Willy Wriggers

Using Situs for the integration of multi-resolution structures

Situs is a modular and widely used software package for the integration of biophysical data across the spatial resolution scales. It has been developed over the last decade with a focus on bridging the resolution gap between atomic structures, coarse-grained models, and volumetric data from low-resolution biophysical origins, such as electron microscopy, tomography, or small-angle scattering. Structural models can be created and refined with various flexible and rigid body docking strategies. The software consists of multiple, stand-alone programs for the format conversion, analysis, visualization, manipulation, and assembly of 3D data sets. The programs have been ported to numerous platforms in both serial and shared memory parallel architectures and can be combined in various ways for specific modeling applications. The modular design facilitates the updating of individual programs and the development of novel application workflows. This review provides an overview of the Situs package as it exists today with an emphasis on functionality and workflows supported by version 2.5.

Using Sculptor and Situs for simultaneous assembly of atomic components into low-resolution shapes

We describe an integrated software system called Sculptor that combines visualization capabilities with molecular modeling algorithms for the analysis of multi-scale data sets. Sculptor features extensive special purpose visualization techniques that are based on modern GPU programming and are capable of representing complex molecular assemblies in real-time. The integration of graphics and modeling offers several advantages. The user interface not only eases the usually steep learning curve of pure algorithmic techniques, but it also permits instant analysis and post-processing of results, as well as the integration of results from external software. Here, we implemented an interactive peak-selection strategy that enables the user to explore a preliminary score landscape generated by the colors tool of Situs. The interactive placement of components, one at a time, is advantageous for low-resolution or ambiguously shaped maps, which are sometimes difficult to interpret by the fully automatic peak selection of colors. For the subsequent refinement of the preliminary models resulting from both interactive and automatic peak selection, we have implemented a novel simultaneous multi-body docking in Sculptor and Situs that softly enforces shape complementarities between components using the normalization of the cross-correlation coefficient. The proposed techniques are freely available in Situs version 2.6 and Sculptor version 2.0.

Conventions and workflows for using Situs.

Recent developments of the Situs software suite for multi-scale modeling are reviewed. Typical workflows and conventions encountered during processing of biophysical data from electron microscopy, tomography or small-angle X-ray scattering are described.

Evolutionary bidirectional expansion for the tracing of alpha helices in cryo-electron microscopy reconstructions.

Cryo-electron microscopy (cryo-EM) enables the imaging of macromolecular complexes in near-native environments at resolutions that often permit the visualization of secondary structure elements. For example, alpha helices frequently show consistent patterns in volumetric maps, exhibiting rod-like structures of high density. Here, we introduce VolTrac (Volume Tracer) - a novel technique for the annotation of alpha-helical density in cryo-EM data sets. VolTrac combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to trace helical regions. Our method takes advantage of the stochastic search by using a genetic algorithm to identify optimal placements for a short cylindrical template, avoiding exploration of already characterized tabu regions. These placements are then utilized as starting positions for the adaptive bidirectional expansion that characterizes the curvature and length of the helical region. The method reliably predicted helices with seven or more residues in experimental and simulated maps at intermediate (4-10Å) resolution. The observed success rates, ranging from 70.6% to 100%, depended on the map resolution and validation parameters. For successful predictions, the helical axes were located within 2Å from known helical axes of atomic structures.

Bend-twist-stretch model for coarse elastic network simulation of biomolecular motion.

The empirical harmonic potential function of elastic network models (ENMs) is augmented by three- and four-body interactions as well as by a parameter-free connection rule. In the new bend-twist-stretch (BTS) model the complexity of the parametrization is shifted from the spatial level of detail to the potential function, enabling an arbitrary coarse graining of the network. Compared to distance cutoff-based Hookean springs, the approach yields a more stable parametrization of coarse-grained ENMs for biomolecular dynamics. Traditional ENMs give rise to unbounded zero-frequency vibrations when (pseudo)atoms are connected to fewer than three neighbors. A large cutoff is therefore chosen in an ENM (about twice the average nearest-neighbor distance), resulting in many false-positive connections that reduce the spatial detail that can be resolved. More importantly, the required three-neighbor connectedness also limits the coarse graining, i.e., the network must be dense, even in the case of low-resolution structures that exhibit few spatial features. The new BTS model achieves such coarse graining by extending the ENM potential to include three-and four-atom interactions (bending and twisting, respectively) in addition to the traditional two-atom stretching. Thus, the BTS model enables reliable modeling of any three-dimensional graph irrespective of the atom connectedness. The additional potential terms were parametrized using continuum elastic theory of elastic rods, and the distance cutoff was replaced by a competitive Hebb connection rule, setting all free parameters in the model. We validate the approach on a carbon-alpha representation of adenylate kinase and illustrate its use with electron microscopy maps of E. coli RNA polymerase, E. coli ribosome, and eukaryotic chaperonin containing T-complex polypeptide 1, which were difficult to model with traditional ENMs. For adenylate kinase, we find excellent reproduction (>90% overlap) of the ENM modes and B factors when BTS is applied to the carbon-alpha representation as well as to coarser descriptions. For the volumetric maps, coarse BTS yields similar motions (70%-90% overlap) to those obtained from significantly denser representations with ENM. Our Python-based algorithms of ENM and BTS implementations are freely available.

An Assembly Model of Rift Valley Fever Virus

Rift Valley fever virus (RVFV) is a bunyavirus endemic to Africa and the Arabian Peninsula that infects humans and livestock. The virus encodes two glycoproteins, Gn and Gc, which represent the major structural antigens and are responsible for host cell receptor binding and fusion. Both glycoproteins are organized on the virus surface as cylindrical hollow spikes that cluster into distinct capsomers with the overall assembly exhibiting an icosahedral symmetry. Currently, no experimental three-dimensional structure for any entire bunyavirus glycoprotein is available. Using fold recognition, we generated molecular models for both RVFV glycoproteins and found significant structural matches between the RVFV Gn protein and the influenza virus hemagglutinin protein and a separate match between RVFV Gc protein and Sindbis virus envelope protein E1. Using these models, the potential interaction and arrangement of both glycoproteins in the RVFV particle was analyzed, by modeling their placement within the cryo-electron microscopy density map of RVFV. We identified four possible arrangements of the glycoproteins in the virion envelope. Each assembly model proposes that the ectodomain of Gn forms the majority of the protruding capsomer and that Gc is involved in formation of the capsomer base. Furthermore, Gc is suggested to facilitate intercapsomer connections. The proposed arrangement of the two glycoproteins on the RVFV surface is similar to that described for the alphavirus E1-E2 proteins. Our models will provide guidance to better understand the assembly process of phleboviruses and such structural studies can also contribute to the design of targeted antivirals.

Automated tracing of filaments in 3D electron tomography reconstructions using Sculptor and Situs

The molecular graphics program Sculptor and the command-line suite Situs are software packages for the integration of biophysical data across spatial resolution scales. Herein, we provide an overview of recently developed tools relevant to cryo-electron tomography (cryo-ET), with an emphasis on functionality supported by Situs 2.7.1 and Sculptor 2.1.1. We describe a work flow for automatically segmenting filaments in cryo-ET maps including denoising, local normalization, feature detection, and tracing. Tomograms of cellular actin networks exhibit both cross-linked and bundled filament densities. Such filamentous regions in cryo-ET data sets can then be segmented using a stochastic template-based search, VolTrac. The approach combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to localize and characterize filamentous regions. The automated filament segmentation by VolTrac compares well to a manual one performed by expert users, and it allows an efficient and reproducible analysis of large data sets. The software is free, open source, and can be used on Linux, Macintosh or Windows computers.

Conserved Intramolecular Interactions Maintain Myosin Interacting-Heads Motifs Explaining Tarantula Muscle Super-Relaxed State Structural Basis.

Tarantula striated muscle is an outstanding system for understanding the molecular organization of myosin filaments. Three-dimensional reconstruction based on cryo-electron microscopy images and single-particle image processing revealed that, in a relaxed state, myosin molecules undergo intramolecular head-head interactions, explaining why head activity switches off. The filament model obtained by rigidly docking a chicken smooth muscle myosin structure to the reconstruction was improved by flexibly fitting an atomic model built by mixing structures from different species to a tilt-corrected 2-nm three-dimensional map of frozen-hydrated tarantula thick filament. We used heavy and light chain sequences from tarantula myosin to build a single-species homology model of two heavy meromyosin interacting-heads motifs (IHMs). The flexibly fitted model includes previously missing loops and shows five intramolecular and five intermolecular interactions that keep the IHM in a compact off structure, forming four helical tracks of IHMs around the backbone. The residues involved in these interactions are oppositely charged, and their sequence conservation suggests that IHM is present across animal species. The new model, PDB 3JBH, explains the structural origin of the ATP turnover rates detected in relaxed tarantula muscle by ascribing the very slow rate to docked unphosphorylated heads, the slow rate to phosphorylated docked heads, and the fast rate to phosphorylated undocked heads. The conservation of intramolecular interactions across animal species and the presence of IHM in bilaterians suggest that a super-relaxed state should be maintained, as it plays a role in saving ATP in skeletal, cardiac, and smooth muscles.

Coarse-Graining Protein Structures With Local Multivariate Features from Molecular Dynamics

A multivariate statistical theory, local feature analysis (LFA), extracts functionally relevant domains from molecular dynamics (MD) trajectories. The LFA representations, like those of principal component analysis (PCA), are low dimensional and provide a reduced basis set for collective motions of simulated proteins, but the local features are sparsely distributed and spatially localized, in contrast to global PCA modes. One key problem in the assignment of local features is the coarse-graining of redundant LFA output functions by means of seed atoms. One can solve the combinatorial problem by adding seed atoms one after another to a growing set, minimizing a reconstruction error at each addition. This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features. Here, we present a novel coarse-graining algorithm for proteins that directly minimizes the mutual correlation of seed atoms by Monte Carlo (MC) simulations. Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics. The well-known undersampling of large-scale motion by short MD simulations is apparent also in our model, but the new coarse-graining offers a major advantage over PCA; converged features are invariant across multiple windows of the trajectory, dividing the protein into converged regions and a smaller number of localized, undersampled regions. In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.

Numerical geometry of map and model assessment.

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8Å) and medium (4-8 Å) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naïve vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent.