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Related Concept Videos

Symmetric Member in Bending01:07

Symmetric Member in Bending

In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
Symmetry01:26

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...
Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...

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Related Experiment Video

Updated: May 29, 2026

Single Particle Cryo-Electron Microscopy: From Sample to Structure
11:52

Single Particle Cryo-Electron Microscopy: From Sample to Structure

Published on: May 29, 2021

Symmetry-restrained flexible fitting for symmetric EM maps.

Kwok-Yan Chan1, James Gumbart, Ryan McGreevy

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.

Structure (London, England : 1993)
|September 7, 2011
PubMed
Summary

We developed a new symmetry-restrained molecular dynamics flexible fitting (MDFF) method. This approach improves atomic-scale structure fitting into cryo-electron microscopy (cryo-EM) maps, especially for low-resolution data.

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Area of Science:

  • Structural Biology
  • Biophysics
  • Computational Biology

Background:

  • Large biological macromolecules often exhibit inherent structural symmetry.
  • Cryo-electron microscopy (cryo-EM) images these complexes in relevant states, but traditional methods struggle with resolution.
  • Existing atomic-scale fitting methods like molecular dynamics flexible fitting (MDFF) depend heavily on map quality.

Purpose of the Study:

  • To develop a novel method that incorporates structural symmetry information into the fitting process.
  • To enhance the accuracy of atomic-scale structure determination from cryo-EM data, particularly at lower resolutions.
  • To improve the quality of fitted structures for symmetric biological complexes.

Main Methods:

  • Developed the symmetry-restrained MDFF method, integrating symmetry knowledge into the fitting potential.
  • Applied MDFF with symmetry restraints to cryo-EM maps of biological complexes.
  • Evaluated the method's performance across three distinct biological systems.

Main Results:

  • The symmetry-restrained MDFF method successfully improved the quality of fitted atomic-scale structures.
  • The benefits were particularly evident when working with medium to low-resolution cryo-EM data.
  • Demonstrated improved structural determination for three different biological systems using the new method.

Conclusions:

  • Incorporating symmetry knowledge into fitting procedures significantly enhances structural determination from cryo-EM maps.
  • Symmetry-restrained MDFF offers a valuable tool for analyzing symmetric macromolecular complexes, especially when high-resolution data is unavailable.
  • This method advances the capability to model complex biological structures with greater accuracy.