Symmetry How do we define symmetry An object

Symmetry

How do we define symmetry • An object invariant under a transformation – Rotation – Translation – Time Lapse – Reflection • How many symmetries does a cube have? 48

Curie’s Principle • If certain causes produce certain effects, then the symmetries of the causes reappear in the effects produces • If certain effects reveal a certain asymmetry, then this asymmetry will be reflected in the causes that give rise to them

An airplane • An airplane has bilateral symmetry • Does half a plane against a wall reproduce the flow past the airplane?

Bifurcation • Symmetry “breaks” by creating an assortment of anti-symmetric states which sum to a symmetric state

Airplane Flying • Has 2 steady states just off direct • Switches between the two due to turbulence or other “imperfections” • The overall “math” is symmetric, though there anti-symmetric solutions

Symmetry in Biology

Gastrulation • Start as spherically symmetric egg • Lose symmetry with division • Regain symmetry with blastula • Lose symmetry as a sphere with a dimple

Breaking of Symmetry • Causes – Difference of Pressure creates inward pressure – Cell-Cell movement • Location selection – Breaking due to pressure will occur where walls are weaker – Cell-Cell movement could be caused by selectively changing cell-cell adhesion

What actually happens? • Cells change their adhesion properties and move via “random” motion • Axis is selected via signaling molecules established at the time of fertilization

Conclusions • Small perturbations away from symmetry can cause substantial effects • Biology often just “pushes” an organism in the correct direction