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)

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 cells in silico – an ensemble of driven damped oscillators 5. Single cell data – periods, phases, gradients, noise

Light synchronizes the clock Regulation of physiology and behavior Clock genes (e.g. Period2) Positive elements activation nucleus SCN-neuron Negative elements inhibition Synchronization of peripheral clocks The system

The circadian oscillator Circadian rhythm Oster et al., 2002 Feedback loopsOscillations Reppert and Weaver, 2001

time [hrs] Luminescence [units] control anti-Cry1 genetic perturbations: RNA interference experiments pharmakological perturbations: Inhibitores time [hrs] Relative Amplitude solvent CKI  inhibitor Fibroblasts as experimental model of the circadianen oscillator

Simplified model of the circadian core oscillator S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer: Biophys. J. 87, (2004)

Wildtype: simulations reproduce period, amplitudes, phase relations Per2 mutant (less positive feedback): arythmic Per2/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, (2005) Problem: How can the internal clock follow changes of the photoperiod? Simulation & PRC: Small free running period & gating allows to track light offset

Suprachiasmatischer Nukleus Optisches Chiasma Hypothalamus 3. Ventrikel 3.ventricle optical chiasm clock-genes (e.g.. Period2) Positive Elements Activation nucleus SCN-Neuron Negative Elements Inhibition Oscillation Synchronisation the system

Suprachiasmatic nucleus  Located in the hypothalamus  Contains about neurons  Circadian pacemaker  Two regions: - Ventro-lateral (VL): VIP, light-sensitive - Dorso-medial (DM): AVP The real challenge: How to synchronize a network of 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

Light entrains VL drives 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

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

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, (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 oscillators are 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 region DM region Prediction from our model: DM region can be phase leading if 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 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

Time [hrs] Luminescence [units] 120 Data generation n = 1 Transfect NIH3T3 fibroblasts with reporter construct Synchronize cells by inducing growth arrest Induce circadian oscillation by serum shock or forskolin Culture cells with luciferase substrate Continuously measure luminescence Per1 E-box_luc Bmal1_luc Circadian oscillation of fibroblasts can be monitored in living cells Experiments in Kramer Lab (Charite)

correlation coefficients: 0.95 significantly different periods despite synchronization

advanced delayed

fast and advanced cells slow and delayed cells