Modeling the mammalian circadian clock

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Modeling the mammalian circadian clock
intracellular feedback loops and synchronization
of neurons
Hanspeter Herzel Institute for Theoretical
Biology Humboldt University Berlin
together
with Sabine Becker-Weimann, Samuel Bernard, Pal
Westermark (ITB), Florian Geier (Freiburg),
Didier Gonze (Brussels), Achim Kramer (Exp.
Chronobiology, Charite), Hitoshi Okamura (Kobe)
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Outlook of the talk

• The system, experimental data
• Modeling intracellular feedbacks, bifurcation
  diagram and
• double mutant
• Entrainment by light for varying photoperiod
• Synchronization of 10000 cells in silico an
  ensemble of
• driven damped oscillators
• 5. Single cell data periods, phases,
  gradients, noise

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Light synchronizes the clock
The system
Regulation of physiology and behavior
Synchronization of peripheral clocks
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The circadian oscillator
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Fibroblasts as experimental modelof the
circadianen oscillator
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Simplified model of the circadian core oscillator
S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer
Biophys. J. 87, 3023-34 (2004)
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Comparison with experimental observations
Wildtype simulations reproduce period,
amplitudes, phase relations Per2 mutant (less
positive feedback) arythmic Per2/Cry2 double
knock-out rescue of oscillations
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Synchronization of circadian clocks to light input
Entrainment zone for different periods and
coupling
Phase-locking of internal variables (mRNA peak)
to sunset for night-active animals
Problem How can the internal clock follow
changes of the photoperiod? Simulation PRC
Small free running period gating allows to
track light offset
F. Geier, S. Becker-Weimann, A. Kramer, H.Herzel
J. Biol. Rhythms, 20, 83-93 (2005)
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The real challenge How to synchronize a network
of 20000 heterogeneous limit cycle oscillators
within a few cycles?
Suprachiasmatic nucleus

• Located in the hypothalamus
• Contains about 10000 neurons
• Circadian pacemaker
• Two regions
• - Ventro-lateral (VL) VIP, light-sensitive
• - Dorso-medial (DM) AVP

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Organotypic SCN slices periods of synchronized
and desynchronized cells
unpublished data from Hitoshi Okamura (Kobe)
analyzed by Pal Westermark
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mPer1-luc bioluminescence in single SCN cells
Experimental findings - Synchronization is
achieved within a few cycles - Phase relations
are re-established after transient
desynchronization - Driven DM region is phase
leading
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Model for the coupling in the SCN

• Ventro-lateral part
• (core)
• Self-sustained
• oscillations
• (synchronized
• oscillations)
• Coupling conveyed
• by VIP, GABA
• Receives light input
• from the retina

• Dorso-medial part
• (shell)
• Damped oscillations
• (unsynchronized
• oscillations)
• No/weak coupling
• Phase leading (4h)
• Receives signal
• from the VL part

Light entrains
VL drives
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Single cell model
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Coupling through the mean field
Neurotransmitter
Mean field
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Coupling through the mean field
Light
L0 in dark phase Lgt0 in light phase
Order parameter
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Coupling two cells through the mean field
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Coupling two cells through the mean field
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Coupling two cells through the mean field
Synchronization requires delicate balance of
coupling and period ratio
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Coupling through the mean field
D. Gonze, S. Bernard, C. Waltermann, A. Kramer,
H. Herzel Biophys. J., 89, 120-129 (2005)
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Transient uncoupling
Note Neurotransmitter level F has positive
mean oscillatory component
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single cell constant mean field
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Coupling through the mean field
fast oscillators are advanced

slow oscillators are delayed
The phases of the oscillators in the coupled
state are uniquely determined by their autonomous
periods
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How circadian oscillators can be synchronized
quickly

• The average value of the coupling agent dampens
  the individual oscillators
• The oscillating part of the mean field drives the
  damped oscillators
• Predictions Internal periods determine the phase
  relations and damping ratio is related to fast
  synchronizability

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Interaction between two populations
Prediction from our model DM region can be
phase leading if its period is shorter
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Experimental single cell data from Hitoshi
Okamura (Kobe)
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Gradients of phases and periods within the SCN
data from Hitoshi Okamura, analyses by Pal
Westermark
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Comparison of synchronized and desynchronized
cells

• Desynchronized cells exhibit
• variable amplitudes and phases
• higher noise level
• ultradian periodicities

synchr.
desynchr.
red desynchronized cells
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Summary and discussion

• mathematical models can describe intracellular
  clock based on transcriptional/translational
  feedback loops
• open problems parameter estimations, origin
  of 6 h delay, which nonlinearities essential?
• possible synchronization mechanism dampening of
  self-sustained single cell oscillations forcing
  by periodic mean field
• open problems alternative scenarios (specific
  PRCs allowing quick and robust synchronization),
  coupling mechanisms (neurotransmitters versus
  synapses versus gap junctions)
• single cell data provide informations about
  gradients of phases and periods, noise, and
  ultradian rhythms

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Nils Blüthgen, Szymon Kielbasa, Branka Cajavec,
Maciej Swat, Sabine Becker-Weimann, Christian
Waltermann, Didier Gonze, Samuel Bernard,
Hanspeter Herzel Institute for Theoretical
Biology, Humboldt-Universität Berlin
Major collaborators Christine Sers, Reinhold
Schäfer, Achim Kramer, Erich Wanker Charite
Berlin, MDC
Support BMBF Networks Proteomics Systems
Biology, SFB Theoretical Biology (A3, A4, A5),
Stifterverband, GK Dynamics and Evolution, EU
Biosimulation
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Data generation
Circadian oscillation of fibroblasts can be
monitored in living cells
Per1 E-box_luc Bmal1_luc
n 1
Experiments in Kramer Lab (Charite)
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correlation coefficients 0.95 significantly
different periods despite synchronization
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advanced
delayed
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slow and delayed cells
fast and advanced cells