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The robust ticking of a circadian clock

The robust ticking of a circadian clock. David Zwicker, Jeroen van Zon, David Lubensky, Pim Altena, Pieter Rein ten Wolde Beijing, July 27, 2010. Synechococcus Elongatus. Introduction: circadian rhythms. In general, circadian rhythms are: Free running ~24 hour oscillations

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The robust ticking of a circadian clock

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  1. The robust ticking of a circadian clock David Zwicker, Jeroen van Zon,David Lubensky, Pim Altena, Pieter Rein ten Wolde Beijing, July 27, 2010 Synechococcus Elongatus

  2. Introduction: circadian rhythms • In general, circadian rhythms are: • Free running ~24 hour oscillations • Entrained to light

  3. Circadian rhythms are very robust • Circadian clocks are extremely stable • higher organisms: cell-cell interactions • clock cyanobacteria stable at single cell level Correlation time: 166 days! Mihalcescu, Hsing, Leibler, Nature (2004)

  4. Key questions: • How does the clock work? • How can it be so stable? Clock cyanobacterium S. elongatus ideal model system

  5. Circadian rhythms: oscillations gene expression • Three genes crucial: kaiA, kaiB, kaiC • kaiBC forms an operon • Expression kaiBC oscillates • Continuous overexpression KaiC represses kaiBC • Temporal overexpression KaiC resets phase C C C C Golden, Johnson, Kondo, Science (1998) kaiBC Transcription-translation cycle (TTC)!

  6. Circadian rhythms: oscillations protein modification • KaiC is hexamer with two phosphorylation sites per monomer • In the dark: no gene expression, yet oscillations of phosphorylation level! Kondo lab, Science (2005A) Protein phosphorylation cycle (PPC)!

  7. KaiC circadian oscillationsin the test tube • Test tube with KaiA, KaiB, KaiC and ATP (and water): oscillations! Kondo lab, Science (2005B) Is the PPC the principal pacemaker?

  8. Oscillations of gene expression without oscillations of phosphorylation level • TTC exists without a PPC! phosphorylation Kondo lab, Genes & Development (2008) gene expression Is the TTC perhaps the pacemaker after all?

  9. Key question: Why does the system have a PPC and a TTC?

  10. Overview PPC in vitro PPC + TTC PPC in vivo TTC in vivo

  11. Overview PPC in vitro PPC + TTC PPC in vivo TTC in vivo

  12. Overview models for PPC • Monomer shuffling: • Emberly & Wingreen (PRL, 2006); Yoda, Eguchi,Terrada, Sasai (PLCB, 2007); Mori et al. (PB, 2007); • Differential affinity or sequestration • Van Zon, Lubensky, Altena, Ten Wolde (PNAS, 2007); Clodong et al. (MSB, 2007); Rust et al. (Science 2007); For overview PPC models, see Markson & O’Shea (FEBS Lett, 2009)

  13. Roadmap to working PPC model • Individual KaiC hexamers phosphorylate and dephosphorylate in a cyclical manner • Action of KaiA and KaiB synchronizes KaiC phosphorylation cycles by differential affinity

  14. Allosteric cycle in KaiC phosphorylation phosphorylated ADP • The subunits of a KaiC hexamer can exist in two conformational states, active and inactive • All subunits switch conformation collectively (MWC model) • ATP/ADP binding to subunits stabilizes the active state • Subunits with ATP bound become phosphorylated • Phosphorylated subunits are preferably in the inactive state unphosphorylated ATP

  15. Allosteric cycle in KaiC phosphorylation ADP Partition function hexamer in state : Fast ATP/ADP binding and unbinding: Free energy of hexamer in state : ATP

  16. Allosteric cycle: thermodynamics ADP Free energy of hexamers: Inactive Active ATP

  17. Allosteric cycle: thermodynamics ADP Free energy system including ATP hydrolysis: ATP

  18. Allosteric cycle: flipping kinetics ADP p = 3 Conformational transition Nucleotide binding Flipping rate depends exponentially on degree of phosphorylation! ATP

  19. Allosteric cycle in KaiC phosphorylation Conformational transition No macroscopic oscillations due to lack of synchronization between the cycle of individual KaiC hexamers!

  20. Synchronization by differential affinity: a toy model • KaiA stimulates phosphorylation of active KaiC • [KaiA] is smaller than [KaiC] • KaiA binds with differential affinity: it binds most strongly to less phosphorylated, active KaiC

  21. Synchronization by differential affinity: a toy model Solve set of ODEs

  22. Synchronization by differential affinity: a toy model KaiA binds and stimulates the laggards!

  23. Full model Kai system: KaiC + KaiA KaiA + KaiC Kageyama et al. Mol. Cell 2006 • KaiA stimulates phosphorylation of active KaiC • Binding of KaiA stabilizes active KaiC

  24. Full model Kai system: KaiC + KaiB KaiC KaiC+KaiB Xu et al. EMBO J. (2003) • KaiB does not stimulate phosphorylation • KaiB stabilizes inactive KaiC by binding it, restoring the cycle

  25. Full model: KaiC + KaiA + KaiB Nakajima et al. Science 2005 • KaiB-KaiC binds to and sequesters KaiA, leading to another form of differential affinity

  26. Phase portrait Changing KaiA Changing KaiB Model Experiment: Kageyama et al. Mol. Cell 2006

  27. Conclusions deterministic PPC model • Oscillations over large range of KaiA and KaiB concentrations • Reproduces experiments on subsets of Kai proteins • Robustness against variations in parameters: temperature compensation (not shown) • Our model makes several testable predictions J. S. van Zon, D. K. Lubensky, P. R. H. Altena, P. R. ten Wolde, PNAS 107, 7420 (2007) http://www.arxiv.org/abs/q-bio.MN/0703009

  28. PPC in vitro: robustness to noise PPC is highly robust against noise!

  29. PPC in vivo: PPC plus constitutive gene expression PPC in vitro PPC + TTC PPC in vivo TTC in vivo

  30. PPC in vivo: PPC plus constitutive gene expression PPC not robust against variations growth rate!

  31. PPC in vivo: PPC plus constitutive gene expression High growth rate: phosphorylation level new KaiC cannot catch up before degradation.

  32. PPC plus TTC PPC in vitro PPC + TTC PPC in vivo TTC in vivo

  33. PPC plus TTC • TTC+PPC highly intertwined • System differs from conventional coupled phase oscillators

  34. PPC plus TTC: robustness PPC plus TTC highly robust.

  35. TTC-only model PPC in vitro PPC + TTC PPC in vivo TTC in vivo

  36. Comparison performance Only PPC+TTC robust over full range growth rates!

  37. PPC - TTC: origin enhanced stability • High copy number PPC • Modification leads to delay • Sharp threshold crossings enhances robustness to noise

  38. Conclusions and outlook • Both TTC plus PPC are needed for robustness against variations in growth rate • Mechanism follows from simple argument on comparison protein decay timescale with oscillation period • Also higher organisms employ protein modification • Test by putting system in E.coli? http://www.arxiv.org/abs/q-bio.MN/1004.2821

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