Dynamical principles of cell-cycle arrest: reversible, irreversible, and mixed strategies

Living cells often alternate between proliferating and nonproliferating states as part of individual or collective strategies to adapt to complex and changing environments. To this aim, they have evolved a biochemical regulatory network enabling them to switch between cell-division cycles (i.e., oscillatory state) and cell-cycle arrests (i.e., steady state) in response to extracellular cues. This can be achieved by means of a variety of bifurcation mechanisms that potentially give rise to qualitatively distinct cell-cycle arrest properties. In this paper, we study the dynamics of a minimal biochemical network model in which a cell-division oscillator and a differentiation switch mutually antagonize. We identify the existence of three biologically plausible bifurcation scenarios organized around a codimension-four swallowtail-homoclinic singularity. As a result, the model exhibits a broad repertoire of cell-cycle arrest properties in terms of reversibility of these arrests, tunability of interdivision time, and ability to track time-varying signals. This dynamic versatility would explain the diversity of cell-cycle arrest strategies developed in different living species and functional contexts.