A Wheel of Fortune: The eukaryotic cell cycle as a tetra-stable excitable system

Progression through the eukaryotic cell cycle is governed by a complex biochemical network controlling the activity of cyclin-dependent kinases. Dynamically, the cell cycle control network can be viewed as a multi-stable system, in which nonlinear feedback loops generate multiple stable attractors, corresponding to distinct cell cycle phases (G1, S, G2, M). Transitions between these states are typically irreversible, ensuring ordered phase progression. However, recent studies of endocycles - variants in which subsets of phases are abrogated - have prompted the development of more general regulatory models, allowing for reversible transitions or the decoupling of autonomous oscillatory modules. The current paper combines minimal ODE modelling, phase plane analysis, and bifurcation theory to demonstrate that two prior frameworks - Newton's Cradle and Latching Gate - are alternative representations of a shared architecture based on mutually regulated oscillators. Leveraging this insight, a generalized model, capturing a broader spectrum of physiological endocycles than previously attempted, is introduced. To provide an intuitive representation of the principles identified by the new model, a 'Wheel of Fortune' analogy for cell cycle dynamics is introduced.