Tertiary and quaternary conformational changes in aspartate transcarbamylase: a normal mode study

Heme and hemoglobin utilization by Mycobacterium tuberculosis

Iron is essential for growth of Mycobacterium tuberculosis (Mtb), but most iron in the human body is stored in heme within hemoglobin. Here, we demonstrate that the substrate-binding protein DppA of the inner membrane Dpp transporter is required for heme and hemoglobin utilization by Mtb. The 1.27 Å crystal structure of DppA shows a tetrapeptide bound in the protein core and a large solvent-exposed crevice for heme binding. Mutation of arginine 179 in this cleft eliminates heme binding to DppA and prevents heme utilization by Mtb. The outer membrane proteins PPE36 and PPE62 are also required for heme and hemoglobin utilization, indicating that these pathways converge at the cell surface of Mtb. Albumin, the most abundant blood protein, binds heme specifically and bypasses the requirements for PPE36, PPE62 and Dpp. Thus, our study reveals albumin-dependent and -independent heme uptake pathways, highlighting the importance of iron acquisition from heme for Mtb.

Combining multi-scale modelling methods to decipher molecular motions of a branching sucrase from glycoside-hydrolase family 70

Among α-transglucosylases from Glycoside-Hydrolase family 70, the ΔN₁₂₃-GB-CD2 enzyme derived from the bifunctional DSR-E from L. citreum NRRL B-1299 is particularly interesting as it was the first described engineered Branching Sucrase, not able to elongate glucan polymers from sucrose substrate. The previously reported overall structural organization of this multi-domain enzyme is an intricate U-shape fold conserved among GH70 enzymes which showed a certain conformational variability of the so-called domain V, assumed to play a role in the control of product structures, in available X-ray structures. Understanding the role of functional dynamics on enzyme reaction and substrate recognition is of utmost interest although it remains a challenge for biophysical methods. By combining long molecular dynamics simulation (1μs) and multiple analyses (NMA, PCA, Morelet Continuous Wavelet Transform and Cross Correlations Dynamics), we investigated here the dynamics of ΔN₁₂₃-GB-CD2 alone and in interaction with sucrose substrate. Overall, our results provide the detailed picture at atomic level of the hierarchy of motions occurring along different timescales and how they are correlated, in agreement with experimental structural data. In particular, detailed analysis of the different structural domains revealed cooperative dynamic behaviors such as twisting, bending and wobbling through anti- and correlated motions, and also two structural hinge regions, of which one was unreported. Several highly flexible loops surrounding the catalytic pocket were also highlighted, suggesting a potential role in the acceptor promiscuity of ΔN123-GBD-CD2. Normal modes and essential dynamics underlined an interesting two-fold dynamic of the catalytic domain A, pivoting about an axis splitting the catalytic gorge in two parts. The comparison of the conformational free energy landscapes using principal component analysis of the enzyme in absence or in presence of sucrose, also revealed a more harmonic basin when sucrose is bound with a shift population of the bending mode, consistent with the substrate binding event.

PLA2-like proteins myotoxic mechanism: a dynamic model description

Phospholipase A₂-like (PLA₂-like) proteins contribute to the development of muscle necrosis in Viperidae snake bites and are not efficiently neutralized by current antivenom treatments. The toxic mechanisms of PLA₂-like proteins are devoid of catalytic activity and not yet fully understood, although structural and functional experiments suggest a dimeric assembly and that the C-terminal residues are essential to myotoxicity. Herein, we characterized the functional mechanism of bothropic PLA₂-like structures related to global and local measurements using the available models in the Protein Data Bank and normal mode molecular dynamics (NM-MD). Those measurements include: (i) new geometric descriptions between their monomers, based on Euler angles; (ii) characterizations of canonical and non-canonical conformations of the C-terminal residues; (iii) accessibility of the hydrophobic channel; (iv) inspection of ligands; and (v) distance of clustered residues to toxin interface of interaction. Thus, we described the allosteric activation of PLA₂-like proteins and hypothesized that the natural movement between monomers, calculated from NM-MD, is related to their membrane disruption mechanism, which is important for future studies of the inhibition process. These methods and strategies can be applied to other proteins to help understand their mechanisms of action.

Computational Analysis of the Molecular Mechanism of RamR Mutations Contributing to Antimicrobial Resistance in Salmonella enterica

Antimicrobial resistance (AMR) in pathogenic microorganisms with multidrug resistance (MDR) constitutes a severe threat to human health. A major causative mechanism of AMR is mediated through the multidrug efflux pump (MEP). The resistance-nodulation-division superfamily (RND family) of Gram-negative bacteria is usually the major cause of MDR in clinical studies. In Salmonella enterica, the RND pump is translated from the acrAB gene, which is regulated by the activator RamA. Many MEP-caused AMR strains have high ramA gene expression due to mutations in RamR, which has a homodimeric structure comprising the dimerization domain and DNA-binding domain (DBD). Three mutations on the dimerization domain, namely Y59H, M84I, and E160D, are far from the DBD; the molecular mechanism through which they influence RamR’s binding affinity to the ramA gene promoter and consequently disrupt RamA remains unclear. The present study conducted molecular dynamics simulations, binding free energy calculations, and normal mode analysis to investigate the mechanism through which Y59H, M84I, and E160D mutations on the dimerization domain influence the binding affinity of RamR to the ramA promoter. The present results suggest that the three mutations alter the RamR structure, resulting in decreased DNA-binding affinity.

Structure-Encoded Global Motions and Their Role in Mediating Protein-Substrate Interactions

Recent structure-based computational studies suggest that, in contrast to the classical description of equilibrium fluctuations as wigglings and jigglings, proteins have access to well-defined spectra of collective motions, called intrinsic dynamics, encoded by their structure under native state conditions. In particular, the global modes of motions (at the low frequency end of the spectrum) are shown by multiple studies to be highly robust to minor differences in the structure or to detailed interactions at the atomic level. These modes, encoded by the overall fold, usually define the mechanisms of interactions with substrates. They can be estimated by low-resolution models such as the elastic network models (ENMs) exclusively based on interresidue contact topology. The ability of ENMs to efficiently assess the global motions intrinsically favored by the overall fold as well as the relevance of these predictions to the dominant changes in structure experimentally observed for a given protein in the presence of different substrates suggest that the intrinsic dynamics plays a role in mediating protein-substrate interactions. These observations underscore the functional significance of structure-encoded dynamics, or the importance of the predisposition to favor functional global modes in the evolutionary selection of structures.

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

ΔΔPT: a comprehensive toolbox for the analysis of protein motion

Background

Normal Mode Analysis is one of the most successful techniques for studying motions in proteins and macromolecules. It can provide information on the mechanism of protein functions, used to aid crystallography and NMR data reconstruction, and calculate protein free energies.

Results

ΔΔPT is a toolbox allowing calculation of elastic network models and principle component analysis. It allows the analysis of pdb files or trajectories taken from; Gromacs, Amber, and DL_POLY. As well as calculation of the normal modes it also allows comparison of the modes with experimental protein motion, variation of modes with mutation or ligand binding, and calculation of molecular dynamic entropies.

Conclusions

This toolbox makes the respective tools available to a wide community of potential NMA users, and allows them unrivalled ability to analyse normal modes using a variety of techniques and current software.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Hybrid approaches to molecular simulation

Molecular dynamics (MD) simulation is an established method for studying the conformational changes that are important for protein function. Recent advances in hardware and software have allowed MD simulations over the same timescales as experiment, improving the agreement between theory and experiment to a large extent. However, running such simulations are costly, in terms of resources, storage, and trajectory analysis. There is still a place for techniques that involve short MD simulations. In order to overcome the sampling paucity of short time-scales, hybrid methods that include some form of MD simulation can exploit certain features of the system of interest, often combining experimental information in surprising ways. Here, we review some recent hybrid approaches to the simulation of proteins.

Computational analysis of a novel mutation in ETFDH gene highlights its long-range effects on the FAD-binding motif

Background

Multiple acyl-coenzyme A dehydrogenase deficiency (MADD) is an autosomal recessive disease caused by the defects in the mitochondrial electron transfer system and the metabolism of fatty acids. Recently, mutations in electron transfer flavoprotein dehydrogenase (ETFDH) gene, encoding electron transfer flavoprotein:ubiquinone oxidoreductase (ETF:QO) have been reported to be the major causes of riboflavin-responsive MADD. To date, no studies have been performed to explore the functional impact of these mutations or their mechanism of disrupting enzyme activity.

Results

High resolution melting (HRM) analysis and sequencing of the entire ETFDH gene revealed a novel mutation (p.Phe128Ser) and the hotspot mutation (p.Ala84Thr) from a patient with MADD. According to the predicted 3D structure of ETF:QO, the two mutations are located within the flavin adenine dinucleotide (FAD) binding domain; however, the two residues do not have direct interactions with the FAD ligand. Using molecular dynamics (MD) simulations and normal mode analysis (NMA), we found that the p.Ala84Thr and p.Phe128Ser mutations are most likely to alter the protein structure near the FAD binding site as well as disrupt the stability of the FAD binding required for the activation of ETF:QO. Intriguingly, NMA revealed that several reported disease-causing mutations in the ETF:QO protein show highly correlated motions with the FAD-binding site.

Conclusions

Based on the present findings, we conclude that the changes made to the amino acids in ETF:QO are likely to influence the FAD-binding stability.

Virtual interface substructure synthesis method for normal mode analysis of super-large molecular complexes at atomic resolution

Normal mode analysis of large biomolecular complexes at atomic resolution remains challenging in computational structure biology due to the requirement of large amount of memory space and central processing unit time. In this paper, we present a method called virtual interface substructure synthesis method or VISSM to calculate approximate normal modes of large biomolecular complexes at atomic resolution. VISSM introduces the subunit interfaces as independent substructures that join contacting molecules so as to keep the integrity of the system. Compared with other approximate methods, VISSM delivers atomic modes with no need of a coarse-graining-then-projection procedure. The method was examined for 54 protein-complexes with the conventional all-atom normal mode analysis using CHARMM simulation program and the overlap of the first 100 low-frequency modes is greater than 0.7 for 49 complexes, indicating its accuracy and reliability. We then applied VISSM to the satellite panicum mosaic virus (SPMV, 78,300 atoms) and to F-actin filament structures of up to 39-mer, 228,813 atoms and found that VISSM calculations capture functionally important conformational changes accessible to these structures at atomic resolution. Our results support the idea that the dynamics of a large biomolecular complex might be understood based on the motions of its component subunits and the way in which subunits bind one another.

A dynamics study of the A-chain of ricin by terahertz vibrational calculation and normal modes analysis

We studied the terahertz (THz) spectroscopy and low frequency normal modes of both apo- and holo- (adenosine monophosphate (AMP)-bound) ricin-A-chain (RTA) as a means to understand the dynamical changes that RTA undergoes upon substrate binding. The calculated THz spectra of apo- and holo-RTAs demonstrated a general intensity suppression upon substrate binding, which is attributed to the reduced number of collective motion in THz region. In normal mode analysis of RTA we find a shearing motion that is shared by both the apo- and holo-RTAs, whereas a breathing motion, and an upward hinge rising and an alpha-G bending characteristic motion are dampened significantly upon AMP binding, suggesting these motions are involved in the necessary flexibility of the active site. In contrast, we find a normal mode motion that separates domains I and II of RTA at the interface that is more common in the holo-protein. We hypothesized that the flexibility of the entrance of RTA can facilitate the entry of rRNA and allow the substrate to adjust its conformation and orientation prior to depurination. This process suggests an rRNA binding pathway which is supplemental the current RTA depurination mechanism.

Toward a molecular understanding of the anisotropic response of proteins to external forces: insights from elastic network models

With recent advances in single-molecule manipulation techniques, it is now possible to measure the mechanical resistance of proteins to external pulling forces applied at specific positions. Remarkably, such recent studies demonstrated that the pulling/stretching forces required to initiate unfolding vary considerably depending on the location of the application of the forces, unraveling residue/position-specific response of proteins to uniaxial tension. Here we show that coarse-grained elastic network models based on the topology of interresidue contacts in the native state can satisfactory explain the relative sizes of such stretching forces exerted on different residue pairs. Despite their simplicity, such models presumably capture a fundamental property that dominates the observed behavior: deformations that can be accommodated by the relatively lower frequency modes of motions intrinsically favored by the structure require weaker forces and vice versa. The mechanical response of proteins to external stress is therefore shown to correlate with the anisotropic fluctuation dynamics intrinsically accessible in the folded state. The dependence on the overall fold implies that evolutionarily related proteins sharing common structural features tend to possess similar mechanical properties. However, the theory cannot explain the differences observed in a number of structurally similar but sequentially distant domains, such as the fibronectin domains.

Terahertz spectroscopy of bacteriorhodopsin and rhodopsin: similarities and differences

We studied the low-frequency terahertz spectroscopy of two photoactive protein systems, rhodopsin and bacteriorhodopsin, as a means to characterize collective low-frequency motions in helical transmembrane proteins. From this work, we found that the nature of the vibrational motions activated by terahertz radiation is surprisingly similar between these two structurally similar proteins. Specifically, at the lowest frequencies probed, the cytoplasmic loop regions of the proteins are highly active; and at the higher terahertz frequencies studied, the extracellular loop regions of the protein systems become vibrationally activated. In the case of bacteriorhodopsin, the calculated terahertz spectra are compared with the experimental terahertz signature. This work illustrates the importance of terahertz spectroscopy to identify vibrational degrees of freedom which correlate to known conformational changes in these proteins.

Picosecond dynamics of T and R forms of aspartate transcarbamylase: A neutron scattering study

E. coli aspartate transcarbamylase (ATCase) is a 310 kDa allosteric enzyme which catalyses the first committed step in pyrimidine biosynthesis. The binding of its substrates, carbamylphosphate and aspartate, induces significant conformational changes. This enzyme shows homotropic cooperative interactions between the catalytic sites for the binding of aspartate. This property is explained by a quaternary structure transition from T state (aspartate low affinity) to R state (aspartate high affinity) accompanied by a 5% increase of radius of gyration of ATCase. The same quaternary structure change is observed upon binding of the bisubstrate analogue PALA (N-(phosphonacetyl)-L-aspartate. Owing to the large incoherent neutron scattering cross-section of the hydrogen atom and the abundance of this element in proteins, inelastic neutron scattering gives a global view of protein dynamics as sensed via the individual motions of its hydrogen atoms. We present neutron scattering results of the local dynamics (few angstroms), at short time (few tens of picoseconds), of ATCase in T and R forms. Compared to the T form, we observe an increased mobility of the protein in the R form that we associate to an increase of accessible surface area to the solvent. Beyond this specific result, this highlights the key role of the accessible surface area (ASA) in dynamic contribution to inelastic neutron data in the picosecond time scale. In particular, we want to stress out (i) that a difference at the picosecond time scale does not allow to conclude to a difference in the dynamics at a longer time scale and to address whether the T state is looser than the R state (ii) how challenging is, any comparison in terms of general dynamics (tense or relaxed) between dynamic values deduced from experimental neutron data on proteins with different sequences and therefore ASA. This caveat holds particularly when comparing dynamics of a mesophile with the corresponding extremophile.

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.

Characterization of protein matrix motions in the Rb. sphaeroides photosynthetic reaction center

We use Normal Mode Analysis to investigate motions in the photosynthetic reaction center (RC) protein. We identify the regions involved in concerted fluctuations of the protein matrix and analyze the normalized amplitudes and the directionality of the first few dominant modes. We also seek to quantify the coupling of normal modes to long-range electron transfer (ET). We find that a quasi-continuous spectrum of protein motions rather than one individual mode contributes to light-driven electron transfer. This is consistent with existing theoretical models (e.g. the spin-boson/dispersed polaron model) for the coupling of the protein and solvent "bath" to charge separation events. [Figure: see text].

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.

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.

Gradient-based direct normal-mode analysis

A formulation of a direct, iterative method for obtaining the lowest eigenvalues and eigenvectors of a Hessian matrix is presented. Similar to the iterative schemes in electronic structure configuration interaction calculations (methods due to Lanczos, Davidson, and others), the mass-weighted Hessian matrix K is not constructed explicitly; instead, its operation on a basis vector (a direction in the 3N Cartesian configuration space of the atoms) is computed based on the principles of dynamical equations of motion. By noting that the time derivative of the gradient vector in the harmonic force field is related to the particles' momenta via dg/dt = Kp, a Hessian-vector product can be computed on the fly by finite differentiation of the gradient along the direction specified by the p vector. Thus, only two evaluations of the gradient are required per Davidson-like iteration per root, which leads to a linear scaling behavior of the computational effort with the number of atoms (provided that the evaluation of the gradient scales linearly). Preliminary results are presented for a 27,000-atom 4He nanodroplet.

Normal mode calculations of icosahedral viruses with full dihedral flexibility by use of molecular symmetry

The study of the dynamics and thermodynamics of small icosahedral virus capsids is an active field of research. Normal mode analysis is one of the computational tools that can provide important insights into the conformational changes of the virus associated with cell entry or caused by changing of the physicochemical environment. Normal mode analysis of virus capsids has been limited due to the size of these systems, which often exceed 50,000 residues. Here we present the first normal mode calculation with full dihedral flexibility of several virus capsids, including poliovirus, rhinovirus, and cowpea chlorotic mottle virus. The calculations were made possible by applying group theoretical methods, which greatly simplified the calculations without any approximation beyond the all-atom force field representations in general use for smaller protein systems. Since a full Cartesian basis set was too large to be handled by the available computer memory, we used a basis set that includes all internal dihedral angles of the system with the exception of the peptide bonds, which were assumed rigid. The fluctuations of the normal modes are shown to correlate well with crystallographic temperature factors. The motions of the first several normal modes of each symmetry type are described. A hinge bending motion in poliovirus was found that may be involved in the mechanism by which bound small molecules inhibit conformational changes of the capsid. Fully flexible normal mode calculations of virus capsids are expected to increase our understanding of virus dynamics and thermodynamics, and can be useful in the refinement of cryo-electron microscopy structures of viruses.

WEBnm@: a web application for normal mode analyses of proteins

Background

Normal mode analysis (NMA) has become the method of choice to investigate the slowest motions in macromolecular systems. NMA is especially useful for large biomolecular assemblies, such as transmembrane channels or virus capsids. NMA relies on the hypothesis that the vibrational normal modes having the lowest frequencies (also named soft modes) describe the largest movements in a protein and are the ones that are functionally relevant.

Results

We developed a web-based server to perform normal modes calculations and different types of analyses. Starting from a structure file provided by the user in the PDB format, the server calculates the normal modes and subsequently offers the user a series of automated calculations; normalized squared atomic displacements, vector field representation and animation of the first six vibrational modes. Each analysis is performed independently from the others and results can be visualized using only a web browser. No additional plug-in or software is required. For users who would like to analyze the results with their favorite software, raw results can also be downloaded. The application is available on . We present here the underlying theory, the application architecture and an illustration of its features using a large transmembrane protein as an example.

Conclusion

We built an efficient and modular web application for normal mode analysis of proteins. Non specialists can easily and rapidly evaluate the degree of flexibility of multi-domain protein assemblies and characterize the large amplitude movements of their domains.

Probing protein mechanics: residue-level properties and their use in defining domains

It is becoming clear that, in addition to structural properties, the mechanical properties of proteins can play an important role in their biological activity. It nevertheless remains difficult to probe these properties experimentally. Whereas single-molecule experiments give access to overall mechanical behavior, notably the impact of end-to-end stretching, it is currently impossible to directly obtain data on more local properties. We propose a theoretical method for probing the mechanical properties of protein structures at the single-amino acid level. This approach can be applied to both all-atom and simplified protein representations. The probing leads to force constants for local deformations and to deformation vectors indicating the paths of least mechanical resistance. It also reveals the mechanical coupling that exists between residues. Results obtained for a variety of proteins show that the calculated force constants vary over a wide range. An analysis of the induced deformations provides information that is distinct from that obtained with measures of atomic fluctuations and is more easily linked to residue-level properties than normal mode analyses or dynamic trajectories. It is also shown that the mechanical information obtained by residue-level probing opens a new route for defining so-called dynamical domains within protein structures.

Diversity and Identity of Mechanical Properties of Icosahedral Viral Capsids Studied with Elastic Network Normal Mode Analysis

We analyze the mechanical properties and putative dynamical fluctuations of a variety of viral capsids comprising different sizes and quasi-equivalent symmetries by performing normal mode analysis using the elastic network model. The expansion of the capsid to a swollen state is studied using normal modes and is compared with the experimentally observed conformational change for three of the viruses for which experimental data exist. We show that a combination of one or two normal modes captures remarkably well the overall translation that dominates the motion between the two conformational states, and reproduces the overall conformational change. We observe for all of the viral capsids that the nature of the modes is different. In particular for the T=7 virus, HK97, for which the shape of the capsid changes from spherical to faceted polyhedra, two modes are necessary to accomplish the conformational transition. In addition, we extend our study to viral capsids with other T numbers, and discuss the similarities and differences in the features of virus capsid conformational dynamics. We note that the pentamers generally have higher flexibility and propensity to move freely from the other capsomers, which facilitates the shape adaptation that may be important in the viral life cycle.

New advances in normal mode analysis of supermolecular complexes and applications to structural refinement

Normal mode analysis is an effective computational method for studying large-amplitude low-frequency molecular deformations that are ubiquitously involved in the functions of biological macromolecules, especially supermolecular complexes. The recent years have witnessed a substantial advance in methodology development in the field. This review is intended to summarize some of the important advances that enable one to simulate deformations of supermolecular complexes at expended resolution- and length-scales, with particular emphasis on the implications in structural refinement against low- to intermediate-resolution structural data such as those from electron cryomicroscopy and fibre diffraction.

Comparative estimation of vibrational entropy changes in proteins through normal modes analysis

We compare the vibrational entropy changes of proteins calculated using a full and a number of approximate normal modes analysis methods. The vibrational entropy differences for three conformational changes and three protein binding interactions were computed. In general, the approximate methods yield good estimates of the vibrational entropy change in a fraction of the time required by full normal modes analysis. The absolute entropies are either overestimated or greatly underestimated, but the difference is sufficiently accurate for some methods. This indicates that some of the approximate methods can give reasonable estimates of the associated vibrational entropy changes, making them suitable for inclusion in free energy calculations.

Analysis of functional motions in Brownian molecular machines with an efficient block normal mode approach: myosin-II and Ca2+ -ATPase

The structural flexibilities of two molecular machines, myosin and Ca(2+)-ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improved implementation of the block normal mode (BNM) approach. The BNM results clearly illustrated that the large-scale conformational transitions implicated in the functional cycles of the two motor systems can be largely captured with a small number of low-frequency normal modes. Therefore, the results support the idea that structural flexibility is an essential part of the construction principle of molecular motors through evolution. Such a feature is expected to be more prevalent in motor proteins than in simpler systems (e.g., signal transduction proteins) because in the former, large-scale conformational transitions often have to occur before the chemical events (e.g., ATP hydrolysis in myosin and ATP binding/phosphorylation in Ca(2+)-ATPase). This highlights the importance of Brownian motions associated with the protein domains that are involved in the functional transitions; in this sense, Brownian molecular machines is an appropriate description of molecular motors, although the normal mode results do not address the origin of the ratchet effect. The results also suggest that it might be more appropriate to describe functional transitions in some molecular motors as intrinsic elastic motions modulating local structural changes in the active site, which in turn gets stabilized by the subsequent chemical events, in contrast with the conventional idea of local changes somehow getting amplified into larger-scale motions. In the case of myosin, for example, we favor the idea that Brownian motions associated with the flexible converter propagates to the Switch I/II region, where the salt-bridge formation gets stabilized by ATP hydrolysis, in contrast with the textbook notion that ATP hydrolysis drives the converter motion. Another useful aspect of the BNM results is that selected low-frequency normal modes have been identified to form a set of collective coordinates that can be used to characterize the progress of a significant fraction of large-scale conformational transitions. Therefore, the present normal mode analysis has provided a stepping-stone toward more elaborate microscopic simulations for addressing critical issues in free energy conversions in molecular machines, such as the coupling and the causal relationship between collective motions and essential local changes at the catalytic active site where ATP hydrolysis occurs.

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.

The role of dynamics in allosteric regulation

The biomolecular conformational changes often associated with allostery are, by definition, dynamic processes. Recent publications have disclosed the role of pre-existing equilibria of conformational substates in this process. In addition, the role of dynamics as an entropic carrier of free energy of allostery has been investigated. Recent work thus shows that dynamics is pivotal to allostery, and that it constitutes much more than just the move from the 'T'-state to the 'R'-state. Emerging computational studies have described the actual pathways of allosteric change.

A normal mode analysis of structural plasticity in the biomolecular motor F(1)-ATPase

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly flexible in the isolated subunit, but more rigid in the alpha(3)beta(3)gamma complex due to interactions with other subunits. The globular domain of the gamma subunit is structurally relatively rigid when isolated and in the alpha(3)beta(3)gamma complex; this is important for its functional role in coupling the F(0) and F(1) complex of ATP synthase and in inducing the conformational changes of the beta subunits in synthesis. Most important, the character of the lowest-frequency modes of the beta(E) subunit is highly correlated with the large beta(E) --> beta(TP) transition. This holds for the C-terminal domain and the nucleotide-binding domain, which undergo significant conformational transitions in the functional cycle of F(1)-ATPase. This is most evident in the ligand-free beta(E) subunit; the flexibility in the nucleotide-binding domain is reduced somewhat in the beta(TP) subunit in the presence of Mg(2+).ATP. The low-frequency modes of the alpha(3)beta(3)gamma complex show that the motions of the globular domain of the gamma subunit and of the C-terminal and nucleotide binding domains of the beta(E) subunits are coupled, in accord with their function. Overall, the normal mode analysis reveals that F(1)-ATPase, like other macromolecular assemblies, has the intrinsic structural flexibility required for its function encoded in its sequence and three-dimensional structure. This inherent plasticity is an essential aspect of assuring a small free energy cost for the large-scale conformational transition that occurs in molecular motors.

Transconformations of the SERCA1 Ca-ATPase: a normal mode study

The transport of Ca(2+) by Ca-ATPase across the sarcoplasmic reticulum membrane is accompanied by several transconformations of the protein. Relying on the already established functional importance of low-frequency modes in dynamics of proteins, we report here a normal mode analysis of the Ca(2+)-ATPase based on the crystallographic structures of the E1Ca(2) and E2TG forms. The lowest-frequency modes reveal that the N and A(+Nter) domains undergo the largest amplitude movements. The dynamical domain analysis performed with the DomainFinder program suggests that they behave as rigid bodies, unlike the highly flexible P domain. We highlight two types of movements of the transmembrane helices: i), a concerted movement around an axis perpendicular to the membrane which "twists open" the lumenal side of the protein and ii), an individual translational and rotational mobility which is of lower amplitude for the helices hosting the calcium binding sites. Among all modes calculated for E1Ca, only three are enough to describe the transition to E2TG; the associated movements involve almost exclusively the A and N domains, reflecting the closure of the cytoplasmic headpiece and high displacement of the L7-8 lumenal loop. Subsequently, we discuss the potential contribution of the remaining low-frequency normal modes to the transconformations occurring within the overall calcium transport cycle.

Comparative modeling of GABA(A) receptors: limits, insights, future developments

GABA(A) receptors are chloride ion channels that mediate fast synaptic transmission and belong to a superfamily of pentameric ligand-gated ion channels. The recently published crystal structure of the acetylcholine binding protein can be used as a template for comparative modeling of the extracellular domain of GABA(A) receptors. In this commentary, difficulties with comparative modeling at low sequence identity are discussed, the degree of structural conservation to be expected within the superfamily is analyzed and numerical estimates of model uncertainties in functional regions are provided. Topography of the binding sites at subunit-interfaces is examined and possible targets for rational mutagenesis studies are suggested. Allosteric motions are considered and a mechanism for mediation of positive cooperativity at the benzodiazepine site is proposed.

A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase

A block normal mode (BNM) algorithm, originally proposed by Tama et al., (Proteins Struct. Func. Genet. 41:1-7, 2000) was implemented into the simulation program CHARMM. The BNM approach projects the hessian matrix into local translation/rotation basis vectors and, therefore, dramatically reduces the size of the matrix involved in diagonalization. In the current work, by constructing the atomic hessian elements required in the projection operation on the fly, the memory requirement for the BNM approach has been significantly reduced from that of standard normal mode analysis and previous implementation of BNM. As a result, low frequency modes, which are of interest in large-scale conformational changes of large proteins or protein-nucleic acid complexes, can be readily obtained. Comparison of the BNM results with standard normal mode analysis for a number of small proteins and nucleic acids indicates that many properties dominated by low frequency motions are well reproduced by BNM; these include atomic fluctuations, the displacement covariance matrix, vibrational entropies, and involvement coefficients for conformational transitions. Preliminary application to a fairly large system, Ca(2+)-ATPase (994 residues), is described as an example. The structural flexibility of the cytoplasmic domains (especially domain N), correlated motions among residues on domain interfaces and displacement patterns for the transmembrane helices observed in the BNM results are discussed in relation to the function of Ca(2+)-ATPase. The current implementation of the BNM approach has paved the way for developing efficient sampling algorithms with molecular dynamics or Monte Carlo for studying long-time scale dynamics of macromolecules.

Inhibitor binding alters the directions of domain motions in HIV-1 reverse transcriptase

Understanding the molecular mechanisms of HIV-1 reverse transcriptase (RT) action and drug inhibition is essential for designing effective antiretroviral therapies. Although comparisons of the different crystal forms of RT give insights into the flexibility of different domains, a direct computational assessment of the effect of inhibitor binding on the collective dynamics of RT is lacking. A structure-based approach is used here for exploring the dynamics of RT in unliganded and inhibitor-bound forms. Non-nucleoside RT inhibitors (NNRTI) are shown to interfere directly with the global hinge-bending mechanism that controls the cooperative motions of the p66 fingers and thumb subdomains. The net effect of nevirapine binding is to change the direction of domain movements rather than suppress their mobilities. The second generation NNRTI, efavirenz, on the other hand, shows the stronger effect of simultaneously reorienting domain motions and obstructing the p66 thumb fluctuations. A second hinge site controlling the global rotational reorientations of the RNase H domain is identified, which could serve as a target for potential inhibitors of RNase H activity.

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

We investigated protein motions using normal modes within a database framework, determining on a large sample the degree to which normal modes anticipate the direction of the observed motion and were useful for motions classification. As a starting point for our analysis, we identified a large number of examples of protein flexibility from a comprehensive set of structural alignments of the proteins in the PDB. Each example consisted of a pair of proteins that were considerably different in structure given their sequence similarity. On each pair, we performed geometric comparisons and adiabatic-mapping interpolations in a high-throughput pipeline, arriving at a final list of 3,814 putative motions and standardized statistics for each. We then computed the normal modes of each motion in this list, determining the linear combination of modes that best approximated the direction of the observed motion. We integrated our new motions and normal mode calculations in the Macromolecular Motions Database, through a new ranking interface at http://molmovdb.org. Based on the normal mode calculations and the interpolations, we identified a new statistic, mode concentration, related to the mathematical concept of information content, which describes the degree to which the direction of the observed motion can be summarized by a few modes. Using this statistic, we were able to determine the fraction of the 3,814 motions where one could anticipate the direction of the actual motion from only a few modes. We also investigated mode concentration in comparison to related statistics on combinations of normal modes and correlated it with quantities characterizing protein flexibility (e.g., maximum backbone displacement or number of mobile atoms). Finally, we evaluated the ability of mode concentration to automatically classify motions into a variety of simple categories (e.g., whether or not they are "fragment-like"), in comparison to motion statistics. This involved the application of decision trees and feature selection (particular machine-learning techniques) to training and testing sets derived from merging the "list" of motions with manually classified ones.

How to describe protein motion without amino acid sequence and atomic coordinates

This paper reports a computational method, the quantized elastic deformational model, that can reliably describe the conformational flexibility of a protein in the absence of the amino acid sequence and atomic coordinates. The essence of this method lies in the fact that, in modeling the functionally important conformational changes such as domain movements, it is possible to abandon the traditional concepts of protein structure (bonds, angles, dihedrals, etc.) and treat the protein as an elastic object. The shape and mass distribution of the object are described by the electron density maps, at various resolutions, from methods such as x-ray diffraction or cryo-electron microscopy. The amplitudes and directionality of the elastic deformational modes of a protein, whose patterns match the biologically relevant conformational changes, can then be derived solely based on the electron density map. The method yields an accurate description of protein dynamics over a wide range of resolutions even as low as 15-20 A at which there is nearly no visually distinguishable internal structures. Therefore, this method dramatically enhances the capability of studying protein motions in structural biology. It is also expected to have ample applications in related fields such as bioinformatics, structural genomics, and proteomics, in which one's ability to extract functional information from the not-so-well-defined structural models is vitally important.

Domain movements in human fatty acid synthase by quantized elastic deformational model

This paper reports the results of applying a computational method called the quantized elastic deformational model, to the determination of conformational flexibility of the supermolecular complex of human fatty acid synthase. The essence of this method is the ability to model large-scale conformational changes such as domain movements by treating the protein as an elastic object without the knowledge of protein primary sequence and atomic coordinates. The calculation was based on the electron density maps of the synthase at 19 A. The results suggest that the synthase is a very flexible molecule. Two types of flexible hinges in the structure were identified. One is an intersubunit hinge formed by the intersubunit connection and the other is an intrasubunit hinge located between domains I and II. Despite the fact that the dimeric synthase has a chemically symmetric structure, large domain movements around the hinge region occur in various directions and allow the molecule to adopt a wide range of conformations. These domain movements are likely to be important in facilitating and regulating the entire palmitate synthesis by coordinating the communication between components of the molecule, for instance, adjusting the distance between various active sites inside the catalytic reaction center. Finally, the ability to describe protein motions of a supermolecular complex, without the information of protein sequence and atomic coordinates, is a major advance in computational modeling of protein dynamics. The method provides an unprecedented ability to model protein motions at such a low resolution of structure.

Intrinsic flexibility and gating mechanism of the potassium channel KcsA

The gating mechanism of the potassium channel KcsA was studied by normal mode analysis. The results provided an atomic description of the locations of the pivot points and the motional features of key structural elements in the gating process. Two pivot points were found in the motions of the inner TM2 helical bundle that directly modulate the size of the central channel pore. One point is an intrasubunit hinge point that sharply divides the structural flexibility between the more rigid selectivity filter and the more mobile peripheral transmembrane helices. Such a division is vital for KcsA because it permits the large-scale motions of transmembrane helices required for the gating and, in the meantime, maintains the rigidity of the filter region essential for the selectivity. The other pivot point is an intersubunit one at which all four TM2 helices are bundled together. During the gating process, each TM2 helix undergoes a lever-like swinging motion pivoting on the intrasubunit hinge, and the entire TM2 bundle undergoes a concerted rotational motion around the central channel axis constrained around the intersubunit bundle point. This series of motions leads to a dramatic enlargement of the intracellular gate without loosening up the structural integrity.

Conformational dynamics of subtilisin-chymotrypsin inhibitor 2 complex by coarse-grained simulations

An off-lattice dynamic Monte Carlo (MC) method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2) and subtilisin in both free and complex forms over two time windows, referring to short and long time scales. The conformational dynamics of backbone bonds analysed from several independent trajectories reveal that: Both the inhibitor and the enzyme are restricted in their bond rotations, excluding a few bonds, upon binding; the effect being greatest for the loop regions, and for the inhibitor. A cooperativity in the near-neighbor bond rotations are observed on both time scales, whereas the cooperative rotations of the bonds far along the sequence appear only in the long time window, and the latter time window is where most of the interactions between the inhibitor and the enzyme are observed. Upon binding, the cooperatively rotating parts of the inhibitor and the enzyme are readjusted compared to their free forms, and new correlations appear. The binding loop, although it is the closest contact region, is not the only part of the inhibitor involved in the interactions with the enzyme. Loops 3 and 8 and the helices F and G in bound enzyme and the binding loop of the inhibitor contribute at the most to the collective motions of whole structure on the slow time scale and are apparently important for enzyme-inhibitor interactions and function. The results in general provide evidence for the contribution of the loops with cooperative motions to the extensive communication network of the complex.