Figure S6 from Multirhythmicity generated by coupling two cellular rhythms

The cell cycle and the circadian clock represent two major cellular rhythms. These rhythms are coupled, since the circadian clock governs the synthesis of several proteins of the network that drives the mammalian cell cycle. Previous analysis of a detailed model for these coupled cellular rhythms showed that the cell cycle can be entrained to oscillate at the circadian period of 24 h, or at a period of 48 h, depending on the autonomous period of the cell cycle and on the coupling strength. Building on these results, we show by means of numerical simulations that multiple stable periodic regimes, i.e. multirhythmicity, may originate from the coupling of the two cellular rhythms. In addition to a unique regime of periodic oscillations, the cell cycle becomes capable of displaying a coexistence between two (birhythmicity) or even three stable periodic regimes (trirhythmicity). Similar results are obtained upon coupling the cell cycle to the circadian clock in various ways, which differ by the nature of the cell cycle proteins controlled by circadian oscillations. In the region of multirhythmicity, the cell cycle coupled to the circadian clock may switch between two and three distinct periodic regimes upon transient perturbation. To which periodic regime, the cell cycle oscillator evolves depends on the magnitude of the perturbation and on the phase at which it is applied. Numerical simulations reveal final state sensitivity, due to the complex structure of attraction basins, as the coupled system evolves alternatively to one or the other periodic regime(s) when progressively changing the magnitude or duration of the transient perturbations, or the initial condition for one of the system's variables. By providing a novel instance of multirhythmicity in a realistic model for coupled cellular rhythms, the results throw light on the conditions in which multiple stable periodic regimes may coexist in biological systems.This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’