Hanspeter Herzel Institute for Theoretical Biology Humboldt University Berlin

1. 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)

2. 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

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

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

5. experiments genetic perturbations: RNA interference pharmakological perturbations: Inhibitores 2500 solvent CKIe inhibitor control anti-Cry1 2000 Luminescence [units] 1500 Relative Amplitude 1000 500 0 24 48 72 96 time [hrs] time [hrs] Fibroblasts as experimental modelof the circadianen oscillator

6. Simplified model of the circadian core oscillator S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer: Biophys. J. 87, 3023-34 (2004)

7. 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

8. 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)

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

10. 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

11. Organotypic SCN slices: periods of synchronized and desynchronized cells unpublished data from Hitoshi Okamura (Kobe) analyzed by Pal Westermark

13. 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

14. 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

15. Single cell model

16. Coupling through the mean field Neurotransmitter Mean field

17. + L(t) Coupling through the mean field Light L=0 in dark phase; L>0 in light phase Order parameter

18. Coupling two cells through the mean field

19. Coupling two cells through the mean field

20. Coupling two cells through the mean field Synchronization requires delicate balance of coupling and period ratio

21. Coupling through the mean field D. Gonze, S. Bernard, C. Waltermann, A. Kramer, H. Herzel: Biophys. J., 89, 120-129 (2005)

22. Transient uncoupling Note: Neurotransmitter level F has positive mean & oscillatory component

23. single cell + constant mean field

24. 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

25. 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

26. VL region DM region Interaction between two populations Prediction from our model: DM region can be phase leading if its period is shorter

28. Experimental single cell data from Hitoshi Okamura (Kobe)

29. Gradients of phases and periods within the SCN data from Hitoshi Okamura, analyses by Pal Westermark

30. Comparison of synchronized and desynchronized cells • Desynchronized cells exhibit: • variable amplitudes and phases • higher noise level • ultradian periodicities synchr. desynchr. red: desynchronized cells

31. 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

32. 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

33. 3000 2000 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 Luminescence [units] 1000 0 0 24 48 72 96 120 Time [hrs] 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)

34. correlation coefficients: 0.95 significantly different periods despite synchronization

35. advanced delayed

36. slow and delayed cells fast and advanced cells