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Related Concept Videos

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...
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
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.
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Unsymmetric Loading of Thin-Walled Members01:23

Unsymmetric Loading of Thin-Walled Members

Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the...

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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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Surprises and pitfalls arising from (pseudo)symmetry.

Peter H Zwart1, Ralf W Grosse-Kunstleve, Andrey A Lebedev

  • 1Berkeley Center for Structural Biology, Lawrence Berkeley National Laboratory, One Cyclotron Road, Building 6R2100, Berkeley, CA 94720, USA. phzwart@lbl.gov

Acta Crystallographica. Section D, Biological Crystallography
|December 21, 2007
PubMed
Summary

Multiple protein molecules in a crystal's asymmetric unit can cause pathologies like twinning and pseudosymmetry. This study introduces a new notation to address space group uncertainties arising from these common crystal defects.

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Area of Science:

  • Crystallography
  • Structural Biology
  • Biophysics

Background:

  • Protein crystals often contain multiple molecules per asymmetric unit.
  • This can lead to crystallographic pathologies including twinning, modulated crystals, and pseudosymmetry.
  • Pseudosymmetry, especially with twinning, complicates accurate space group determination.

Purpose of the Study:

  • To present the background of common crystallographic pathologies.
  • To introduce a novel notation for describing space groups in unusual settings.
  • To clarify space group determination in the presence of crystal defects.

Main Methods:

  • Literature review of common crystallographic pathologies.
  • Development of a new notation system for space groups.
  • Analysis of examples from scientific literature and the Protein Data Bank.

Main Results:

  • Detailed explanation of pathologies arising from multiple molecules per asymmetric unit.
  • Introduction of a new, standardized notation for non-standard space group settings.
  • Demonstration of the notation's utility with real-world crystallographic data.

Conclusions:

  • The proposed notation aids in resolving space group ambiguities caused by crystal pathologies.
  • Understanding these pathologies is crucial for accurate protein structure determination.
  • The new notation facilitates clearer communication and data interpretation in structural biology.