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Overview of current research (Declan Bates)

IEEE Colloquium on Control in Systems Biology, University of Sheffield, 26th March 2007. Overview of current research (Declan Bates) Robustness of deterministic & stochastic models of D. discoideum cAMP oscillations (Jongrae Kim) Research supported by:.

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Overview of current research (Declan Bates)

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

  2. 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. 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. 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. Dictyostelium discoideum From http://www.ruf.rice.edu/~evolve

  6. Dictyostelium discoideum extra-cellular intracellular Maeda, et al, Science, Vol. 304 (875), May 2004

  7. NH2 C N 5´ C N O C HC 1´ 4´ C CH C C 3´ 2´ N N H O O O C C -O O O O O O P P P O- O- O- Basic Molecular Biology • Basic Elements Base : Adenine Sugar Phosphate: Triphosphate

  8. NH2 C N C N HC C CH 5´ O N N C H O O O 1´ 4´ C C 3´ 2´ O O O O O O P P P C C O- O- O- Basic Molecular Biology • ATP (Adenosine TriPhosphate) OH OH

  9. NH2 C N C N HC C CH 5´ O N N C H O 1´ 4´ C C 3´ 2´ O O P C C O O OH Basic Molecular Biology • Cyclic 3´, 5´- AMP (Cyclic Adenosine MonoPhosphate) adenylate cyclase (ACA) ACA

  10. NH2 C N C N HC C CH 5´ O N N C H O 1´ 4´ C C 3´ 2´ O O P C C O- Basic Molecular Biology • 5´ AMP cAMP phosphodiesterase phosphodiesterase OH OH

  11. Laub-Loomis 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 • Laub-Loomis cAMP Oscillation model

  12. Robustness Analysis: deterministic model 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 • Linear analysis

  13. Robustness Analysis: deterministic model • Linear periodically time-varying • Discretise

  14. Robustness Analysis: deterministic model

  15. Robustness Analysis: deterministic model The system is guaranteed to be stable inside of the following range:

  16. Robustness Analysis: deterministic model • Nonlinear Optimisation Problem Yes : Increase No : Decrease Does the time response with produce a limit cycle?

  17. 1.5 1 0.5 0 1 2 3 4 5 6 1.5 1 0.5 0 1 2 3 4 5 6 1.5 1 0.5 0 1 2 3 4 5 6 Robustness Analysis: deterministic model • Nonlinear Optimisation Problem [Internal cAMP] Oscillation

  18. Robustness Analysis: stochastic model • Stochastic model

  19. …….. Robustness Analysis: stochastic model • 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. Propensity function

  20. Robustness Analysis: stochastic model • Result: Oscillations re-emerge for the worst parameter combination! Maeda, et al, Science, Vol. 304 (875), May 2004

  21. Robustness Analysis: stochastic model • Is the stochastic model robust to variations in the parameters and initial conditions?

  22. Robustness Analysis: stochastic model • cAMP oscillations of multiple cells:

  23. Robustness Analysis: stochastic model • Synchronisation through external cAMP

  24. Robustness Analysis: stochastic model

  25. 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. Robustness Analysis: stochastic model • 100-cells

  27. Robustness Analysis: stochastic model • Power Spectrum

  28. 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

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