Related Experiment Video
Updated: Jul 13, 2026
09:23
Assessing Two-dimensional Crystallization Trials of Small Membrane Proteins for Structural Biology Studies by Electron Crystallography
Published on: October 29, 2010
Symmetry: A guide to its application in 2D electron crystallography
Michael J Landsberg1, Ben Hankamer
1Institute for Molecular Bioscience, Queensland Biosciences Precinct, The University of Queensland, Brisbane, Qld 4072, Australia. m.landsberg@imb.uq.edu.au
Journal of Structural Biology
|August 21, 2007
Summary
This review explains 2D crystallographic symmetry for macromolecular structure studies. It covers symmetry operations, plane groups, and their application in 2D electron crystallography for 3D structure determination.
Area of Science:
- Crystallography
- Structural Biology
- Electron Microscopy
Background:
- Crystallographic symmetry is fundamental to understanding crystal structure.
- 2D electron crystallography provides insights into macromolecular structures.
- Symmetry analysis is crucial for accurate 3D structure determination from 2D projections.
Purpose of the Study:
- To provide a comprehensive summary of 2D crystallographic symmetry.
- To detail symmetry operations, notation, and plane groups relevant to 2D crystals.
- To guide the identification and application of symmetry in 2D crystal images for 3D structure determination.
Main Methods:
- Review of crystallographic symmetry principles in 2D.
- Explanation of symmetry operations and common notation.
- Discussion of crystallographic plane groups and theoretical methods.
Main Results:
- Defined molecular point symmetries and 2D crystallographic symmetry operations.
- Summarized 2D crystallographic plane groups and relevant theoretical methods.
- Highlighted considerations for applying symmetry in 2D crystal imaging for 3D structure determination.
Conclusions:
- 2D crystallographic symmetry is essential for macromolecular structure analysis.
- Understanding symmetry operations and plane groups aids in 2D electron crystallography.
- Accurate symmetry identification in 2D projections is key for reliable 3D structure determination.
Related Concept Videos
01:27Symmetry 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...
01:29Crystallographic Point Groups
Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
01:26Symmetry
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...
01:24The Seven Crystal Systems: Overview
Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
02:18X-ray Crystallography
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
02:25Chirality
Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...