Bridging between normal mode analysis and elastic network models

Normal mode analysis (NMA) has been a powerful tool for studying protein dynamics. Elastic network models (ENM), through their simplicity, have made normal mode computations accessible to a much broader research community and for many more biomolecular systems. The drawback of ENMs, however, is that they are less accurate than NMA. In this work, through steps of simplification that starts with NMA and ends with ENMs we build a tight connection between NMA and ENMs. In the process of bridging between the two, we have also discovered several high‐quality simplified models. Our best simplified model has a mean correlation with the original NMA that is as high as 0.88. In addition, the model is force‐field independent and does not require energy minimization, and thus can be applied directly to experimental structures. Another benefit of drawing the connection is a clearer understanding why ENMs work well and how it can be further improved. We discovered that can be greatly enhanced by including an additional torsional term and a geometry term. Proteins 2014; 82:2157–2168. © 2014 Wiley Periodicals, Inc.     

Identification of dynamical correlations within the myosin motor domain by the normal mode analysis of an elastic network model

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

Acyl carrier protein structural classification and normal mode analysis

All acyl carrier protein primary and tertiary structures were gathered into the ThYme database. They are classified into 16 families by amino acid sequence similarity, with members of the different families having sequences with statistically highly significant differences. These classifications are supported by tertiary structure superposition analysis. Tertiary structures from a number of families are very similar, suggesting that these families may come from a single distant ancestor. Normal vibrational mode analysis was conducted on experimentally determined freestanding structures, showing greater fluctuations at chain termini and loops than in most helices. Their modes overlap more so within families than between different families. The tertiary structures of three acyl carrier protein families that lacked any known structures were predicted as well.     

Comparison of intrinsic dynamics of cytochrome p450 proteins using normal mode analysis

Cytochrome P450 enzymes are hemeproteins that catalyze the monooxygenation of a wide‐range of structurally diverse substrates of endogenous and exogenous origin. These heme monooxygenases receive electrons from NADH/NADPH via electron transfer proteins. The cytochrome P450 enzymes, which constitute a diverse superfamily of more than 8,700 proteins, share a common tertiary fold but < 25% sequence identity. Based on their electron transfer protein partner, cytochrome P450 proteins are classified into six broad classes. Traditional methods of protein classification are based on the canonical paradigm that attributes proteins’ function to their three‐dimensional structure, which is determined by their primary structure that is the amino acid sequence. It is increasingly recognized that protein dynamics play an important role in molecular recognition and catalytic activity. As the mobility of a protein is an intrinsic property that is encrypted in its primary structure, we examined if different classes of cytochrome P450 enzymes display any unique patterns of intrinsic mobility. Normal mode analysis was performed to characterize the intrinsic dynamics of five classes of cytochrome P450 proteins. The present study revealed that cytochrome P450 enzymes share a strong dynamic similarity (root mean squared inner product > 55% and Bhattacharyya coefficient > 80%), despite the low sequence identity (< 25%) and sequence similarity (< 50%) across the cytochrome P450 superfamily. Noticeable differences in C_α atom fluctuations of structural elements responsible for substrate binding were noticed. These differences in residue fluctuations might be crucial for substrate selectivity in these enzymes.     

High-throughput modeling and analysis of protein structural dynamics

Protein function is a dynamic property closely related to the conformational mechanisms of protein structure in its physiological environment. To understand and control the function of target proteins, it becomes increasingly important to develop methods and tools for predicting collective motions at the molecular level. In this article, we review computational methods for predicting conformational dynamics and discuss software tools for data analysis. In particular, we discuss a high-throughput, web-based system called iGNM for protein structural dynamics. iGNM contains a database of protein motions for more than 20 000 PDB structures and supports online calculations for newly deposited PDB structures or user-modified structures. iGNM allows dynamics analysis of protein structures ranging from enzymes to large complexes and assemblies, and enables the exploration of protein sequence-structure-dynamics-function relations.     

Large scale motions in a biosensor protein glucose oxidase: a combined approach by QENS, normal mode analysis, and molecular dynamics studies

The characteristics of the glucose oxidase were studied using a combination of experimental and theoretical techniques. Quasi elastic neutron scattering experiments were used to obtain the vibrational frequencies of the protein. These were compared to theoretical results obtained by normal mode analysis. Results indicate a good match between the experimental and theoretical values. Molecular dynamic simulation with covariant analysis was used to study the structure and dynamics of glucose oxidase. Various parameters like the radius of gyration, root mean square fluctuations, solvent accessibility were studied for evaluating the structural stability of the protein. The frequency of vibration calculated from the three methods is used to derive the large scale motions. Theses studies were used to predict the suitable lysine residues for linkage with carbon nanotubes.     

Diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network normal mode analysis

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

Flexible fitting to cryo-electron microscopy maps with coarse-grained elastic network models

Cryo-electron microscopy has become an important tool for protein structure determination in recent decades. Since proteins may exist in multiple conformational states, combining high resolution X-ray or NMR structures with cryo-electron microscopy maps is a useful approach to obtain proteins in different functional states. Flexible fitting methods used in cryo-electron microscopy aim to obtain an unknown protein conformation from a high resolution structure and a cryo-electron microscopy map. Since all-atom flexible fitting is computationally expensive, many efficient flexible fitting algorithms that utilize coarse-grained elastic network models have been proposed. In this study, we investigated performance of three coarse-grained elastic network model-based flexible fitting methods (EMFF, iModFit, NMFF) using 25 protein pairs at four resolutions. This study shows that the application of coarse-grained elastic network models to flexible fitting of cryo-electron microscopy maps can provide fast and fruitful models of various conformational states of proteins.     

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse‐grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass‐weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well‐known proteins of which both closed and open conformations are available as well as three α‐helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.     

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

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

Structural compliance: A new metric for protein flexibility

Proteins are the active players in performing essential molecular activities throughout biology, and their dynamics has been broadly demonstrated to relate to their mechanisms. The intrinsic fluctuations have often been used to represent their dynamics and then compared to the experimental B-factors. However, proteins do not move in a vacuum and their motions are modulated by solvent that can impose forces on the structure. In this paper, we introduce a new structural concept, which has been called the structural compliance, for the evaluation of the global and local deformability of the protein structure in response to intramolecular and solvent forces. Based on the application of pairwise pulling forces to a protein elastic network, this structural quantity has been computed and sometimes is even found to yield an improved correlation with the experimental B-factors, meaning that it may serve as a better metric for protein flexibility. The inverse of structural compliance, namely the structural stiffness, has also been defined, which shows a clear anticorrelation with the experimental data. Although the present applications are made to proteins, this approach can also be applied to other biomolecular structures such as RNA. This present study considers only elastic network models, but the approach could be applied further to conventional atomic molecular dynamics. Compliance is found to have a slightly better agreement with the experimental B-factors, perhaps reflecting its bias toward the effects of local perturbations, in contrast to mean square fluctuations. The code for calculating protein compliance and stiffness is freely accessible at https://jerniganlab.github.io/Software/PACKMAN/Tutorials/compliance .     

Toward the mechanism of dynamical couplings and translocation in hepatitis C virus NS3 helicase using elastic network model

Hepatitis C virus NS3 helicase is an enzyme that unwinds double-stranded polynucleotides in an ATP-dependent reaction. It provides a promising target for small molecule therapeutic agents against hepatitis C. Design of such drugs requires a thorough understanding of the dynamical nature of the mechanochemical functioning of the helicase. Despite recent progress, the detailed mechanism of the coupling between ATPase activity and helicase activity remains unclear. Based on an elastic network model (ENM), we apply two computational analysis tools to probe the dynamical mechanism underlying the allosteric coupling between ATP binding and polynucleotide binding in this enzyme. The correlation analysis identifies a network of hot-spot residues that dynamically couple the ATP-binding site and the polynucleotide-binding site. Several of these key residues have been found by mutational experiments as functionally important, while our analysis also reveals previously unexplored hot-spot residues that are potential targets for future mutational studies. The conformational changes between different crystal structures of NS3 helicase are found to be dominated by the lowest frequency mode solved from the ENM. This mode corresponds to a hinge motion of the highly flexible domain 2. This motion simultaneously modulates the opening/closing of the domains 1-2 cleft where ATP binds, and the domains 2-3 cleft where the polynucleotide binds. Additionally, a small twisting motion of domain 1, observed in both mode 1 and the computed ATP binding induced conformational change, fine-tunes the binding affinity of the domains 1-3 interface for the polynucleotide. The combination of these motions facilitates the translocation of a single-stranded polynucleotide in an inchworm-like manner.     

A comparative study of dynamic structures between phage 434 Cro and repressor proteins by normal mode analysis

Two DNA binding proteins, Cro and the amino-terminal domain of the repressor of bacteriophage 434 (434 Cro and 434 repressor) that regulate gene expression and contain a helix-turn-helix (HTH) motif responsible for their site-specific DNA recognition adopt very similar three-dimensional structures when compared to each other. To reveal structural differences between these two similar proteins, their dynamic structures, as examined by normal mode analysis, are compared in this paper. Two kinds of structural data, one for the monomer and the other for a complex with DNA, for each protein, are used in the analyses. From a comparison between the monomers it is found that the interactions of Ala-24 in 434 Cro or Val-24 in 434 repressor, both located in the HTH motif, with residues 44, 47, 48, and 51 located in the domain facing the motif, and the interactions between residues 17, 18, 28, and 32, located in the HTH motif, cause significant differences in the correlative motions of these residues. From the comparison between the monomer and the complex with DNA for each protein, it was found that the first helix in the HTH motif is distorted in the complex form. While the residues in the HTH motif in 434 Cro have relatively larger positive correlation coefficients of motions with other residues within the HTH motif, such correlations are not large in the HTH motif of 434 repressor. It is suggestive to their specificity because the 434 repressor is less specific than 434 Cro. Although a structural comparison of proteins has been performed mainly from a static or geometrical point of view, this study demonstrates that the comparison from a dynamic point of view, using the normal mode analysis, is useful and convenient to explore a difference that is difficult to find only from a geometrical point of view, especially for proteins very similar in structure. © 1996 Wiley-Liss, Inc.     

Insights from the molecular docking analysis of colistin with the PmrA protein model from Acinetobacter baumannii

Acinetobacter baumannii (AB) is one of the most common causes of nosocomial infections. Therefore, it is of interest to design and develop drugs against Acinetobacter baumannii. A strain of AB showing MIC 32 µg/ml against colistin was isolated from a hospital environment in Iran. Hence, we document data to glean insights from the molecular docking analysis of colistin with the PmrA protein from this bacterium.     

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

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

Dynamic structures of globular proteins with respect to correlative movements of residues calculated in the normal mode analysis

Dynamic structures of globular proteins are studied on the basis of correlative movements of residues around their native conformations, which are computed by means of the normal mode analysis. To describe the dynamic structures of a protein, the core regions moving with strong positive or negative correlations to other regions of the polypeptide chain are detected from the correlation maps of the movements of residues. Such core regions are different, according to the definition, from the regions defined from a geometrical point of view, such as secondary structures, domains, modules, and so on. The core regions are actually detected for four proteins, myoglobin, Bence-Jones protein, flavodoxin, and hen egg-white lysozyme, with different folding types from each other. The results show that some of them coincide with the secondary structures, domains, or modules, but others do not. Then, the dynamic structure of each protein is discussed in terms of the dynamic cores detected, as compared with the secondary structures, domains, and modules.     

Comparison of protein-protein interactions in serine protease-inhibitor and antibody-antigen complexes: implications for the protein docking problem

The protein-protein interaction energy of 12 nonhomologous serine protease-inhibitor and 15 antibody-antigen complexes is calculated using a molecular mechanics formalism and dissected in terms of the main-chain vs. side-chain contribution, nonrotameric side-chain contributions, and amino acid residue type involvement in the interface interaction. There are major differences in the interactions of the two types of protein-protein complex. Protease-inhibitor complexes interact predominantly through a main-chain-main-chain mechanism while antibody-antigen complexes interact predominantly through a side-chain-side-chain or a side-chain-main-chain mechanism. However, there is no simple correlation between the main-chain-main-chain interaction energy and the percentage of main-chain surface area buried on binding. The interaction energy is equally effected by the presence of nonrotameric side-chain conformations, which constitute approximately 20% of the interaction energy. The ability to reproduce the interface interaction energy of the crystal structure if original side-chain conformations are removed from the calculation is much greater in the protease-inhibitor complexes than the antibody-antigen complexes. The success of a rotameric model for protein-protein docking appears dependent on the extent of the main-chain-main-chain contribution to binding. Analysis of (1) residue type and (2) residue pair interactions at the interface show that antibody-antigen interactions are very restricted with over 70% of the antibody energy attributable to just six residue types (Tyr > Asp > Asn > Ser > Glu > Trp) in agreement with previous studies on residue propensity. However, it is found here that 50% of the antigen energy is attributable to just four residue types (Arg = Lys > Asn > Asp). On average just 12 residue pair interactions (6%) contribute over 40% of the favorable interaction energy in the antibody-antigen complexes, with charge-charge and charge/polar-tyrosine interactions being prominent. In contrast protease inhibitors use a diverse set of residue types and residue pair interactions.