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A mean field Ising model for cortical rotation in amphibian one cell stage embryos
by
Jack A. Tuszynski
University of Alberta
Coauthors: Richard Gordon (University of Manitoba, gordonr@cc.umanitoba.ca)
The fertilized amphibian egg is ideal for mathematical analysis, with its apparently spherically symmetric cortex (membrane and a few microns of attached cytoskeleton), and initially axially symmetric, bottom heavy stratified yolk and cytoplasm inside. Before the first cell division, the cortex rotates 30deg. It is believed that the rotation is driven by microtubule motors and/or polymerization of microtubules attached to the inner surface of the cortex. While these microtubules are initially randomly oriented, they take on a common orientation by the end of the cortical rotation. The basic interaction appears to be two way: the microtubules drive the cortical rotation, leading to sloshing of the yolk and cytoplasm, and the fluid motion aligns the microtubules in such a way as to enhance the rotation. The startup is stochastic in nature. We model this interaction by a mean field Ising model, but due to the coupling between the microtubules, the actual “field” is equal to the mean field, giving the model an unusual precision. Here we show what can be gleaned from observed stochastic rotational trajectories using this model, and how the model is altered if nearest neighbor microtubule-microtubule interactions are included.
Date received: May 4, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawd-51.