Analyzing various models of Circadian Clock and Cell Cycle coupling

1. Analyzing various models of Circadian Clock and Cell Cycle coupling Alessandro Romanel, Heike Siebert, Sylvain Soliman, Denis Thieffry

2. Cell cycle engine Cell cycle DNA replication ODEs model: Novák & Tyson (2004) J Theor Biol 230:563-579. S G1 Boolean model: Faure et al. (2006) Bioinformatics G2 M mitosis

3. Mammalian Circadian Clock Circadian Clock translation transcription rhythmic metabolism and behavior clock controlled genes Time Delayed Negative Feedback Loop POSITIVEELEMENTS BMAL1/CLK Per Cry NEGATIVEELEMENTS translation transcription clock genes

4. Coupling Matsuo et al. (2003) SCIENCE 302:255-259

5. Coupling Calzone and Soliman (2006) INRIA RR5835 CIRCADIAN CLOCK Cdk4/CycD CELL CYCLE Rb Wee1 E2F Cdk2/CycE p55cdc Kip1 Cdk2/CycA Cdc2/CycB Zámborszky et al. (2007) J Biol Rhythms 22(6):542-53. Novák & Tyson (2004) J Theor Biol 230:563-579. Cdh1

6. BlenX BlenX Programming language of concurrent interacting processes with typed interaction sites, based on Beta-binders (Priami & Quaglia)

7. BlenX BlenX BlenX interaction capabilities change internal behaviour x : B x : B x : B x : B x : A x : A x : A x : A P x!().P P Q Q x?().Q P Q A A A B B B A B inter x : A x : A x : C ch(x,C).P P P A A A split x : A x : D x : E P Q R complex decomplex A D E

8. From ODEs to BlenX Computational Analysis of Mammalian Cell Division Gated by a Circadian Clock: Quantized Cell Cycles and Cell Size Control Zámborszky J, Hong CI and Csikász-Nagy A A model for restriction point control of the mammalian cell cycle Novák B, Tyson JJ From Odes to Language-based, executable models of Biological Systems Palmisano A, Mura I, Priami C We translated the ODEs coupled model of Cell Cycle and Circadian Clock into a BlenX program

9. Original Model Uncoupled Cell Cycle Time Distr. Coupled MDT=16h MDT=16h Nagoshi (2004) Cell 119:693-705 MDT=24h MDT=24h Klevecz (1976) PNAS 73:4012-4016

10. Fourier analysis of stochastic simulations • FT converts stochastic time series to frequency spectrum • Multiple runs produce a distribution which converges • Statistical measures characterise distribution • ρ1 and ρ2 are measures of stochasticity • ρ1 = ρ2 = 0 corresponds to completely random behaviour 400 cycles log(peak/mean) µ = time series mean coefficient of variance rho2 rho1

11. Fourier Analysis Uncoupled Coupled MDT=16h MDT=16h MDT=24h MDT=24h

12. Coupling increases noise

13. Extending the model Biological data points to additional couplings including a link back from the Cell cycle to the Circadian Clock This requires a more detailed description of both parts of the model

14. Extending the Cell Cycle A model for restriction point control of the mammalian cell cycle Novák B, Tyson JJ Conradie R, Bruggeman FJ, Ciliberto A, Csikász-Nagy A, Novák B, Westerhoff HV, Snoep JL, Submitted 2008

15. Unpacked Model Cell Cycle Time Distr. Uncoupled Coupled MDT=16h MDT=16h MDT=24h MDT=24h

16. Comparing Original and Unpacked models

17. Extending the Circadian Clock PER Per mRNA PER PER/PER BMAL1 / CLK INACTIVE COMPLEX Preitner, N., et .al (2002) Cell 110:251–260 Sato, T. et. al (2004) Neuron 43:527–537 BMAL1 mRNA

18. KInfer Lecca P, Palmisano A, Priami C, Sanguinetti G, ACM SAC 2009 • If the optimization of the likelihood function built on the rate equations of the model returns parameters that do not reproduce - within the experimental errors - the experimental time-courses, there is a disagreement between the model and the experiments, that suggest the need to revise/extend the model. BMAL1 / CLK ROR RevErb BMAL1 mRNA

19. RB multiphosphorylation x:A x:D x:E x:P x:S x:B CycA CycD CycE E2Fp E2F CycB a:P1 b:P2 d:P4 x:CB a:S1 b:S2 c:S3 c:P3 d:S4 e:S5 e:P5 RB x:00000 x:00100 x:00101 x:11111

20. Network Analysis string.embl.de Further extensions of the model 49 nodes p53 p53 Wee1 CKII aggregate model 12 nodes CycB, Kip1, Rb Wee1 Bmal1/Clock All molecules in current model 25 nodes Cdk2, Kip1 Wee1 Bmal1, Clock Addition of DNA damage pathway 29 nodes p53 Wee1 Per1 Highest degree Highest betweenness Betweenness ≈ Relative importance Degree ≈ Connectedness

21. …once upon a time… …in Dagstuhl…

22. Combining complementary approaches and tools • CoSBi Lab • BlenX modelling • stochastic simulation and Fourier analysis • parameter inference • BIOCHAM • reaction based • model checking (boolean, stochastic, continuous) • GINsim • logical modeling • attractor identification • feedback circuit analysis

23. Combining complementary approaches and tools Revised boolean model Boolean model ODEs GINsim CoSBi Lab BIOCHAM GINML SBML Influence graph regulatory graph BlenX reactions

24. Conclusions • Before Dagstuhl: • Flexibility and modularity of BlenX language allowed us to extend and analyze the stochastic behavior of a coupled model of Cell Cycle and Circadian Clock • We investigated several models at different levels of abstraction • The refined model reveals the effectiveness of the language in modeling various complex interaction scenarios in a simple way • Our analysis identifies holes in our current biological knowledge and suggests further directions of research • During Dagstuhl: • Delineated a PIPELINE from ODEs -> BlenX -> Reactions -> Regulatory graphs • Better understanding on the different abstractions. Towards a fully detailed model as a common reference • Refined logical model and better understanding on the gating mechanism (phase locking)

25. Prospects Extension of the model, consideration of additional couplings (p21, M-phase transcription inhibition,…) Use of model checking capabilities of BIOCHAM Use GINsim and BIOCHAM to design new experiments to run and analyse in CoSBi Lab Long term goals… Cancer treatment (chronotherapeutics) Lévi (2006) Cancer Causes Control 17:611-621

26. Acknowledgements Tommaso Mazza Sean Sedwards Alida Palmisano Paolo Ballarini Attila Csikász-Nagy Roberto Larcher Paola Lecca Adrien Faure (TAGC) Ivan Mura Ferenc Jordán Judit Zámborszky

27. Questions?