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.
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