Stability of \({p:q}\) Temporally Clustered Population Structures in the Cell Cycle with Asymmetric Division

Abstract. Budding yeast has been observed for many years to exhibit stable metabolic oscillations in certain bioreactor experiments and some of these oscillations are known to involve the cell cycle and temporal clustering, i.e., groups of cells traversing the cycle in near synchrony. In budding yeast, division is asymmetric: it produces two nonidentical cells, namely a larger mother and a smaller daughter. A mother cell may be able to reach the next division more quickly than a daughter. Previous studies have suggested that this disparity may cause there to exist periodic temporally clustered solutions in which there are [Formula: see text] mother clusters and [Formula: see text] daughter clusters for [Formula: see text]. We study a population model of the cell cycle in which cells in one region of the cell cycle may negatively influence the progress of cells in another region, resulting in temporal clustering. We demonstrate numerically in simple simulations that [Formula: see text] periodic configurations can form spontaneously from a disordered population. As the main result, we prove analytically in the models that certain types of [Formula: see text] clustered solutions can exist and be linearly asymptotically stable.