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Modeling the mammalian circadian clock –intracellular feedback loops and
synchronization of neurons
Hanspeter HerzelInstitute for Theoretical BiologyHumboldt 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
1. The system, experimental data
2. Modeling intracellular feedbacks, bifurcation diagram and double mutant
3. Entrainment by light for varying photoperiod
4. 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 synchronizesthe clock
Regulation ofphysiology and behavior
Clock genes(e.g. Period2)
Positiveelements
activation
nucleus
SCN-neuron
Negativeelements
inhibition
Synchronization ofperipheral clocks
The system
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The circadian oscillator
Circadian rhythm
Oster et al., 2002
Feedback loopsOscillations
Reppert and Weaver, 2001
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controlanti-Cry1
genetic perturbations:RNA interference
experiments
pharmakological perturbations:Inhibitores
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Fibroblasts as experimental modelof the circadianen oscillator
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Simplified model of thecircadian core oscillator
S. Becker-Weimann, J. Wolf, H. Herzel,
A. Kramer: Biophys. J. 87, 3023-34 (2004)
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Wildtype: simulations reproduce period, amplitudes, phase relationsPer2 mutant (less positive feedback): arythmicPer2/Cry2 double knock-out: rescue of oscillations
Comparison with experimental observations
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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
F. Geier, S. Becker-Weimann, A. Kramer, H.Herzel: J. Biol. Rhythms, 20, 83-93 (2005)
Problem: How can the internal clock follow changes of the photoperiod?
Simulation & PRC: Small free running period & gating allows to track light offset
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SuprachiasmatischerNukleus
Optisches Chiasma
Hypothalamus
3. Ventrikel
3.ventricle
optical chiasm
clock-genes(e.g.. Period2)
PositiveElements
Activation
nucleus
SCN-Neuron
NegativeElements
Inhibition
Oscillation Synchronisation
the system
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Suprachiasmatic nucleus
Located in the hypothalamus
Contains about 10000 neurons
Circadian pacemaker
Two regions:
- Ventro-lateral (VL): VIP, light-sensitive
- Dorso-medial (DM): AVP
The real challenge: How to synchronize a network of 20000 heterogeneous limit cycle oscillators within a few cycles?
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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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Lightentrains
VLdrives
Model for the coupling in the SCN
Ventro-lateral part(core)
Self-sustainedoscillations
(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
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Single cell model
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Coupling through the mean field
Mean field
Neurotransmitter
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Order parameter
Coupling through the mean field
Light+ L(t)
L=0 in dark phase; L>0 in light phase
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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
The phases of the oscillators in the coupled state are uniquely determined by their autonomous periods
slow oscillators are delayed
fast oscillatorsare advanced
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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
VL regionDM region
Prediction from our model:
DM region can be phase leadingif 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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Modeling Signaling Cascades and Gene Regulation
Nils Blüthgen, Szymon Kielbasa, Branka Cajavec, Maciej Swat, Sabine Becker-Weimann, Christian Waltermann, Didier Gonze, Samuel Bernard, Hanspeter HerzelInstitute 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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24 48 72 96
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Transfect NIH3T3 fibroblastswith reporter construct
Synchronize cells by inducinggrowth arrest
Induce circadian oscillation byserum shock or forskolin
Culture cells with luciferase substrate
Continuously measure luminescence
Per1 E-box_lucBmal1_luc
Circadian oscillation of fibroblasts
can be monitored in living cells
Experiments in Kramer Lab (Charite)
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correlation coefficients: 0.95
significantly different periodsdespite synchronization
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advanced
delayed
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fast andadvanced cells
slow and delayed cells