substrate specificity; however, this residue did not contribute to allostery of prolidase. R293S mutation resulted in the disappearance of the allosteric behaviour yielding a Hill constant of 0.98 while the wild type had a constant of 1.58. In addition, the R293S mutation suppressed the substrate inhibition that was observed in other mutants and wild type. The K(m) value of R293S was 2.9-fold larger and V(max) was approximately 50% less as compared to the wild type. The results indicated that Arg293 increased the affinity for substrates while introducing allosteric behaviour and substrate inhibition. Computer modelling suggested that negative charges on the loop structure interacted with Arg293 and Ser307 to maintain these characteristics. It was, therefore, concluded that Arg293, His303, Ser307 and the loop contributed to the enzyme's allosteric characteristics.

Global dynamics of newly constructed oligonucleosomes of conventional and variant H2A.Z histone

Background

Complexes of nucleosomes, which often occur in the gene promoter areas, are one of the fundamental levels of chromatin organization and thus are important for transcription regulation. Investigating the dynamic structure of a single nucleosome as well as nucleosome complexes is important for understanding transcription within chromatin. In a previous work, we highlighted the influence of histone variants on the functional dynamics of a single nucleosome using normal mode analysis developed by Bahar et al. The present work further analyzes the dynamics of nucleosome complexes (nucleosome oligomers or oligonucleosomes) such as dimer, trimer and tetramer (beads on a string model) with conventional core histones as well as with the H2A.Z histone variant using normal mode analysis.

Results

The global dynamics of oligonucleosomes reveal larger amplitude of motion within the nucleosomes that contain the H2A.Z variant with in-planar and out-of-planar fluctuations as the common mode of relaxation. The docking region of H2A.Z and the L1:L1 interactions between H2A.Z monomers of nucleosome (that are responsible for the highly stable nucleosome containing variant H2A.Z-histone) are highly dynamic throughout the first two dynamic modes.

Conclusion

Dissection of the dynamics of oligonucleosomes discloses in-plane as well as out-of-plane fluctuations as the common mode of relaxation throughout the global motions. The dynamics of individual nucleosomes and the combination of the relaxation mechanisms expressed by the individual nucleosome are quite interesting and highly dependent on the number of nucleosome fragments present in the complexes. Distortions generated by the non-planar dynamics influence the DNA conformation, and hence the histone-DNA interactions significantly alter the dynamics of the DNA. The variant H2A.Z histone is a major source of weaker intra- and inter-molecular correlations resulting in more disordered motions.

Protein mechanics: a route from structure to function

In order to better understand the mechanical properties of proteins, we have developed simulation tools which enable these properties to be analysed on a residue-by-residue basis. Although these calculations are relatively expensive with all-atom protein models, good results can be obtained much faster using coarse-grained approaches. The results show that proteins are surprisingly heterogeneous from a mechanical point of view and that functionally important residues often exhibit unusual mechanical behaviour. This finding offers a novel means for detecting functional sites and also potentially provides a route for understanding the links between structure and function in more general terms.

Locating the active sites of enzymes using mechanical properties

We have applied the calculation of mechanical properties to a dataset of almost 100 enzymes to determine the extent to which catalytic residues have distinct properties. Specifically, we have calculated force constants describing the ease of moving any given amino acid residue with respect to the other residues in the protein. The results show that catalytic residues are invariably associated with high force constants. Choosing an appropriate cutoff enables the detection of roughly 80% of catalytic residues with only 25% of false positives. It is shown that neither multidomain structures, nor the presence or absence of bound ligands hinder successful detections. It is however noted that active sites near the protein surface are more difficult to detect and that non-catalytic, but structurally key residues may also exhibit high force constants.

Packing regularities in biological structures relate to their dynamics

The high packing density inside proteins leads to certain geometric regularities and also is one of the most important contributors to the high extent of cooperativity manifested by proteins in their cohesive domain motions. The orientations between neighboring nonbonded residues in proteins substantially follow the similar geometric regularities, regardless of whether the residues are on the surface or buried, a direct result of hydrophobicity forces. These orientations are relatively fixed and correspond closely to small deformations from those of the face-centered cubic lattice, which is the way in which identical spheres pack at the highest density. Packing density also is related to the extent of conservation of residues, and we show this relationship for residue packing densities by averaging over a large sample or residue packings. There are three regimes: (1) over a broad range of packing densities the relationship between sequence entropy and inverse packing density is nearly linear, (2) over a limited range of low packing densities the sequence entropy is nearly constant, and (3) at extremely low packing densities the sequence entropy is highly variable. These packing results provide important justification for the simple elastic network models that have been shown for a large number of proteins to represent protein dynamics so successfully, even when the models are extremely coarse grained. Elastic network models for polymeric chains are simple and could be combined with these protein elastic networks to represent partially denatured parts of proteins. Finally, we show results of applications of the elastic network model to study the functional motions of the ribosome, based on its known structure. These results indicate expected correlations among its components for the step-wise processing steps in protein synthesis, and suggest ways to use these elastic network models to develop more detailed mechanisms, an important possibility because most experiments yield only static structures.

Structural dynamics of nucleosome core particle: comparison with nucleosomes containing histone variants

The present study provides insights on the dominant mechanisms of motions of the nucleosome core particle and the changes in its functional dynamics in response to histone variants. Comparative analysis of the global dynamics of nucleosomes with native and variant H2A histones, using normal mode analysis revealed that the dynamics of the nucleosome is highly symmetric, and its interaction with the nucleosomal DNA plays a vital role in its regulation. The collective dynamics of nucleosomes are predicted to be dominated by two types of large-scale motions: (1) a global stretching-compression of nucleosome along the dyad axis by which the nucleosome undergoes a breathing motion with a massive distortion of nucleosomal DNA, modulated by histone-DNA interactions; and (2) the flipping (or bending) of both the sides of the nucleosome in an out-of-plane fashion with respect to the dyad axis, originated by the highly dynamic N-termini of H3 and (H2A.Z-H2B) dimer in agreement with the experimentally observed perturbed dynamics of the particular N-terminus under physiological conditions. In general, the nucleosomes with variant histones exhibit higher mobilities and weaker correlations between internal motions compared to the nucleosome containing ordinary histones. The differences are more pronounced at the L1 and L2 loops of the respective monomers H2B and H2A, and at the N-termini of the monomers H3 and H4, all of which closely interact with the wrapping DNA.

Low-frequency normal modes that describe allosteric transitions in biological nanomachines are robust to sequence variations

By representing the high-resolution crystal structures of a number of enzymes using the elastic network model, it has been shown that only a few low-frequency normal modes are needed to describe the large-scale domain movements that are triggered by ligand binding. Here we explore a link between the nearly invariant nature of the modes that describe functional dynamics at the mesoscopic level and the large evolutionary sequence variations at the residue level. By using a structural perturbation method (SPM), which probes the residue-specific response to perturbations (or mutations), we identify a sparse network of strongly conserved residues that transmit allosteric signals in three structurally unrelated biological nanomachines, namely, DNA polymerase, myosin motor, and the Escherichia coli chaperonin. Based on the response of every mode to perturbations, which are generated by interchanging specific sequence pairs in a multiple sequence alignment, we show that the functionally relevant low-frequency modes are most robust to sequence variations. Our work shows that robustness of dynamical modes at the mesoscopic level is encoded in the structure through a sparse network of residues that transmit allosteric signals.

Allosteric communication between alpha and beta subunits of tryptophan synthase: modelling the open-closed transition of the alpha subunit

Ligand binding to the alpha-subunit of the alpha2beta2 complex of tryptophan synthase induces the alphaloop6 closure over the alpha-active site. This conformational change is associated with the formation of a hydrogen bond between alphaGly181 NH group and betaSer178 carbonyl oxygen, a key event for the triggering of intersubunit allosteric signals. Mutation of betaSer178 to Pro and alphaGly181 to Pro, Ala, Phe and Val abolishes the ligand-induced intersubunit communication. Molecular dynamics methods were applied to simulate the conformation of the highly flexible and crystallographically undetectable open state of alphaloop6 in the wild type and in the alpha181 mutants. The open conformation of alphaloop6 is favoured in the wild type enzyme in the absence of alpha-ligands, and in the alpha181 mutants both in the presence and absence of bound ligands. A very good correlation was found between the extent of limited tryptic proteolysis and both the hydrogen bond distance between alphaX181 and betaSer178, obtained from the molecular dynamics simulation, and the hydrogen bond strength, evaluated by HINT, an empirical force field that takes into account both enthalpic and entropic contributions. Comparison of the open and closed conformations of alphaloop6 suggests a pathway for substrate entrance into the alpha-active site and provides an explanation for the limited catalytic efficiency of the open state.

Investigating the local flexibility of functional residues in hemoproteins

It is now widely accepted that protein function depends not only on structure, but also on flexibility. However, the way mechanical properties contribute to catalytic mechanisms remains unclear. Here, we propose a method for investigating local flexibility within protein structures that combines a reduced protein representation with Brownian dynamics simulations. An analysis of residue fluctuations during the dynamics simulation yields a rigidity profile for the protein made up of force constants describing the ease of displacing each residue with respect to the rest of the structure. This approach has been applied to the analysis of a set of hemoproteins, one of the functionally most diverse protein families. Six proteins containing one or two heme groups have been studied, paying particular attention to the mechanical properties of the active-site residues. The calculated rigidity profiles show that active site residues are generally associated with high force constants and thus rigidly held in place. This observation also holds for diheme proteins if their mechanical properties are analyzed domain by domain. We note, however, that residues other than those in the active site can also have high force constants, as in the case of residues belonging to the folding nucleus of c-type hemoproteins.

Large-amplitude fast motions in double-stranded DNA driven by solvent thermal fluctuations

The nature of the internal dynamics of double-stranded DNA in aqueous environment remains to be established. We consider the motions to stem from thermal fluctuations/dissipations of the harmonic modes of beads (bases and sugars) in a cylindrical geometry that are tracked through the stochastic Langevin trajectories; these are characterized by parameters obtained from published data. The present approach has allowed a comparative study of the dynamics for DNA lengths in the range of 20-600 base pairs. For this range, we find that rotational motions about directions parallel to the helix axis (opening, twist) and perpendicular to it (propeller-twist, roll) contribute significantly to the dynamics. For a 20-mer at a solvent viscosity of 1 cP, the calculated fluorescence anisotropy profile exhibits a fast decay in the subnanosecond range due to large-amplitude fluctuations at the mesoscopic level. This feature reproduces the experimental behavior well, and suggests a possible way for the initiation of biological processes: they may be suddenly triggered on this scale through the occurrence of favorable thermal fluctuations. This analysis also reveals that, as is the case for a 20-mer, the dynamics of longer N-mers are dominated by internal motions, and are modulated by the viscosity of the solvent, in agreement with our previous experimental observations. Moreover, the model indicates that occurrence of partially concerted rotations of the bases due to thermal fluctuations can possibly be sustained over a DNA length of the order of 100 A at 1 ns, suggesting a possible mechanism for action-at-a-distance in transcription.

Coupling of structural fluctuations to deamidation reaction in triosephosphate isomerase by Gaussian network model

We study the structural fluctuations of triosephosphate isomerase (TIM) by an elastic model, namely, the Gaussian network model (GNM), to identify a network of coupled motions in the allosteric communication between its deamidation and catalytic sites, and the promoting motions for the deamidation activity. For this, three TIM structures have been studied: one crystal structure and two model structures designed to describe different putative models for the deamidation reaction taking place at the subunit interface. The structural fluctuations have been mapped on the functional properties; then the differences in the fluctuations between the two models in relation to the deamidation reaction have been considered. The results demonstrate that the qualitative picture of the mean-square fluctuations and the correlations between the fluctuations are similar in both, but the differences may affect the observed barrier height of the deamidation reaction. The higher packing density at regions close to deamidation sites, reflected by the high-frequency fluctuating residues in the respective regions, the stronger positive correlation between the fluctuations of the deamidation sites, and enhanced positive correlation of the primary deamidation site with the extended vicinity of the catalytic region on the juxtaposed unit promote the probability of the deamidation reaction. The results in general emphasize the importance of structural fluctuations in enzyme reactions, as well as proposing the present methodology as a plausible approach for studies on the network of coupled promoting motions in protein functions.

Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP(5)A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of (15)N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg(+2)*ATP + AMP --> Mg(+2)*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time tau( perpendicular) and low order parameters, and fast (picoseconds) motions with correlation time tau( parallel) and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP(5)A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, tau( parallel) and tau( perpendicular) are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time tau( perpendicular), is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.

Comparison of tRNA motions in the free and ribosomal bound structures

A general method is presented that allows the separation of the rigid body motions from the nonrigid body motions of structural subunits when bound in a complex. The application presented considers the motions of the tRNAs: free, bound to the ribosome and to a synthase. We observe that both the rigid body and nonrigid body motions of the structural subunits are highly controlled by the large ribosomal assembly and are important for the functional motions of the assembly. For the intact ribosome, its major parts, the 30S and the 50S subunits, are found to have counterrotational motions in the first few slowest modes, which are consistent with the experimentally observed ratchet motion. The tRNAs are found to have on average approximately 72-75% rigid body motions and principally translational motions within the first 100 slow modes of the complex. Although the three tRNAs exhibit different apparent total motions, after the rigid body motions are removed, the remaining internal motions of all three tRNAs are essentially the same. The direction of the translational motions of the tRNAs are in the same direction as the requisite translocation step, especially in the first slowest mode. Surprisingly the small intrinsically flexible mRNA has all of its internal motions completely inhibited and shows mainly a rigid-body translation in the slow modes of the ribosome complex. On the other hand, the required nonrigid body motions of the tRNA during translocation reveal that the anticodon-stem-loop, as well as the acceptor arm, of the tRNA enjoy a large mobility but act as rigid structural units. In summary, the ribosome exerts its control by enforcing rigidity in the functional parts of the tRNAs as well as in the mRNA.

iGNM: a database of protein functional motions based on Gaussian Network Model

MOTIVATION

The knowledge of protein structure is not sufficient for understanding and controlling its function. Function is a dynamic property. Although protein structural information has been rapidly accumulating in databases, little effort has been invested to date toward systematically characterizing protein dynamics. The recent success of analytical methods based on elastic network models, and in particular the Gaussian Network Model (GNM), permits us to perform a high-throughput analysis of the collective dynamics of proteins.

RESULTS

We computed the GNM dynamics for 20 058 structures from the Protein Data Bank, and generated information on the equilibrium dynamics at the level of individual residues. The results are stored on a web-based system called iGNM and configured so as to permit the users to visualize or download the results through a standard web browser using a simple search engine. Static and animated images for describing the conformational mobility of proteins over a broad range of normal modes are accessible, along with an online calculation engine available for newly deposited structures. A case study of the dynamics of 20 non-homologous hydrolases is presented to illustrate the utility of the iGNM database for identifying key residues that control the cooperative motions and revealing the connection between collective dynamics and catalytic activity.

Collective motions of RNA polymerases. Analysis of core enzyme, elongation complex and holoenzyme

The anisotropic network model (ANM), a coarse-grained normal mode analysis, is used to study the vibrational dynamics of RNA polymerases (RNAP) around the native states. The theoretical temperature factors obtained from ANM are in conformity with the experimental values for yeast and bacterial RNAP structures in free and complex forms. In the low-frequency collective modes that are related to biological function, both bacterial and yeast RNAPs with a crab claw shape display an opening/closing of the cleft due to the rigid-body motion of the clamp (bottom pincer), which has been also predicted by experiments, together with the motion of the top pincer. Even though slightly lower fluctuations are observed in the elongation complex of yeast RNAP, similar clamp motion still exists in collective modes, which should be concerted with the flexible switches and the bridge helix in driving the transcription process, pointing at the possibility of a ratchet-like mechanism. Two different bacterial holoenzyme (HE) structures are studied, which may have functional significance at different stages of transcription initiation. In a specific closed conformation of the HE, the clamp and top pincer are highly immobilized due to interactions with the sigma subunit. In contrast, the deformation of the top pincer is not inhibited in a relatively open conformation of another HE, which may help load the DNA into the cleft during transcription initiation, even though the clamp motion is still inhibited.