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

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Normal mode dynamics of voltage-gated K(+) channels: gating principle, opening mechanism, and inhibition

Voltage-dependent potassium channels open in response to changes in membrane potential and become partially inactivated upon binding of inhibitors. Here we calculate normal mode motion of two voltage-dependent K(+) channels, KvAP and Shaker, and their complexes with inhibitors and address the gating principle, opening mechanism, and inhibition. The normal modes indicate that pore expansion and channel opening is correlated with a displacement of the arginine gating charges and a tilting of the voltage-sensor paddles. Normal modes of Shaker in complex with agitoxin, which blocks the central pore, do not display significantly altered paddle tilting and pore expansion. In contrast, normal modes of Shaker in complex with hanatoxin, which binds to the voltage sensor paddle, display decreased paddle tilting and pore expansion. This study presents a unified motion for the gating principle and channel opening, and offers insight into the voltage sensor paddle motion and its inhibition.

In silico study on multidrug resistance conferred by I223R/H275Y double mutant neuraminidase

It was recently reported that an I223R/H275Y double mutant of neuraminidase (NA) creates a multidrug-resistant form of the pandemic influenza A (H1N1) virus. However, a comprehensive understanding of the molecular mechanisms is still lacking. We conducted a systematic in silico study to explore the structural basis underlying this multidrug resistance. By molecular docking analyses and molecular dynamics (MD) simulations, we compared various biochemical and biophysical properties of the wild type, the I223R single mutant and the I223R/H275Y double mutant NA with two inhibitors, zanamivir (ZMR) and oseltamivir (G39). The binding free energy of oseltamivir with all types of NA was substantially lower than its zanamivir counterpart. On the other hand, the binding free energy of each inhibitor with wild type NA was generally higher than that with mutant NAs. MD simulation outcomes exemplify distinct patterns for oseltamivir and zanamivir with all types of NA. In particular, the stronger resistance of the double mutant NA relative to the wild and single mutant types can be ascribed to the overall looser but locally more compact structure of the former. Specifically, as a whole the double mutant NA adapts to the larger gyration radius and greater distance between charged atom groups, which is contrary to the pattern in the local binding site region. The enhanced resistance of all types of NA to oseltamivir rather than zanamivir might be accounted for similarly. We expect these findings to provide significant insights into improving inhibitors for the multidrug-resistant neuraminidase of H1N1 influenza viruses.

Analysis of protein conformational transitions using elastic network model

In this chapter, we demonstrate the usage of a coarse-grained elastic network model to analyze protein conformational transitions in the NS3 helicase (NS3hel) of Hepatitis C virus (HCV). This analysis allows us to identify and visualize collective domain motions involved in the conformational transitions and predict the order of structural events during the transitions. It is highly efficient and applicable to many multi-domain protein structures which undergo large conformational changes to fulfill their functions. This method is made available through a Web server ( http://enm.lobos.nih.gov ).

Aligning experimental and theoretical anisotropic B-factors: water models, normal-mode analysis methods, and metrics

The strength of X-ray crystallography in providing the information for protein dynamics has been under appreciated. The anisotropic B-factors (ADPs) from high-resolution structures are invaluable in studying the relationship among structure, dynamics, and function. Here, starting from an in-depth evaluation of the metrics used for comparing the overlap between two ellipsoids, we applied normal-mode analysis (NMA) to predict the theoretical ADPs and then align them with experimental results. Adding an extra layer of explicitly treated water on protein surface significantly improved the energy minimization results and better reproduced the anisotropy of experimental ADPs. In comparing experimental and theoretical ADPs, we focused on the overlap in shape, the alignment of dominant directions, and the similarity in magnitude. The choices of water molecules, NMA methods, and the metrics for evaluating the overlap of ADPs determined final results. This study provides useful information for exploring the physical basis and the application potential of experimental ADPs.

Principal component analysis: a method for determining the essential dynamics of proteins

It has become commonplace to employ principal component analysis to reveal the most important motions in proteins. This method is more commonly known by its acronym, PCA. While most popular molecular dynamics packages inevitably provide PCA tools to analyze protein trajectories, researchers often make inferences of their results without having insight into how to make interpretations, and they are often unaware of limitations and generalizations of such analysis. Here we review best practices for applying standard PCA, describe useful variants, discuss why one may wish to make comparison studies, and describe a set of metrics that make comparisons possible. In practice, one will be forced to make inferences about the essential dynamics of a protein without having the desired amount of samples. Therefore, considerable time is spent on describing how to judge the significance of results, highlighting pitfalls. The topic of PCA is reviewed from the perspective of many practical considerations, and useful recipes are provided.

The intrinsic dynamics of Cse1p and Xpot elucidated by coarse-grained models

Cse1p and Xpot are two karyopherin proteins that transport the corresponding cargos during the nucleocytoplasmic transport. We utilized Elastic Network Model (ENM) and Finite Element Analysis (FEA) to study their conformational dynamics. These dynamics were interpreted by their intrinsic modes that played key roles in the flexibility of karyopherins, which further affected the binding affinities. The findings included that it was the karyopherin's versatile conformations composed of the same superhelices of HEAT repeats that produced different degrees of functional flexibilities. We presented evidence that these coarse-grained methods could help to elucidate the biological function behind the structures of the two karyopherins.

Conformational changes in DNA-binding proteins: relationships with precomplex features and contributions to specificity and stability

Both Proteins and DNA undergo conformational changes in order to form functional complexes and also to facilitate interactions with other molecules. These changes have direct implications for the stability and specificity of the complex, as well as the cooperativity of interactions between multiple entities. In this work, we have extensively analyzed conformational changes in DNA-binding proteins by superimposing DNA-bound and unbound pairs of protein structures in a curated database of 90 proteins. We manually examined each of these pairs, unified the authors' annotations, and summarized our observations by classifying conformational changes into six structural categories. We explored a relationship between conformational changes and functional classes, binding motifs, target specificity, biophysical features of unbound proteins, and stability of the complex. In addition, we have also investigated the degree to which the intrinsic flexibility can explain conformational changes in a subset of 52 proteins with high quality coordinate data. Our results indicate that conformational changes in DNA-binding proteins contribute significantly to both the stability of the complex and the specificity of targets recognized by them. We also conclude that most conformational changes occur in proteins interacting with specific DNA targets, even though unbound protein structures may have sufficient information to interact with DNA in a nonspecific manner.

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

SCEDS: protein fragments for molecular replacement in Phaser

A method is described for generating protein fragments suitable for use as molecular-replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of C(α) atoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lower R factor after ten cycles of all-atom refinement with REFMAC5 than the original template structure. The method has been implemented in the software Phaser.

Elastic network normal mode dynamics reveal the GPCR activation mechanism

G-protein-coupled receptors (GPCR) are a family of membrane-embedded metabotropic receptors which translate extracellular ligand binding into an intracellular response. Here, we calculate the motion of several GPCR family members such as the M2 and M3 muscarinic acetylcholine receptors, the A2A adenosine receptor, the β2 -adrenergic receptor, and the CXCR4 chemokine receptor using elastic network normal modes. The normal modes reveal a dilation and a contraction of the GPCR vestibule associated with ligand passage, and activation, respectively. Contraction of the vestibule on the extracellular side is correlated with cavity formation of the G-protein binding pocket on the intracellular side, which initiates intracellular signaling. Interestingly, the normal modes of rhodopsin do not correlate well with the motion of other GPCR family members. Electrostatic potential calculation of the GPCRs reveal a negatively charged field around the ligand binding site acting as a siphon to draw-in positively charged ligands on the membrane surface. Altogether, these results expose the GPCR activation mechanism and show how conformational changes on the cell surface side of the receptor are allosterically translated into structural changes on the inside.

Structure of a truncation mutant of the nuclear export factor CRM1 provides insights into the auto-inhibitory role of its C-terminal helix

Chromosome region maintenance 1/exportin1/Xpo1 (CRM1) associates with the GTPase Ran to mediate the nuclear export of proteins bearing a leucine-rich nuclear export signal (NES). CRM1 consists of helical hairpin HEAT repeats and a C-terminal helical extension (C-extension) that inhibits the binding of NES-bearing cargos. We report the crystal structure and small-angle X-ray scattering analysis of a human CRM1 mutant with enhanced NES-binding activity due to deletion of the C-extension. We show that loss of the C-extension leads to a repositioning of CRM1's C-terminal repeats and to a more extended overall conformation. Normal mode analysis predicts reduced rigidity for the deletion mutant, consistent with an observed decrease in thermal stability. Point mutations that destabilize the C-extension shift CRM1 to the more extended conformation, reduce thermal stability, and enhance NES-binding activity. These findings suggest that an important mechanism by which the C-extension regulates CRM1's cargo-binding affinity is by modulating the conformation and flexibility of its HEAT repeats.

Structural analysis and ion translocation mechanisms of the muscle-type acetylcholine receptor channel

PURPOSE

The aim of this work is to analyze the conformational changes in the acetylcholine receptor caused by channel opening and to investigate the electrostatic profile during ion translocation through the channel.

METHODS

A computational model of the human muscle-type acetylcholine receptor (AChR) was built and used to analyze channel structure and its interactions with different ions. Using the Torpedo AChR crystal structure as a homologous template, the 3D structure of the human muscle-type AChR was reconstructed.

RESULTS

This first model is optimized and an open structure of the channel is generated using Normal Mode Analysis in order to assess morphologic and energetic differences between open and closed structures. In addition, the issue of ion translocation is investigated in further detail. Results elucidate different aspects of the channel: channel gate structure, channel interactions with translocating ions, differences between muscle-type AChR and previous neuronal-type AChR models.

CONCLUSIONS

The model constructed here is ideal for further computational studies on muscle-type AChR and its pathologic mutations.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

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.

Normal mode analysis based on an elastic network model for biomolecules in the Protein Data Bank, which uses dihedral angles as independent variables

We have developed a computer program, named PDBETA, that performs normal mode analysis (NMA) based on an elastic network model that uses dihedral angles as independent variables. Taking advantage of the relatively small number of degrees of freedom required to describe a molecular structure in dihedral angle space and a simple potential-energy function independent of atom types, we aimed to develop a program applicable to a full-atom system of any molecule in the Protein Data Bank (PDB). The algorithm for NMA used in PDBETA is the same as the computer program FEDER/2, developed previously. Therefore, the main challenge in developing PDBETA was to find a method that can automatically convert PDB data into molecular structure information in dihedral angle space. Here, we illustrate the performance of PDBETA with a protein-DNA complex, a protein-tRNA complex, and some non-protein small molecules, and show that the atomic fluctuations calculated by PDBETA reproduce the temperature factor data of these molecules in the PDB. A comparison was also made with elastic-network-model based NMA in a Cartesian-coordinate system.

Structure-based simulations of the translocation mechanism of the hepatitis C virus NS3 helicase along single-stranded nucleic acid

The NS3 helicase of Hepatitis C virus is an ATP-fueled molecular motor that can translocate along single-stranded (ss) nucleic acid, and unwind double-stranded nucleic acids. It makes a promising antiviral target and an important prototype system for helicase research. Despite recent progress, the detailed mechanism of NS3 helicase remains unknown. In this study, we have combined coarse-grained (CG) and atomistic simulations to probe the translocation mechanism of NS3 helicase along ssDNA. At the residue level of detail, our CG simulations have captured functionally important interdomain motions of NS3 helicase and reproduced single-base translocation of NS3 helicase along ssDNA in the 3'-5' direction, which is in good agreement with experimental data and the inchworm model. By combining the CG simulations with residue-specific perturbations to protein-DNA interactions, we have identified a number of key residues important to the translocation machinery that agree with previous structural and mutational studies. Additionally, our atomistic simulations with targeted molecular dynamics have corroborated the findings of CG simulations and further revealed key protein-DNA hydrogen bonds that break/form during the transitions. This study offers, to our knowledge, the most detailed and realistic simulations of translocation mechanism of NS3 helicase. The simulation protocol established in this study will be useful for designing inhibitors that target the translocation machinery of NS3 helicase, and for simulations of a variety of nucleic-acid-based molecular motors.

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).

Elastic network models: theoretical and empirical foundations

Fifteen years ago, Monique Tirion showed that the low-frequency normal modes of a protein are not significantly altered when nonbonded interactions are replaced by Hookean springs, for all atom pairs whose distance is smaller than a given cutoff value. Since then, it has been shown that coarse-grained versions of Tirion's model are able to provide fair insights on many dynamical properties of biological macromolecules. In this chapter, theoretical tools required for studying these so-called Elastic Network Models are described, focusing on practical issues and, in particular, on possible artifacts. Then, an overview of some typical results that have been obtained by studying such models is given.

Coarse-grained and all-atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen-binding protein composed of four subunits (α1, α2, β1, and β2), is a well-known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse-grained (CG) modeling, all-atom simulation, and structural data from X-ray crystallography and wide-angle X-ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot-spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all-atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all-atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Protein flexibility and conformational states of Leishmania antigen eIF-4A: identification of a novel plausible protein adjuvant using comparative genomics and molecular modeling

Recent homology modeling studies have identified specific residues (epitope) of the Leishmania RNA helicase protein (LmeIF) that stimulates production of IL-12 cytokine. However, question remains concerning how LmeIF's N-terminal moiety initiates adjuvant effects. Extensive molecular modeling combining the normal mode analysis (NMA) and molecular dynamics simulations, in the present study, has demonstrated that the LmeIF structure may exist in two different forms corresponding to the extended and collapsed (closed) states of the entire structure. The computational results showed that the two domains of the LmeIF structure tend to undergo large fluctuations in a concerted fashion and have strong effect on the solvent accessible surface of the epitope situated on the N-terminal structure. The conformational freedom of the C-terminal domains may explain why the entire LmeIF protein is not as active as the N-terminal moiety. Thereafter, a comparative genome analysis with subsequent homology modeling and molecular electrostatic potential (MEP) techniques allowed us to predict a novel and plausible RNA helicase (LI-helicase) from the Listeria source with adjuvant property as observed for the Leishmania eIF-4A protein. The structural folding and MEP maps revealed similar topologies of the epitope of both LmeIF and LI-helicase proteins and striking identity in the local disposition of the charged groups. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:7.

Coarse-grained modeling of the structural states and transition underlying the powerstroke of dynein motor domain

This study aims to model a minimal dynein motor domain capable of motor function, which consists of the linker domain, six AAA+ modules (AAA1-AAA6), coiled coil stalk, and C-terminus domain. To this end, we have used the newly solved X-ray structures of dynein motor domain to perform a coarse-grained modeling of dynein's post- and pre-powerstroke conformation and the conformational transition between them. First, we have used normal mode analysis to identify a single normal mode that captures the coupled motions of AAA1-AAA2 closing and linker domain rotation, which enables the ATP-driven recovery stroke of dynein. Second, based on the post-powerstroke conformation solved crystallographically, we have modeled dynein's pre-powerstroke conformation by computationally inducing AAA1-AAA2 closing and sliding of coiled coil stalk, and the resulting model features a linker domain near the pre-powerstroke position and a slightly tilted stalk. Third, we have modeled the conformational transition from pre- to post-powerstroke conformation, which predicts a clear sequence of structural events that couple microtubule binding, powerstroke and product release, and supports a signaling path from stalk to AAA1 via AAA3 and AAA4. Finally, we have found that a closed AAA3-AAA4 interface (compatible with nucleotide binding) is essential to the mechano-chemical coupling in dynein. Our modeling not only offers unprecedented structural insights to the motor function of dynein as described by past single-molecule, fluorescence resonance energy transfer, and electron microscopy studies, but also provides new predictions for future experiments to test.

Conservation of functionally important global motions in an enzyme superfamily across varying quaternary structures

The α-d-phosphohexomutase superfamily comprises enzymes involved in carbohydrate metabolism that are found in all kingdoms of life. Recent biophysical studies have shown for the first time that several of these enzymes exist as dimers in solution, prompting an examination of the oligomeric state of all proteins of known structure in the superfamily (11 different proteins; 31 crystal structures) via computational and experimental analyses. We find that these proteins range in quaternary structure from monomers to tetramers, with 6 of the 11 known structures being likely oligomers. The oligomeric state of these proteins not only is associated in some cases with enzyme subgroup (i.e., substrate specificity) but also appears to depend on domain of life, with the two archaeal proteins existing as higher-order oligomers. Within the oligomers, three distinct interfaces are observed, one of which is found in both archaeal and bacterial proteins. Normal mode analysis shows that the topological arrangement of the oligomers permits domain 4 of each protomer to move independently as required for catalysis. Our analysis suggests that the advantages associated with protein flexibility in this enzyme family are of sufficient importance to be maintained during the evolution of multiple independent oligomers. This study is one of the first showing that global motions may be conserved not only within protein families but also across members of a superfamily with varying oligomeric structures.

Conformational analysis of Clostridium difficile toxin B and its implications for substrate recognition

Clostridium difficile (C. difficile) is an opportunistic pathogen that can cause potentially lethal hospital-acquired infections. The cellular damage that it causes is the result of two large clostridial cytotoxins: TcdA and TcdB which act by glucosylating cytosolic G-proteins, mis-regulation of which induces apoptosis. TcdB is a large flexible protein that appears to undergo significant structural rearrangement upon accommodation of its substrates: UDP-glucose and a Rho-family GTPase. To characterize the conformational space of TcdB, we applied normal mode and hinge-region analysis, followed by long-timescale unbiased molecular dynamics. In order to examine the TcdB and RhoA interaction, macromolecular docking and simulation of the TcdB/RhoA complex was performed. Generalized Masked Delaunay analysis of the simulations determined the extent of significant motions. This combination of methods elucidated a wide range of motions within TcdB that are reiterated in both the low-cost normal mode analysis and the extensive MD simulation. Of particular interest are the coupled motions between a peripheral 4-helix bundle and a small loop in the active site that must rearrange to allow RhoA entry to the catalytic site. These extensive coupled motions are indicative of TcdB using a conformational capture mechanism for substrate accommodation.

Density-cluster NMA: A new protein decomposition technique for coarse-grained normal mode analysis

Normal mode analysis has emerged as a useful technique for investigating protein motions on long time scales. This is largely due to the advent of coarse-graining techniques, particularly Hooke's Law-based potentials and the rotational-translational blocking (RTB) method for reducing the size of the force-constant matrix, the Hessian. Here we present a new method for domain decomposition for use in RTB that is based on hierarchical clustering of atomic density gradients, which we call Density-Cluster RTB (DCRTB). The method reduces the number of degrees of freedom by 85-90% compared with the standard blocking approaches. We compared the normal modes from DCRTB against standard RTB using 1-4 residues in sequence in a single block, with good agreement between the two methods. We also show that Density-Cluster RTB and standard RTB perform well in capturing the experimentally determined direction of conformational change. Significantly, we report superior correlation of DCRTB with B-factors compared with 1-4 residue per block RTB. Finally, we show significant reduction in computational cost for Density-Cluster RTB that is nearly 100-fold for many examples.

Tightening of the ATP-binding sites induces the opening of P2X receptor channels

The opening of ligand-gated ion channels in response to agonist binding is a fundamental process in biology. In ATP-gated P2X receptors, little is known about the molecular events that couple ATP binding to channel opening. In this paper, we identify structural changes of the ATP site accompanying the P2X2 receptor activation by engineering extracellular zinc bridges at putative mobile regions as revealed by normal mode analysis. We provide evidence that tightening of the ATP sites shaped like open 'jaws' induces opening of the P2X ion channel. We show that ATP binding favours jaw tightening, whereas binding of a competitive antagonist prevents gating induced by this movement. Our data reveal the inherent dynamic of the binding jaw, and provide new structural insights into the mechanism of P2X receptor activation.

The dynamic stator stalk of rotary ATPases

Rotary ATPases couple ATP hydrolysis/synthesis with proton translocation across biological membranes and so are central components of the biological energy conversion machinery. Their peripheral stalks are essential components that counteract torque generated by rotation of the central stalk during ATP synthesis or hydrolysis. Here we present a 2.25-Å resolution crystal structure of the peripheral stalk from Thermus thermophilus A-type ATPase/synthase. We identify bending and twisting motions inherent within the structure that accommodate and complement a radial wobbling of the ATPase headgroup as it progresses through its catalytic cycles, while still retaining azimuthal stiffness necessary to counteract rotation of the central stalk. The conformational freedom of the peripheral stalk is dictated by its unusual right-handed coiled-coil architecture, which is in principle conserved across all rotary ATPases. In context of the intact enzyme, the dynamics of the peripheral stalks provides a potential mechanism for cooperativity between distant parts of rotary ATPases.

The peripheral stalks of rotary ATPases counteract torque generated by rotation of the central stalk during ATP synthesis or hydrolysis. Stewart et al. report the crystal structure of an A-type ATPase/synthase peripheral stalk and identify bending and twisting motions that permit the radial wobbling of the headgroup.

Vinculin motion modes analysis with elastic network model

Vinculin is an important protein for the linkage between adhesion molecules and the actin cytoskeleton. The activation mechanism of vinculin is still controversial. In order to provide useful information for a better understanding of its activation, we analyze the motion mode of vinculin with elastic network model in this work. The results show that, to some extent, the five domains will present structural rigidity in the motion process. The differences between the structure fluctuations of these domains are significant. When vinculin interacted with other partners, the central long alpha-helix of the first domain becomes bent. This bending deformation can weaken the interaction between the first domain and the tail domain. This motion mode of the first domain is in good agreement with the information extracted from some realistic complex structures. With the aid of the anisotropy elastic network mode, we analyze the motion directions of these domains. The fourth domain has a rotational motion. This rotation is favorable for the releasing of the tail domain from the pincer-like clamp, which is formed by the first and the third domain. All these motion modes are an inherent feature of the structure, and these modes mainly depend on the topology character of the structure.

Rapid simulation of protein motion: merging flexibility, rigidity and normal mode analyses

Protein function frequently involves conformational changes with large amplitude on timescales which are difficult and computationally expensive to access using molecular dynamics. In this paper, we report on the combination of three computationally inexpensive simulation methods--normal mode analysis using the elastic network model, rigidity analysis using the pebble game algorithm, and geometric simulation of protein motion--to explore conformational change along normal mode eigenvectors. Using a combination of ElNemo and First/Froda software, large-amplitude motions in proteins with hundreds or thousands of residues can be rapidly explored within minutes using desktop computing resources. We apply the method to a representative set of six proteins covering a range of sizes and structural characteristics and show that the method identifies specific types of motion in each case and determines their amplitude limits.

Normal mode-based approaches in receptor ensemble docking

Explicitly accounting for target flexibility in docking still constitutes a difficult challenge due to the high dimensionality of the conformational space to be sampled. This especially applies to the high-throughput scenario, where the screening of hundreds of thousands compounds takes place. The use of multiple receptor conformations (MRCs) to perform ensemble docking in a sequential fashion is a simple but powerful approach that allows to incorporate binding site structural diversity in the docking process. Whenever enough experimental structures to build a diverse ensemble are not available, normal mode analysis provides an appealing and efficient approach to in silico generate MRCs by distortion along few low-frequency modes that represent collective mid- and large-scale displacements. In this way, the dimension of the conformational space to be sampled is heavily reduced. This methodology is especially suited to incorporate target flexibility at the backbone level. In this chapter, the main components of normal mode-based approaches in the context of ensemble docking are presented and explained, including the theoretical and practical considerations needed for the successful development and implementation of this methodology.

Optimized torsion-angle normal modes reproduce conformational changes more accurately than cartesian modes

We present what to our knowledge is a new method of optimized torsion-angle normal-mode analysis, in which the normal modes move along curved paths in Cartesian space. We show that optimized torsion-angle normal modes reproduce protein conformational changes more accurately than Cartesian normal modes. We also show that orthogonalizing the displacement vectors from torsion-angle normal-mode analysis and projecting them as straight lines in Cartesian space does not lead to better performance than Cartesian normal modes. Clearly, protein motion is more naturally described by curved paths in Cartesian space.

Insights into the structural stability of Bax from molecular dynamics simulations at high temperatures

Bax is a member of the Bcl-2 protein family that participates in mitochondrion-mediated apoptosis. In the early stages of the apoptotic pathway, this protein migrates from the cytosol to the outer mitochondrial membrane, where it is inserted and usually oligomerizes, making cytochrome c-compatible pores. Although several cellular and structural studies have been reported, a description of the stability of Bax at the molecular level remains elusive. This article reports molecular dynamics simulations of monomeric Bax at 300, 400, and 500 K, focusing on the most relevant structural changes and relating them to biological experimental results. Bax gradually loses its α-helices when it is submitted to high temperatures, yet it maintains its globular conformation. The resistance of Bax to adopt an extended conformation could be due to several interactions that were found to be responsible for maintaining the structural stability of this protein. Among these interactions, we found salt bridges, hydrophobic interactions, and hydrogen bonds. Remarkably, salt bridges were the most relevant to prevent the elongation of the structure. In addition, the analysis of our results suggests which conformational movements are implicated in the activation/oligomerization of Bax. This atomistic description might have important implications for understanding the functionality and stability of Bax in vitro as well as within the cellular environment.

Predicting protein ligand binding motions with the conformation explorer

BACKGROUND

Knowledge of the structure of proteins bound to known or potential ligands is crucial for biological understanding and drug design. Often the 3D structure of the protein is available in some conformation, but binding the ligand of interest may involve a large scale conformational change which is difficult to predict with existing methods.

RESULTS

We describe how to generate ligand binding conformations of proteins that move by hinge bending, the largest class of motions. First, we predict the location of the hinge between domains. Second, we apply an Euler rotation to one of the domains about the hinge point. Third, we compute a short-time dynamical trajectory using Molecular Dynamics to equilibrate the protein and ligand and correct unnatural atomic positions. Fourth, we score the generated structures using a novel fitness function which favors closed or holo structures. By iterating the second through fourth steps we systematically minimize the fitness function, thus predicting the conformational change required for small ligand binding for five well studied proteins.

CONCLUSIONS

We demonstrate that the method in most cases successfully predicts the holo conformation given only an apo structure.

Changes in dynamics upon oligomerization regulate substrate binding and allostery in amino acid kinase family members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities.

Protein function requires a three-dimensional structure with specific dynamic features for catalytic and binding events, and, in many cases, the structure results from the assembly of more than one polypeptide chain (also called monomer or subunit) to form an oligomer or multimer. Proteins such as hemoglobin or chaperonin GroEL are oligomers formed by 2 and 14 subunits, respectively, whereas virus capsids are multimers composed of hundreds of monomers. In these cases, the architecture of the interface between the subunits and the overall assembly geometry are essential in determining the functional motions that these sophisticated structures are able to perform under physiological conditions. Here we present results from our computational study of the large-amplitude motions of dimeric and hexameric proteins that belong to the Amino Acid Kinase family. Our study reveals that the monomers in these oligomeric proteins are arranged in such a way that the oligomer inherits the intrinsic dynamic features of its components. The packing geometry additionally confers the ability to perform highly cooperative conformational changes that involve all monomers and enable the biological activity of the multimer. The study highlights the significance of the quaternary design in favoring the oligomer dynamics that enables ligand-binding and allosteric regulation functions.

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Characterizing protein motions from structure

To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.

Ligand-induced conformational change of a protein reproduced by a linear combination of displacement vectors obtained from normal mode analysis

The conformational change of a protein upon ligand binding was examined by normal mode analysis (NMA) based on an elastic-network model (ENM) for a full-atom system using dihedral angles as independent variables. Specifically, we investigated the extent to which conformational change vectors of atoms from an apo form to a holo form of a protein can be represented by a linear combination of the displacement vectors of atoms in the apo form calculated for the lowest-frequency m normal modes (m=1, 2,…, 20). In this analysis, the latter vectors were best fitted to the former ones by the least-squares method. Twenty-two paired proteins in the holo and apo forms, including three dimer pairs, were examined. The results showed that, in most cases, the conformational change vectors were reproduced well by a linear combination of the displacement vectors of a small number of low-frequency normal modes. The conformational change around an active site was reproduced as well as the entire conformational change, except for some proteins that only undergo significant conformational changes around active sites. The weighting factors for 20 normal modes optimized by the least-squares fitting characterize the conformational changes upon ligand binding for these proteins. The conformational changes sampled around the apo form of a protein by the linear combination of the displacement vectors obtained by ENM-based NMA may help solve the flexible-docking problem of a protein with another molecule because the results presented herein suggest that they have a relatively high probability of being involved in an actual conformational change.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.

Mechanism of kinase inactivation and nonbinding of FRATide to GSK3β due to K85M mutation: molecular dynamics simulation and normal mode analysis

As a serine/threonine protein kinase, glycogen synthase kinase 3β (GSK3β) is an essential component of several cellular processes, including insulin, growth factor, and Wnt signaling. The conserved K85 is important to GSK3β activity and FRATide binding. To elucidate the mechanisms concerning kinase inactivation and nonbinding of FRATide to GSK3β, molecular dynamics (MD) simulation, molecular mechanics generalized Born/surface area (MM_GBSA) calculation, and normal mode analysis (NMA) were performed on both the wild-type (WT) and the K85M mutation of the GSK3β-FRATide complex. The results revealed that the periodic open-closed conformational change of the G loop, together with the compact conformation of the RD pocket, was disturbed in the K85M mutant, in contrast to those in the WT. This in turn caused inhibition of GSK3β. Specifically, the correct folding pattern of GSK3β was disrupted in the K85M mutant, resulting in the loss of two key hydrogen bonds between K214 of FRATide and E290 and K292 of GSK3β, respectively. Furthermore, MM_GBSA calculations indicated that the K85M mutation could lead to a less energy-favorable GSK3β-FRATide complex. In addition, NMA demonstrated that the "rocking" of the N- and C-terminal domains of GSK3β, which coordinates the mutual movement of both lobes, inducing the opening and closing of the active site of GSK3β, which may assist the entry of ATP into the ATP binding site and the release of the ADP product. Strikingly, this phenomenon was not clearly observed in the K85M mutation. This study provides a structural basis for the effect of the K85M mutation on the GSK3β-FRATide complex.

Normal modes of prion proteins: from native to infectious particle

Prion proteins (PrP) are the infectious agent in transmissible spongiform encephalopathies (i.e., mad cow disease). To be infectious, prion proteins must undergo a conformational change involving a decrease in α-helical content along with an increase in β-strand content. This conformational change was evaluated by means of elastic normal modes. Elastic normal modes show a diminution of two α-helices by one and two residues, as well as an extension of two β-strands by three residues each, which could instigate the conformational change. The conformational change occurs in a region that is compatible with immunological studies, and it is observed more frequently in mutant prions that are prone to conversion than in wild-type prions because of differences in their starting structures, which are amplified through normal modes. These findings are valuable for our comprehension of the conversion mechanism associated with the conformational change in prion proteins.

ReplicOpter: a replicate optimizer for flexible docking

We present a computationally efficient method for flexible refinement of docking predictions that reflects observed motions within a protein's structural class. Using structural homologs, we derive deformation models that capture likely motions. The models or "replicates" typically align along a rigid core, with a handful of flexible loops, linkers and tails. A few replicates can generate a much larger number of conformers, by exchanging each flexible region independently of the others. In this way, 10 replicates of a protein having 6 flexible regions can be used to generate a million conformations of a molecule. While this has obvious advantages in terms of sampling, the cost of assessing energies at every conformer is prohibitive, particularly when both molecules are flexible. Our approach addresses this combinatorial explosion, using key assumptions to compress the sampling by many orders of magnitude. ReplicOpter can perform hierarchical clustering from a list of rigid docking predictions and find nearby structures to any promising cluster representatives. These predicted complexes can then be refined and rescored. ReplicOpter's scoring function includes a Lennard-Jones potential softened using the Anderson-Chandler-Weeks decomposition, a desolvation term derived from the Atomic Contact Energy function, Coulombic electrostatics, hydrogen bonding, and terms to model pi-pi and pi-cation interactions. ReplicOpter has performed well on several recent CAPRI systems. We are presently benchmarking ReplicOpter on the complete docking benchmark set to fully establish its utility in refining rigid docking predictions and identifying near-native solutions.

CAPRI targets T29-T42: proving ground for new docking procedures

The critical assessment of protein interactions (CAPRI) experiment provides a unique opportunity for unbiased assessment of docking procedures. The recent CAPRI targets T29-T42 entailed docking of bound, unbound, and modeled structures, presenting a wide range of prediction difficulty. We submitted accurate predictions for targets T40, T41, and T42, a good prediction for T32 and acceptable predictions for T29 and T34. The accuracy of our docking results generally matched the prediction difficulty; hence, docking of modeled proteins produced less accurate results. However, there were interesting exceptions: an accurate prediction was submitted for the dimer of modeled tetratricopeptide repeat (T42) and only an acceptable prediction for the bound/unbound case T29. The ensembles of docking models produced in the scans included an acceptable or better prediction for every target. We show here that our recently developed postscan reevaluation procedure, which tests propensity and solvation measures of the whole interface and the interface core, successfully distinguished these predictions from false docking models. For enzyme-inhibitor targets, we show that the distance of the interface from the enzyme's centroid ranked high native like docking models. Also, for one case we demonstrate that docking of an ensemble of conformers produced by normal modes analysis can improve the accuracy of the prediction.

Large-scale comparison of protein essential dynamics from molecular dynamics simulations and coarse-grained normal mode analyses

A large-scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse-grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low-frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD.

Coarse-grained representation of protein flexibility. Foundations, successes, and shortcomings

Flexibility is the key magnitude to understand the variety of functions of proteins. Unfortunately, its experimental study is quite difficult, and in fact, most experimental procedures are designed to reduce flexibility and allow a better definition of the structure. Theoretical approaches have become then the alternative but face serious timescale problems, since many biologically relevant deformation movements happen in a timescale that is far beyond the possibility of current atomistic models. In this complex scenario, coarse-grained simulation methods have emerged as a powerful and inexpensive alternative. Along this chapter, we will review these coarse-grained methods, and explain their physical foundations and their range of applicability.

Flexibility of the exportins Cse1p and Xpot depicted by elastic network model

Nucleocytoplasmic transport in eukaryotic cells involves many interactions between macromolecules, and has been an active area for many researchers. However, the precise mechanism still evades us and more efforts are needed to better understand it. In this study, the authors investigated exportins (Cse1p and Xpot) by elastic network interpolation (ENI) and elastic network based normal mode analysis (EN-NMA). Results of the study on Cse1p were in good agreement with the results obtained by molecular dynamics simulation in another study but with the benefit of time-efficiency. First, a formation of ring closure obtained by ENI was observed. Second, HEAT 1 to 3 and HEAT 14 to 17 had the largest values of root mean square deviation (RMSD) which indicated the flexibility of Cse1p during the transition. In the case of Xpot, a possible pathway from nuclear state to cytoplasmic state was shown, and the predicted pathway was also quantitatively analyzed in terms of RMSD. The results suggested two flexible regions of Xpot that might be important to the transporting mechanism. Moreover, the dominant mode of Xpot in the nuclear state obtained by EN-NMA not only showed the tendency to match the predicted pathway to the cytoplasmic state of Xpot, but also displayed the flexible regions of Xpot. A time-efficient computational approach was presented in this paper and the results indicated that the flexibility of tested exportins might be required to perform the biological function of transporting cargos.

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions of various biological nanomachines. Coarse-grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse-grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP-driven transitions in three important biological nanomachines (myosin, F(1) ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines.

SwarmDock and the use of normal modes in protein-protein docking

Here is presented an investigation of the use of normal modes in protein-protein docking, both in theory and in practice. Upper limits of the ability of normal modes to capture the unbound to bound conformational change are calculated on a large test set, with particular focus on the binding interface, the subset of residues from which the binding energy is calculated. Further, the SwarmDock algorithm is presented, to demonstrate that the modelling of conformational change as a linear combination of normal modes is an effective method of modelling flexibility in protein-protein docking.