Design Principles for Phase-splitting Behaviour of Coupled Cellular Oscillators: Clues from Hamsters with 'split' Circadian Rhythms

Overview

Journal J R Soc Interface

Specialties Biology
Biomedical Engineering
Biophysics

Date 2007 Dec 14

PMID 18077247

Citations 12

Authors

Premananda Indic

William J Schwartz

David Paydarfar

Affiliations

Soon will be listed here.

Abstract

Nonlinear interactions among coupled cellular oscillators are likely to underlie a variety of complex rhythmic behaviours. Here we consider the case of one such behaviour, a doubling of rhythm frequency caused by the spontaneous splitting of a population of synchronized oscillators into two subgroups each oscillating in anti-phase (phase-splitting). An example of biological phase-splitting is the frequency doubling of the circadian locomotor rhythm in hamsters housed in constant light, in which the pacemaker in the suprachiasmatic nucleus (SCN) is reconfigured with its left and right halves oscillating in anti-phase. We apply the theory of coupled phase oscillators to show that stable phase-splitting requires the presence of negative coupling terms, through delayed and/or inhibitory interactions. We also find that the inclusion of real biological constraints (that the SCN contains a finite number of non-identical noisy oscillators) implies the existence of an underlying non-uniform network architecture, in which the population of oscillators must interact through at least two types of connections. We propose that a key design principle for the frequency doubling of a population of biological oscillators is inhomogeneity of oscillator coupling.

Citing Articles

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding.

Schmal C J Comp Physiol A Neuroethol Sens Neural Behav Physiol. 2023; 210(4):549-564.

PMID: 37659985 PMC: 11226496. DOI: 10.1007/s00359-023-01669-z.

Synchronization, clustering, and weak chimeras in a densely coupled transcription-based oscillator model for split circadian rhythms.

Luis Ocampo-Espindola J, Nikhil K, Li J, Herzog E, Kiss I Chaos. 2023; 33(8).

PMID: 37535024 PMC: 10403273. DOI: 10.1063/5.0156135.

Network Structure of the Master Clock Is Important for Its Primary Function.

Gu C, Li J, Zhou J, Yang H, Rohling J Front Physiol. 2021; 12:678391.

PMID: 34483953 PMC: 8415478. DOI: 10.3389/fphys.2021.678391.

Nonlinear phenomena in models of the circadian clock.

van Soest I, Del Olmo M, Schmal C, Herzel H J R Soc Interface. 2020; 17(170):20200556.

PMID: 32993432 PMC: 7536064. DOI: 10.1098/rsif.2020.0556.

Two-Community Noisy Kuramoto Model Suggests Mechanism for Splitting in the Suprachiasmatic Nucleus.

Rohling J, Meylahn J J Biol Rhythms. 2020; 35(2):158-166.

PMID: 31969025 PMC: 7031819. DOI: 10.1177/0748730419898314.

References

Pavlidis T . Populations of biochemical oscillators as circadian clocks. J Theor Biol. 1971; 33(2):319-38. DOI: 10.1016/0022-5193(71)90070-1. View

Kunz H, Achermann P . Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators. J Theor Biol. 2003; 224(1):63-78. DOI: 10.1016/s0022-5193(03)00141-3. View

Herzog E, Takahashi J, Block G . Clock controls circadian period in isolated suprachiasmatic nucleus neurons. Nat Neurosci. 1999; 1(8):708-13. DOI: 10.1038/3708. View

To T, Henson M, Herzog E, Doyle 3rd F . A molecular model for intercellular synchronization in the mammalian circadian clock. Biophys J. 2007; 92(11):3792-803. PMC: 1868999. DOI: 10.1529/biophysj.106.094086. View

Sim C, Forger D . Modeling the electrophysiology of suprachiasmatic nucleus neurons. J Biol Rhythms. 2007; 22(5):445-53. DOI: 10.1177/0748730407306041. View

Duncan M, Deveraux A . Age-related changes in circadian responses to dark pulses. Am J Physiol Regul Integr Comp Physiol. 2000; 279(2):R586-90. DOI: 10.1152/ajpregu.2000.279.2.R586. View

Schaap J, Meijer J . Opposing effects of behavioural activity and light on neurons of the suprachiasmatic nucleus. Eur J Neurosci. 2001; 13(10):1955-62. DOI: 10.1046/j.0953-816x.2001.01561.x. View

Grillner S, Halbertsma J, Nilsson J, Thorstensson A . The adaptation to speed in human locomotion. Brain Res. 1979; 165(1):177-82. DOI: 10.1016/0006-8993(79)90059-3. View

Diez-Noguera A . A functional model of the circadian system based on the degree of intercommunication in a complex system. Am J Physiol. 1994; 267(4 Pt 2):R1118-35. DOI: 10.1152/ajpregu.1994.267.4.R1118. View

10.

Liu C, Weaver D, Strogatz S, Reppert S . Cellular construction of a circadian clock: period determination in the suprachiasmatic nuclei. Cell. 1997; 91(6):855-60. DOI: 10.1016/s0092-8674(00)80473-0. View

11.

Kawato M, Suzuki R . Two coupled neural oscillators as a model of the circadian pacemaker. J Theor Biol. 1980; 86(3):547-75. DOI: 10.1016/0022-5193(80)90352-5. View

12.

Hansel D, Mato G, Meunier C . Synchrony in excitatory neural networks. Neural Comput. 1995; 7(2):307-37. DOI: 10.1162/neco.1995.7.2.307. View

13.

Auffeves A, Maioli P, Meunier T, Gleyzes S, Nogues G, Brune M . Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity. Phys Rev Lett. 2003; 91(23):230405. DOI: 10.1103/PhysRevLett.91.230405. View

14.

Hansel , Mato , MEUNIER . Clustering and slow switching in globally coupled phase oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993; 48(5):3470-3477. DOI: 10.1103/physreve.48.3470. View

15.

Daan S, Berde C . Two coupled oscillators: simulations of the circadian pacemaker in mammalian activity rhythms. J Theor Biol. 1978; 70(3):297-313. DOI: 10.1016/0022-5193(78)90378-8. View

16.

Tavakoli-Nezhad M, Schwartz W . c-Fos expression in the brains of behaviorally "split" hamsters in constant light: calling attention to a dorsolateral region of the suprachiasmatic nucleus and the medial division of the lateral habenula. J Biol Rhythms. 2005; 20(5):419-29. PMC: 1380273. DOI: 10.1177/0748730405278443. View

17.

Becker-Weimann S, Wolf J, Herzel H, Kramer A . Modeling feedback loops of the Mammalian circadian oscillator. Biophys J. 2004; 87(5):3023-34. PMC: 1304775. DOI: 10.1529/biophysj.104.040824. View

18.

Gonze D, Bernard S, Waltermann C, Kramer A, Herzel H . Spontaneous synchronization of coupled circadian oscillators. Biophys J. 2005; 89(1):120-9. PMC: 1366510. DOI: 10.1529/biophysj.104.058388. View

19.

Welsh D, Logothetis D, Meister M, Reppert S . Individual neurons dissociated from rat suprachiasmatic nucleus express independently phased circadian firing rhythms. Neuron. 1995; 14(4):697-706. DOI: 10.1016/0896-6273(95)90214-7. View

20.

Silver R, Schwartz W . The suprachiasmatic nucleus is a functionally heterogeneous timekeeping organ. Methods Enzymol. 2005; 393:451-65. PMC: 1364538. DOI: 10.1016/S0076-6879(05)93022-X. View