Multi-rhythmicity generated by coupling two cellular rhythms.

Jie Yan,Albert Goldbeter

doi:10.1098/rsif.2018.0835

Abstract

The cell cycle and the circadian clock represent two major cellular rhythms, which are coupled because the circadian clock governs the synthesis of several proteins of the network that drives the mammalian cell cycle. Analysis of a detailed model for these coupled cellular rhythms previously showed that the cell cycle can be entrained 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. We show by means of numerical simulations that multiple stable periodic regimes, i.e. multi-rhythmicity, may originate from the coupling of the two cellular rhythms. In these conditions, the cell cycle can evolve to any one of two (birhythmicity) or three stable periodic regimes (trirhythmicity). When applied at the right phase, transient perturbations of appropriate duration and magnitude can induce the switch between the different oscillatory states. Such switching is characterized by final state sensitivity, which originates from the complex structure of the attraction basins. By providing a novel instance of multi-rhythmicity in a realistic model for the coupling of two major cellular rhythms, the results throw light on the conditions in which multiple stable periodic regimes may coexist in biological systems.

Highlights

Besides oscillations, spatial patterns and propagating waves, the coexistence between multiple attractors represents a major mode of self-organization in nonlinear systems [1,2,3,4]
After summarizing the results previously obtained for the effects of this coupling on the dynamics of the cell cycle, such as entrainment and complex oscillations, we investigate the occurrence of birhythmicity and trirhythmicity in §§3 and 4, respectively
We explored in further detail the entrainment domains to search for evidence of multiple periodic regimes in the case where the cell cycle is coupled to the circadian clock via Wee1 only, via cyclin E only, or via both Wee1 and cyclin E

Summary

Introduction

Spatial patterns and propagating waves, the coexistence between multiple attractors represents a major mode of self-organization in nonlinear systems [1,2,3,4]. The transition between two stable oscillatory regimes was observed in models for two oscillatory enzyme reactions coupled in series [18] or in parallel [21], a product-activated enzyme reaction with substrate recycling [19], cyclic AMP signalling in Dictyostelium amoebae based on receptor desensitization [20], the circadian clock network in Drosophila [23], the mammalian cell cycle [24,25] and the p53–Mdm oscillatory network [26] In these systems, birhythmicity generally arises from the interplay between two endogenous oscillatory mechanisms. We report a novel mechanism for the occurrence of bi- and trirhythmicity in a realistic model for the coupling between two major cellular rhythms: the circadian clock network producing self-sustained oscillations with a period close to 24 h and the oscillatory biochemical network driving the mammalian cell cycle. We present evidence for the occurrence of birhythmicity and trirhythmicity as a result of the coupling of the cell cycle to the circadian clock

Birhythmicity: coexistence of two periodic attractors

Trirhythmicity: coexistence of three periodic attractors

Switching between multiple periodic attractors

Discussion

52. Feillet C et al 2014 Phase locking and multiple