Circadian rhythms are archetypal examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are also affected by the cell’s mechanical environment. Here, we extend a standard biochemical model of circadian rhythmicity to include mechanical effects in a parametric manner. Using experimental observations to constrain the model, we suggest specific ways in which the mechanical signal might affect the clock. Additionally, a bifurcation analysis of the system predicts that these mechanical signals need to be within an optimal range for circadian oscillations to occur.
REFERENCES
1.
A.
Goldbeter
, Biochemical Oscillations and Cellular Rhythms
(Cambridge University Press
, 1996
).2.
M. H.
Hastings
, A. B.
Reddy
, and E. S.
Maywood
, “A clockwork web: Circadian timing in brain and periphery, in health and disease
,” Nat. Rev. Neurosci.
4
, 649
–661
(2003
). 3.
J. S.
Takahashi
, “Transcriptional architecture of the mammalian circadian clock
,” Nat. Rev. Genet.
18
, 164
–179
(2017
). 4.
N.
Kronfeld-Schor
and T.
Dayan
, “Partitioning of time as an ecological resource
,” Annu. Rev. Ecol. Evol. Syst.
34
, 153
–181
(2003
). 5.
S.
Yamaguchi
, H.
Isejima
, T.
Matsuo
, R.
Okura
, K.
Yagita
, M.
Kobayashi
, and H.
Okamura
, “Synchronization of cellular clocks in the suprachiasmatic nucleus
,” Science
302
, 1408
–1412
(2003
). 6.
J. A.
Mohawk
, C. B.
Green
, and J. S.
Takahashi
, “Central and peripheral circadian clocks in mammals
,” Annu. Rev. Neurosci.
35
, 445
–462
(2012
). 7.
A. T.
Winfree
, “Biological rhythms and the behavior of populations of coupled oscillators,” J. Theoret. Biol.
16
, 1542
(1967
). 8.
Y.
Kuramoto
, “Self-entrainment of a population of coupled non-linear oscillators,” in International Symposium on Mathematical Problems in Theoretical Physics, edited by H. Araki (Springer, Berlin, 1975), pp. 420–422.9.
N.
Kopell
and G.
Ermentrout
, “Coupled oscillators and the design of central pattern generators
,” Math. Biosci.
90
, 87
–109
(1988
). 10.
A.
Pikovsky
, M.
Rosenblum
, and J.
Kurths
, Synchronization: A Universal Concept in Nonlinear Sciences
(Cambridge University Press
, 2001
).11.
S.
Boccaletti
, J.
Kurths
, G.
Osipov
, D.
Valladares
, and C.
Zhou
, “The synchronization of chaotic systems
,” Phys. Rep.
366
, 1
–101
(2002
). 12.
A.
Arenas
, A.
Díaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, “Synchronization in complex networks
,” Phys. Rep.
469
, 93
–153
(2008
). 13.
H. R.
Ueda
, K.
Hirose
, and M.
Iino
, “Intercellular coupling mechanism for synchronized and noise-resistant circadian oscillators
,” J. Theor. Biol.
216
, 501
–512
(2002
). 14.
D.
Gonze
, S.
Bernard
, C.
Waltermann
, A.
Kramer
, and H.
Herzel
, “Spontaneous synchronization of coupled circadian oscillators
,” Biophys. J.
89
, 120
–129
(2005
). 15.
S.
Bernard
, D.
Gonze
, B.
Čajavec
, H.
Herzel
, and A.
Kramer
, “Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus
,” PLoS Comput. Biol.
3
, e68
(2007
). 16.
T.-L.
To
, M. A.
Henson
, E. D.
Herzog
, and F. J.
Doyle
, “A molecular model for intercellular synchronization in the mammalian circadian clock
,” Biophys. J.
92
, 3792
–3803
(2007
). 17.
U.
Abraham
, A. E.
Granada
, P. O.
Westermark
, M.
Heine
, A.
Kramer
, and H.
Herzel
, “Coupling governs entrainment range of circadian clocks
,” Mol. Syst. Biol.
6
, 438
(2010
). 18.
O.
Burckard
, M.
Teboul
, F.
Delaunay
, and M.
Chaves
, “Cycle dynamics and synchronization in a coupled network of peripheral circadian clocks
,” Interface Focus
12
, 20210087
(2022
). 19.
S.
Dupont
, L.
Morsut
, M.
Aragona
, E.
Enzo
, S.
Giulitti
, M.
Cordenonsi
, F.
Zanconato
, J.
Le Digabel
, M.
Forcato
, S.
Bicciato
, N.
Elvassore
, and S.
Piccolo
, “Role of YAP/TAZ in mechanotransduction
,” Nature
474
, 179
–184
(2011
). 20.
I. G.
Macara
, “Transport into and out of the nucleus
,” Microbiol. Mol. Biol. Rev.
65
, 570
–594
(2001
). 21.
J. F.
Abenza
, L.
Rossetti
, M.
Mouelhi
, J.
Burgués
, I.
Andreu
, K.
Kennedy
, P.
Roca-Cusachs
, S.
Marco
, J.
García-Ojalvo
, and X.
Trepat
, “Mechanical control of the mammalian circadian clock via YAP/TAZ and TEAD,” bioRxiv (2022), https://doi.org/10.1101/2022.02.04.47883022.
A.
Relógio
, P. O.
Westermark
, T.
Wallach
, K.
Schellenberg
, A.
Kramer
, and H.
Herzel
, “Tuning the mammalian circadian clock: Robust synergy of two loops
,” PLoS Comput. Biol.
7
, e1002309
(2011
). 23.
H.
Cho
, X.
Zhao
, M.
Hatori
, R. T.
Yu
, G. D.
Barish
, M. T.
Lam
, L. W.
Chong
, L.
Ditacchio
, A. R.
Atkins
, C. K.
Glass
, C.
Liddle
, J.
Auwerx
, M.
Downes
, S.
Panda
, and R. M.
Evans
, “Regulation of circadian behaviour and metabolism by REV-ERB-
and REV-ERB-
,” Nature
485
, 123
–127
(2012
). 24.
C.
Hsiao
, M.
Lampe
, S.
Nillasithanukroh
, W.
Han
, X.
Lian
, and S. P.
Palecek
, “Human pluripotent stem cell culture density modulates YAP signaling
,” Biotechnol. J.
11
, 662
–675
(2016
). 25.
B. C.
Goodwin
, “Oscillatory behavior in enzymatic control processes
,” Adv. Enzym. Regul.
3
, 425
–437
(1965
). 26.
E.
Ullner
, J.
Buceta
, A.
Díez-Noguera
, and J.
García-Ojalvo
, “Noise-induced coherence in multicellular circadian clocks
,” Biophys. J.
96
, 3573
–3581
(2009
). 27.
B.
Ananthasubramaniam
, C.
Schmal
, and H.
Herzel
, “Amplitude effects allow short jet lags and large seasonal phase shifts in minimal clock models
,” J. Mol. Biol.
432
, 3722
–3737
(2020
). 28.
R.
Milo
, R.
Phillips
, and N.
Orme
, Cell Biology by the Numbers
(Garland Science
, 2008
).29.
B.
Zhao
, X.
Ye
, J.
Yu
, L.
Li
, W.
Li
, S.
Li
, J.
Yu
, J. D.
Lin
, C. Y.
Wang
, A. M.
Chinnaiyan
, Z. C.
Lai
, and K. L.
Guan
, “TEAD mediates YAP-dependent gene induction and growth control
,” Genes Dev.
22
, 1962
–1971
(2008
). 30.
F.
Zanconato
, M.
Forcato
, G.
Battilana
, L.
Azzolin
, E.
Quaranta
, B.
Bodega
, A.
Rosato
, S.
Bicciato
, M.
Cordenonsi
, and S.
Piccolo
, “Genome-wide association between YAP/TAZ/TEAD and AP-1 at enhancers drives oncogenic growth
,” Nat. Cell. Biol.
17
, 1218
–1227
(2015
). 31.
D. H.
Lee
, J. O.
Park
, T. S.
Kim
, S. K.
Kim
, T. H.
Kim
, M. C.
Kim
, G. S.
Park
, J. H.
Kim
, S.
Kuninaka
, E. N.
Olson
, H.
Saya
, S. Y.
Kim
, H.
Lee
, and D. S.
Lim
, “LATS-YAP/TAZ controls lineage specification by regulating TGF
signaling and Hnf4
expression during liver development
,” Nat. Commun.
7
, 11961
(2016
). 32.
A.
Rivera-Reyes
et al., “YAP1 enhances NF-
B-dependent and independent effects on clock-mediated unfolded protein responses and autophagy in sarcoma
,” Cell Death Dis.
9
, 1108
(2018
). 33.
P.
Rajbhandari
et al., “Cross-cohort analysis identifies a TEAD4-MYCN positive-feedback loop as the core regulatory element of high-risk neuroblastoma
,” Cancer Discov.
8
, 582
–599
(2018
). 34.
B.
Ermentrout
, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students
(Society for Industrial and Applied Mathematics
, 2002
).35.
T. R.
Maarleveld
, B. G.
Olivier
, and F. J.
Bruggeman
, “StochPy: A comprehensive, user-friendly tool for simulating stochastic biological processes
,” PLoS One
8
, e79345
(2013
). 36.
D. T.
Gillespie
, “Stochastic simulation of chemical kinetics
,” Annu. Rev. Phys. Chem.
58
, 35
–55
(2007
). 37.
F. Y.
Rodríguez
and A. P.
Muñuzuri
, “A goodwin model modification and its interactions in complex networks
,” Entropy
25
, 894
(2023
). 38.
A.
Neiman
, P. I.
Saparin
, and L.
Stone
, “Coherence resonance at noisy precursors of bifurcations in nonlinear dynamical systems
,” Phys. Rev. E
56
, 270
–273
(1997
). 39.
S.
Almeida
, M.
Chaves
, and F.
Delaunay
, “Transcription-based circadian mechanism controls the duration of molecular clock states in response to signaling inputs
,” J. Theor. Biol.
484
, 110015
(2020
). 40.
M.
del Olmo
, C.
Schmal
, C.
Mizaikoff
, S.
Grabe
, C.
Gabriel
, A.
Kramer
, and H.
Herzel
, “Are circadian amplitudes and periods correlated? a new twist in the story,” bioRxiv (2023), doi:10.1101/2023.05.17.54113941.
J. D.
Murray
, Mathematical Biology. I. An Introduction
, 3rd ed. (Springer
, 2002
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
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