A mean field Ising model for cortical rotation in amphibian one-cell stage embryos

Abstract

We propose a new physical mechanism of cortical rotation generation in one-cell embryos of amphibians based on a phase transition in the ensemble of microtubules localized to the cortical region of the cell interior. Microtubules, protein polymers formed from tubulin heterodimers, are highly negatively charged, which results in strong electrostatic interactions over tens of nanometers, even in the presence of counterions that partially screen electrostatic interactions. A simplified model that offers a plausible representation of these effects is based on the Ising Hamiltonian, which has been robustly applied to explain a wide range of order–disorder transitions in physics, chemistry and other sciences. An Ising model phase transition, especially with the supercooperative flow alignment effect of global rotation of the cortex, provides an alternative to models of cortical rotation based on microtubule polymerization or motor molecules. Insofar as there is any reality to the concept that microtubules are involved in consciousness, we propose that cortical rotation in the one-cell embryo is a better place to look for the purported microtubule entanglement or coherence properties than the adult brain.