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)

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

Light synchronizesthe clock

Regulation ofphysiology and behavior

Clock genes(e.g. Period2)

Positiveelements

activation

nucleus

SCN-neuron

Negativeelements

inhibition

Synchronization ofperipheral clocks

The system

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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solventCKI inhibitor

Fibroblasts as experimental modelof the circadianen oscillator

Simplified model of thecircadian core oscillator

S. Becker-Weimann, J. Wolf, H. Herzel,

A. Kramer: Biophys. J. 87, 3023-34 (2004)

Wildtype: simulations reproduce period, amplitudes, phase relationsPer2 mutant (less positive feedback): arythmicPer2/Cry2 double knock-out: rescue of oscillations

Comparison with experimental observations

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

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

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?

Organotypic SCN slices: periods of synchronized and desynchronized cells

unpublished data from Hitoshi Okamura (Kobe) analyzed by Pal Westermark

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

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

Single cell model

Coupling through the mean field

Mean field

Neurotransmitter

Order parameter

Coupling through the mean field

Light+ L(t)

L=0 in dark phase; L>0 in light phase

Coupling two cells through the mean field

Coupling two cells through the mean field

Coupling two cells through the mean field

Synchronization requires delicate balance of coupling and period ratio

Coupling through the mean field

D. Gonze, S. Bernard, C. Waltermann, A. Kramer, H. Herzel: Biophys. J., 89, 120-129 (2005)

Transient uncoupling

Note: Neurotransmitter level F has positive mean & oscillatory component

single cell + constant mean field

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

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

Interaction between two populations

VL regionDM region

Prediction from our model:

DM region can be phase leadingif its period is shorter

Experimental single cell data from Hitoshi Okamura (Kobe)

Gradients of phases and periods within the SCN

data from Hitoshi Okamura, analyses by Pal Westermark

Comparison of synchronized and desynchronized cells

Desynchronized cells exhibit: -variable amplitudes and phases

-higher noise level

-ultradian periodicities

synchr.

desynchr.

red: desynchronized cells

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

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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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)

correlation coefficients: 0.95

significantly different periodsdespite synchronization

advanced

delayed

fast andadvanced cells

slow and delayed cells