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Symmetry

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...

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Biological membranes show uneven distribution of different types of lipids in the inner and outer layers, resulting in transverse asymmetric membranes. The treatment of the erythrocyte membrane with the enzyme phospholipase confirmed the asymmetric nature of the lipid bilayer. The enzyme hydrolyzes lipids into fatty acids and hydrophilic groups. The phospholipase acts only on the outer layer of the membrane, while the inner layer remains intact. The phospholipase treatment resulted in 80%...

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The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...

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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...

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Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

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Published on: January 15, 2016

What's left in asymmetry?

Sherry Aw¹, Michael Levin

¹Biological and Biomedical Sciences Program, Harvard Medical School, Boston, Massachusetts 02115, USA.

Developmental Dynamics : an Official Publication of the American Association of Anatomists

|May 21, 2008

Summary

Left-right asymmetry in embryonic development involves complex signaling pathways. New research highlights critical knowledge gaps and proposes 12 key questions for future studies on developmental biology and morphogenesis.

Area of Science:

Developmental Biology
Morphogenesis
Evolutionary Biology

Background:

Left-right (LR) patterning is crucial for embryonic development, integrating evolutionary and cellular signaling.
Significant progress has been made in understanding molecular mechanisms in model organisms over the past 15 years.
Despite advances, fundamental uncertainties persist regarding specific mechanisms, cross-phyla unity, and unexplored research avenues.

Purpose of the Study:

To identify critical knowledge gaps in the field of left-right asymmetry.
To propose fundamental questions for future research in developmental biology.
To highlight the importance of underutilized data sources for understanding asymmetry.

Main Methods:

Review and synthesis of existing literature on LR asymmetry.

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Last Updated: Jul 5, 2026

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

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Symmetric Bihemispheric Postmortem Brain Cutting to Study Healthy and Pathological Brain Conditions in Humans

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Analysis of data from clinical syndromes, cryptic asymmetries, and bilateral gynandromorphs.

Identification of key unresolved questions in the field.

Main Results:

Several fundamental uncertainties remain regarding the detailed mechanisms of LR patterning.
A lack of conceptual unity exists across different phyla concerning asymmetry.
Clinical data and rare asymmetries reveal crucial gaps in current understanding.
Twelve significant questions are identified as opportunities for major advances.

Conclusions:

The field of LR asymmetry requires a broader perspective beyond popular model systems.
Clinical syndromes and cryptic asymmetries offer vital insights into fundamental gaps.
Addressing the proposed 12 questions will drive significant progress in understanding morphogenesis and developmental biology.