Comparative Study of Thermal Remodeling of Viruses with Icosahedral and Helical Symmetry

Study of the possibilities of virions and viral proteins modifications and structural remodeling is an important problem of the modern molecular virology. A technique of heat treatment of rod-shaped tobacco mosaic virus that allowed producing structurally modified spherical particles consisting of the virus coat protein was previously developed in our laboratory. These particles possessed unique adsorption and immunogenic properties and were successfully used to develop a new candidate vaccine against rubella virus. Later, the possibility of thermal remodeling of the filamentous virions of potato virus X was demonstrated. The present work reports a comparative study of thermal remodeling of viruses with different structure belonging to various taxonomic groups. The generation of structurally modified spherical particles by the heat treatment of rod-shaped virions with helical symmetry (dolichos enation mosaic virus and barley stripe mosaic virus) has been demonstrated. The dependence of the size of spherical particles derived from dolichos enation mosaic virus on the initial virus concentration was revealed. The process of thermal remodeling of the filamentous virions and virus-like particles of alternanthera mosaic virus was studied. Heat treatment of plant viruses with icosahedral symmetry was shown to cause no morphological changes.     

Viral capsid equilibrium dynamics reveals nonuniform elastic properties

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.     

Internal structural anisotropy of spherical viruses studied with magnetic birefringence

Six so called spherical viruses (four plant and two animal) are shown to exhibit magnetically induced birefringence in solution. They must therefore be magnetically and optically anisotropic. This is attributed to static structural anisotropy of the interiors as neither natural shape nor field-induced deformations are likely causes. Thus at least part of these virus cores have a symmetry differing from that of their capsids. An estimate of the average orientation of the RNA bases is given for the plant viruses: turnip yellow mosaic, bromegrass mosaic, tomato bushy stunt and turnip crinkle. The packing geometry of the nucleic acid/protein cores of adenovirus and probably influenza virus are anisotropic but to an extent that cannot be quantified.     

Loop motions of triosephosphate isomerase observed with elastic networks

The internal dynamics of triosephosphate isomerase have been investigated with elastic networks, with and without a substrate bound. The slowest modes of motion involve large domain motions but also a loop motion that conforms to the changes observed between the crystal structures and . Our computations confirm that the different motions of this loop are important in several of the computed slowest modes. We have shown that elastic network computations on this protein system can combine atoms for the functional parts of the structure with coarse-grained (cg) representations of the remainder of the structure in several different ways. Similar loop motions are seen with elastic network models for atomistic and mixed cg models. The loop motions are reproduced with an overlap of 0.75-0.79 by combining the four slowest modes of motion for the free and complex forms of the enzyme.     

Normal mode analysis with molecular geometry restraints: bridging molecular mechanics and elastic models

A new method for normal mode analysis is reported for all-atom structures using molecular geometry restraints (MGR). Similar to common molecular mechanics force fields, the MGR potential contains short- and long-range terms. The short-range terms are defined by molecular geometry, i.e., bond lengths, angles and dihedrals; the long-range term is similar to that in elastic network models. Each interaction term uses a single force constant parameter, and is determined by fitting against a set of known structures. Tests on proteins/non-proteins show that MGR can produce low frequency eigenvectors closer to all-atom force-field-based methods than conventional elastic network models. Moreover, the “tip effect”, found in low frequency eigenvectors in elastic network models, is reduced in MGR to the same level of the modes produced by force-field-based methods. The results suggest that molecular geometry plays an important role, in addition to molecular shape, in determining low frequency deformational motions. MGR does not require initial energy minimization, and is applicable to almost any structure, including the one with missing atoms, bad contacts, or bad geometries, frequently observed in low-resolution structure determination and refinement. The method bridges the two major representations in normal mode analyses, i.e., the molecular mechanics models and elastic network models.     

hdANM: a new comprehensive dynamics model for protein hinges

Hinge motions are essential for many protein functions, and their dynamics are important to understand underlying biological mechanisms. The ways that these motions are represented by various computational methods differ significantly. By focusing on a specific class of motion, we have developed a new hinge-domain anisotropic network model (hdANM) that is based on the prior identification of flexible hinges and rigid domains in the protein structure and the subsequent generation of global hinge motions. This yields a set of motions in which the relative translations and rotations of the rigid domains are modulated and controlled by the deformation of the flexible hinges, leading to a more restricted, specific view of these motions. hdANM is the first model, to our knowledge, that combines information about protein hinges and domains to model the characteristic hinge motions of a protein. The motions predicted with this new elastic network model provide important conceptual advantages for understanding the underlying biological mechanisms. As a matter of fact, the generated hinge movements are found to resemble the expected mechanisms required for the biological functions of diverse proteins. Another advantage of this model is that the domain-level coarse graining makes it significantly more computationally efficient, enabling the generation of hinge motions within even the largest molecular assemblies, such as those from cryo-electron microscopy. hdANM is also comprehensive as it can perform in the same way as the well-known protein dynamics models (anisotropic network model, rotations-translations of blocks, and nonlinear rigid block normal mode analysis), depending on the definition of flexible and rigid parts in the protein structure and on whether the motions are extrapolated in a linear or nonlinear fashion. Furthermore, our results indicate that hdANM produces more realistic motions as compared to the anisotropic network model. hdANM is an open-source software, freely available, and hosted on a user-friendly website.     

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.     

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.     

Normal modes of symmetric protein assemblies. Application to the tobacco mosaic virus protein disk.

We use group theoretical methods to study the molecular dynamics of symmetric protein multimers in the harmonic or quasiharmonic approximation. The method explicitly includes the long-range correlations between protein subunits. It can thus address collective dynamic effects, such as cooperativity between subunits. The n lowest-frequency normal modes of each individual subunit are combined into symmetry coordinates for the entire multimer. The Hessian of the potential energy is thereby reduced to a series of blocks of order n or 2n. In the quasiharmonic approximation, the covariance matrix of the atomic oscillations is reduced to the same block structure by an analogous set of symmetry coordinates. The method is applied to one layer of the tobacco mosaic virus protein disk in vacuo, to gain insight into the role of conformational fluctuations and electrostatics in tobacco mosaic virus assembly. The system has 78,000 classical, positional, degrees of freedom, yet the calculation is reduced by symmetry to a problem of order 4,600. Normal modes in the 0-100 cm-1 range were calculated. The calculated correlations extend mainly from each subunit to its nearest neighbors. The network of core helices has weak correlations with the rest of the structure. Similarly, the inner loops 90-108 are uncorrelated with the rest of the structure. Thus, the model predicts that the dielectric response in the RNA-binding region is mainly due to the loops alone.     

Structure of flexible filamentous plant viruses

Flexible filamentous viruses make up a large fraction of the known plant viruses, but in comparison with those of other viruses, very little is known about their structures. We have used fiber diffraction, cryo-electron microscopy, and scanning transmission electron microscopy to determine the symmetry of a potyvirus, soybean mosaic virus; to confirm the symmetry of a potexvirus, potato virus X; and to determine the low-resolution structures of both viruses. We conclude that these viruses and, by implication, most or all flexible filamentous plant viruses share a common coat protein fold and helical symmetry, with slightly less than 9 subunits per helical turn.     

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.     

Gating mechanisms of mechanosensitive channels of large conductance, II: systematic study of conformational transitions

Part II of this study is based on the continuum mechanics-based molecular dynamics-decorated finite element method (MDeFEM) framework established in Part I. In Part II, the gating pathways of Escherichia coli-MscL channels under various basic deformation modes are simulated. Upon equibiaxial tension (which is verified to be the most effective mode for gating), the MDeFEM results agree well with both experiments and all-atom simulations in literature, as well as the analytical continuum models and elastic network models developed in Part I. Different levels of model sophistication and effects of structural motifs are explored in detail, where the importance of mechanical roles of transmembrane helices, cytoplasmic helices, and loops are discussed. The conformation transitions under complex membrane deformations are predicted, including bending, torsion, cooperativity, patch clamp, and indentation. Compared to atom-based molecular dynamics simulations and elastic network models, the MDeFEM framework is unusually well-suited for simulating complex deformations at large length scales. The versatile hierarchical framework can be further applied to simulate the gating transition of other mechanosensitive channels and other biological processes where mechanical perturbation is important.     

Comparison of mode analyses at different resolutions applied to nucleic acid systems

More than two decades of different types of mode analyses has shown that these techniques can be useful in describing large-scale motions in protein systems. A number of mode analyses are available and include quasiharmonics, classical normal mode, block normal mode, and the elastic network model. Each of these methods has been validated for protein systems and this variety allows researchers to choose the technique that gives the best compromise between computational cost and the level of detail in the calculation. These same techniques have not been systematically tested for nucleic acid systems, however. Given the differences in interactions and structural features between nucleic acid and protein systems, the validity of these techniques in the protein regime cannot be directly translated into validity in the nucleic acid realm. In this work, we investigate the usefulness of the above mode analyses as applied to two RNA systems, i.e., the hammerhead ribozyme and a guanine riboswitch. We show that classical normal-mode analysis can match the magnitude and direction of residue fluctuations from the more detailed, anharmonic technique, quasiharmonic analysis of a molecular dynamics trajectory. The block normal-mode approximation is shown to hold in the nucleic acid systems studied. Only the mode analysis at the lowest level of detail, the elastic network model, produced mixed results in our calculations. We present data that suggest that the elastic network model, with the popular parameterization, is not best suited for systems that do not have a close packed structure; this observation also hints at why the elastic network model has been found to be valid for many globular protein systems. The different behaviors of block normal-mode analysis and the elastic network model, which invoke similar degrees of coarse-graining to the dynamics but use different potentials, suggest the importance of applying a heterogeneous potential function in a robust analysis of the dynamics of biomolecules, especially those that are not closely packed. In addition to these comparisons, we briefly discuss insights into the conformational space available to the hammerhead ribozyme.     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Signal propagation in proteins and relation to equilibrium fluctuations

Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models.     

Obtaining and characterization of spherical particles—new biogenic platforms

The technique of obtaining spherical particles from rod-like plant virus, tobacco mosaic virus, in a preparative scale was developed. The conditions of tobacco mosaic virus isolation for obtaining spherical particles were selected. Spherical particles were examined by methods of electron microscopy, nanoparticle tracking analysis, and dynamic light scattering. Information about inner structure of spherical particles was obtained. High electron density of spherical particles was demonstrated. The analysis of ultrathin sections showed that spherical particles are homogenous within and do not contain any cavities.     

Primary structure of belladonna mottle virus coat protein

The coat protein of belladonna mottle virus (a tymovirus) was cleaved by trypsin and chymotrypsin, and the peptides were separated by high performance liquid chromatography using a combination of gel permeation, reverse phase, and ion pair chromatography. The peptides were sequenced manually using the 4-N, N-dimethylaminoazobenzene-4'-isothiocyanate/phenyl isothiocyanate double-coupling method. The chymotryptic peptides were aligned by overlapping sequences of tryptic peptides and by homology with another tymovirus, eggplant mosaic virus. The belladonna mottle virus is more closely related to eggplant mosaic virus than to turnip yellow mosaic virus, the type member of this group, as evident from the sequence homologies of 57 and 32%, respectively. The accumulation of basic residues at the amino terminus implicated in RNA-protein interactions in many spherical plant viruses was absent in all the three sequences. Interestingly, the amino-terminal region is the least conserved among the tymoviruses. The longest stretch of conserved sequence between belladonna mottle virus and eggplant mosaic virus was residues 34-44, whereas it was residues 96-102 in the case of belladonna mottle virus and turnip yellow mosaic virus. A tetrapeptide in the region (residues 154-157) was found to be common for all the three sequences. It is possible that these conserved regions (residues 34-44, 96-102, 154-157) are involved in either intersubunit or RNA-protein interactions.     

The requirement for mechanical coupling between head and S2 domains in smooth muscle myosin ATPase regulation and its implications for dimeric motor function

A combination of experimental structural data, homology modelling and elastic network normal mode analysis is used to explore how coupled motions between the two myosin heads and the dimerization domain (S2) in smooth muscle myosin II determine the domain movements required to achieve the inhibited state of this ATP-dependent molecular motor. These physical models rationalize the empirical requirement for at least two heptads of non-coiled alpha-helix at the junction between the myosin heads and S2, and the dependence of regulation on S2 length. The results correlate well with biochemical data regarding altered conformational-dependent solubility and stability. Structural models of the conformational transition between putative active states and the inhibited state show that torsional flexibility of the S2 alpha-helices is a key mechanical requirement for myosin II regulation. These torsional motions of the myosin heads about their coiled coil alpha-helices affect the S2 domain structure, which reciprocally affects the motions of the myosin heads. This inter-relationship may explain a large body of data on function of molecular motors that form dimers through a coiled-coil domain.