Title: Optimal segregation of proteins: phase transitions and symmetry breaking,
Abstract: Asymmetric segregation of key proteins at cell division -- be it a beneficial
or deleterious protein -- is ubiquitous in unicellular organisms and often
considered as an evolved trait to increase fitness in a stressed environment.
Here, 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
proteins which decrease the single-cell growth rate. 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.