Combining electron microscopy and comparative protein structure modeling

Recently, advances have been made in methods and applications that integrate electron microscopy density maps and comparative modeling to produce atomic structures of macromolecular assemblies. Electron microscopy can benefit from comparative modeling through the fitting of comparative models into electron microscopy density maps. Also, comparative modeling can benefit from electron microscopy through the use of intermediate-resolution density maps in fold recognition, template selection and sequence-structure alignment.     

Trans‐generational effects of maternal rearing density on offspring development time in a parasitoid wasp

Maternal pre‐reproductive experience can impose phenotypic changes on offspring traits. These modifications may result from physiological constraints, although they can also increase the adaptation of offspring to their anticipated environment. Distinguishing between the two interpretations is often difficult. The effects of virgin female rearing density on their longevity and the characteristics of their male offspring are explored in the polyembryonic parasitoid wasp Copidosoma koehleri (Blanchard) (Encyrtidae: Hymenoptera). High rearing density may adversely affect maternal physiology or, alternatively, act as a cue for anticipated competition during the lives of the mothers and their offspring. Male offspring of group‐reared females reach pupation significantly sooner than male offspring of females reared alone. This accelerated development may provide an advantage when competition from superparasitising individuals is expected. The lifespan of high‐density females is longer than that of singly‐reared females, and their male offspring survive longer, suggesting that crowded rearing does not reduce the fitness of females or offspring. The shortened development time of male offspring may reflect an adaptive epigenetic response to predicted competitive conditions.     

Cryo‐EM model validation using independent map reconstructions

An increasing number of cryo‐electron microscopy (cryo‐EM) density maps are being generated with suitable resolution to trace the protein backbone and guide sidechain placement. Generating and evaluating atomic models based on such maps would be greatly facilitated by independent validation metrics for assessing the fit of the models to the data. We describe such a metric based on the fit of atomic models with independent test maps from single particle reconstructions not used in model refinement. The metric provides a means to determine the proper balance between the fit to the density and model energy and stereochemistry during refinement, and is likely to be useful in determining values of model building and refinement metaparameters quite generally.     

Combined approaches to flexible fitting and assessment in virus capsids undergoing conformational change

Fitting of atomic components into electron cryo-microscopy (cryoEM) density maps is routinely used to understand the structure and function of macromolecular machines. Many fitting methods have been developed, but a standard protocol for successful fitting and assessment of fitted models has yet to be agreed upon among the experts in the field. Here, we created and tested a protocol that highlights important issues related to homology modelling, density map segmentation, rigid and flexible fitting, as well as the assessment of fits. As part of it, we use two different flexible fitting methods (Flex-EM and iMODfit) and demonstrate how combining the analysis of multiple fits and model assessment could result in an improved model. The protocol is applied to the case of the mature and empty capsids of Coxsackievirus A7 (CAV7) by flexibly fitting homology models into the corresponding cryoEM density maps at 8.2 and 6.1 Å resolution. As a result, and due to the improved homology models (derived from recently solved crystal structures of a close homolog – EV71 capsid – in mature and empty forms), the final models present an improvement over previously published models. In close agreement with the capsid expansion observed in the EV71 structures, the new CAV7 models reveal that the expansion is accompanied by ∼5° counterclockwise rotation of the asymmetric unit, predominantly contributed by the capsid protein VP1. The protocol could be applied not only to viral capsids but also to many other complexes characterised by a combination of atomic structure modelling and cryoEM density fitting.     

Cryo-electron microscopy modeling by the molecular dynamics flexible fitting method

The increasing power and popularity of cryo-electron microscopy (cryo-EM) in structural biology brought about the development of so-called hybrid methods, which permit the interpretation of cryo-EM density maps beyond their nominal resolution in terms of atomic models. The Cryo-EM Modeling Challenge 2010 is the first community effort to bring together developers of hybrid methods as well as cryo-EM experimentalists. Participating in the challenge, the molecular dynamics flexible fitting (MDFF) method was applied to a number of cryo-EM density maps. The results are described here with special emphasis on the use of symmetry-based restraints to improve the quality of atomic models derived from density maps of symmetric complexes; on a comparison of the stereochemical quality of atomic models resulting from different hybrid methods; and on application of MDFF to electron crystallography data.     

Refinement of Protein Structures into Low-Resolution Density Maps Using Rosetta

We describe a method based on Rosetta structure refinement for generating high-resolution, all-atom protein models from electron cryomicroscopy density maps. A local measure of the fit of a model to the density is used to directly guide structure refinement and to identify regions incompatible with the density that are then targeted for extensive rebuilding. Over a range of test cases using both simulated and experimentally generated data, the method consistently increases the accuracy of starting models generated either by comparative modeling or by hand-tracing the density. The method can achieve near-atomic resolution starting from density maps at 4-6 Å resolution.     

Modelling habitat distributions for multiple species using phylogenetics

In this paper, we describe an empirical approach to model community structure using phylogenetic signals. That approach combines information about the species (i.e. traits and phylogeny) with information about the habitat (i.e. environmental conditions and spatial distribution of sampling sites) and their interactions to predict the species responses (e.g. the local densities). As an application, we use the approach to model fish densities in rivers. In the model, the different species and size classes were described using a functional trait, body length, and phylogenetic eigenvectors maps whereas the sites were described using water velocity, depth, substrate composition, macrophyte cover, degree‐days, total phosphorus, and spatial eigenvector maps. The model (estimated using a regularised Poisson‐family generalised linear modelling approach) fitted the data well (likelihood‐based R²_adj = 0.512) and showed fair predictive power (likelihood‐based cross‐validation R² = 0.283) to predict the density of fish pertaining to 48 species totalling 143 combinations of species and size classes in 15 unregulated Canadian rivers. Using the model as a baseline to estimate the effect of flow regulation on community composition, we found that, with few exceptions, the densities of most fish species were lower in regulated than in unregulated rivers. Phylogenetics have been proposed to study community structure, but this is, to our knowledge, the first time phylogenetic information is used explicitly for numerical habitat modelling. We expect that models of that type will be in increasing demand now that development projects are routinely assessed through impact studies.     

On methylene‐bridged cysteine and lysine residues in proteins

Cysteine residues ubiquitously stabilize tertiary and quaternary protein structure by formation of disulfide bridges. Here we investigate another linking interaction that involves sulfhydryl groups of cysteines, namely intra‐ and intermolecular methylene‐bridges between cysteine and lysine residues. A number of crystal structures possessing such a linkage were identified in the Protein Data Bank. Inspection of the electron density maps and re‐refinement of the nominated structures unequivocally confirmed the presence of Lys‐CH₂‐Cys bonds in several cases.     

Review of studies on biomass-density relationships (including self-thinning lines) in seaweeds: Main contributions and persisting misconceptions

Ecological models relating biomass and density are relatively simple to calculate and offer information on, for example, the interactions among organisms and size constraints. Biomass‐density relationships have mostly been studied for terrestrial plants, but recently they have also been increasingly investigated for seaweeds. Unfortunately, a number of misconceptions have limited the overall contribution of algal studies to biomass‐density theory in general. Aiming to improve this situation, the present paper first summarizes the current knowledge on biomass‐density theory, particularly focusing on the main concepts that, with varying degrees of validity, exist in the published literature: the self‐thinning rule (in its boundary and dynamic interpretations), the interspecific biomass‐density relationship, and the ultimate biomass‐density line. Afterwards, the present paper provides a critical review of past biomass‐density studies on seaweeds. The main contributions of studies on clonal and unitary species are discussed, while the misconceptions that persist to these days are identified in order to help future studies to be based on solid grounds.     

A novel three-dimensional variant of the watershed transform for segmentation of electron density maps

Electron density maps at moderate resolution are often difficult to interpret due to the lack of recognizable features. This is especially true for electron tomograms that suffer in addition to the resolution limitation from low signal-to-noise ratios. Reliable segmentation of such maps into smaller, manageable units can greatly facilitate interpretation. Here, we present a segmentation approach targeting three-dimensional electron density maps derived by electron microscopy. The approach consists of a novel three-dimensional variant of the immersion-based watershed algorithm. We tested the algorithm on calculated data and applied it to a wide variety of electron density maps ranging from reconstructions of single macromolecules to tomograms of subcellular structures. The results indicate that the algorithm is reliable, efficient, accurate, and applicable to a wide variety of biological problems.     

Cryo‐EM map interpretation and protein model‐building using iterative map segmentation

A procedure for building protein chains into maps produced by single‐particle electron cryo‐microscopy (cryo‐EM) is described. The procedure is similar to the way an experienced structural biologist might analyze a map, focusing first on secondary structure elements such as helices and sheets, then varying the contour level to identify connections between these elements. Since the high density in a map typically follows the main‐chain of the protein, the main‐chain connection between secondary structure elements can often be identified as the unbranched path between them with the highest minimum value along the path. This chain‐tracing procedure is then combined with finding side‐chain positions based on the presence of density extending away from the main path of the chain, allowing generation of a C_α model. The C_α model is converted to an all‐atom model and is refined against the map. We show that this procedure is as effective as other existing methods for interpretation of cryo‐EM maps and that it is considerably faster and produces models with fewer chain breaks than our previous methods that were based on approaches developed for crystallographic maps.     

Guidelines for evaluating performance of oyster habitat restoration

Restoration of degraded ecosystems is an important societal goal, yet inadequate monitoring and the absence of clear performance metrics are common criticisms of many habitat restoration projects. Funding limitations can prevent adequate monitoring, but we suggest that the lack of accepted metrics to address the diversity of restoration objectives also presents a serious challenge to the monitoring of restoration projects. A working group with experience in designing and monitoring oyster reef projects was used to develop standardized monitoring metrics, units, and performance criteria that would allow for comparison among restoration sites and projects of various construction types. A set of four universal metrics (reef areal dimensions, reef height, oyster density, and oyster size–frequency distribution) and a set of three universal environmental variables (water temperature, salinity, and dissolved oxygen) are recommended to be monitored for all oyster habitat restoration projects regardless of their goal(s). In addition, restoration goal‐based metrics specific to four commonly cited ecosystem service‐based restoration goals are recommended, along with an optional set of seven supplemental ancillary metrics that could provide information useful to the interpretation of prerestoration and postrestoration monitoring data. Widespread adoption of a common set of metrics with standardized techniques and units to assess well‐defined goals not only allows practitioners to gauge the performance of their own projects but also allows for comparison among projects, which is both essential to the advancement of the field of oyster restoration and can provide new knowledge about the structure and ecological function of oyster reef ecosystems.     

A core-weighted fitting method for docking atomic structures into low-resolution maps: application to cryo-electron microscopy

Cryo-electron microscopy of "single particles" is a powerful method to analyze structures of large macromolecular assemblies that are not amenable to investigation by traditional X-ray crystallographic methods. A key step in these studies is to obtain atomic interpretations of multiprotein complexes by fitting atomic structures of individual components into maps obtained from electron microscopic data. Here, we report the use of a "core-weighting" method, combined with a grid-threading Monte Carlo (GTMC) approach for this purpose. The "core" of an individual structure is defined to represent the part where the density distribution is least likely to be altered by other components that comprise the macromolecular assembly of interest. The performance of the method has been evaluated by its ability to determine the correct fit of (i) the alpha-chain of the T-cell receptor variable domain into a simulated map of the alphabeta complex at resolutions between 5 and 40 A, and (ii) the E2 catalytic domain of the pyruvate dehydrogenase into an experimentally determined map, at 14 A resolution, of the icosahedral complex formed by 60 copies of this enzyme. Using the X-ray structures of the two test cases as references, we demonstrate that, in contrast to more traditional methods, the combination of the core-weighting method and the grid-threading Monte Carlo approach can identify the correct fit reliably and rapidly from the low-resolution maps that are typical of structures determined with the use of single-particle electron microscopy.     

Gorgon and pathwalking: macromolecular modeling tools for subnanometer resolution density maps

The complex interplay of proteins and other molecules, often in the form of large transitory assemblies, are critical to cellular function. Today, X-ray crystallography and electron cryo-microscopy (cryo-EM) are routinely used to image these macromolecular complexes, though often at limited resolutions. Despite the rapidly growing number of macromolecular structures, few tools exist for modeling and annotating structures in the range of 3-10 ? resolution. To address this need, we have developed a number of utilities specifically targeting subnanometer resolution density maps. As part of the 2010 Cryo-EM Modeling Challenge, we demonstrated two of our latest de novo modeling tools, Pathwalking and Gorgon, as well as a tool for secondary structure identification (SSEHunter) and a new rigid-body/flexible fitting tool in Gorgon. In total, we submitted 30 structural models from ten different subnanometer resolution data sets in four of the six challenge categories. Each of our utlities produced accurate structural models and annotations across the various density maps. In the end, the utilities that we present here offer users a robust toolkit for analyzing and modeling protein structure in macromolecular assemblies at non-atomic resolutions.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Using surface envelopes to constrain molecular modeling

Molecular density information (as measured by electron microscopic reconstructions or crystallographic density maps) can be a powerful source of information for molecular modeling. Molecular density constrains models by specifying where atoms should and should not be. Low-resolution density information can often be obtained relatively quickly, and there is a need for methods that use it effectively. We have previously described a method for scoring molecular models with surface envelopes to discriminate between plausible and implausible fits. We showed that we could successfully filter out models with the wrong shape based on this discrimination power. Ideally, however, surface information should be used during the modeling process to constrain the conformations that are sampled. In this paper, we describe an extension of our method for using shape information during computational modeling. We use the envelope scoring metric as part of an objective function in a global optimization that also optimizes distances and angles while avoiding collisions. We systematically tested surface representations of proteins (using all nonhydrogen heavy atoms) with different abundance of distance information and showed that the root mean square deviation (RMSD) of models built with envelope information is consistently improved, particularly in data sets with relatively small sets of short-range distances.     

Experimental charge density from electron microscopic maps

The charge density (CD) distribution of an atom is the difference per unit volume between the positive charge of its nucleus and the distribution of the negative charges carried by the electrons that are associated with it. The CDs of the atoms in macromolecules are responsible for their electrostatic potential (ESP) distributions, which can now be visualized using cryo‐electron microscopy at high resolution. CD maps can be recovered from experimental ESP density maps using the negative Laplacian operation. CD maps are easier to interpret than ESP maps because they are less sensitive to long‐range electrostatic effects. An ESP‐to‐CD conversion involves multiplication of amplitudes of structure factors as Fourier transforms of these maps in reciprocal space by 1/d², where d is the resolution of reflections. In principle, it should be possible to determine the charges carried by the individual atoms in macromolecules by comparing experimental CD maps with experimental ESP maps.     

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.     

Optimising long‐term monitoring projects for species distribution modelling: how atlas data may help

Long‐term biodiversity monitoring data are mainly used to estimate changes in species occupancy or abundance over time, but they may also be incorporated into predictive models to document species distributions in space. Although changes in occupancy or abundance may be estimated from a relatively limited number of sampling units, small sample size may lead to inaccurate spatial models and maps of predicted species distributions. We provide a methodological approach to estimate the minimum sample size needed in monitoring projects to produce accurate species distribution models and maps. The method assumes that monitoring data are not yet available when sampling strategies are to be designed and is based on external distribution data from atlas projects. Atlas data are typically collected in a large number of sampling units during a restricted timeframe and are often similar in nature to the information gathered from long‐term monitoring projects. The large number of sampling units in atlas projects makes it possible to simulate a broad gradient of sample sizes in monitoring data and to examine how the number of sampling units influences the accuracy of the models. We apply the method to several bird species using data from a regional breeding bird atlas. We explore the effect of prevalence, range size and habitat specialization of the species on the sample size needed to generate accurate models. Model accuracy is sensitive to particularly small sample sizes and levels off beyond a sufficiently large number of sampling units that varies among species depending mainly on their prevalence. The integration of spatial modelling techniques into monitoring projects is a cost‐effective approach as it offers the possibility to estimate the dynamics of species distributions in space and over time. We believe our innovative method will help in the sampling design of future monitoring projects aiming to achieve such integration.