Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

Abstract

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

How artificial intelligence enables modeling and simulation of biological networks to accelerate drug discovery

“…The interactions between system components are critically dependent on network architecture, or topology, which brings about emergent properties and behaviors so that phenotypic traits arise from the collective action of genes (and conversely, genetic diversity results in a variety of phenotypes). Collective phenomena include steady-state multiplicity (e.g., bistability), hysteresis, oscillations, whose details are outside the scope of this paper [for reviews, see (Goldbeter, 2018;Goldbeter and Yan, 2022)]. As for the relevance in drug discovery, the deterministic nature of ODE-based model simulation has the critical advantage of allowing the study of "emergence" in terms of quantitatively monitoring and analyzing the phenotypic response of the whole biological system to pharmacological, genetic, environmental, or pathophysiological perturbations.…”

Time-keeping and decision-making in living cells: Part I

“…Jiménez et al [ 18 ] lead off the collection with a valuable survey of entrainment among biological oscillators, focusing on six representative examples: the circadian clock, the cell cycle, mitotic exit (Cdc14 endocycles), cardiac pacemaker cells (Ca 2+ /cyclic AMP (cAMP) oscillations), glycolytic oscillations and inflammatory responses (nuclear factor-κB (NFκB) oscillations). Next, Goldbeter & Yan [ 19 ] present a masterly review of multi-rhythmicity (two or more simultaneously stable oscillatory states in models of biochemical reaction networks) and multi-synchronization (two or more simultaneously stable modes of synchronization of coupled biological oscillators). Examples are drawn from cAMP signalling, circadian rhythms and cell cycle oscillations.…”

Time-keeping and decision-making in living cells: Part II

“…Jimenez et al [ 1 ] provided a valuable survey of entrainment among biological oscillators, focusing on the circadian clock, the cell cycle, cardiac pacemaker cells, glycolytic oscillations and inflammatory responses. Goldbeter & Yan [ 2 ] presented a masterly review of multi-rhythmicity (two or more simultaneously stable oscillatory states) and multi-synchronization (two or more simultaneously stable modes of synchronization), with examples drawn from cyclic AMP signalling, circadian rhythms and cell cycle oscillations. Burckard et al [ 3 ] provided new results on the synchronization of peripheral circadian clocks by intercellular communication between two cells or in small clusters of cells.…”