1. Computational Modeling of Circadian Rhythms Christian Hong Department of Genetics YGTLC, New York, 2007

2. Circadian Rhythm Physiological events that recur with a frequency of about 24 hours. (circa, “approximately,” and dies, “day”) Examples: • Sleep wake cycles • Metabolic and gastrointestinal activities • Core and skin temperature rhythms • Kidney and hormonal rhythms • Behavior and mental performance of organisms

3. Endogenous Rhythm Human Being in Constant Light Time of Day 24:00 12:00 24:00 12:00 24:00 0 10 20 Days Sleep Episodes

4. Temperature Compensation in Euglenagracilis Period (hr) Temperature (°C)

5. Phase Response Curve in Drosophila (Pittendrigh, 1967) 12 Phase Advance (hrs) 6 0 Phase Delay (hrs) 24 hr 6 12 0 10 20 30 40 Subjective night Subjective day Subjective night Hours Since Last (12 hour) Entraining Pulse

6. Importance of Circadian Rhythms Robust functional activities of circadian clock are essential for the health of an organism. • Sleep deprivations are harmful or even fatal. • Higher rate of tumorgenesis is observed in clockless mice. • Chronic jet-lag is associated with higher mortality rate in aged mice. • Sudden infant death syndrome (SIDS) occurs during sleep. • Temporary insomnia is a result of changed phase relationships of the internal clock to the external time cues (i.e. shift workers). • Sleep disturbances are often observed in schizophrenic and epileptic patients. • Manic depressive patients also show sleep disorder phenotype. • In the U.S., roughly 45 - 60 million people complain about chronic or occasional sleep disturbances.

7. Circadian rhythms are everywhere

8. Clock mechanism in fruit fly Young and Kay, 2001

9. Are you sure? • NO! • Need rigorous mathematical • models based on realistic • biochemistry of control • system. • Two models: • Simple model • Complex and realistic model

10. Simplified Wiring Diagram of Drosophila ClockTyson et al. (1999) Biophys J. per-mRNA mRNA PER PER DBT PER2 (stable) PER-P mRNA PER mRNA & Protein Level Time (hr)

11. Realistic Model of Neurospora Clock

12. Schafmeier et al. Cell, 122, 2005, 235-246 Wild-type simulations

13. Mutant Simulations Aronson et al. Science, 263, 1994, 1578-1584

14. + Inducer A Inducer/DD 0 1 2 3 4 5 6 7 8 12 16 20 (Hr) + Inducer B Inducer/DD 0 1 2 3 4 5 6 7 8 12 16 20 (Hr) - Inducer B DD 0 1 2 3 4 5 6 7 8 12 16 20 (Hr) Predictions and Model Validations B A:B A

15. Summary • Circadian rhythms are controlled by complex molecular mechanisms consisting of multiple feedback loops. 2. It is difficult to understand the mechanistic details of circadian rhythms with intuition alone. • Mathematical models: • Provide a better understanding of complex systems. • Simulate hypothesis prior to experiments. • Propose novel hypotheses from mathematical analysis. • Evaluations and validations of mathematical models. • Reproduction of both wild-type and mutant phenotypes. • Experimental validations of model hypotheses.

16. Acknowledgements Supported by National Academies Keck Futures Initiative Fund

17. Neurospora crassa as a model organism for circadian rhythms Garceau et. al. (Cell, 1997)

18. Phase Plane at vp=30 1.5 Stable limit cycle mRNA Unstable steady state mRNA nullcline Protein nullcline 0 70 Protein

19. Phase Plane at vp=3 12 Stable steady state Unstable steady states mRNA mRNA nullcline Protein nullcline 0 40 Protein

20. Hysteresis & Oscillation 90 SNIC Hopf Bifurcation PER Protein Oscillatory Region Saddle Nodes stable unstable 0 100 vp (translational efficiency)

21. Testing the existence of autocatalysis with inducible FRQ promoter QA Construction Aronson et. al. (Science, 1994)

22. 6. Almost any parameter in the model could be adopted for the role of the “resetting” component. 7. If this idea is appealing to anyone other than ourselves, then we should propose some likely molecular candidates and mechanisms for the “resetting hypothesis” and seek direct experimental evidence for this proposal.