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Cryo-electron tomography maps often exhibit considerable noise and anisotropic resolution, due to the low-dose requirements and the missing wedge in Fourier space. These spurious features are visually unappealing and, more importantly, prevent an automated segmentation of geometric shapes, requiring a subjective and labor-intensive manual tracing. We developed a novel computational strategy for objectively denoising and correcting missing-wedge artifacts in homogeneous specimen areas of tomograms, where it is assumed that a template repeats itself across the volume under consideration, as happens in the case of filaments. In our deconvolution approach, we use a template and a map of corresponding template locations, allowing us to compensate for the information lost in the missing wedge. We applied the method to tomograms of actin-filament bundles of inner-ear stereocilia, which are critical for the senses of hearing and balance. In addition, we demonstrate that our method can be used for cell membrane detection.

Electron cryo-tomography allows for high-resolution imaging of stereocilia in their native state. Because their actin filaments have a higher degree of order, we imaged stereocilia from mice lacking the actin crosslinker plastin 1 (PLS1). We found that while stereocilia actin filaments run 13 nm apart in parallel for long distances, there were gaps of significant size that were stochastically distributed throughout the actin core. Actin crosslinkers were distributed through the stereocilium, but did not occupy all possible binding sites. At stereocilia tips, protein density extended beyond actin filaments, especially on the side of the tip where a tip link is expected to anchor. Along the shaft, repeating density was observed that corresponds to actin-to-membrane connectors. In the taper region, most actin filaments terminated near the plasma membrane. The remaining filaments twisted together to make a tighter bundle than was present in the shaft region; the spacing between them decreased from 13 nm to 9 nm, and the apparent filament diameter decreased from 6.4 to 4.8 nm. Our models illustrate detailed features of distinct structural domains that are present within the stereocilium.

Cryo-electron tomography maps often exhibit considerable noise and anisotropic resolution, due to the low-dose requirements and the missing wedge in Fourier space. These spurious features are visually unappealing and, more importantly, prevent an automated segmentation of geometric shapes, requiring a highly subjective, labor-intensive manual tracing. We developed a novel computational strategy for objectively denoising and correcting missing-wedge artifacts in the special but important case of repetitive basic shapes, such as filamentous structures. In this approach, we use the template and a non-negative "location map" to constrain the deconvolution scheme, allowing us to recover, to a considerable degree, the information lost in the missing wedge. We applied our method to data of actin-filament bundles of inner-ear stereocilia, which are critical in hearing transduction processes, and found a much better overlap with the experimental map than manual tracing was able to achieve, confirming that the latter is subject to visual interpretation errors. In addition, we demonstrate that our method can also be used for membrane detection.

Electron cryo-tomography allows for high-resolution imaging of stereocilia in their native state. Because their actin filaments have a higher degree of order, we imaged stereocilia from mice lacking the actin crosslinker plastin 1 (PLS1). We found that while stereocilia actin filaments run 13 nm apart in parallel for long distances, there were gaps of significant size that were stochastically distributed throughout the actin core. Actin crosslinkers were distributed through the stereocilium, but did not occupy all possible binding sites. At stereocilia tips, protein density extended beyond actin filaments, especially on the side of the tip where a tip link should anchor. Along the shaft, repeating density was observed that corresponds to actin-to-membrane connectors. In the taper region, most actin filaments terminated near the plasma membrane. The remaining filaments twisted together to make a tighter bundle than was present in the shaft region; the spacing between them decreased from 13 nm to 9 nm. Our models illustrate detailed features of distinct structural domains that are present within the stereocilium.

In this paper, we present the construction of several aggregates of tetrahedra. Each construction is obtained by performing rotations on an initial set of tetrahedra that either (1) contains gaps between adjacent tetrahedra, or (2) exhibits an aperiodic nature. Following this rotation, gaps of the former case are &ldquo, closed&rdquo, (in the sense that faces of adjacent tetrahedra are brought into contact to form a &ldquo, face junction&rdquo, ), while translational and rotational symmetries are obtained in the latter case. In all cases, an angular displacement of &beta, = arccos 3 ϕ &minus, 1 / 4 (or a closely related angle), where ϕ = 1 + 5 / 2 is the golden ratio, is observed between faces of a junction. Additionally, the overall number of plane classes, defined as the number of distinct facial orientations in the collection of tetrahedra, is reduced following the transformation. Finally, we present several &ldquo, curiosities&rdquo, involving the structures discussed here with the goal of inspiring the reader&rsquo, s interest in constructions of this nature and their attending, interesting properties.

The Boerdijk&ndash, Coxeter helix is a helical structure of tetrahedra which possesses no non-trivial translational or rotational symmetries. In this document, we develop a procedure by which this structure is modified to obtain both translational and rotational (upon projection) symmetries along/about its central axis. We show by construction that a helix can be obtained whose shortest period is any whole number of tetrahedra greater than one except six, while a period of six necessarily entails a shorter period. We give explicit examples of two particular forms related to the pentagonal and icosahedral aggregates of tetrahedra as well as Buckminster Fuller&rsquo, s &ldquo, jitterbug transformation&rdquo

We introduce a fast information matching (FIM) method for transforming time domain data into spatial images through handshaking between fast and slow degrees of freedom. The analytics takes advantage of the detailed time series available from biomolecular computer simulations, and it yields spatial heat maps that can be visualized on 3D molecular structures or in the form of interaction networks. The speed of our efficient mutual information solver is on the order of a basic Pearson cross-correlation calculation. We demonstrate that the FIM method is superior to linear cross-correlation for the detection of nonlinear dependence in challenging situations where measures for the global dynamics (the “activity”) diverge. The analytics is applied to the detection of hinge-bending hot spots and to the prediction of pairwise contacts between residues that are relevant for the global activity exhibited by the molecular dynamics (MD) trajectories. Application examples from various MD laboratories include the millisecond bovine pancreatic trypsin inhibitor (BPTI) trajectory using canonical MD, a Gaussian accelerated MD folding trajectory of chignolin, and the heat-induced unfolding of engrailed homeodomain (EnHD). The FIM implementation will be freely disseminated with our open-source package, TimeScapes.

Background Dramatic progress has recently been made in cryo-electron microscopy technologies, which now make possible the reconstruction of a growing number of biomolecular structures to near-atomic resolution. However, the need persists for fitting and refinement approaches that address those cases that require modeling assistance. Methods In this paper, we describe algorithms to optimize the performance of such medium-resolution refinement methods. These algorithms aim to automatically optimize the parameters that define the density shape of the flexibly fitted model, as well as the time-dependent damper cutoff distance. Atomic distance constraints can be prescribed for cases where extra containment of parts of the structure is helpful, such as in regions where the density map is poorly defined. Also, we propose a simple stopping criterion that estimates the probable onset of overfitting during the simulation. Results The new set of algorithms produce more accurate fitting and refinement results, and yield a faster rate of convergence of the trajectory toward the fitted conformation. The latter is also more reliable due to the overfitting warning provided to the user. Conclusions The algorithms described here were implemented in the new Damped-Dynamics Flexible Fitting simulation tool “DDforge” in the Situs package.

Our development of a Fast (Mutual) Information Matching (FIM) of molecular dynamics time series data led us to the general problem of how to accurately estimate the probability density function of a random variable, especially in cases of very uneven samples. Here, we propose a novel Balanced Adaptive Density Estimation (BADE) method that effectively optimizes the amount of smoothing at each point. To do this, BADE relies on an efficient nearest-neighbor search which results in good scaling for large data sizes. Our tests on simulated data show that BADE exhibits equal or better accuracy than existing methods, and visual tests on univariate and bivariate experimental data show that the results are also aesthetically pleasing. This is due in part to the use of a visual criterion for setting the smoothing level of the density estimate. Our results suggest that BADE offers an attractive new take on the fundamental density estimation problem in statistics. We have applied it in the accompanying paper on molecular dynamics simulations of membrane pore formation. We also expect BADE to be generally useful for low-dimensional applications in other statistical application domains such as bioinformatics, signal processing and econometrics.

Cryo-electron microscopy (cryo-EM) is an important biophysical technique that produces three-dimensional (3D) density maps at different resolutions. Because more and more models are being produced from cryo-EM density maps, validation of the models is becoming important. We propose a method for measuring local agreement between a model and the density map using the central axis of the helix. This method was tested using 19 helices from cryo-EM density maps between 5.5 A and 7.2 A resolution and 94 helices from simulated density maps. This method distinguished most of the well-fitting helices, although challenges exist for shorter helices. Validation, protein structure, secondary structure, image, fitting, cryo-electron microscopy

An Icosahedral Quasicrystal as a Packing of Regular Tetrahedra F. Fang∗, J. Kovacs, G. Sadler and K. Irwin Quantum Gravity Research We present the construction of a dense, quasicrystalline packing of regular tetrahedra with icosahedral symmetry. This quasicrystalline packing was achieved through two independent approaches. The first approach originates in the Elser–Sloane 4D quasicrystal. A 3D slice of the quasicrystal contains a few types of prototiles. An initial structure is obtained by decorating these prototiles with tetrahedra. This initial structure is then modified using the Elser–Sloane quasicrystal itself as a guide. The second approach proceeds by decorating the prolate and oblate rhombohedra in a 3-dimensional Ammann tiling. The resulting quasicrystal has a packing density of 59.783%. We also show a variant of the quasicrystal that has just 10 “plane classes” (compared with the 190 of the original), defined as the total number of distinct orientations of the planes in which the faces of the tetrahedra are contained. This small number of plane classes was achieved by a certain “golden rotation” of the tetrahedra.

In fitting atomic structures into EM maps, it often happens that the map corresponds to a different conformation of the structure. We have developed a new methodology to handle these situations that preserves the covalent geometry of the structure and allows the modeling of large deformations. The first goal is achieved by working in generalized coordinates (positional and internal coordinates), and the second by avoiding harmonic potentials. Instead, we use dampers (shock absorbers) between every pair of atoms, combined with a force field that attracts the atomic structure toward incompletely occupied regions of the EM map. The trajectory obtained by integrating the resulting equations of motion converges to a conformation that, in our validation cases, was very close to the target atomic structure. Compared to current methods, our approach is more efficient and robust against wrong solutions and to overfitting, and does not require user intervention or subjective decisions. Applications to the computation of transition pathways between known conformers, homology and loop modeling, as well as protein docking, are also discussed.

We have extended Miedema's model to the modelling of free-energy diagrams in ternary alloys and applied the extended model to obtain a thermodynamic characterization of the glass formation range in Mg–Cu–Y. A structural term has been added in the calculation of the free energy of formation of solid solutions. By assuming that amorphization competes with formation of the hcp and fcc solid solutions, we have evaluated the region of compositions in which the system can be amorphized by quenching or casting of the liquid alloy. Equations of analytical geometry are proposed to search for regions of coexistence of amorphous and solid solutions, which could not be found for this ternary alloy. Heats of glass crystallisation have been calculated. The results of our model are in reasonable agreement with experimental data.

Inspired by the current representation of the ligand-receptor binding process, a normal-mode-based methodology is presented to incorporate receptor flexibility in ligand docking and virtual screening. However, the systematic representation of the deformation space grows geometrically with the number of modes, and furthermore, midscale loop rearrangements like those found in protein kinase binding pockets cannot be accounted for with the first lowest-frequency modes. We thus introduced a measure of relevance of normal modes on a given region of interest and showed that only very few modes in the low-frequency range are necessary and sufficient to describe loop flexibility in cAMP-dependent protein kinase. We used this approach to generate an ensemble of representative receptor backbone conformations by perturbing the structure along a combination of relevant modes. Each ensemble conformation is complexed with known non-native binders to optimize the position of the binding-pocket side chains through a full flexible docking procedure. The multiple receptor conformations thus obtained are used in a small-scale virtual screening using receptor ensemble docking. We evaluated this algorithm on holo and apo structures of cAMP-dependent protein kinase that exhibit backbone rearrangements on two independent loop regions close to the binding pocket. Docking accuracy is improved, since the ligands considered in the virtual screening docked within 1.5 A to at least one of the structures. The discrimination between binders and nonbinders is also enhanced, as shown by the improvement of the enrichment factor. This constitutes a new step toward the systematic integration of flexible ligand-flexible receptor docking tools in structure-based drug discovery.

Topology-representing networks (TRNs) generate reduced models of biomolecules and thereby facilitate the 5tting of molecular fragments into large macromolecular complexes. The components of such complexes undergo a wide range of motions, and shapes observed at low resolution often deviate from the known atomic structures. What is required for the modeling of such motions is a combination of global shape constraints based on the low-resolution data with a local modeling of atomic interactions. We present a novel Motion Capture Network that freezes inessential degrees of freedom to maintain the stereochemistryof an atomic model. TRN-based deformable models retain much of the mechanical properties of biological macromolecules. The elastic models yield a decomposition of the predicted motion into vibrational normal modes and are amenable to interactive manipulation with haptic rendering software. c

The 'fast rotational matching' method (an approach to find the three rotational degrees of freedom in matching problems using just one three-dimensional FFT) is extended to the full six-dimensional (rotation and translation) matching scenario between two three-dimensional objects. By recasting this problem into a formulation involving five angles and just one translational parameter, it was possible to accelerate, by means of fast Fourier transforms, five of the six degrees of freedom of the problem. This method was successfully applied to the docking of atomic structures of components into three-dimensional low-resolution density maps. Timing comparisons performed with our method and with 'fast translational matching' (the standard way to accelerate the translational parameters utilizing fast Fourier transforms) demonstrates that the performance gain can reach several orders of magnitude, especially for large map sizes. This gain can be particularly advantageous for spherical- and toroidal-shaped maps, since the scanning range of the translational parameter would be significantly constrained in these cases. The method can also be harnessed to the complementary surface (or 'exterior docking') problem and to pattern recognition in image processing.

As the existing literature reports, when Zircaloy-2 and Zircaloy-4 are irradiated at intermediate temperatures with high-energy neutrons, a crystalline to amorphous phase transition occurs, coincidental with a preferential depletion of Fe at the periphery of the Zr(Fe,Cr) 2 intermetallic particles. In order to describe these phenomena, relative phase stability criteria combined with a balance between the rate of irradiation damage and irradiation enhanced diffusion leading back to a modified or new state should be considered. Aiming at this suggested study, in this work we calculate the metastable free-energy diagram of the ternary Zr–Fe–Cr system. The free energies of formation of the metastable amorphous and solid solution phases and of the stable Zr(Fe,Cr) 2 compound have been calculated using Miedema's model. By solving equations of analytical geometry, regions of metastable equilibria and their tie-lines are defined, linking the hcp-Zr-rich solid solution with the Zr–Fe–Cr amorphous phase, and the latter with the irradiation-energized compound. Composition profiles, reported in the literature, were measured on partially and completely amorphized particles, and also in the case when the latter experienced microcrystallization with solute reversion, that is, with the Fe concentration increased during post-irradiation heat treatments. Those composition profiles define a path along a calculated tie-line, deviating near the crystalline core/amorphous crown interface toward low Fe concentrations. The analysis in the present work suggests that the microstructure in irradiated Zircaloy tends to reach a new radiation-induced metastable co-existence of phases.

Mutations in cardiac myosin binding protein C (cMyBP-C) are the most common cause of hypertrophic cardiomyopathy affecting millions of people worldwide. Recent studies established that the N-terminal domains (NTDs) of cMyBP-C (e.g., C0, C1, M, and C2) can bind to and activate or inhibit the thin filament (TF). However, the molecular mechanism(s) by which NTDs modulate interaction of myosin with the TF remains unknown. Recently, we demonstrated that despite being structural homologs, C0 and C1 NTDs exhibit different patterns of binding on the surface of F-actin. Moreover, we showed that C1 but not C0 can activate the TF by means of shifting the tropomyosin (Tm) cable from the “closed” to the “open” structural state via direct interaction with Tm. Here we used cryo electron microscopy and image analysis to reveal how C0 and C1 Ig-domains connected by the Proline/Alanine-linker communicate with each other when interacting with the TF in tandem. Our results show that C0 binds to the front of actin subdomain-1 in two distinct modes, and that in these two modes C0 has different effect on the interaction of C1 domain with both actin filament and Tm cable. In one mode C0 enhances the activating effect of C1 domain so that the Tm cable is shifted towards the subdomain-4 of actin to an even larger extent than found in the “open” state of Tm. In the second mode C0 reverses the activation effect of C1 by means of disrupting the interaction of C1 with Tm. Importantly, we demonstrate that the two domains communicate with each other allosterically through the actin filament. Our data suggest that the internal dynamics of the actin molecule is essential for the regulation of the actomyosin interaction in cardiac muscle. We propose a mechanism by which cMyBP-C may modulate actomyosin interactions in cardiac muscle.

The amorphization of Mg-Cu-Sn alloys with various compositions has been studied using the melt-spinning technique, with particular emphasis on the magnesium-rich corner of the ternary phase diagram. The results have been interpreted in terms of Miedema's theory, which highlights competition between the amorphous phase and crystalline solid solutions. Competition by ordered intermetallic compounds has also to be considered in order to explain the restricted amorphization region found in these experiments.

Summary Mediator, a large (21 polypeptides, MW ∼1 MDa) complex conserved throughout eukaryotes, plays an essential role in control of gene expression by conveying regulatory signals that influence the activity of the preinitiation complex. However, the precise mode of interaction between Mediator and RNA polymerase II (RNAPII), and the mechanism of regulation by Mediator remain elusive. We used cryo-electron microscopy and reconstituted in vitro transcription assays to characterize a transcriptionally-active complex including the Mediator Head module and components of a minimum preinitiation complex (RNAPII, TFIIF, TFIIB, TBP, and promoter DNA). Our results reveal how the Head interacts with RNAPII, affecting its conformation and function.

Gap junction channels connect the cytoplasms of adjacent cells through the end-to-end docking of hexameric hemichannels called connexons. Each connexon is formed by a ring of 24 a-helices that are staggered by 301 with respect to those in the apposed connexon. Current evidence suggests that the two connexons are docked by interdigitated, antiparallel b strands across the extracellular gap. The second extracellular loop, E2, guides selectivity in docking between connexons formed by different isoforms. There is considerably more sequence variability of the N-terminal portion of E2, suggesting that this region dictates connexon coupling. Mutagenesis, biochemical, dye-transfer and electrophysiological data, combined with computational studies, have suggested possible assignments for the four transmembrane a-helices within each subunit. Most current models assign M3 as the major pore-lining helix. Mapping of human mutations onto a C a model suggested that native helix packing is important for the formation of fully functional channels. Nevertheless, a mutant in which the M4 helix has been replaced with polyalanine is functional, suggesting that M4 is located on the perimeter of the channel. In spite of this substantial progress in understanding the structural biology of gap junction channels, an experimentally determined structure at atomic resolution will be essential to confirm these concepts. r 2007 Elsevier Ltd. All rights reserved.

Motivation: Efficient fitting tools are needed to take advantage of a fast growth of atomic models of protein domains from crystallography or comparative modeling, and low-resolution density maps of larger molecular assemblies. Here, we report a novel fitting algorithm for the exhaustive and fast overlay of partial high-resolution models into a low-resolution density map. The method incorporates a fast rotational search based on spherical harmonics (SH) combined with a simple translational scanning. Results: This novel combination makes it possible to accurately dock atomic structures into low-resolution electron-density maps in times ranging from seconds to a few minutes. The high-efficiency achieved with simulated and experimental test cases preserves the exhaustiveness needed in these heterogeneous-resolution merging tools. The results demonstrate its efficiency, robustness and high-throughput coverage. Availability: Contact: pablo@cib.csic.es Supplementary information: Supplementary data are available at Bioinformatics online.

The normal modes of a molecule are utilized, in conjunction with classical conformal vector field theory, to define a function that measures the capability of the molecule to deform at each of its residues. An efficient algorithm is presented to calculate the local chain deformability from the set of normal modes of vibration. This is done by considering each mode as an off-grid sample of a deformation vector field. Predictions of deformability are compared with experimental data in the form of dihedral angle differences between two conformations of ten kinases by using a modified correlation function. Deformability calculations correlate well with experimental results and validate the applicability of this method to protein flexibility predictions. © 2004 Wiley-Liss, Inc., DOE; Grant number: DE-FG03-00ER6304. P.C. was supported by Fundación BBVA

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.

A navigation system for an autonomous mobile robot is described, which is basically probabilistic. The sensing of the environment is made through a rangefinder, each measurement updating an occupancy grid, which is the internal representation of the robot's environment. The vehicle uses only local information for path planning and obstacle avoidance, searching for the path of minimum cost to the goal. The robot's position and orientation estimates are corrected after each scan of the environment by making a least square fit between the internal map and the set of observed points. Results of computer simulations are shown.

Integral membrane proteins pose a major challenge for protein-structure prediction because only approximately 100 high-resolution structures are available currently, thereby impeding the development of rules or empirical potentials to predict the packing of transmembrane alpha-helices. However, when an intermediate-resolution electron microscopy (EM) map is available, it can be used to provide restraints which, in combination with a suitable computational protocol, make structure prediction feasible. In this work we present such a protocol, which proceeds in three stages: 1), generation of an ensemble of alpha-helices by flexible fitting into each of the density rods in the low-resolution EM map, spanning a range of rotational angles around the main helical axes and translational shifts along the density rods; 2), fast optimization of side chains and scoring of the resulting conformations; and 3), refinement of the lowest-scoring conformations with internal coordinate mechanics, by optimizing the van der Waals, electrostatics, hydrogen bonding, torsional, and solvation energy contributions. In addition, our method implements a penalty term through a so-called tethering map, derived from the EM map, which restrains the positions of the alpha-helices. The protocol was validated on three test cases: GpA, KcsA, and MscL.

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