A simple mechanism for spontaneous and induced cell polarization during asymmetric cell division

Symmetry breaking phenomena not only occurs in physical and chemical systems.
In biology this effect is encountered in many different contexts either in
single cells or in hole organisms. In single cells, this phenomenon is known
as cell polarization and is responsible, e.g., for an effect know as asymmetric
cell division. Cell polarization during asymmetric cell division has been
intensively studied in embryos of the worm Caenorhabditis elegans. In embryos
of this worm, and prior to the first cell division, the distribution of some
characteristic proteins becomes asymmetrical. This asymmetric distribution of
proteins in distinct anterior and posterior domains is responsible for the
different fates that each daughter cells has after the asymmetric cell
division. Motivated by recent experimental evidence, here we present a simple
two-variable, mass conserved reaction-diffusion system that describes the
distribution of the characteristic proteins. The model exhibits a symmetry-
breaking mechanism that leads to protein segregation and accounts for many
experimental observations done in C. elegans and other organisms. We show that
this spontaneous symmetry breaking is induced by a mechanism similar to a
Turing instability. However, in our model the wavelength of the fastest
growing spatial pattern is always equal to the system size.