Fast fitting of atomic structures to low-resolution electron density maps by surface overlap maximization

The complexities of X-ray crystallography and NMR spectroscopy for large protein complexes, and the comparative ease of approaches such as electron microscopy mean that low-resolution structures are often available long before their atomic resolution equivalents. To help bridge this gap in knowledge, we present 3SOM: an approach for finding the best fit of atomic resolution structures into lower-resolution density maps through surface overlap maximization. High-resolution templates (i.e. partial structures or models for multi-subunit complexes) and targets (lower-resolution maps) are initially represented as iso-surfaces. The latter are used first in a fast search for transformations that superimpose a significant portion of the target surface onto the template surface, which is quantified as surface overlap. The vast search space is reduced by considering key vectors that capture local surface information. The set of transformations with the highest surface overlap scores are then re-ranked by using more sophisticated scores including cross-correlation. We give a number of examples to illustrate the efficiency of the method and its restrictions. For targets for which partial complexes are available, the speed and performance of the method make it an attractive complement to existing methods, as many different hypotheses can be tested quickly on a single processor.     

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.     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

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.     

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.     

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.     

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.