1. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Overview of current research (Declan Bates) Robustness of deterministic & stochastic models of D. discoideum cAMP oscillations (Jongrae Kim) Research supported by: Systems Biology Lab www.sblab.org Declan Bates Pat Heslop-Harrison Ian Postlethwaite Jongrae Kim Najl Valeyev Prathyush Menon IEEE Colloquium on Control in Systems Biology, University of Sheffield, 26th March 2007

2. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Overview of current research Combined in silico and in vitro robustness analysis of biochemical networks: –cAMP oscillations in fields of chemotactic Dictyostelium cells –Regulation of gene expression in the tryptophan operon of E.coli Multisite protein-ligand interactions: –Modelling mechanisms underlying multifunctional target regulation by multisite proteins –Selective and differential activation of Ca2+-CaM targets Reverse engineering biomolecular networks: –Methods for inferring network architectures –Dealing with noise in time-series data Projects with external collaborators: –Modelling and analysis of mechanisms underlying inflammation (with Dr. Michael Seed, William Harvey Research Institute) –Pathophysiological modelling of hypoxaemia (with Dr. Jonathan Hardman, University of Nottingham) J. Kim, D.G. Bates, I. Postlethwaite, L. Ma and P. Iglesias, "Robustness Analysis of Biochemical Network Models", IET Systems Biology, 2006 N.V. Valeyev, P. Heslop-Harrison, I. Postlethwaite, N. Kotov, and D.G. Bates, ``Multiple binding sites make proteins multifunctional'', FEBS-SysBio2007, Gosau, Austria, 2007. J. Kim, D.G. Bates, P. Heslop-Harrison, I. Postlethwaite and K.-H. Cho, "Least-Squares Methods for Identifying Biochemical Regulatory Networks from Noisy Measurements", BMC Bioinformatics, 2007

3. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org IEEE UK&RI Control Systems Chapter, Colloquium on Control in Systems Biology University of Sheffield, Sheffield, UK, 26 th March 2006 Robustness of Deterministic & Stochastic Models of D. discoideum cAMP Oscillations Jongrae Kim *,‡,Ian Postlethwaite *,‡, Pat Heslop-Harrison †,‡, Declan G. Bates *,‡ *Control & Instrumentation Research Group, Dept. of Engineering, University of Leicester, Leicester, UK † Department of Biology, University of Leicester, Leicester, UK ‡ Systems Biology Lab., University of Leicester, Leicester, UK, www.sblab.org

4. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Outline Introduction –Dictyostelium discoideum –basic molecular biology –Laub-Loomis model Robustness Analysis –the deterministic model  Worst-case parameter combination –the stochastic model  converting from a deterministic to a stochastic model  synchronisation of cAMP oscillations Conclusions

5. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Dictyostelium discoideum From http://www.ruf.rice.edu/~evolve

6. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Dictyostelium discoideum extra-cellular intracellular Maeda, et al, Science, Vol. 304 (875), May 2004

7. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Basic Molecular Biology Basic Elements C O C C C C 1´1´ 2´2´ 3´3´ 4´4´ 5´ C C N N C CH N HC N H NH 2 P O O-O- O O Sugar Base : Adenine Phosphate: Triphosphate P O O-O- O O P O O-O- O -O-O

8. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Basic Molecular Biology ATP (Adenosine TriPhosphate) C C N N C CH N HC N H NH 2 C O C C C C 1´1´ 2´2´ 3´3´ 4´4´ 5´ P O O-O- O O P O O-O- O O P O O-O- O O OH

9. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Basic Molecular Biology Cyclic 3´, 5´- AMP (Cyclic Adenosine MonoPhosphate) C C N N C CH N HC N H NH 2 C O C C C C 1´1´ 2´2´ 3´3´ 4´4´ 5´ P O O O O O OH adenylate cyclase (ACA) ACA

10. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Basic Molecular Biology 5´ AMP cAMP phosphodiesterase C C N N C CH N HC N H NH 2 C O C C C C 1´1´ 2´2´ 3´3´ 4´4´ 5´ P O O-O- O O OH cAMP ACA CAR1 ERK2 REG A PKA phosphodiesterase

11. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Laub-Loomis Model Laub-Loomis cAMP Oscillation model “the model is robust in that 25-fold changes in the kinetic constants linking the activities have only minor effects on the predicted frequency” “two-fold changes make little difference in either the frequency or amplitude of the oscillations in enzymatic activities” Laub & Loomis, Molecular Biology of the Cell, 1998

12. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model Linear analysis Kim, J., Bates, D. G., Postlethwaite, I., Ma L. and Iglesias P.A., "Robustness Analysis of Biochemical Network Models", Vol 153, No. 3, IET Systems Biology, May 2006, pp. 96-104

13. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model Linear periodically time-varying Discretise

14. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model

15. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model The system is guaranteed to be stable inside of the following range:

16. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model Nonlinear Optimisation Problem Does the time response with produce a limit cycle? Yes : Increase No : Decrease

17. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: deterministic model Nonlinear Optimisation Problem [Internal cAMP] Oscillation

18. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Stochastic model

19. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Stochastic simulation: Gillespie’s-direct method –S1. When does the next reaction occur? (Probability that each reaction occurs during ) (Probability that no reaction occurs from to ) –S2. Which reaction happens from to ? –S3. Set the current time and go to the step S1. Robustness Analysis: stochastic model Propensity function ……..

20. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Result: Oscillations re-emerge for the worst parameter combination! Maeda, et al, Science, Vol. 304 (875), May 2004

21. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Is the stochastic model robust to variations in the parameters and initial conditions?

22. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model cAMP oscillations of multiple cells:

23. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Synchronisation through external cAMP

24. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model

25. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Synchronisation with more cells: Chemical Langevin Equation Formulate the increment with matching the mean and the variance up to the first-order of

26. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model 100-cells

27. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Robustness Analysis: stochastic model Power Spectrum

28. Systems Biology Lab, University of Leicester, Leicester, UK, www.sblab.org Conclusions Robustness analysis of oscillations in biological systems: –Deterministic and stochastic models may exhibit radically different levels of robustness –Deterministic and stochastic models not equivalent even for high molecular concentrations Analysis provides an explanation for the robustness of D. discoideum cAMP oscillations: –Individual cells: Stochastic fluctuation –Culture cells: Synchronisation between cells Qualitative changes of D. discoideum cells to a slug initiated by the internal cAMP concentration change