Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic

A skewed-momenta method to efficiently generate conformational-transition trajectories

We present a novel computational method, the skewed-momenta method (Skew'M), which applies a bias to the Maxwell distribution of initial momenta used to generate ensembles of trajectories. As a result, conformational transitions are accentuated and kinetic properties are calculated more effectively. The connection to the related puddle jumping method is discussed. A reweighting scheme permits the exact calculation of kinetic properties. Applications are presented for the rapid calculation of rate constants for molecular isomerization, and for the efficient reconstruction of free-energy profiles using a straightforward modification of the Jarzynski identity.

Allosteric transitions in the chaperonin GroEL are captured by a dominant normal mode that is most robust to sequence variations

The Escherichia coli chaperonin GroEL, which helps proteins to fold, consists of two heptameric rings stacked back-to-back. During the reaction cycle GroEL undergoes a series of allosteric transitions triggered by ligand (substrate protein, ATP, and the cochaperonin GroES) binding. Based on an elastic network model of the bullet-shaped double-ring chaperonin GroEL-(ADP)(7)-GroES structure (R''T state), we perform a normal mode analysis to explore the energetically favorable collective motions encoded in the R''T structure. By comparing each normal mode with the observed conformational changes in the R''T --> TR'' transition, a single dominant normal mode provides a simple description of this highly intricate allosteric transition. A detailed analysis of this relatively high-frequency mode describes the structural and dynamic changes that underlie the positive intra-ring and negative inter-ring cooperativity. The dynamics embedded in the dominant mode entails highly concerted structural motions with approximate preservation of sevenfold symmetry within each ring and negatively correlated ones between the two rings. The dominant normal mode (in comparison with the other modes) is robust to parametric perturbations caused by sequence variations, which validates its functional importance. Response of the dominant mode to local changes that mimic mutations using the structural perturbation method technique leads to a wiring diagram that identifies a network of key residues that regulate the allosteric transitions. Many of these residues are located in intersubunit interfaces, and may therefore play a critical role in transmitting allosteric signals between subunits.

MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape

The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.

Hinge Atlas: relating protein sequence to sites of structural flexibility

Background

Relating features of protein sequences to structural hinges is important for identifying domain boundaries, understanding structure-function relationships, and designing flexibility into proteins. Efforts in this field have been hampered by the lack of a proper dataset for studying characteristics of hinges.

Results

Using the Molecular Motions Database we have created a Hinge Atlas of manually annotated hinges and a statistical formalism for calculating the enrichment of various types of residues in these hinges.

Conclusion

We found various correlations between hinges and sequence features. Some of these are expected; for instance, we found that hinges tend to occur on the surface and in coils and turns and to be enriched with small and hydrophilic residues. Others are less obvious and intuitive. In particular, we found that hinges tend to coincide with active sites, but unlike the latter they are not at all conserved in evolution. We evaluate the potential for hinge prediction based on sequence.

Motions play an important role in catalysis and protein-ligand interactions. Hinge bending motions comprise the largest class of known motions. Therefore it is important to relate the hinge location to sequence features such as residue type, physicochemical class, secondary structure, solvent exposure, evolutionary conservation, and proximity to active sites. To do this, we first generated the Hinge Atlas, a set of protein motions with the hinge locations manually annotated, and then studied the coincidence of these features with the hinge location. We found that all of the features have bearing on the hinge location. Most interestingly, we found that hinges tend to occur at or near active sites and yet unlike the latter are not conserved. Less surprisingly, we found that hinge residues tend to be small, not hydrophobic or aliphatic, and occur in turns and random coils on the surface. A functional sequence based hinge predictor was made which uses some of the data generated in this study. The Hinge Atlas is made available to the community for further flexibility studies.

Binding induced conformational changes of proteins correlate with their intrinsic fluctuations: a case study of antibodies

Background

How antibodies recognize and bind to antigens can not be totally explained by rigid shape and electrostatic complimentarity models. Alternatively, pre-existing equilibrium hypothesis states that the native state of an antibody is not defined by a single rigid conformation but instead with an ensemble of similar conformations that co-exist at equilibrium. Antigens bind to one of the preferred conformations making this conformation more abundant shifting the equilibrium.

Results

Here, two antibodies, a germline antibody of 36–65 Fab and a monoclonal antibody, SPE7 are studied in detail to elucidate the mechanism of antibody-antigen recognition and to understand how a single antibody recognizes different antigens. An elastic network model, Anisotropic Network Model (ANM) is used in the calculations. Pre-existing equilibrium is not restricted to apply to antibodies. Intrinsic fluctuations of eight proteins, from different classes of proteins, such as enzymes, binding and transport proteins are investigated to test the suitability of the method. The intrinsic fluctuations are compared with the experimentally observed ligand induced conformational changes of these proteins. The results show that the intrinsic fluctuations obtained by theoretical methods correlate with structural changes observed when a ligand is bound to the protein. The decomposition of the total fluctuations serves to identify the different individual modes of motion, ranging from the most cooperative ones involving the overall structure, to the most localized ones.

Conclusion

Results suggest that the pre-equilibrium concept holds for antibodies and the promiscuity of antibodies can also be explained this hypothesis: a limited number of conformational states driven by intrinsic motions of an antibody might be adequate to bind to different antigens.

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.

Anharmonicity and self-similarity of the free energy landscape of protein G

The near-native free-energy landscape of protein G is investigated through 0.4-micros-long atomistic molecular dynamics simulations in an explicit solvent. A theoretical and computational framework is used to assess the time dependence of salient thermodynamical features. While the quasiharmonic character of the free energy is found to degrade in a few ns, the slow modes display a very mild dependence on the trajectory duration. This property originates from a striking self-similarity of the free-energy landscape embodied by the consistency of the principal directions of the local minima, where the system dwells for several ns, and of the virtual jumps connecting them.

Modular architecture of protein structures and allosteric communications: potential implications for signaling proteins and regulatory linkages

BACKGROUND

Allosteric communications are vital for cellular signaling. Here we explore a relationship between protein architectural organization and shortcuts in signaling pathways.

RESULTS

We show that protein domains consist of modules interconnected by residues that mediate signaling through the shortest pathways. These mediating residues tend to be located at the inter-modular boundaries, which are more rigid and display a larger number of long-range interactions than intra-modular regions. The inter-modular boundaries contain most of the residues centrally conserved in the protein fold, which may be crucial for information transfer between amino acids. Our approach to modular decomposition relies on a representation of protein structures as residue-interacting networks, and removal of the most central residue contacts, which are assumed to be crucial for allosteric communications. The modular decomposition of 100 multi-domain protein structures indicates that modules constitute the building blocks of domains. The analysis of 13 allosteric proteins revealed that modules characterize experimentally identified functional regions. Based on the study of an additional functionally annotated dataset of 115 proteins, we propose that high-modularity modules include functional sites and are the basic functional units. We provide examples (the Galphas subunit and P450 cytochromes) to illustrate that the modular architecture of active sites is linked to their functional specialization.

CONCLUSION

Our method decomposes protein structures into modules, allowing the study of signal transmission between functional sites. A modular configuration might be advantageous: it allows signaling proteins to expand their regulatory linkages and may elicit a broader range of control mechanisms either via modular combinations or through modulation of inter-modular linkages.

Interpreting Correlated Motions Using Normal Mode Analysis

With the increased popularity of normal mode analyses in structural biology, it is important to carefully consider how to best utilize the results for gaining biological insights without over interpretation. The discussion in this article argues that for the purpose of identifying correlated motions in biomolecules, a case separate from concomitant conformational changes of structural motifs, it is generally important to use a large number of normal modes. This is illustrated through three increasingly complex examples. The simplest case includes two bilinearly coupled harmonic oscillators and serves as a straightforward problem where the important considerations are explicit and transparent. The argument is then generalized to include a system of N-coupled harmonic oscillators and finally to a realistic biomolecule. Although a small number of normal modes are useful for probing structural flexibility, it is clear that a much larger number of modes are required for properly investigating correlated motions in biomolecules.

Flexible fitting in 3D-EM with incomplete data on superfamily variability

We present a substantial improvement of S-flexfit, our recently proposed method for flexible fitting in three dimensional electron microscopy (3D-EM) at a resolution range of 8-12A, together with a comparison of the method capabilities with Normal Mode Analysis (NMA), application examples and a user's guide. S-flexfit uses the evolutionary information contained in protein domain databases like CATH, by means of the structural alignment of the elements of a protein superfamily. The added development is based on a recent extension of the Singular Value Decomposition (SVD) algorithm specifically designed for situations with missing data: Incremental Singular Value Decomposition (ISVD). ISVD can manage gaps and allows considering more aminoacids in the structural alignment of a superfamily, extending the range of application and producing better models for the fitting step of our methodology. Our previous SVD-based flexible fitting approach can only take into account positions with no gaps in the alignment, being appropriate when the superfamily members are relatively similar and there are few gaps. However, with new data coming from structural proteomics works, the later situation is becoming less likely, making ISVD the technique of choice for further works. We present the results of using ISVD in the process of flexible fitting with both simulated and experimental 3D-EM maps (GroEL and Poliovirus 135S cell entry intermediate).

Hierarchical and multi-resolution representation of protein flexibility

MOTIVATION

Conformational rearrangements during molecular interactions are observed in a wide range of biological systems. However, computational methods that aim at simulating and predicting molecular interactions are still largely ignoring the flexible nature of biological macromolecules as the number of degrees of freedom is computationally intractable when using brute force representations.

RESULTS

In this article, we present a computational data structure called the Flexibility Tree (FT) that enables a multi-resolution and hierarchical encoding of molecular flexibility. This tree-like data structure allows the encoding of relatively small, yet complex sub-spaces of a protein's conformational space. These conformational sub-spaces are parameterized by a small number of variables and can be searched efficiently using standard global search techniques. The FT structure makes it straightforward to combine and nest a wide variety of motion types such as hinge, shear, twist, screw, rotameric side chains, normal modes and essential dynamics. Moreover, the ability to assign shapes to the nodes in a FT allows the interactive manipulation of flexible protein shapes and the interactive visualization of the impact of conformational changes on the protein's overall shape. We describe the design of the FT and illustrate the construction of such trees to hierarchically combine motion information obtained from a variety of sources ranging from experiment to user intuition, and describing conformational changes at different biological scales. We show that the combination of various types of motion helps refine the encoded conformational sub-spaces to include experimentally determined structures, and we demonstrate searching these sub-spaces for specific conformations.

NOMAD-Ref: visualization, deformation and refinement of macromolecular structures based on all-atom normal mode analysis

Normal mode analysis (NMA) is an efficient way to study collective motions in biomolecules that bypasses the computational costs and many limitations associated with full dynamics simulations. The NOMAD-Ref web server presented here provides tools for online calculation of the normal modes of large molecules (up to 100 000 atoms) maintaining a full all-atom representation of their structures, as well as access to a number of programs that utilize these collective motions for deformation and refinement of biomolecular structures. Applications include the generation of sets of decoys with correct stereochemistry but arbitrary large amplitude movements, the quantification of the overlap between alternative conformations of a molecule, refinement of structures against experimental data, such as X-ray diffraction structure factors or Cryo-EM maps and optimization of docked complexes by modeling receptor/ligand flexibility through normal mode motions. The server can be accessed at the URL .

Anisotropic network model: systematic evaluation and a new web interface

MOTIVATION

The Anisotropic Network Model (ANM) is a simple yet powerful model for normal mode analysis of proteins. Despite its broad use for exploring biomolecular collective motions, ANM has not been systematically evaluated to date. A lack of a convenient interface has been an additional obstacle for easy usage.

RESULTS

ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability. Residue fluctuations in globular proteins are shown to be more accurately predicted than those in nonglobular proteins, and core residues are more accurately described than solvent-exposed ones. Significant improvement in agreement with experiments is observed with increase in the resolution of the examined structure. A new server for ANM calculations is presented, which offers flexible options for controlling model parameters and output formats, interactive animation of collective modes and advanced graphical features.

AVAILABILITY

ANM server (http://www.ccbb.pitt.edu/anm)

Multiple-basin energy landscapes for large-amplitude conformational motions of proteins: Structure-based molecular dynamics simulations

Biomolecules often undergo large-amplitude motions when they bind or release other molecules. Unlike macroscopic machines, these biomolecular machines can partially disassemble (unfold) and then reassemble (fold) during such transitions. Here we put forward a minimal structure-based model, the "multiple-basin model," that can directly be used for molecular dynamics simulation of even very large biomolecular systems so long as the endpoints of the conformational change are known. We investigate the model by simulating large-scale motions of four proteins: glutamine-binding protein, S100A6, dihydrofolate reductase, and HIV-1 protease. The mechanisms of conformational transition depend on the protein basin topologies and change with temperature near the folding transition. The conformational transition rate varies linearly with driving force over a fairly large range. This linearity appears to be a consequence of partial unfolding during the conformational transition.

The role of protein dynamics in thymidylate synthase catalysis: variants of conserved 2'-deoxyuridine 5'-monophosphate (dUMP)-binding Tyr-261

The enzyme thymidylate synthase (TS) catalyzes the reductive methylation of 2'-deoxyuridine 5'-monophosphate (dUMP) to 2'-deoxythymidine 5'-monophosphate. Using kinetic and X-ray crystallography experiments, we have examined the role of the highly conserved Tyr-261 in the catalytic mechanism of TS. While Tyr-261 is distant from the site of methyl transfer, mutants at this position show a marked decrease in enzymatic activity. Given that Tyr-261 forms a hydrogen bond with the dUMP 3'-O, we hypothesized that this interaction would be important for substrate binding, orientation, and specificity. Our results, surprisingly, show that Tyr-261 contributes little to these features of the mechanism of TS. However, the residue is part of the structural core of closed ternary complexes of TS, and conservation of the size and shape of the Tyr side chain is essential for maintaining wild-type values of kcat/Km. Moderate increases in Km values for both the substrate and cofactor upon mutation of Tyr-261 arise mainly from destabilization of the active conformation of a loop containing a dUMP-binding arginine. Besides binding dUMP, this loop has a key role in stabilizing the closed conformation of the enzyme and in shielding the active site from the bulk solvent during catalysis. Changes to atomic vibrations in crystals of a ternary complex of Escherichia coli Tyr261Trp are associated with a greater than 2000-fold drop in kcat/Km. These results underline the important contribution of dynamics to catalysis in TS.

Modeling activated states of GPCRs: the rhodopsin template

Activation of G Protein-Coupled Receptors (GPCRs) is an allosteric mechanism triggered by ligand binding and resulting in conformational changes transduced by the transmembrane domain. Models of the activated forms of GPCRs have become increasingly necessary for the development of a clear understanding of signal propagation into the cell. Experimental evidence points to a multiplicity of conformations related to the activation of the receptor, rendered important physiologically by the suggestion that different conformations may be responsible for coupling to different signaling pathways. In contrast to the inactive state of rhodopsin (RHO) for which several high quality X-ray structures are available, the structure-related information for the active states of rhodopsin and all other GPCRs is indirect. We have collected and stored such information in a repository we maintain for activation-specific structural data available for rhodopsin-like GPCRs, http://www.physiology.med.cornell.edu/GPCRactivation/gpcrindex.html . Using these data as structural constraints, we have applied Simulated Annealing Molecular Dynamics to construct a number of different active state models of RHO starting from the known inactive structure. The common features of the models indicate that TM3 and TM5 play an important role in activation, in addition to the well-established rearrangement of TM6. Some of the structural changes observed in these models occur in regions that were not involved in the constraints, and have not been previously tested experimentally; they emerge as interesting candidates for further experimental exploration of the conformational space of activated GPCRs. We show that none of the normal modes calculated from the inactive structure has a dominant contribution along the path of conformational rearrangement from inactive to the active forms of RHO in the models. This result may differentiate rhodopsin from other GPCRs, and the reasons for this difference are discussed in the context of the structural properties and the physiological function of the protein.

Identifying sequence regions undergoing conformational change via predicted continuum secondary structure

MOTIVATION

Conformational flexibility is essential to the function of many proteins, e.g. catalytic activity. To assist efforts in determining and exploring the functional properties of a protein, it is desirable to automatically identify regions that are prone to undergo conformational changes. It was recently shown that a probabilistic predictor of continuum secondary structure is more accurate than categorical predictors for structurally ambivalent sequence regions, suggesting that such models are suited to characterize protein flexibility.

RESULTS

We develop a computational method for identifying regions that are prone to conformational change directly from the amino acid sequence. The method uses the entropy of the probabilistic output of an 8-class continuum secondary structure predictor. Results for 171 unique amino acid sequences with well-characterized variable structure (identified in the 'Macromolecular movements database') indicate that the method is highly sensitive at identifying flexible protein regions, but false positives remain a problem. The method can be used to explore conformational flexibility of proteins (including hypothetical or synthetic ones) whose structure is yet to be determined experimentally.

AVAILABILITY

The predictor, sequence data and supplementary studies are available at http://pprowler.itee.uq.edu.au/sspred/ and are free for academic use.

Flexibility in a drug transport accessory protein: molecular dynamics simulations of MexA

Drug resistance in gram-negative bacteria may be conferred via efflux through a tripartite complex of an inner membrane pump, an outer membrane pore, and a periplasmic adaptor protein. These are AcrB, TolC, and AcrA, respectively, in Escherichia coli. In Pseudomonas aerugonisa, their homologs are MexB, OprM, and MexA. Defining the interdomain dynamics of the adaptor protein is essential to understanding the mechanism of complex formation. Extended (25 ns) molecular dynamics simulations of MexA have been performed to determine such interdomain dynamics. Analysis of conformational drift demonstrates substantial motions of the three domains of MexA relative to one another. Principal components analysis reveals a hinge-bending motion and rotation of the alpha-helical hairpin relative to the other domains to be the two dominant motions. These two motions provide an element of considerable flexibility which is likely to be exploited in the adaptor function of MexA.

A method for finding candidate conformations for molecular replacement using relative rotation between domains of a known structure

This paper presents a methodology to obtain candidate conformations of multidomain proteins for use in molecular replacement. For each separate domain, the orientational relationship between the template and the target structure is obtained using standard molecular replacement. The orientational relationships of the domains are then used to calculate the relative rotation between the domains in the target conformation by using pose-estimation techniques from the field of robotics and computer vision. With the angle of relative rotation between the domains as a cost function, iterative normal-mode analysis is used to drive the template structure to a candidate conformation that matches the X-ray crystallographic data obtained for the target conformation. The selection of the correct intra-protein domain orientations from among the many spurious maxima in the rotation function (including orientations obtained from domains in symmetry mates rather than within the same copy of the protein) presents a challenge. This problem is resolved by checking R factors of each domain, measuring the absolute value of relative rotation between domains, and evaluating the cost value after each candidate conformation is driven to convergence with iterative NMA. As a validation, the proposed method is applied to three test proteins: ribose-binding protein, lactoferrin and calcium ATPase. In each test case, the orientation and translation of the final candidate conformation in the unit cell are generated correctly from the suggested procedure. The results show that the proposed method can yield viable candidate conformations for use in molecular replacement and can reveal the structural details and pose of the target conformation in the crystallographic unit cell.

The Database of Macromolecular Motions: new features added at the decade mark

The database of molecular motions, MolMovDB (), has been in existence for the past decade. It classifies macromolecular motions and provides tools to interpolate between two conformations (the Morph Server) and predict possible motions in a single structure. In 2005, we expanded the services offered on MolMovDB. In particular, we further developed the Morph Server to produce improved interpolations between two submitted structures. We added support for multiple chains to the original adiabatic mapping interpolation, allowing the analysis of subunit motions. We also added the option of using FRODA interpolation, which allows for more complex pathways, potentially overcoming steric barriers. We added an interface to a hinge prediction service, which acts on single structures and predicts likely residue points for flexibility. We developed tools to relate such points of flexibility in a structure to particular key residue positions, i.e. active sites or highly conserved positions. Lastly, we began relating our motion classification scheme to function using descriptions from the Gene Ontology Consortium.

Functional modes of proteins are among the most robust

It is shown that a small subset of modes which are likely to be involved in protein functional motions of large amplitude can be determined by retaining the most robust normal modes obtained using different protein models. This result should prove helpful in the context of several applications proposed recently, like for solving difficult molecular replacement problems or for fitting atomic structures into low-resolution electron density maps. It may also pave the way for the development of methods allowing us to predict such motions accurately.

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.

The Allosteric Mechanism of Yeast Chorismate Mutase: A Dynamic Analysis

The effector-regulated allosteric mechanism of yeast chorismate mutase (YCM) was studied by normal mode analysis and targeted molecular dynamics. The normal mode analysis shows that the conformational change between YCM in the R state and in the T state can be represented by a relatively small number of low-frequency modes. This suggests that the transition is coded in the structure and is likely to have a low energetic barrier. Quantitative comparisons (i.e. frequencies) between the low-frequency modes of YCM with and without effectors (modeled structures) reveal that the binding of Trp increases the global flexibility, whereas Tyr decreases global flexibility. The targeted molecular dynamics simulation of substrate analog release from the YCM active site suggests that a series of residues are critical for orienting and "recruiting" the substrate. The simulation led to the switching of a series of substrate-release-coupled salt-bridge partners in the ligand-binding domain; similar changes occur in the transition between YCM R-state and T-state crystal structures. Thus, the normal mode analysis and targeted molecular dynamics results provide evidence that the effectors regulate YCM activity by influencing the global flexibility. The change in flexibility is coupled to the binding of substrate to the T state and release of the product from the R state, respectively.

Normal mode analysis of the horseradish peroxidase collective motions: Correlation with spectroscopically observed heme distortions

Horseradish peroxidase C is a class III peroxidase whose structure is stabilized by the presence of two endogenous calcium atoms. Calcium removal has been shown to decrease the enzymatic activity of the enzyme and significantly affect the spectroscopically detectable properties of the heme, such as the spin state of the iron, heme normal modes, and distortions from planarity. In this work, we report on normal mode analysis (NMA) performed on models subjected to 2 ns of molecular dynamics simulations to describe the effect of calcium removal on protein collective motions and to investigate the correlation between active site (heme) and protein matrix fluctuations. We show that in the native peroxidase model, heme fluctuations are correlated to matrix fluctuations while they are not in the calcium-depleted model.

Rotation of DNA around intact strand in human topoisomerase I implies distinct mechanisms for positive and negative supercoil relaxation

Topoisomerases are enzymes of quintessence to the upkeep of superhelical DNA, and are vital for replication, transcription and recombination. An atomic-resolution model for human topoisomerase I in covalent complex with DNA is simulated using molecular dynamics with external potentials that mimic torque and bias the DNA duplex downstream of a single-strand cut to rotate around the intact strand, according to the prevailing enzymatic mechanism. The simulations reveal the first dynamical picture of how topoisomerase accommodates large-scale motion of DNA as it changes its supercoiling state, and indicate that relaxation of positive and negative supercoils are fundamentally different. To relax positive supercoils, two separate domains (the 'lips') of the protein open up by about 10-14 A, whereas to relax negative supercoils, a continuous loop connecting the upper and lower parts (and which was a hinge for opening the lips) stretches about 12 A while the lips remain unseparated. Normal mode analysis is additionally used to characterize the functional flexibility of the protein. Remarkably, the same combination of low-frequency eigenvectors exhibit the dominant contribution for both rotation mechanisms through a see-saw motion. The simulated mechanisms suggest mutations to control the relaxation of either type of supercoiling selectively and advance a hypothesis for the debated role of the N-terminal domain in supercoil relaxation.

Coupled protein domain motion in Taq polymerase revealed by neutron spin-echo spectroscopy

Long-range conformational changes in proteins are ubiquitous in biology for the transmission and amplification of signals; such conformational changes can be triggered by small-amplitude, nanosecond protein domain motion. Understanding how conformational changes are initiated requires the characterization of protein domain motion on these timescales and on length scales comparable to protein dimensions. Using neutron spin-echo spectroscopy (NSE), normal mode analysis, and a statistical-mechanical framework, we reveal overdamped, coupled domain motion within DNA polymerase I from Thermus aquaticus (Taq polymerase). This protein utilizes correlated domain dynamics over 70 angstroms to coordinate nucleotide synthesis and cleavage during DNA synthesis and repair. We show that NSE spectroscopy can determine the domain mobility tensor, which determines the degree of dynamical coupling between domains. The mobility tensor defines the domain velocity response to a force applied to it or to another domain, just as the sails of a sailboat determine its velocity given the applied wind force. The NSE results provide insights into the nature of protein domain motion that are not appreciated by conventional biophysical techniques.

A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information

A sparser but more efficient connection rule (called a bond-cutoff method) for a simplified alpha-carbon coarse-grained elastic network model is presented. One of conventional connection rules for elastic network models is the distance-cutoff method, where virtual springs connect an alpha-carbon with all neighbor alpha-carbons within predefined distance-cutoff value. However, though the maximum interaction distance between alpha-carbons is reported as 7 angstroms, this cutoff value can make the elastic network unstable in many cases of protein structures. Thus, a larger cutoff value (>11 angstroms) is often used to establish a stable elastic network model in previous researches. To overcome this problem, a connection rule for backbone model is proposed, which satisfies the minimum condition to stabilize an elastic network. Based on the backbone connections, each type of chemical interactions is considered and added to the elastic network model: disulfide bonds, hydrogen bonds, and salt-bridges. In addition, the van der Waals forces between alpha-carbons are modeled by using the distance-cutoff method. With the proposed connection rule, one can make an elastic network model with less than 7 angstroms distance cutoff, which can reveal protein flexibility more sharply. Moreover, the normal modes from the new elastic network model can reflect conformational changes of a given protein better than ones by the distance-cutoff method. This method can save the computational cost when calculating normal modes of a given protein structure, because it can reduce the total number of connections. As a validation, six example proteins are tested. Computational times and the overlap values between the conformational change and infinitesimal motion calculated by normal mode analysis are presented. Those animations are also available at UMass Morph Server (http://biomechanics.ecs.umass.edu/umms.html).

Comparative molecular dynamics-Similar folds and similar motions?

Proteins possessing the same fold may undergo similar motions, particularly if these motions involve large conformational transitions. The increasing amounts of structural data provide a useful starting point with which to test this hypothesis. We have performed a total of 0.29 micros of molecular dynamics across a series of proteins within the same fold family (periplasmic binding proteinlike) in order to address to what extent similarity of motion exists. Analysis of the local conformational space on these timescales (10-20 ns) revealed that the behavior of the proteins could be readily distinguished between an apo-state and a ligand-bound state. Moreover, analysis of the root-mean-square fluctuations reveals that the presence of the ligand exerts a stabilizing effect on the protein, with similar motions occurring, but with reduced magnitude. Furthermore, the conformational space in the presence of the ligand appears to be dictated by sequence but not by the type of ligand present. In contrast, apo-simulations showed considerable overlap of conformational space across the fold as a result of their ability to undergo larger fluctuations. Indeed, we observed several transitions from different simulations between states corresponding to the closed-cleft and open-cleft forms of the fold, with the predominant motions being conserved across the different proteins. Thus, large-scale conformational changes do indeed appear to be conserved across this fold architecture, but smaller conformational motions appear to reflect the differences in sequence and local fold.

Usefulness and limitations of normal mode analysis in modeling dynamics of biomolecular complexes

Various types of large-amplitude molecular deformation are ubiquitously involved in the functions of biological macromolecules, especially supramolecular complexes. They can be very effectively analyzed by normal mode analysis with well-established procedures. However, despite its enormous success in numerous applications, certain issues related to the applications of normal mode analysis require further discussion. In this review, the author addresses some common issues so as to raise the awareness of the usefulness and limitations of the method in the general community of structural biology.

Comparison of mode analyses at different resolutions applied to nucleic acid systems

More than two decades of different types of mode analyses has shown that these techniques can be useful in describing large-scale motions in protein systems. A number of mode analyses are available and include quasiharmonics, classical normal mode, block normal mode, and the elastic network model. Each of these methods has been validated for protein systems and this variety allows researchers to choose the technique that gives the best compromise between computational cost and the level of detail in the calculation. These same techniques have not been systematically tested for nucleic acid systems, however. Given the differences in interactions and structural features between nucleic acid and protein systems, the validity of these techniques in the protein regime cannot be directly translated into validity in the nucleic acid realm. In this work, we investigate the usefulness of the above mode analyses as applied to two RNA systems, i.e., the hammerhead ribozyme and a guanine riboswitch. We show that classical normal-mode analysis can match the magnitude and direction of residue fluctuations from the more detailed, anharmonic technique, quasiharmonic analysis of a molecular dynamics trajectory. The block normal-mode approximation is shown to hold in the nucleic acid systems studied. Only the mode analysis at the lowest level of detail, the elastic network model, produced mixed results in our calculations. We present data that suggest that the elastic network model, with the popular parameterization, is not best suited for systems that do not have a close packed structure; this observation also hints at why the elastic network model has been found to be valid for many globular protein systems. The different behaviors of block normal-mode analysis and the elastic network model, which invoke similar degrees of coarse-graining to the dynamics but use different potentials, suggest the importance of applying a heterogeneous potential function in a robust analysis of the dynamics of biomolecules, especially those that are not closely packed. In addition to these comparisons, we briefly discuss insights into the conformational space available to the hammerhead ribozyme.

Refinement of docked protein-ligand and protein-DNA structures using low frequency normal mode amplitude optimization

Prediction of structural changes resulting from complex formation, both in ligands and receptors, is an important and unsolved problem in structural biology. In this work, we use all-atom normal modes calculated with the Elastic Network Model as a basis set to model structural flexibility during formation of macromolecular complexes and refine the non-bonded intermolecular energy between the two partners (protein–ligand or protein–DNA) along 5–10 of the lowest frequency normal mode directions. The method handles motions unrelated to the docking transparently by first applying the modes that improve non-bonded energy most and optionally restraining amplitudes; in addition, the method can correct small errors in the ligand position when the first six rigid-body modes are switched on. For a test set of six protein receptors that show an open-to-close transition when binding small ligands, our refinement scheme reduces the protein coordinate cRMS by 0.3–3.2 Å. For two test cases of DNA structures interacting with proteins, the program correctly refines the docked B-DNA starting form into the expected bent DNA, reducing the DNA cRMS from 8.4 to 4.8 Å and from 8.7 to 5.4 Å, respectively. A public web server implementation of the refinement method is available at .

The role of shape in determining molecular motions

We examined the role of molecular shape in determining the patterns of low-frequency deformational motions of biological macromolecules. The low-frequency subspace of eigenvectors in normal mode analysis was found to be robustly similar upon randomization of the Hessian matrix elements as long as the structure of the matrix is maintained, which indicates that the global shape of molecules plays a more dominant role in determining the highly anisotropic low-frequency motions than the absolute values of stiffness and directionality of local interactions. The results provided a quantitative foundation for the validity of elastic normal mode analysis.

Normal modes for predicting protein motions: a comprehensive database assessment and associated Web tool

We carry out an extensive statistical study of the applicability of normal modes to the prediction of mobile regions in proteins. In particular, we assess the degree to which the observed motions found in a comprehensive data set of 377 nonredundant motions can be modeled by a single normal-mode vibration. We describe each motion in our data set by vectors connecting corresponding atoms in two crystallographically known conformations. We then measure the geometric overlap of these motion vectors with the displacement vectors of the lowest-frequency mode, for one of the conformations. Our study suggests that the lowest mode contains useful information about the parts of a protein that move most (i.e., have the largest amplitudes) and about the direction of this movement. Based on our findings, we developed a Web tool for motion prediction (available from http://molmovdb.org/nma) and apply it here to four representative motions--from bacteriorhodopsin, calmodulin, insulin, and T7 RNA polymerase.

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.

Normal mode analysis suggests a quaternary twist model for the nicotinic receptor gating mechanism

We present a three-dimensional model of the homopentameric alpha7 nicotinic acetylcholine receptor (nAChR), that includes the extracellular and membrane domains, developed by comparative modeling on the basis of: 1), the x-ray crystal structure of the snail acetylcholine binding protein, an homolog of the extracellular domain of nAChRs; and 2), cryo-electron microscopy data of the membrane domain collected on Torpedo marmorata nAChRs. We performed normal mode analysis on the complete three-dimensional model to explore protein flexibility. Among the first 10 lowest frequency modes, only the first mode produces a structural reorganization compatible with channel gating: a wide opening of the channel pore caused by a concerted symmetrical quaternary twist motion of the protein with opposing rotations of the upper (extracellular) and lower (transmembrane) domains. Still, significant reorganizations are observed within each subunit, that involve their bending at the domain interface, an increase of angle between the two beta-sheets composing the extracellular domain, the internal beta-sheet being significantly correlated to the movement of the M2 alpha-helical segment. This global symmetrical twist motion of the pentameric protein complex, which resembles the opening transition of other multimeric ion channels, reasonably accounts for the available experimental data and thus likely describes the nAChR gating process.

Protein structural change upon ligand binding: linear response theory

A simple formula based on linear response theory is proposed to explain and predict the structural change of proteins upon ligand binding. By regarding ligand binding as an external perturbation, the structural change as a response is described by atomic fluctuations in the ligand-free form and the protein-ligand interactions. The results for three protein systems of various sizes are consistent with the observations in the crystal structures, confirming the validity of the linear relationship between the equilibrium fluctuations and the structural change upon ligand binding.

Identification of Dynamical Correlations within the Myosin Motor Domain by the Normal Mode Analysis of an Elastic Network Model

In order to systematically analyze functionally relevant dynamical correlations within macromolecular complexes, we have developed computational methods based on the normal mode analysis of an elastic network model. First, we define two types of dynamical correlations (fluctuation-based and density-based), which are computed by summing up contributions from all low-frequency normal modes up to a given cutoff. Then we use them to select dynamically important "hinge residues" whose elastic distortion affects the fluctuations of a large number of residues. Second, in order to clarify long-range dynamical correlations, we decompose the dynamical correlations to individual normal modes to identify the most relevant modes. We have applied these methods to the analysis of the motor domain of Dictyostelium myosin and have obtained the following three interesting results that shed light on its mechanism of force generation: first, we find the hinge residues are distributed over several key inter-subdomain joints (including the nucleotide-binding pocket, the relay helix, the SH1 helix, the strut between the upper 50 kDa and the lower 50 kDa subdomains), which is consistent with their hypothesized roles in modulating functionally relevant inter-subdomain conformational changes; second, a single mode 7 (for structure 1VOM) is found to dominate the fluctuation-based correlations between the converter/strut and the nucleotide-binding pocket, revealing a surprising simplicity for their intriguing roles in the force generation mechanism; finally, we find a negative density-based correlation between the strut and the nucleotide-binding pocket, which is consistent with the hypothesized signaling pathway that links the actin-binding site's opening/closing with the nucleotide-binding pocket's closing/opening.

Predictions of protein flexibility: first-order measures

The normal modes of a molecule are utilized, in conjunction with classical conformal vector field theory, to define a function that measures the capability of the molecule to deform at each of its residues. An efficient algorithm is presented to calculate the local chain deformability from the set of normal modes of vibration. This is done by considering each mode as an off-grid sample of a deformation vector field. Predictions of deformability are compared with experimental data in the form of dihedral angle differences between two conformations of ten kinases by using a modified correlation function. Deformability calculations correlate well with experimental results and validate the applicability of this method to protein flexibility predictions.

An analysis of core deformations in protein superfamilies

An analysis is presented on how structural cores modify their shape across homologous proteins, and whether or not a relationship exists between these structural changes and the vibrational normal modes that proteins experience as a result of the topological constraints imposed by the fold. A set of 35 representative, well-populated protein families is studied. The evolutionary directions of deformation are obtained by using multiple structural alignments to superimpose the structures and extract a conserved core, together with principal components analysis to extract the main deformation modes from the three-dimensional superimposition. In parallel, a low-resolution normal mode analysis technique is employed to study the properties of the mechanical core plasticity of these same families. We show that the evolutionary deformations span a low dimensional space of 4-5 dimensions on average. A statistically significant correspondence exists between these principal deformations and the approximately 20 slowest vibrational modes accessible to a particular topology. We conclude that, to a significant extent, the structural response of a protein topology to sequence changes takes place by means of collective deformations along combinations of a small number of low-frequency modes. The findings have implications in structure prediction by homology modeling.

Evolutionary epitopes of Hsp90 and p23: implications for their interaction

The amino-terminal domain (N-domain) of Hsp90 represents the ATP binding site and is important for interaction with its cochaperone, p23. Whereas some evidence suggests that p23 may bind to this domain in an ATP-dependent manner and that this process requires the dimerization of two N-domains, the interaction sites between them and the molecular mechanism of coupling these two events to p23 binding remain unsolved. As a first step toward establishing the interaction mechanism, we used the evolutionary tracing (ET) method [Lichtarge, O., Bourne, H. R., and Cohen, F. E. (1996) J. Mol. Biol. 257, 342-358] to identify the putative functional surfaces of Hsp90 and p23, and combined with protein-protein docking techniques, to predict their binding interface. Both evolutionarily privileged surfaces of Hsp90 and p23 identified by ET appear on this putative interface. An analysis of the complex model produced using the ET results combined with available experimental data highlights a putative conformational pathway in the ATP binding domain of Hsp90, where a series of conformational changes transfer the ATP-induced N-domain dimerization signal for the binding of p23. In this pathway, the closure of "lid" may result in reorientation of the helix alpha1 and the following loop (residues 10-27 in yeast Hsp90), which will expose more hydrophobic surface, and thus triggers the dimerization of N-domain.

Global ribosome motions revealed with elastic network model

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at.

MoViES: molecular vibrations evaluation server for analysis of fluctuational dynamics of proteins and nucleic acids

Analysis of vibrational motions and thermal fluctuational dynamics is a widely used approach for studying structural, dynamic and functional properties of proteins and nucleic acids. Development of a freely accessible web server for computation of vibrational and thermal fluctuational dynamics of biomolecules is thus useful for facilitating the relevant studies. We have developed a computer program for computing vibrational normal modes and thermal fluctuational properties of proteins and nucleic acids and applied it in several studies. In our program, vibrational normal modes are computed by using modified AMBER molecular mechanics force fields, and thermal fluctuational properties are computed by means of a self-consistent harmonic approximation method. A web version of our program, MoViES (Molecular Vibrations Evaluation Server), was set up to facilitate the use of our program to study vibrational dynamics of proteins and nucleic acids. This software was tested on selected proteins, which show that the computed normal modes and thermal fluctuational bond disruption probabilities are consistent with experimental findings and other normal mode computations. MoViES can be accessed at http://ang.cz3.nus.edu.sg/cgi-bin/prog/norm.pl.

ElNemo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement

Normal mode analysis (NMA) is a powerful tool for predicting the possible movements of a given macromolecule. It has been shown recently that half of the known protein movements can be modelled by using at most two low-frequency normal modes. Applications of NMA cover wide areas of structural biology, such as the study of protein conformational changes upon ligand binding, membrane channel opening and closure, potential movements of the ribosome, and viral capsid maturation. Another, newly emerging field of NMA is related to protein structure determination by X-ray crystallography, where normal mode perturbed models are used as templates for diffraction data phasing through molecular replacement (MR). Here we present ElNémo, a web interface to the Elastic Network Model that provides a fast and simple tool to compute, visualize and analyse low-frequency normal modes of large macro-molecules and to generate a large number of different starting models for use in MR. Due to the 'rotation-translation-block' (RTB) approximation implemented in ElNémo, there is virtually no upper limit to the size of the proteins that can be treated. Upon input of a protein structure in Protein Data Bank (PDB) format, ElNémo computes its 100 lowest-frequency modes and produces a comprehensive set of descriptive parameters and visualizations, such as the degree of collectivity of movement, residue mean square displacements, distance fluctuation maps, and the correlation between observed and normal-mode-derived atomic displacement parameters (B-factors). Any number of normal mode perturbed models for MR can be generated for download. If two conformations of the same (or a homologous) protein are available, ElNémo identifies the normal modes that contribute most to the corresponding protein movement. The web server can be freely accessed at http://igs-server.cnrs-mrs.fr/elnemo/index.html.

Statistical and visual morph movie analysis of crystallographic mutant selection bias in protein mutation resource data

Structural studies of the effects of non-silent mutations on protein conformational change are an important key in deciphering the language that relates protein amino acid primary structure to tertiary structure. Elsewhere, we presented the Protein Mutant Resource (PMR) database, a set of online tools that systematically identified groups of related mutant structures in the Protein DataBank (PDB), accurately inferred mutant classifications in the Gene Ontology using an innovative, statistically rigorous data-mining algorithm with more general applicability, and illustrated the relationship of these mutant structures via an intuitive user interface. Here, we perform a comprehensive statistical analysis of the effect of PMR mutations on protein tertiary structure. We find that, although the PMR does contain spectacular examples of conformational change, in general there is a counter-intuitive inverse relationship between conformational change (measured as C-alpha displacement or RMS of the core structure) and the number of mutations in a structure. That is, point mutations by structural biologists present in the PDB contrast naturally evolved mutations. We compare the frequency of mutations in the PMR/PDB datasets against the accepted PAM250 natural amino acid mutation frequency to confirm these observations. We generated morph movies from PMR structure pairs using technology previously developed for the Macromolecular Motions Database (http://molmovdb.org), allowing bioinformaticians, geneticists, protein engineers, and rational drug designers to analyze visually the mechanisms of protein conformational change and distinguish between conformational change due to motions (e.g., ligand binding) and mutations. The PMR morph movies and statistics can be freely viewed from the PMR website, http://pmr.sdsc.edu.

On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models

As more and more structures of macromolecular complexes get solved in different conditions, it has become apparent that flexibility is an inherent part of their biological function. Normal mode analysis using simplified models of proteins such as the elastic network model has proved very effective in showing that many of the structural transitions derived from a survey of the Protein Data Bank can be explained by just a few of the lowest-frequency normal modes. In this work, normal modes are used to carry out medium- or low-resolution structural refinement, enforcing collective and large-amplitude movements that are beyond the reach of existing methods. Refinement is carried out in reciprocal space with respect to the normal mode amplitudes, by using standard conjugate-gradient minimization. Several tests on synthetic diffraction data whose mode concentration follows the one of real movements observed in the Protein Data Bank have shown that the radius of convergence is larger than the one of rigid-body refinement. Tests with experimental diffraction data for the same protein in different environments also led to refined structural models showing drastic reduction of the rms deviation with the target model. Because the structural transition is described by very few parameters, over-fitting of real experimental data is easily detected by using a cross-validation test. The method has also been applied to the refinement of atomic models into molecular envelopes and could readily be used to fit large macromolecular complex rearrangements into cryo-electron microscopy-reconstructed images as well as small-angle x-ray scattering-derived envelopes.

Flexibility of β-sheets: Principal component analysis of database protein structures

Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold (e.g., coiled coils and beta-barrels). Recent work has quantified the flexibility of alpha-helices using a principal component analysis (PCA) of database helical structures (J. Mol. Bio. 2003, 327, pp. 229-237). Here, we extend the analysis to beta-sheet flexibility using PCA on a database of beta-sheet structures. For sheets of varying dimension and geometry, we find two dominant modes of flexibility: twist and bend. The distributions of amplitudes for these modes are found to be Gaussian and independent, suggesting that the PCA twist and bend modes can be identified as the soft elastic normal modes of sheets. We consider the scaling of mode eigenvalues with sheet size and find that parallel beta-sheets are more rigid than antiparallel sheets over the entire range studied. Finally, we discuss the application of our PCA results to modeling and design of beta-sheet proteins.

Allosteric Changes in Protein Structure Computed by a Simple Mechanical Model: Hemoglobin T↔R2 Transition

Information on protein dynamics has been usually inferred from spectroscopic studies of parts of the proteins, or indirectly from the comparison of the conformations assumed in the presence of different substrates or ligands. While molecular simulations also provide information on protein dynamics, they usually suffer from incomplete sampling of conformational space, and become prohibitively expensive when exploring the collective dynamics of large macromolecular structures. Here, we explore the dynamics of a well-studied allosteric protein, hemoglobin (Hb), to show that a simple mechanical model based on Gaussian fluctuations of residues can efficiently predict the transition between the tense (T, unliganded) and relaxed (R or R2, O(2) or CO-bound) forms of Hb. The passage from T into R2 is shown to be favored by the global mode of motion, which, in turn is driven by entropic effects. The major difference between the dynamics of the T and R2 forms is the loss of the hinge-bending role of alpha(1)-beta(2) (or alpha(2)-beta(1)) interfacial residues at alpha Phe36-His45 and beta Thr87-Asn102 in the R2 form, which implies a decreased cooperativity in the higher affinity (R2) form of Hb, consistent with many experimental studies. The involvement of the proximal histidine beta His92 in this hinge region suggests that the allosteric propagation of the local structural changes (induced upon O(2) binding) into global ones occur via hinge regions. This is the first demonstration that there is an intrinsic tendency of Hb to undergo T-->R2 transition, induced by purely elastic forces of entropic origin that are uniquely defined for the particular contact topology of the T form.

Dynamical properties of the MscL of Escherichia coli: a normal mode analysis

The mechanosensitive channel (MscL) is an integral membrane protein which gates in response to membrane tension. Physiological data have shown that the gating transition involves a very large change in the conformation, and that the open state of the channel forms a large non-specific pore with a high conductance. The Escherichia coli channel structure was first modeled by homology modeling, starting with the X-ray structure of the homologous from Mycobacterium tuberculosis. Then, the dynamical and conformational properties of the channel were explored, using normal mode analysis. Such an analysis was also performed with the different structures proposed recently by Sukharev and co-workers. Similar dynamical behaviors are observed, which are characteristic of the channel architecture, subtle differences being due to the different relative positioning of the structural elements. The ability of particular regions of the channel to deform is discussed with respect to the functional and structural properties, implied in the gating process. Our results show that the first step of the gating mechanism can be described with three low-frequency modes only. The movement associated to these modes is clearly an iris-like movement involving both tilt and twist rotation.