Isochron-based phase response analysis of circadian rhythms.

Circadian rhythms possess the ability to robustly entrain to the environmental cycles. This ability relies on the phase synchronization of circadian rhythm gene regulation to different environmental cues, of which light is the most obvious and important. The elucidation of the mechanism of circadian entrainment requires an understanding of circadian phase behavior. This article presents two phase analyses of oscillatory systems for infinitesimal and finite perturbations based on isochrons as a phase metric of a limit cycle. The phase response curve of circadian rhythm can be computed from the results of the analyses. The application to a mechanistic Drosophila circadian rhythm model gives experimentally testable hypotheses for the control mechanisms of circadian phase responses and evidence for the role of phase and period modulations in circadian photic entrainment.

[1]  S. Daan,et al.  The Art of Entrainment , 2003, Journal of biological rhythms.

[2]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[3]  T. Page,et al.  History dependence of circadian pacemaker period in the cockroach. , 2001, Journal of insect physiology.

[4]  Christina D. Smolke,et al.  Coordinated, Differential Expression of Two Genes through Directed mRNA Cleavage and Stabilization by Secondary Structures , 2000, Applied and Environmental Microbiology.

[5]  Daniel B. Forger,et al.  A detailed predictive model of the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[6]  G. Stephanopoulos,et al.  Tuning genetic control through promoter engineering. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[7]  R. Moore,et al.  Circadian rhythms: basic neurobiology and clinical applications. , 1997, Annual review of medicine.

[8]  Steve A. Kay,et al.  Circadian rhythm genetics: from flies to mice to humans , 2000, Nature Genetics.

[9]  Francis J. Doyle,et al.  Sensitivity analysis of oscillatory (bio)chemical systems , 2005, Comput. Chem. Eng..

[10]  Zuwei Qian,et al.  A light-entrainment mechanism for the Drosophila circadian clock , 1996, Nature.

[11]  R. Foster,et al.  Entrainment of Circadian Programs , 2003, Chronobiology international.

[12]  S. Daan,et al.  Colin Pittendrigh, Jürgen Aschoff, and the Natural Entrainment of Circadian Systems , 2000, Journal of biological rhythms.

[13]  A. Goldbeter,et al.  Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora , 1999, Journal of biological rhythms.

[14]  Aftereffects of Entrainment on the Period of the Pacemaker in the Eye of the Mollusk Bulla gouldiana , 1997, Journal of biological rhythms.

[15]  Hua Wu,et al.  Parametric sensitivity in chemical systems , 1999 .

[16]  Jeffrey C. Hall,et al.  Genes and biological rhythms , 1987 .

[17]  Mark A. Kramer,et al.  Sensitivity analysis of limit cycles with application to the Brusselator , 1984 .

[18]  G. Ermentrout,et al.  Multiple pulse interactions and averaging in systems of coupled neural oscillators , 1991 .

[19]  D A Rand,et al.  Design principles underlying circadian clocks , 2004, Journal of The Royal Society Interface.

[20]  A. Goldbeter,et al.  A Model for Circadian Rhythms in Drosophila Incorporating the Formation of a Complex between the PER and TIM Proteins , 1998, Journal of biological rhythms.

[21]  Eric Shea-Brown,et al.  On the Phase Reduction and Response Dynamics of Neural Oscillator Populations , 2004, Neural Computation.

[22]  A. Sehgal,et al.  Molecular components of the circadian system in Drosophila. , 2001, Annual review of physiology.

[23]  José Halloy,et al.  Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour. , 2003, Comptes rendus biologies.

[24]  S. Daan,et al.  Accuracy of Circadian Entrainment under Fluctuating Light Conditions: Contributions of Phase and Period Responses , 1999, Journal of biological rhythms.

[25]  Daniel B. Forger,et al.  Stochastic simulation of the mammalian circadian clock. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[26]  B. Ingalls,et al.  Autonomously oscillating biochemical systems: parametric sensitivity of extrema and period. , 2004, Systems biology.

[27]  J. Tyson,et al.  A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. , 1999, Biophysical journal.

[28]  J. Stelling,et al.  Robustness of Cellular Functions , 2004, Cell.

[29]  Vijay Kumar Sharma,et al.  Entrainment Properties of the Locomotor Activity Rhythm of Drosophila melanogaster Under Different Photoperiodic Regimens , 2004 .

[30]  C. Pittendrigh,et al.  Circadian rhythms and the circadian organization of living systems. , 1960, Cold Spring Harbor symposia on quantitative biology.

[31]  M. W. Young,et al.  Light-Induced Degradation of TIMELESS and Entrainment of the Drosophila Circadian Clock , 1996, Science.

[32]  D. Boivin,et al.  A molecular perspective of human circadian rhythm disorders , 2003, Brain Research Reviews.

[33]  A. Goldbeter,et al.  Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms. , 2004, Journal of Theoretical Biology.

[34]  J. Doyle,et al.  Bow Ties, Metabolism and Disease , 2022 .

[35]  Yang Cao,et al.  Sensitivity analysis of discrete stochastic systems. , 2005, Biophysical journal.

[36]  M. Kramer,et al.  Sensitivity analysis of oscillatory systems , 1984 .

[37]  M. Smit,et al.  Secondary structure of the ribosome binding site determines translational efficiency: a quantitative analysis. , 1990 .

[38]  A. Díez-Noguera,et al.  History-Dependent Changes in Entrainment of the Activity Rhythm in the Syrian Hamster (Mesocricetus auratus) , 2006, Journal of biological rhythms.

[39]  J. Stelling,et al.  Robustness properties of circadian clock architectures. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[40]  W. V. Loscutoff,et al.  General sensitivity theory , 1972 .

[41]  A. Winfree.  The geometry of biological time , 1991 .

[42]  C. Johnson,et al.  Forty years of PRCs--what have we learned? , 1999, Chronobiology international.