The Sum of Squares Law

We show that when projecting an edge-transitive N-dimensional polytope onto anM-dimensional subspace of R^N, the sums of the squares of the original and projected edges are in the ratio N=M

A Balanced Approach to Adaptive Probability Density Estimation

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 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

Comparing an Atomic Model or Structure to a Corresponding Cryo-Electron Microscopy Image at the Central Axis of a Helix

Three-dimensional density maps of biological specimens from cryo-electron microscopy (cryo-EM) can be interpreted in the form of atomic models that are modeled into the density, or they can be compared to known atomic structures. When the central axis of a helix is detectable in a cryo-EM density map, it is possible to quantify the agreement between this central axis and a central axis calculated from the atomic model or structure. We propose a novel arc-length association method to compare the two axes reliably. This method was applied to 79 helices in simulated density maps and six case studies using cryo-EM maps at 6.4-7.7 Å resolution. The arc-length association method is then compared to three existing measures that evaluate the separation of two helical axes: a two-way distance between point sets, the length difference between two axes, and the individual amino acid detection accuracy. The results show that our proposed method sensitively distinguishes lateral and longitudinal discrepancies between the two axes, which makes the method particularly suitable for the systematic investigation of cryo-EM map-model pairs

Accurate Flexible Refinement of Atomic Models Against Medium-Resolution cryo-EM Maps Using Damped Dynamics

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

Tracing Actin Filament Bundles in Three-Dimensional Electron Tomography Density Maps of Hair Cell Stereocilia

Cryo-electron tomography (cryo-ET) is a powerful method of visualizing the three-dimensional organization of supramolecular complexes, such as the cytoskeleton, in their native cell and tissue contexts. Due to its minimal electron dose and reconstruction artifacts arising from the missing wedge during data collection, cryo-ET typically results in noisy density maps that display anisotropic XY versus Z resolution. Molecular crowding further exacerbates the challenge of automatically detecting supramolecular complexes, such as the actin bundle in hair cell stereocilia. Stereocilia are pivotal to the mechanoelectrical transduction process in inner ear sensory epithelial hair cells. Given the complexity and dense arrangement of actin bundles, traditional approaches to filament detection and tracing have failed in these cases. In this study, we introduce BundleTrac, an effective method to trace hundreds of filaments in a bundle. A comparison between BundleTrac and manually tracing the actin filaments in a stereocilium showed that BundleTrac accurately built 326 of 330 filaments (98.8%), with an overall cross-distance of 1.3 voxels for the 330 filaments. BundleTrac is an effective semi-automatic modeling approach in which a seed point is provided for each filament and the rest of the filament is computationally identified. We also demonstrate the potential of a denoising method that uses a polynomial regression to address the resolution and high-noise anisotropic environment of the density map

Conformation and concerted dynamics of the integrin-binding site and the C-terminal region of echistatin revealed by homonuclear NMR

Echistatin is a potent antagonist of the integrins αvβ3, α5β1 and αIIbβ3. Its full inhibitory activity depends on an RGD (Arg-Gly- Asp) motif expressed at the tip of the integrin-binding loop and on its C-terminal tail. Previous NMR structures of echistatin showed a poorly defined integrin-recognition sequence and an incomplete C-terminal tail, which left the molecular basis of the functional synergy between the RGD loop and the C-terminal region unresolved. We report a high-resolution structure of echistatin and an analysis of its internal motions by off-resonance ROESY (rotating-frame Overhauser enhancement spectroscopy). The fulllength C-terminal polypeptide is visible as a β-hairpin running parallel to the RGD loop and exposing at the tip residues Pro43, His44 and Lys45. The side chains of the amino acids of the RGD motif have well-defined conformations. The integrin-binding loop displays an overall movement with maximal amplitude of 30◦. Internal angular motions in the 100–300 ps timescale indicate increased flexibility for the backbone atoms at the base of the integrin- recognition loop. In addition, backbone atoms of the amino acids Ala23 (flanking the R24GD26 tripeptide) and Asp26 of the integrin-binding motif showed increased angular mobility, suggesting the existence of major and minor hinge effects at the base and the tip, respectively, of the RGD loop. A strong network of NOEs (nuclear Overhauser effects) between residues of the RGD loop and the C-terminal tail indicate concerted motions between these two functional regions. A full-length echistatin– αvβ3 docking model suggests that echistatin’s C-terminal amino acids may contact αv-subunit residues and provides new insights to delineate structure–function [email protected]; [email protected]; [email protected]; [email protected]

Reasons for the use of masks in open areas after the Peruvian government announced that it will no longer be mandatory in the context of COVID-19 in 2022

Introduction: In Peru, a high proportion of fully immunized people against COVID-19 has been achieved, which has mitigated the severity of the disease. Thus, under the recommendation of experts, the Peruvian government issued Supreme Decree 118-2022-PCM, which indicated that the use of masks is optional in open and ventilated enclosed spaces as of October 1, 2022. Objective: The aim of the present study was to find out the reasons why people continued to wear masks even though it was not mandatory in outdoor environments. Methods: A total of 335 people participated, with an average age of 26.11 years (73.1% women). A data collection form was prepared where sociodemographic and health information was requested; in addition, the question "Why do you continue to wear mask despite it being optional in open and closed ventilated spaces?" was included. The data obtained from the last open question of the instrument was analyzed by means of a discursive textual analysis (DTA) and an exploratory analysis through IRAMUTEQ. Results: Results indicate that people continue to wear masks, despite the lifting of the restrictions, to avoid contagion of COVID-19 and other respiratory diseases. In addition, the prevention of possible infection and transmission of the virus also focused on the family and vulnerable people. Discussion: It is concluded that the practice of wearing masks may be influenced by individual perceptions of risk and interpretations of responsibility and solidarity towards others

How does a cadaver model work for testing ultrasound diagnostic capability for rheumatic-like tendon damage?

To establish whether a cadaver model can serve as an effective surrogate for the detection of tendon damage characteristic of rheumatoid arthritis (RA). In addition, we evaluated intraobserver and interobserver agreement in the grading of RA-like tendon tears shown by US, as well as the concordance between the US findings and the surgically induced lesions in the cadaver model. RA-like tendon damage was surgically induced in the tibialis anterior tendon (TAT) and tibialis posterior tendon (TPT) of ten ankle/foot fresh-frozen cadaveric specimens. Of the 20 tendons examined, six were randomly assigned a surgically induced partial tear; six a complete tear; and eight left undamaged. Three rheumatologists, experts in musculoskeletal US, assessed from 1 to 5 the quality of US imaging of the cadaveric models on a Likert scale. Tendons were then categorized as having either no damage, (0); partial tear, (1); or complete tear (2). All 20 tendons were blindly and independently evaluated twice, over two rounds, by each of the three observers. Overall, technical performance was satisfactory for all items in the two rounds (all values over 2.9 in a Likert scale 1-5). Intraobserver and interobserver agreement for US grading of tendon damage was good (mean κ values 0.62 and 0.71, respectively), with greater reliability found in the TAT than the TPT. Concordance between US findings and experimental tendon lesions was acceptable (70-100 %), again greater for the TAT than for the TPT. A cadaver model with surgically created tendon damage can be useful in evaluating US metric properties of RA tendon lesions