Elastic network models capture the motions apparent within ensembles of RNA structures

The role of structure and dynamics in mechanisms for RNA becomes increasingly important. Computational approaches using simple dynamics models have been successful at predicting the motions of proteins and are often applied to ribonucleo-protein complexes but have not been thoroughly tested for well-packed nucleic acid structures. In order to characterize a true set of motions, we investigate the apparent motions from 16 ensembles of experimentally determined RNA structures. These indicate a relatively limited set of motions that are captured by a small set of principal components (PCs). These limited motions closely resemble the motions computed from low frequency normal modes from elastic network models (ENMs), either at atomic or coarse-grained resolution. Various ENM model types, parameters, and structure representations are tested here against the experimental RNA structural ensembles, exposing differences between models for proteins and for folded RNAs. Differences in performance are seen, depending on the structure alignment algorithm used to generate PCs, modulating the apparent utility of ENMs but not significantly impacting their ability to generate functional motions. The loss of dynamical information upon coarse-graining is somewhat larger for RNAs than for globular proteins, indicating, perhaps, the lower cooperativity of the less densely packed RNA. However, the RNA structures show less sensitivity to the elastic network model parameters than do proteins. These findings further demonstrate the utility of ENMs and the appropriateness of their application to well-packed RNA-only structures, justifying their use for studying the dynamics of ribonucleo-proteins, such as the ribosome and regulatory RNAs.     

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 network of dynamically conserved residues deciphers the motions of maltose transporter

The maltose transporter of Escherichia coli is a member of the ATP‐binding cassette (ABC) transporter superfamily. The crystal structures of maltose transporter MalK have been determined for distinct conformations in the presence and absence of the ligand ATP, and other interacting proteins. Using the distinct MalK structures, normal mode analysis was performed to understand the dynamics behavior of the system. A network of dynamically important residues was obtained from the normal mode analysis and the analysis of point mutation on the normal modes. Our results suggest that the intradomain rotation occurs earlier than the interdomain rotation during the maltose‐binding protein (MBP)‐driven conformational changes of MalK. We inquire if protein motion and functional‐driven evolutionary conservation are related. The sequence conservation of MalK was analyzed to derive a network of evolutionarily important residues. There are highly significant correlations between protein sequence and protein dynamics in many regions on the maltose transporter MalK, suggesting a link between the protein evolution and dynamics. The significant overlaps between the network of dynamically important residues and the network of evolutionarily important residues form a network of dynamically conserved residues. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

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.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.     

Conventional NMA as a better standard for evaluating elastic network models

Normal mode analysis (NMA) is an important tool for studying protein dynamics. Because of the complexity of conventional NMA that uses an all‐atom model and a semi‐empirical force field, many simplified NMA models have been developed, some of which are known as elastic network models. The quality of these simplified NMA models was assessed mostly by evaluating their predictions against experimental B‐factors, and rarely by comparing them with the original NMA. In this work, we take the effort to create a publicly accessible dataset of proteins with their minimized structures, NMA modes, and mean‐square fluctuations. Then, for the first time, we evaluate the quality of individual normal modes of several widely used elastic network models by comparing them with the conventional NMA. Our results demonstrate that the conventional NMA presents a better and more complete evaluation measure of the quality of elastic network models. This realization should be very helpful in improving current or designing new, higher quality elastic network models. Moreover, using the conventional NMA as the standard of evaluation, a number of interesting and significant insights into the elastic network models are gained. Proteins 2015; 83:259–267. © 2014 Wiley Periodicals, Inc.     

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.     

Multi-resolution contour-based fitting of macromolecular structures

A novel contour-based matching criterion is presented for the quantitative docking of high-resolution structures of components into low-resolution maps of macromolecular complexes. The proposed Laplacian filter is combined with a six-dimensional search using fast Fourier transforms to rapidly scan the rigid-body degrees of freedom of a probe molecule relative to a fixed target density map. A comparison of the docking performance with the standard cross-correlation criterion demonstrates that contour matching with the Laplacian filter significantly extends the viable resolution range of correlation-based fitting to resolutions as low as 30 A. The gain in docking precision at medium to low resolution (15-30 A) is critical for image reconstructions from electron microscopy (EM). The new algorithm enables for the first time the reliable docking of smaller molecular components into EM densities of large biomolecular assemblies at such low resolutions. As an example of the practical effectiveness of contour-based fitting, a new pseudo-atomic model of a microtubule was constructed from a 20 A resolution EM map and from atomic structures of alpha and beta tubulin subunits.     

Molecular motions and conformational changes of HPPK

6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) belongs to a class of catalytic enzymes involved in phosphoryl transfer and is a new target for the development of novel antimicrobial agents. In the present study, the fundamental consideration is to view the overall structure of HPPK as a network of interacting residues and to extract the most cooperative collective motions that define its global dynamics. A coarse-grained model, harmonically constrained according to HPPK's crystal structure is used. Four crystal structures of HPPK (one apo and three holo forms with different nucleotide and pterin analogs) are studied with the goal of providing insights about the function-dynamic correlation and ligand induced conformational changes. The dynamic differences are examined between HPPK's apo- and holo-forms, because they are involved in the catalytic reaction steps. Our results indicate that the palm-like structure of HPPK is nearly rigid, whereas the two flexible loops: L2 (residues 43-53) and L3 (residues 82-92) exhibit the most concerted motions for ligand recognition and presumably, catalysis. These two flexible loops are involved in the recognition of HPPKs nucleotide and pterin ligands, whereas the rigid palm region is associated with binding of these cognate ligands. Six domains of collective motions are identified, comprised of structurally close but not necessarily sequential residues. Two of these domains correspond to the flexible loops (L2 and L3), whereas the remaining domains correspond to the rigid part of the molecule.     

Dynamics alignment: comparison of protein dynamics in the SCOP database

A novel methodology for comparison of protein dynamics is presented. Protein dynamics is calculated using the Gaussian network model and the modes of motion are globally aligned using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. The alignment is fast and can be used to analyze large sets of proteins. The methodology is applied to the four major classes of the SCOP database: "all alpha proteins," "all beta proteins," "alpha and beta proteins," and "alpha/beta proteins". We show that different domains may have similar global dynamics. In addition, we report that the dynamics of "all alpha proteins" domains are less specific to structural variations within a given fold or superfamily compared with the other classes. We report that domain pairs with the most similar and the least similar global dynamics tend to be of similar length. The significance of the methodology is that it suggests a new and efficient way of mapping between the global structural features of protein families/subfamilies and their encoded dynamics.     

On the relationship between the protein structure and protein dynamics

Recently, we have developed a method (Shih et al., Proteins: Structure, Function, and Bioinformatics 2007;68: 34-38) to compute correlation of fluctuations of proteins. This method, referred to as the protein fixed-point (PFP) model, is based on the positional vectors of atoms issuing from the fixed point, which is the point of the least fluctuations in proteins. One corollary from this model is that atoms lying on the same shell centered at the fixed point will have the same thermal fluctuations. In practice, this model provides a convenient way to compute the average dynamical properties of proteins directly from the geometrical shapes of proteins without the need of any mechanical models, and hence no trajectory integration or sophisticated matrix operations are needed. As a result, it is more efficient than molecular dynamics simulation or normal mode analysis. Though in the previous study the PFP model has been successfully applied to a number of proteins of various folds, it is not clear to what extent this model will be applied. In this article, we have carried out the comprehensive analysis of the PFP model for a dataset comprising 972 high-resolution X-ray structures with pairwise sequence identity or=0.5. Our result shows that the fixed-point model is indeed quite general and will be a useful tool for high throughput analysis of dynamical properties of proteins.     

Gating and conduction of nano-channel forming proteins: a computational approach

Monitoring conformational changes in ion channels is essential to understand their gating mechanism. Here, we explore the structural dynamics of four outer membrane proteins with different structures and functions in the slowest nonzero modes of vibration. Normal mode analysis was performed on the modified elastic network model of channel in the membrane. According to our results, when membrane proteins were analyzed in the dominant mode, the composed pores, TolC and α-hemolysin showed large motions at the intramembrane β-barrel region while, in other porins, OmpA and OmpF, largest motions observed in the region of external flexible loops. A criterion based on equipartition theorem was used to measure the possible amplitude of vibration in channel forming proteins. The current approach complements theoretical and experimental techniques including HOLE, Molecular Dynamics (MD), and voltage clamp used to address the channel’s structure and dynamics and provides the means to conduct a theoretical simultaneous study of the structure and function of the channel.

An animated interactive 3D complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:3     

Large‐scale analysis of the dynamics of enzymes

Protein enzymes enable the cell to execute chemical reactions in short time by accelerating the rate of the reactions in a selective manner. The motions or dynamics of the enzymes are essential for their function. Comparison of the dynamics of a set of 1247 nonhomologous enzymes was performed. For each enzyme, the slowest modes of motion are calculated using the Gaussian network model (GNM) and they are globally aligned. Alignment is done using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. Only 96 pairs of proteins were identified to have three similar GNM slow modes with 63 of them having a similar structure. The most frequent slowest mode of motion describes a two domains anticorrelated motion that characterizes at least 23% of the enzymes. Therefore, dynamics uniqueness cannot be accounted for by the slowest mode itself but rather by the combination of several slow modes. Different quaternary structure packing can restrain the motion of enzyme subunits differently and may serve as another mechanism that increases the dynamics uniqueness. Proteins 2013; 81:1910–1918. © 2013 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.     

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.     

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.     

Dynamics of the trimeric AcrB transporter protein inferred from a B-factor analysis of the crystal structure

The Escherichia coli AcrB multidrug transporter recognizes a wide range of toxic chemicals and actively extrudes them from cells. The molecular basis of multidrug transport in AcrB remains unknown. Herein, we describe normal mode analyses to study important regions for drug recognition and extrusion in this transporter. Based on the X-ray structure of AcrB, an elastic network model has been able to correct errors arising from crystal imperfection in the experimental B-factors. The results allow us to understand the functional dynamics of this membrane protein. It is expected that this technique can be applied to other membrane proteins with known structures.     

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.     

Opening and closing of a toroidal group II chaperonin revealed by a symmetry constrained elastic network model

Recently, the atomic structures of both the closed and open forms of Group 2 chaperonin protein Mm‐cpn were revealed through crystallography and cryo‐electron microscopy. This toroidal‐like chaperonin is composed of two eightfold rings that face back‐to‐back. To gain a computational advantage, we used a symmetry constrained elastic network model (SCENM), which requires only a repeated subunit structure and its symmetric connectivity to neighboring subunits to simulate the entire system. In the case of chaperonin, only six subunits (i.e., three from each ring) were used out of the eight subunits comprising each ring. A smooth and symmetric pathway between the open and closed conformations was generated by elastic network interpolation (ENI). To support this result, we also performed a symmetry‐constrained normal mode analysis (NMA), which revealed the intrinsic vibration features of the given structures. The NMA and ENI results for the representative single subunit were duplicated according to the symmetry pattern to reconstruct the entire assembly. To test the feasibility of the symmetry model, its results were also compared with those obtained from the full model. This study allowed the folding mechanism of chaperonin Mm‐cpn to be elucidated by SCENM in a timely manner.