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

Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

This article presents a novel finite element formulation for the Biot equation using low-order elements. Additionally, an extra degree of freedom is introduced to treat the volumetric locking steaming from the effective response of the medium; its balance equation is also stabilized. The accuracy of the proposed formulation is demonstrated by means of numerical analyses.Peer ReviewedPostprint (author's final draft

MOTIF-EM: an automated computational tool for identifying conserved regions in CryoEM structures

We present a new, first-of-its-kind, fully automated computational tool MOTIF-EM for identifying regions or domains or motifs in cryoEM maps of large macromolecular assemblies (such as chaperonins, viruses, etc.) that remain conformationally conserved. As a by-product, regions in structures that are not conserved are revealed: this can indicate local molecular flexibility related to biological activity. MOTIF-EM takes cryoEM volumetric maps as inputs. The technique used by MOTIF-EM to detect conserved sub-structures is inspired by a recent breakthrough in 2D object recognition. The technique works by constructing rotationally invariant, low-dimensional representations of local regions in the input cryoEM maps. Correspondences are established between the reduced representations (by comparing them using a simple metric) across the input maps. The correspondences are clustered using hash tables and graph theory is used to retrieve conserved structural domains or motifs. MOTIF-EM has been used to extract conserved domains occurring in large macromolecular assembly maps, including as those of viruses P22 and epsilon 15, Ribosome 70S, GroEL, that remain structurally conserved in different functional states. Our method can also been used to build atomic models for some maps. We also used MOTIF-EM to identify the conserved folds shared among dsDNA bacteriophages HK97, Epsilon 15, and ô29, though they have low-sequence similarity

Nonlinearity of Mechanochemical Motions in Motor Proteins

The assumption of linear response of protein molecules to thermal noise or structural perturbations, such as ligand binding or detachment, is broadly used in the studies of protein dynamics. Conformational motions in proteins are traditionally analyzed in terms of normal modes and experimental data on thermal fluctuations in such macromolecules is also usually interpreted in terms of the excitation of normal modes. We have chosen two important protein motors - myosin V and kinesin KIF1A - and performed numerical investigations of their conformational relaxation properties within the coarse-grained elastic network approximation. We have found that the linearity assumption is deficient for ligand-induced conformational motions and can even be violated for characteristic thermal fluctuations. The deficiency is particularly pronounced in KIF1A where the normal mode description fails completely in describing functional mechanochemical motions. These results indicate that important assumptions of the theory of protein dynamics may need to be reconsidered. Neither a single normal mode, nor a superposition of such modes yield an approximation of strongly nonlinear dynamics.Comment: 10 pages, 6 figure

Complementary hydro-mechanical coupled finite/discrete element and microseismic modelling to predict hydraulic fracture propagation in tight shale reservoirs

This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretization. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretization. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microsesimic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology

FitEM2EM—Tools for Low Resolution Study of Macromolecular Assembly and Dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top

Conformational Reorganization of the SARS Coronavirus Spike Following Receptor Binding: Implications for Membrane Fusion

The SARS coronavirus (SARS-CoV) spike is the largest known viral spike molecule, and shares a similar function with all class 1 viral fusion proteins. Previous structural studies of membrane fusion proteins have largely used crystallography of static molecular fragments, in isolation of their transmembrane domains. In this study we have produced purified, irradiated SARS-CoV virions that retain their morphology, and are fusogenic in cell culture. We used cryo-electron microscopy and image processing to investigate conformational changes that occur in the entire spike of intact virions when they bind to the viral receptor, angiotensin-converting enzyme 2 (ACE2). We have shown that ACE2 binding results in structural changes that appear to be the initial step in viral membrane fusion, and precisely localized the receptor-binding and fusion core domains within the entire spike. Furthermore, our results show that receptor binding and subsequent membrane fusion are distinct steps, and that each spike can bind up to three ACE2 molecules. The SARS-CoV spike provides an ideal model system to study receptor binding and membrane fusion in the native state, employing cryo-electron microscopy and single-particle image analysis

Using least median of squares for structural superposition of flexible proteins

<p>Abstract</p> <p>Background</p> <p>The conventional superposition methods use an ordinary least squares (LS) fit for structural comparison of two different conformations of the same protein. The main problem of the LS fit that it is sensitive to outliers, i.e. large displacements of the original structures superimposed.</p> <p>Results</p> <p>To overcome this problem, we present a new algorithm to overlap two protein conformations by their atomic coordinates using a robust statistics technique: least median of squares (LMS). In order to effectively approximate the LMS optimization, the forward search technique is utilized. Our algorithm can automatically detect and superimpose the rigid core regions of two conformations with small or large displacements. In contrast, most existing superposition techniques strongly depend on the initial LS estimating for the entire atom sets of proteins. They may fail on structural superposition of two conformations with large displacements. The presented LMS fit can be considered as an alternative and complementary tool for structural superposition.</p> <p>Conclusion</p> <p>The proposed algorithm is robust and does not require any prior knowledge of the flexible regions. Furthermore, we show that the LMS fit can be extended to multiple level superposition between two conformations with several rigid domains. Our fit tool has produced successful superpositions when applied to proteins for which two conformations are known. The binary executable program for Windows platform, tested examples, and database are available from <url>https://engineering.purdue.edu/PRECISE/LMSfit</url>.</p

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