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

Peptide Inhibitors Targeting the Neisseria gonorrhoeae Pivotal Anaerobic Respiration Factor AniA

Neisseria gonorrhoeae causes the sexually transmitted infection gonorrhea, which is highly prevalent worldwide and has a major impact on reproductive and neonatal health. The superbug status of N. gonorrhoeae necessitates the development of drugs with different mechanisms of action. Here, we focused on targeting the nitrite reductase AniA, which is a pivotal component of N. gonorrhoeae anaerobic respiration and biofilm formation. Our studies showed that gonococci expressing AniA containing the altered catalytic residues D137A and H280A failed to grow under anaerobic conditions, demonstrating that the nitrite reductase function is essential. To facilitate the pharmacological targeting of AniA, new crystal structures of AniA were refined to 1.90-Å and 2.35-Å resolutions, and a phage display approach with libraries expressing randomized linear dodecameric peptides or heptameric peptides flanked by a pair of cysteine residues was utilized. Biopanning experiments led to the identification of 29 unique peptides, with 1 of them, C7-3, being identified multiple times. Evaluation of their ability to interact with AniA using enzyme-linked immunosorbent assay and computational docking studies revealed that C7-3 was the most promising inhibitor, binding near the type 2 copper site of the enzyme, which is responsible for interaction with nitrite. Subsequent enzymatic assays and biolayer interferometry with a synthetic C7-3 and its derivatives, C7-3m1 and C7-3m2, demonstrated potent inhibition of AniA. Finally, the MIC₅₀ value of C7-3 and C7-3m2 against anaerobically grown N. gonorrhoeae was 0.6 mM. We present the first peptide inhibitors of AniA, an enzyme that should be further exploited for antigonococcal drug development.

The Intrinsic Dynamics and Unfolding Process of an Antibody Fab Fragment Revealed by Elastic Network Model

Antibodies have been increasingly used as pharmaceuticals in clinical treatment. Thermal stability and unfolding process are important properties that must be considered in antibody design. In this paper, the structure-encoded dynamical properties and the unfolding process of the Fab fragment of the phosphocholine-binding antibody McPC603 are investigated by use of the normal mode analysis of Gaussian network model (GNM). Firstly, the temperature factors for the residues of the protein were calculated with GNM and then compared with the experimental measurements. A good result was obtained, which provides the validity for the use of GNM to study the dynamical properties of the protein. Then, with this approach, the mean-square fluctuation (MSF) of the residues, as well as the MSF in the internal distance (MSFID) between all pairwise residues, was calculated to investigate the mobility and flexibility of the protein, respectively. It is found that the mobility and flexibility of the constant regions are higher than those of the variable regions, and the six complementarity-determining regions (CDRs) in the variable regions also exhibit relative large mobility and flexibility. The large amplitude motions of the CDRs are considered to be associated with the immune function of the antibody. In addition, the unfolding process of the protein was simulated by iterative use of the GNM. In our method, only the topology of protein native structure is taken into account, and the protein unfolding process is simulated through breaking the native contacts one by one according to the MSFID values between the residues. It is found that the flexible regions tend to unfold earlier. The sequence of the unfolding events obtained by our method is consistent with the hydrogen-deuterium exchange experimental results. Our studies imply that the unfolding behavior of the Fab fragment of antibody McPc603 is largely determined by the intrinsic dynamics of the protein.

Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models

Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations—how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Proteins and other biomolecules are not static but are constantly in motion. Moreover, they possess intrinsic collective motion patterns that are tightly linked to their functions. Thus, an accurate and detailed description of their motions can provide deep insights into their functional mechanisms. For large protein complexes with hundreds of thousands of atoms or more, an atomic level description of the motions can be computationally prohibitive, and so coarse-grained models with fewer structural details are often used instead. However, there can be a big gap between the quality of motions derived from atomic models and those from coarse-grained models. In this work, we solve an important problem in protein dynamics studies: how to preserve the atomic-level accuracy in describing molecular motions while using coarse-grained models? We accomplish this by developing a novel iterative matrix projection method that dramatically speeds up the computations. This method is significant since it promises accurate descriptions of protein motions approaching an all-atom level even for the largest biomolecular complexes. Results shown here for a large molecular chaperonin demonstrate how this can provide new insights into its functional process.

Structural insight into the binding complex: β-arrestin/CCR5 complex

The chemokine receptor 5 (CCR5) belongs to the superfamily of serpentine G protein-coupled receptors (GPCRs). The DRY motif (Asp, Arg, Tyr) of the intracellular loop 2 (ICL2), which is highly conserved in the GPCRs has been shown to be essential for the stability of folding of CCR5 and the interaction with β-arrestin. But the molecular mechanism by which it recognizes and interacts with β-arrestin has not been elucidated. In the present study, we described the active state of the β-arrestin structure using normal mode analysis and characterized the binding cleft of CCR5-ICL2 with β-arrestin using SABRE© docking tool and molecular dynamics simulation. Based on our computational results, we proposed a mode of binding between the ICL2 loop of CCR5 and β-arrestin structure, and modeled the energetically stable β-arrestin/CCR5 complex. In view of CCR5's importance as a therapeutic target for the treatment of HIV, this observation provides novel insight into the β-arrestin/CCR5 pathway. As a result, the current computational study of the detailed β-arrestin/CCR5 binding complex could provide the rationale for the development of next generation of HIV peptide inhibitors as therapeutic agents.

Localized lipid packing of transmembrane domains impedes integrin clustering

Integrin clustering plays a pivotal role in a host of cell functions. Hetero-dimeric integrin adhesion receptors regulate cell migration, survival, and differentiation by communicating signals bidirectionally across the plasma membrane. Thus far, crystallographic structures of integrin components are solved only separately, and for some integrin types. Also, the sequence of interactions that leads to signal transduction remains ambiguous. Particularly, it remains controversial whether the homo-dimerization of integrin transmembrane domains occurs following the integrin activation (i.e. when integrin ectodomain is stretched out) or if it regulates integrin clustering. This study employs molecular dynamics modeling approaches to address these questions in molecular details and sheds light on the crucial effect of the plasma membrane. Conducting a normal mode analysis of the intact αllbβ3 integrin, it is demonstrated that the ectodomain and transmembrane-cytoplasmic domains are connected via a membrane-proximal hinge region, thus merely transmembrane-cytoplasmic domains are modeled. By measuring the free energy change and force required to form integrin homo-oligomers, this study suggests that the β-subunit homo-oligomerization potentially regulates integrin clustering, as opposed to α-subunit, which appears to be a poor regulator for the clustering process. If α-subunits are to regulate the clustering they should overcome a high-energy barrier formed by a stable lipid pack around them. Finally, an outside-in activation-clustering scenario is speculated, explaining how further loading the already-active integrin affects its homo-oligomerization so that focal adhesions grow in size.

Focal adhesions are complex, dynamic structures of multiple proteins that act as the cell's mechanical anchorage to its surrounding. Integrins are proteins linking the cell inner and outer environments, which act as a bridge that crosses the cell membrane. Integrins respond to mechanical loads exerted to them by changing their conformations. Several diseases, such as atherosclerosis and different types of cancer, are caused by altered function of integrins. Essential to the formation of focal adhesions is the process of integrin clustering. Bidirectional integrin signaling involves conformational changes in this protein, clustering, and finally the assembly of a large intracellular adhesion complex. Integrin clustering is defined as the interaction of integrins to form lateral assemblies that eventually lead to focal adhesion formation. The effect of the plasma membrane on formation of integrin clusters has been largely neglected in current literature; subsequently some apparently contradictory data has been reported by a number of researchers in the field. Using a molecular dynamics modeling approach, a computational method that simulates systems in a full-atomic scale, we probe the role of the plasma membrane in integrin clustering and hypothesize a clustering scenario that explains the relationship between integrin activation and focal adhesion growth.

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).

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.

Motion and flexibility in human cytochrome p450 aromatase

The crystal structures of human placental aromatase in complex with the substrate androstenedione and exemestane have revealed an androgen-specific active site and the structural basis for higher order organization. However, X-ray structures do not provide accounts of movements due to short-range fluctuations, ligand binding and protein-protein association. In this work, we conduct normal mode analysis (NMA) revealing the intrinsic fluctuations of aromatase, deduce the internal modes in membrane-free and membrane-integrated monomers as well as the intermolecular modes in oligomers, and propose a quaternary organization for the endoplasmic reticulum (ER) membrane integration. Dynamics of the crystallographic oligomers from NMA is found to be in agreement with the isotropic thermal factors from the X-ray analysis. Calculations of the root mean square fluctuations of the C-alpha atoms from their equilibrium positions confirm that the rigid-core structure of aromatase is intrinsic regardless of the changes in steroid binding interactions, and that aromatase self-association does not deteriorate the rigidity of the catalytic cleft. Furthermore, NMA on membrane-integrated aromatase shows that the internal modes in all likelihood contribute to breathing of the active site access channel. The collective intermolecular hinge bending and twisting modes provide the flexibility in the quaternary association necessary for membrane integration of the aromatase oligomers. Taken together, fluctuations of the active site, the access channel, and the heme-proximal cavity, and a dynamic quaternary organization could all be essential components of the functional aromatase in its role as an ER membrane-embedded steroidogenic enzyme.

Elastic network model-based normal mode analysis reveals the conformational couplings in the tripartite AcrAB-TolC multidrug efflux complex

The AcrAB-TolC drug efflux system, energized by proton movement down the transmembrane electrochemical gradient, is responsible for the resistance of the organism to a wide range of drugs. Experimental data suggest functional roles of each part of the assembly, but the detailed working mechanism of this machinery remains elusive. We used elastic network-based normal mode analysis (NMA) to explore the conformational dynamics of the AcrAB-TolC complex. The intrinsic flexibilities of the pore domain in AcrB monomer conform to the previously proposed three-step functionally rotating mechanism for asymmetric AcrB trimer. Conformational couplings across monomers in the AcrB trimer were observed, and the coupling between the transmembrane domain and the other parts of AcrB are strengthened through trimeric assembly. In the tripartite AcrAB-TolC assembly obtained through molecular docking, concerted motions were observed not only at the direct contact interfaces between various components but also between distant parts of the whole complex. The presence of AcrA was shown to significantly strengthen the motional couplings between AcrB and TolC. Overall, NMA revealed an allosteric network in the AcAB-TolC efflux system, which provides hints to our understanding of its detailed working mechanism.

Accurate prediction of the bound form of the Akt pleckstrin homology domain using normal mode analysis to explore structural flexibility

Molecular docking is often performed with rigid receptors. This can be a serious limitation, since the receptor often differs between bound and unbound forms or between bound forms with different ligands. We recently developed a normal-mode based docking method and showed that it is possible to obtain reasonable estimates of the complexed form of the pleckstrin homology (PH) domain of Akt, starting with the free form of the receptor. With inositol (1,3,4,5)-tetrakisphosphate (IP4) as the ligand the docked results agree with the known high-resolution X-ray crystal structure of the IP4-Akt PH domain complex. We also tested our methods with PH4, SC66, and PIT-1, several recently designed PH domain inhibitors. The results are shown to be consistent with available experimental data and previous modeling studies. The method we described can be used for molecular docking analysis even when only an approximation of the experimental structure or model is known.

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.

A molecular dynamics investigation of vinculin activation

Vinculin activation plays a critical role in focal adhesion initiation and formation. In its native state, vinculin is in an autoinhibitory conformation in which domain 1 prevents interaction of the vinculin tail domain with actin by steric hindrance. Once activated, vinculin is able to interact with both actin and talin. Several hypotheses have been put forth addressing the mechanisms of vinculin activation. One set of studies suggests that vinculin interaction with talin is sufficient to cause activation, whereas another set of studies suggests that a simultaneous interaction with several binding partners is necessary to achieve vinculin activation. Using molecular-dynamics (MD) simulations, we investigate the mechanisms of vinculin activation and suggest both a trajectory of conformational changes leading to vinculin activation, and key structural features that are likely involved in stabilizing the autoinhibited conformation. Assuming that the simultaneous interaction of vinculin with both actin and talin causes a stretching force on vinculin, and that vinculin activation results from a removal of steric hindrance blocking the actin-binding sites, we simulate with MD the stretching and activation of vinculin. The MD simulations are further confirmed by normal-mode analysis and simulation after residue modification. Taken together, the results of these simulations suggest that bending of the vinculin-binding-site region in vinculin away from the vinculin tail is the likely trajectory of vinculin activation.

Group theory and biomolecular conformation: I. Mathematical and computational models

Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes.

Shape-Dependent Global Deformation Modes of Large Protein Structures

Conformational changes are central to the functioning of pore-forming proteins that open and close their molecular gates in response to external stimuli such as pH, ionic strength, membrane voltage or ligand binding. Normal mode analysis (NMA) is used to identify and characterize the slowest motions in the gA, KcsA, ClC-ec1, LacY and LeuT(Aa) proteins at the onset of gating. Global deformation modes of the essentially cylindrical gA, KcsA, LacY and LeuT(Aa) biomolecules are reminiscent of global twisting, transverse and longitudinal motions in a homogeneous elastic rod. The ClC-ec1 protein executes a splaying motion in the plane perpendicular to the lipid bilayer. These global collective deformations are determined by protein shape. New methods, all-atom Monte Carlo Normal Mode Following and its simplification using a rotation-translation of protein blocks (RTB), are described and applied to gain insight into the nature of gating transitions in gA and KcsA. These studies demonstrate the severe limitations of standard NMA in characterizing the structural rearrangements associated with gating transitions. Comparison of all-atom and RTB transition pathways in gA clearly illustrates the impact of the rigid protein block approximation and the need to include all degrees of freedom and their relaxation in computational studies of protein gating. The effects of atomic level structure, pH, hydrogen bonding and charged residues on the large scale conformational changes associated with gating transitions are discussed.

FiberDock: Flexible induced-fit backbone refinement in molecular docking

Upon binding, proteins undergo conformational changes. These changes often prevent rigid-body docking methods from predicting the 3D structure of a complex from the unbound conformations of its proteins. Handling protein backbone flexibility is a major challenge for docking methodologies, as backbone flexibility adds a huge number of degrees of freedom to the search space, and therefore considerably increases the running time of docking algorithms. Normal mode analysis permits description of protein flexibility as a linear combination of discrete movements (modes). Low-frequency modes usually describe the large-scale conformational changes of the protein. Therefore, many docking methods model backbone flexibility by using only few modes, which have the lowest frequencies. However, studies show that due to molecular interactions, many proteins also undergo local and small-scale conformational changes, which are described by high-frequency normal modes. Here we present a new method, FiberDock, for docking refinement which models backbone flexibility by an unlimited number of normal modes. The method iteratively minimizes the structure of the flexible protein along the most relevant modes. The relevance of a mode is calculated according to the correlation between the chemical forces, applied on each atom, and the translation vector of each atom, according to the normal mode. The results show that the method successfully models backbone movements that occur during molecular interactions and considerably improves the accuracy and the ranking of rigid-docking models of protein-protein complexes. A web server for the FiberDock method is available at: http://bioinfo3d.cs.tau.ac.il/FiberDock.

Higher susceptibility to halothane modulation in open- than in closed-channel alpha4beta2 nAChR revealed by molecular dynamics simulations

The neuronal alpha4beta2 nicotinic acetylcholine receptor (nAChR) is a potential molecular target for general anesthetics. It is unclear, however, whether anesthetic action produces the same effect on the open and closed channels. Computations parallel to our previous open channel study (J. Phys. Chem. B 2009, 113, 12581) were performed on the closed-channel alpha4beta2 nAChR to investigate the conformation-dependent anesthetic effects on channel structures and dynamics. Flexible ligand docking and over 20 ns molecular dynamics simulations revealed similar halothane-binding sites in the closed and open channels. The sites with relatively high binding affinities (approximately -6.0 kcal/mol) were identified at the interface of extracellular (EC) and transmembrane (TM) domains or at the interface between alpha4 and beta2 subunits. Despite similar sites for halothane binding, the closed-channel conformation showed much less sensitivity than the open channel to the structural and dynamical perturbations from halothane. Compared to the systems without anesthetics, the amount of water inside the pore decreased by 22% in the presence of halothane in the open channel but only by 6% in the closed channel. Comparison of the nonbonded interactions at the EC/TM interfaces suggested that the beta2 subunits were more prone than the alpha4 subunits to halothane binding. In addition, our data support the notion that halothane exerts its effect by disturbing the quaternary structure and dynamics of the channel. The study concludes that sensitivity and global dynamics responsiveness of alpha4beta2 nAChR to halothane are conformation dependent. The effect of halothane on the global dynamics of the open-channel conformation might also account for the action of other inhaled general anesthetics.

General anesthetic binding to neuronal alpha4beta2 nicotinic acetylcholine receptor and its effects on global dynamics

The neuronal alpha4beta2 nicotinic acetylcholine receptor (nAChR) is a target for general anesthetics. Currently available experimental structural information is inadequate to understand where anesthetics bind and how they modulate the receptor motions essential to function. Using our published open-channel structure model of alpha4beta2 nAChR, we identified and evaluated six amphiphilic interaction sites for the volatile anesthetic halothane via flexible ligand docking and subsequent 20-ns molecular dynamics simulations. Halothane binding energies ranged from -6.8 to -2.4 kcal/mol. The primary binding sites were located at the interface of extracellular and transmembrane domains, where halothane perturbed conformations of, and widened the gap among, the Cys loop, the beta1-beta2 loop, and the TM2-TM3 linker. The halothane with the highest binding affinity at the interface between the alpha4 and beta2 subunits altered interactions between the protein and nearby lipids by competing for hydrogen bonds. Gaussian network model analyses of the alpha4beta2 nAChR structures at the end of 20-ns simulations in the absence or presence of halothane revealed profound changes in protein residue mobility. The concerted motions critical to protein function were also perturbed considerably. Halothane's effect on protein dynamics was not confined to the residues adjacent to the binding sites, indicating an action on a more global scale.

Coarse-grained modeling of allosteric regulation in protein receptors

Allosteric regulation provides highly specific ligand recognition and signaling by transmembrane protein receptors. Unlike functions of protein molecular machines that rely on large-scale conformational transitions, signal transduction in receptors appears to be mediated by more subtle structural motions that are difficult to identify. We describe a theoretical model for allosteric regulation in receptors that addresses a fundamental riddle of signaling: What are the structural origins of the receptor agonism (specific signaling response to ligand binding)? The model suggests that different signaling pathways in bovine rhodopsin or human beta(2)-adrenergic receptor can be mediated by specific structural motions in the receptors. We discuss implications for understanding the receptor agonism, particularly the recently observed "biased agonism" (selected activation of specific signaling pathways), and for developing rational structure-based drug-design strategies.

Molecular mechanics of the alpha-actinin rod domain: bending, torsional, and extensional behavior

α-Actinin is an actin crosslinking molecule that can serve as a scaffold and maintain dynamic actin filament networks. As a crosslinker in the stressed cytoskeleton, α-actinin can retain conformation, function, and strength. α-Actinin has an actin binding domain and a calmodulin homology domain separated by a long rod domain. Using molecular dynamics and normal mode analysis, we suggest that the α-actinin rod domain has flexible terminal regions which can twist and extend under mechanical stress, yet has a highly rigid interior region stabilized by aromatic packing within each spectrin repeat, by electrostatic interactions between the spectrin repeats, and by strong salt bridges between its two anti-parallel monomers. By exploring the natural vibrations of the α-actinin rod domain and by conducting bending molecular dynamics simulations we also predict that bending of the rod domain is possible with minimal force. We introduce computational methods for analyzing the torsional strain of molecules using rotating constraints. Molecular dynamics extension of the α-actinin rod is also performed, demonstrating transduction of the unfolding forces across salt bridges to the associated monomer of the α-actinin rod domain.

The cell interacts with its environment in both biochemical and mechanical ways. In this study we explore one of the ways in which the cell interacts mechanically with its environment. α-Actinin is a cytoskeletal crosslinker: it functions to scaffold the cytoskeletal actin filaments that provide mechanical reinforcement to the cell. In its functional environment α-actinin is exposed to a multitude of mechanical stresses as it attaches itself to a dynamic network of actin filaments. The actin filaments extend, rotate, and bend the α-actinin crosslinkers. In this study we employ molecular dynamics techniques to understand the structural characteristics of α-actinin that underlie its ability to provide a scaffold in such a stressed environment. We analyzed the natural frequencies of α-actinin and simulated force-induced bending, extension, and twisting. Our results suggest that α-actinin has structural flexibility facilitating crosslinking in a dynamic environment and also structural rigidity stabilizing the linkage in the stressed environment. We have discovered novel natural bending movements of the rod domain that enhance its function as a crosslinker. We have also demonstrated the specific structural characteristics of α-actinin that give it the previously suggested property of having partial flexibility. Our results enhance the understanding of structural mechanics in the cytoskeletal molecules.

Structural improvement of unliganded simian immunodeficiency virus gp120 core by normal-mode-based X-ray crystallographic refinement

The envelope protein gp120/gp41 of simian and human immunodeficiency viruses plays a critical role in viral entry into host cells. However, the extraordinarily high structural flexibility and heavy glycosylation of the protein have presented enormous difficulties in the pursuit of high-resolution structural investigation of some of its conformational states. An unliganded and fully glycosylated gp120 core structure was recently determined to 4.0 A resolution. The rather low data-to-parameter ratio limited refinement efforts in the original structure determination. In this work, refinement of this gp120 core structure was carried out using a normal-mode-based refinement method that has been shown in previous studies to be effective in improving models of a supramolecular complex at 3.42 A resolution and of a membrane protein at 3.2 A resolution. By using only the first four nonzero lowest-frequency normal modes to construct the anisotropic thermal parameters, combined with manual adjustments and standard positional refinement using REFMAC5, the structural model of the gp120 core was significantly improved in many aspects, including substantial decreases in R factors, better fitting of several flexible regions in electron-density maps, the addition of five new sugar rings at four glycan chains and an excellent correlation of the B-factor distribution with known structural flexibility. These results further underscore the effectiveness of this normal-mode-based method in improving models of protein and nonprotein components in low-resolution X-ray structures.

Principles of flexible protein-protein docking

Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.

Signaling pathways of PDZ2 domain: a molecular dynamics interaction correlation analysis

PDZ domains are found in many signaling proteins. One of their functions is to provide scaffolds for forming membrane-associated protein complexes by binding to the carboxyl termini of their partners. PDZ domains are thought also to play a signal transduction role by propagating the information that binding has occurred to remote sites. In this study, a molecular dynamics (MD) simulation-based approach, referred to as an interaction correlation analysis, is applied to the PDZ2 domain to identify the possible signal transduction pathways. A residue correlation matrix is constructed from the interaction energy correlations between all residue pairs obtained from the MD simulations. Two continuous interaction pathways, starting at the ligand binding pocket, are identified by a hierarchical clustering analysis of the residue correlation matrix. One pathway is mainly localized at the N-terminal side of helix alpha1 and the adjacent C-terminus of loop beta1-beta2. The other pathway is perpendicular to the central beta-sheet and extends toward the side of PDZ2 domain opposite to the ligand binding pocket. The results complement previous studies based on multiple sequence analysis, NMR, and MD simulations. Importantly, they reveal the energetic origin of the long-range coupling. The PDZ2 results, as well as the earlier rhodopsin analysis, show that the interaction correlation analysis is a robust approach for determining pathways of intramolecular signal transduction.

Rods-on-string idealization captures semiflexible filament dynamics

We present an approach to modeling the two-dimensional Brownian dynamics of semiflexible filaments in the worm-model description as uniform, isotropic, and continuously flexible. Experimental observations increasingly show that the mechanical behavior of semiflexible filament networks departs from conventional knowledge. A force-balance-based dynamic simulation of the filament networks has multiple advantages as an approach to understanding their anomalous mechanics. However, a major disadvantage is the difficulty of capturing filament hydrodynamics and bending mechanics in a computationally efficient and physically consistent manner. To that end, we propose a strategy for modeling semiflexible filaments which involves idealizing a semiflexible filament as a contiguous string of flexible rods, and considering the Brownian forces on it as Einsteinian-like point normal and tangential forces. By idealizing the filament as a string of rods, we avoid the complex hydrodynamic treatment involved in beads-on-string idealizations, and implement large-deflection beam mechanics and filament inextensibility in a natural manner, while reducing the computational size of the problem. By considering the Brownian forces as point normal and tangential forces, we decompose the Brownian forces on straight and curved segments into a combination of classical resultant forces and couples whose distribution is shown to be governed by the rod diffusion coefficients. The decomposition allows solution of the Euler beam equations to second-order continuity between segments and fifth-order continuity within segments. We show that the approach is physically consistent by capturing multiple Brownian phenomena ranging from the rigid to the semiflexible limit: the translational and rotational diffusion of rigid rods; the thermal fluctuation of semirigid cantilever filaments; and the shape, bending, and time relaxation of freely diffusing, semiflexible actin filaments.

A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography

In this article, we report a method for coarse-grained normal mode analysis called the minimalist network model. The main features of the method are that it can deliver accurate low-frequency modes on structures without undergoing initial energy minimization and that it also retains the details of molecular interactions. The method does not require any additional adjustable parameters after coarse graining and is computationally very fast. Tests on modeling the experimentally measured anisotropic displacement parameters in biomolecular x-ray crystallography demonstrate that the method can consistently perform better than other commonly used methods including our own one. We expect this method to be effective for applications such as structural refinement and conformational sampling.

Folding of small helical proteins assisted by small-angle X-ray scattering profiles

This paper reports a computational method for folding small helical proteins. The goal was to determine the overall topology of proteins given secondary structure assignment on sequence. In doing so, a Monte Carlo protocol, which combines coarse-grained normal modes and a Hamiltonian at a different scale, was developed to enhance sampling. In addition to the knowledge-based potential functions, a small-angle X-ray scattering (SAXS) profile was also used as a weak constraint for guiding the folding. The algorithm can deliver structural models with overall correct topology, which makes them similar to those of 5 approximately 6 A cryo-EM density maps. The success could contribute to make the SAXS technique a fast and inexpensive solution-phase experimental method for determining the overall topology of small, soluble, but noncrystallizable, helical proteins.

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

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

The conformational coupling and translocation mechanism of vitamin B12 ATP-binding cassette transporter BtuCD

ATP-binding cassette transporter BtuCD mediating vitamin B(12) uptake in Escherichia coli couples the energy of ATP hydrolysis to the translocation of vitamin B(12) across the membrane into the cell. Elastic normal mode analysis of BtuCD demonstrates that the simultaneous substrate trapping at periplasmic cavity and ATP binding at the ATP-binding cassette (BtuD) dimer proceeds readily along the lowest energy pathway. The transport power stroke is attributed to ATP-hydrolysis-induced opening of the nucleotide-binding domain dimer, which is coupled to conformational rearrangement of transmembrane domain (BtuC) helices leading to the closing at the periplasmic side and opening at the cytoplasmic gate. Simultaneous hydrolysis of two ATP is supported by the fact that antisymmetric movement of BtuD dimer implying alternating hydrolysis cannot induce effective conformational change of the translocation pathway. A plausible mechanism of translocation cycle is proposed in which the possible effect of the association of periplasmic binding protein BtuF to the transporter is also considered.

Dynamics of heteropentameric nicotinic acetylcholine receptor: implications of the gating mechanism

The dynamics characteristics of the currently available structure of Torpedo nicotinic acetylcholine receptor (nAChR), including the extracellular, transmembrane, and intracellular domains (ICDs), were analyzed using the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM). We found that a symmetric quaternary twist motion, reported previously in the literature in a homopentameric receptor (Cheng et al. J Mol Biol 2006;355:310-324; Taly et al. Biophys J 2005;88:3954-3965), occurred also in the heteropentameric Torpedo nAChR. We believe, however, that the symmetric twist alone is not sufficient to explain a large body of experimental data indicating asymmetry and subunit nonequivalence during gating. Here we report our results supporting the hypothesis that a combination of symmetric and asymmetric motions opens the gate. We show that the asymmetric motion involves tilting of the TM2 helices. Furthermore, our study reveals three additional aspects of channel dynamics: (1) loop A serves as an allosteric mediator between the ligand binding loops and those at the domain interface, particularly the linker between TM2 and TM3; (2) the ICD can modulate the pore dynamics and thus should not be neglected in gating studies; and (3) the F loops, which are peculiarly longer and poorly-conserved in non-alpha-subunits, have important dynamical implications.

Normal mode refinement of anisotropic thermal parameters for a supramolecular complex at 3.42-A crystallographic resolution

Here we report a normal-mode-based protocol for modeling anisotropic thermal motions of proteins in x-ray crystallographic refinement. The foundation for this protocol is a recently developed elastic normal mode analysis that produces much more accurate eigenvectors without the tip effect. The effectiveness of the procedure is demonstrated on the refinement of a 3.42-A structure of formiminotransferase cyclodeaminase, a 0.5-MDa homooctameric enzyme. Using an order of magnitude fewer adjustable thermal parameters than the conventional isotropic refinement, this protocol resulted in a decrease of the values of R(cryst) and R(free) and improvements of the density map. Several poorly resolved regions in the original isotropically refined structure became clearer so that missing side chains were fitted easily and mistraced backbone was corrected. Moreover, the distribution of anisotropic thermal ellipsoids revealed functionally important structure flexibility. This normal-mode-based refinement is an effective way of describing anisotropic thermal motions in x-ray structures and is particularly attractive for the refinement of very large and flexible supramolecular complexes at moderate resolutions.

Crystal structures of the substrate free-enzyme, and reaction intermediate of the HAD superfamily member, haloacid dehalogenase DehIVa from Burkholderia cepacia MBA4

DehIVa is a haloacid dehalogenase (EC 3.8.1.2) from the soil and water borne bacterium Burkholderia cepacia MBA4, which belongs to the functionally variable haloacid dehalogenase (HAD) superfamily of enzymes. The haloacid dehalogenases catalyse the removal of halides from haloacids resulting in a hydroxlated product. These enzymes are of interest for their potential to degrade recalcitrant halogenated environmental pollutants and their use in the synthesis of industrial chemicals. The haloacid dehalogenases utilise a nucleophilic attack on the substrate by an aspartic acid residue to form an enzyme-substrate ester bond and concomitantly cleaving of the carbon-halide bond and release of a hydroxylated product following ester hydrolysis. We present the crystal structures of both the substrate-free DehIVa refined to 1.93 A resolution and DehIVa covalently bound to l-2-monochloropropanoate trapped as a reaction intermediate, refined to 2.7 A resolution. Electron density consistent with a previously unidentified yet anticipated water molecule in the active site poised to donate its hydroxyl group to the product and its proton to the catalytic Asp11 is evident. It has been unclear how substrate enters the active site of this and related enzymes. The results of normal mode analysis (NMA) are presented and suggest a means whereby the predicted global dynamics of the enzyme allow for entry of the substrate into the active site. In the context of these results, the possible role of Arg42 and Asn178 in a "lock down" mechanism affecting active site access is discussed. In silico substrate docking of enantiomeric substrates has been examined in order to evaluate the enzymes enantioselectivity.

Protein fluctuations and breakdown of time-scale separation in rate theories

A long-time fluctuation correlation function with a power-law form has been observed in recent single-molecule experiments by the Xie group. By analyzing the dynamics of an elastic network model (ENM) under white noise, we show that the observed long-time memory kernel can be explained by the discrepancy between the experimentally measured coordinate (or the coordinate directly coupled to protein function) and the minimum energy path of the system. Consequently, the dynamics of the measured collective coordinate has contributions from degrees of freedoms with a broad distribution of time scales. Our study also implies that the widely used ENM Hamiltonian should be viewed as a coarse-grained model of a protein over a rugged energy landscape. Large effective drag coefficients are needed to describe protein dynamics with the ENM's.

A natural coarse graining for simulating large biomolecular motion

Various coarse graining schemes have been proposed to speed up computer simulations of the motion within large biomolecules, which can contain hundreds of thousands of atoms. We point out here that there is a very natural way of doing this, using the rigid regions identified within a biomolecule as the coarse grain elements. Subsequently, computer resources can be concentrated on the flexible connections between the rigid units. Examples of the use of such techniques are given for the protein barnase and the maltodextrin binding protein, using the geometric simulation technique FRODA and the rigidity enhanced elastic network model RCNMA to compute mobilities and atomic displacements.

A New Method for Coarse-Grained Elastic Normal-Mode Analysis

In this paper, we report a new method for coarse-grained elastic normal-mode analysis. The purpose is to overcome a long-standing problem in the conventional analysis called the tip effect that makes the motional patterns (eigenvectors) of some low-frequency modes irrational. The new method retains the merits of a conventional method such as not requiring lengthy initial energy minimization, which always distorts structures, and also delivers substantially more accurate low-frequency modes with no tip effect for proteins of any size. This improvement of modes is crucial for certain types of applications such as structural refinement or normal-mode-based sampling.

Slow protein conformational dynamics from multiple experimental structures: the helix/sheet transition of arc repressor

Conformational transitions underlie the function of many biomolecular systems. Resolving intermediate structural changes, however, is challenging for both experiments and all-atom simulations because the duration of transitions is short relative to the lifetime of the stable species. Simplified descriptions based on a single experimental structure, such as elastic network models or Gō models, are not immediately applicable. Here, we develop a general method that combines multiple coarse-grained models to capture slow conformational transitions. Individually, each model describes one of the experimental structures; together, they approximate the complete energy surface. We demonstrate the method for the helix-to-sheet transition in Arc repressor N11L. We find that the transition involves the partial unfolding of the switch region, and rapid refolding into the alternate structure. Transient local unfolding is consistent with the low hydrogen exchange protection factors of the switch region. Also in agreement with experiment, the isomerization occurs independently of the global folding/dimerization transition.

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.

Making ATP

We present a mesoscopic model for ATP synthesis by F(1)F(o) ATPase. The model combines the existing experimental knowledge of the F(1) enzyme into a consistent mathematical model that illuminates how the stages in synthesis are related to the protein structure. For example, the model illuminates how specific interactions between the gamma, epsilon, and alpha(3)beta(3) subunits couple the F(o) motor to events at the catalytic sites. The model also elucidates the origin of ADP inhibition of F(1) in its hydrolysis mode. The methodology we develop for constructing the structure-based model should prove useful in modeling other protein motors.

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.

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.

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

MOTIVATION

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

RESULTS

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