Optimal segregation of proteins: phase transitions and symmetry breaking

In stressed environments, microbial cells such as bacteria or yeast utilize various mechanisms to survive. One important mechanism is the asymmetric segregation of key proteins at cell division, placing one of the two daughter cells in a more favorable condition. We provide a general framework to describe the evolutionary origin of this asymmetric segregation. We compute the population fitness as a function of the protein segregation asymmetry a and show that the value of a which optimizes the population growth manifests a phase transition between symmetric and asymmetric partitioning phases. Surprisingly, the nature of phase transition is different for the case of beneficial proteins as opposed to deleterious proteins: a smooth (second order) transition from purely symmetric to asymmetric segregation is found in the former, while a sharp transition occurs in the latter. Our study elucidates the optimization problem faced by evolution in the context of protein segregation and motivates further investigation of asymmetric protein segregation in biological systems.