Bayesian inference for three-dimensional helical reconstruction using a soft-body model

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Masataka Ohashi ◽  
Shin-ichi Maeda ◽  
Chikara Sato
Keyword(s):  
Bayesian Inference ◽  
Three Dimensional ◽  
Soft Body ◽  
Body Model ◽  
Helical Reconstruction

scholarly journals Three-dimensional structure of a single filament in the Limulus acrosomal bundle: scruin binds to homologous helix-loop-beta motifs in actin

1994 ◽  
Vol 124 (3) ◽  
pp. 341-350 ◽  
Author(s):  
MF Schmid ◽  
JM Agris ◽  
J Jakana ◽  
P Matsudaira ◽  
W Chiu
Keyword(s):  
Actin Filament ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Unit Cell ◽  
Dimensional Structure ◽  
Single Filament ◽  
Three Dimensional Structure ◽  
Helical Reconstruction

Frozen, hydrated acrosomal bundles from Limulus sperm were imaged with a 400 kV electron cryomicroscope. Segments of this long bundle can be studied as a P1 crystal with a unit cell containing an acrosomal filament with 28 actin and 28 scruin molecules in 13 helical turns. A novel computational procedure was developed to extract single columns of superimposed acrosomal filaments from the distinctive crystallographic view. Helical reconstruction was used to generate a three-dimensional structure of this computationally isolated acrosomal filament. The scruin molecule is organized into two domains which contact two actin subunits in different strands of the same actin filament. A correlation of Holmes' actin filament model to the density in our acrosomal filament map shows that actin subdomains 1, 2, and 3 match the model density closely. However, actin subdomain 4 matches rather poorly, suggesting that interactions with scruin may have altered actin conformation. Scruin makes extensive interactions with helix-loop-beta motifs in subdomain 3 of one actin subunit and in subdomain 1 of a consecutive actin subunit along the genetic filament helix. These two actin subdomains are structurally homologous and are closely spaced along the actin filament. Our model suggests that scruin, which is derived from a tandemly duplicated gene, has evolved to bind structurally homologous but non-identical positions across two consecutive actin subunits.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

2020 ◽  
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Uncertainty Quantification ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
User Interest ◽  
Operation Conditions ◽  
Random Material Properties

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

scholarly journals Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
Amit Singer
Keyword(s):  
Bayesian Inference ◽  
Theoretical Foundation ◽  
Three Dimensional ◽  
Electron Cryomicroscopy ◽  
High Frequencies ◽  
X Ray ◽  
X Ray Crystallography ◽  
Bayesian Inference Framework ◽  
Higher Order Spectra ◽  
Mathematical Derivation

The power spectrum of proteins at high frequencies is remarkably well described by the flat Wilson statistics. Wilson statistics therefore plays a significant role in X-ray crystallography and more recently in electron cryomicroscopy (cryo-EM). Specifically, modern computational methods for three-dimensional map sharpening and atomic modelling of macromolecules by single-particle cryo-EM are based on Wilson statistics. Here the first rigorous mathematical derivation of Wilson statistics is provided. The derivation pinpoints the regime of validity of Wilson statistics in terms of the size of the macromolecule. Moreover, the analysis naturally leads to generalizations of the statistics to covariance and higher-order spectra. These in turn provide a theoretical foundation for assumptions underlying the widespread Bayesian inference framework for three-dimensional refinement and for explaining the limitations of autocorrelation-based methods in cryo-EM.

On Some Particularities of the Axisymmetric Wave Propagation in the Initially Twisted Circular Compound Cylinders

2010 ◽  
Author(s):  
Surkay Akbarov ◽  
Mugan Guliev ◽  
Tamer Kepceler
Keyword(s):  
Wave Propagation ◽  
Solution Method ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Body Model ◽  
Axisymmetric Wave ◽  
Piecewise Homogeneous Body ◽  
Linearized Theory ◽  
New Type ◽  
Circular Compound

This paper investigates some particularities related with the influence of the magnitude of the initial twisting of the axisymmetric wave propagation in the initially twisted circular bi-material compounded cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed. The numerical results are further presented and discussed. In particular, the mechanism of the arising of the new type modes caused by the initial twisting of the circular compounded cylinders is established.

Quantifying Segmental Contributions to Center-of-Mass Motion During Dynamic Continuous Support Surface Perturbations Using Simplified Estimation Models

2020 ◽  
Vol 36 (4) ◽  
pp. 198-208
Author(s):  
Alison Schinkel-Ivy ◽  
Vicki Komisar ◽  
Carolyn A. Duncan
Keyword(s):  
Balance Control ◽  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Whole Body ◽  
Mass Motion ◽  
Support Surface ◽  
Body Segments ◽  
Body Model ◽  
Full Body

Investigating balance reactions following continuous, multidirectional, support surface perturbations is essential for improving our understanding of balance control in moving environments. Segmental motions are often incorporated into rapid balance reactions following external perturbations to balance, although the effects of these motions during complex, continuous perturbations have not been assessed. This study aimed to quantify the contributions of body segments (ie, trunk, head, upper extremity, and lower extremity) to the control of center-of-mass (COM) movement during continuous, multidirectional, support surface perturbations. Three-dimensional, whole-body kinematics were captured while 10 participants experienced 5 minutes of perturbations. Anteroposterior, mediolateral, and vertical COM position and velocity were calculated using a full-body model and 7 models with reduced numbers of segments, which were compared with the full-body model. With removal of body segments, errors relative to the full-body model increased, while relationship strength decreased. The inclusion of body segments appeared to affect COM measures, particularly COM velocity. Findings suggest that the body segments may provide a means of improving the control of COM motion, primarily its velocity, during continuous, multidirectional perturbations, and constitute a step toward improving our understanding of how the limbs contribute to balance control in moving environments.

Statics of Laminated and Fibrous Composites With Curved Structures

1992 ◽  
Vol 45 (2) ◽  
pp. 17-34 ◽  
Author(s):  
S. D. Akbarov ◽  
A. N. Guz’
Keyword(s):  
Composite Material ◽  
Solid Body ◽  
Three Dimensional ◽  
Local Distribution ◽  
Homogeneous Body ◽  
Deformable Solid ◽  
Body Model ◽  
Curved Structures ◽  
Piecewise Homogeneous Body ◽  
Deformable Solid Body

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.

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