Population Structures with Positive Feedback and Asymmetric Division

In bioreactor experiments, budding yeast can manifest stable metabolic oscillations. In some instances these oscillations involve the cell cycle and are associated with a dynamical phenomenon called temporal clustering. Since yeast divide asymmetrically, mother cells may be able to divide sooner than the smaller daughter cells. We show that asymmetric division plus positive feedback can result in stable temporal clustering. In this scenario, the cells self-organize into $p$ clusters of mother cells and $q$ clusters of daughter cells, $p \le q$. In simple numerical simulations of a population model with asymmetric division and positive feedback, we show that $p:q$ periodic arrangements form spontaneously from random populations of cells. Our main result is that these structures can be stable.