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Internal Noise Coherence Resonance in mesoscopic chemical oscillation systems

Internal Noise Coherence Resonance in mesoscopic chemical oscillation systems. Zhonghuai Hou ( 侯中怀 ) Perugia ， SR2008 Email: hzhlj@ustc.edu.cn Department of Chemical Physics Hefei National Lab for Physical Science at Microscale University of Science & Technology of China (USTC).

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Internal Noise Coherence Resonance in mesoscopic chemical oscillation systems

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  1. Internal Noise Coherence Resonance in mesoscopic chemical oscillation systems Zhonghuai Hou (侯中怀) Perugia，SR2008 Email: hzhlj@ustc.edu.cn Department of Chemical Physics Hefei National Lab for Physical Science at Microscale University of Science & Technology of China (USTC)

  2. Our Research Interests • Nonlinear Dynamics in Mesoscopic Chemical Systems • Dynamics of Complex Networks • Nonequilibrium Thermodynamics of Small Systems (Fluctuation Theorem) • Multiscale Modeling of Complex Systems Nonequilibrium +Nonlinear+ Complexity

  3. Outline • Introduction  the question • Internal Noise Coherence Resonance • Stochastic Normal Form Theory as well as its applications • Conclusion

  4. Nonlinear Chemical Dynamics Two or more stable states under same external constraints Aperiodic/Initial condition sensitivity/strange attractor… Travelling/Target/Spiral/Soliton … waves Temporally Periodic Variations of Concentrations Stationary spatial structures in reaction-diffusion systems Strange Attractor The Lorenz System Chemical turbulence CO+O2 on Pt Surface Science 2001 Reactive/Inactive bistabe CO+O2 on Pt filed tip PRL1999 Calcium Spiral Wave in Cardiac Tissues Nature 1998 Turing Pattern BZ Reaction System PNAS 2003 Synthetic transcriptional oscillator (Repressilator) Nature 2002 Cellular Pattern CO Oxidation on Pt PRL 2001 PEEM Image CO Oxidation on Pt PRL 1995 Rate Oscillation CO+O2 Nano-particle Catal.Today 2003 Genetic Toggle Switch In E. Coli Nature 2000 • far-from equilibrium, self-organized, complex, spatio-temporal structures • Oscillation • Multistability • Patterns • Waves • Chaos

  5. Mesoscopic Reaction System Molecular Fluctuation N, V (Small) ? Chemical Oscillation Regularity Stochasticity Nonlinear Chemical Dynamics • Heterogeneous catalysis - field emitter tips - nanostructured composite surface - small metal particles • Sub-cellular reactions - gene expression - ion-channel gating - calcium signaling ……

  6. We already know ... • Noise Induced Pattern Transition • Disorder sustained spiral waves • Taming Chaos by Topological Disorder • Ordering Bursting Chaos in Neuron Networks • M. Wang, Z.Hou, H.Xin. ChemPhysChem 7，579( 2006); Z.Hou, et al., PRL 81, 2854 (1998) Z.Hou, et al., PRL 89, 280601 (2002) F. Qi, Z.Hou, H. Xin, PRL 91, 064102 (2003) • Noise and disorder play constructive roles in nonlinear systems

  7. Modeling of Chemical Oscillations • Macroscopic level: Deterministic, Cont. N Species, M reaction channels, well-stirred in V Reaction j: Rate: Hopf bifurcation leads to oscillation

  8. Modeling of Chemical Oscillations Exactly Kinetic Monte Carlo Simulation (KMC) Gillespie’s algorithm Approximately Internal Noise Deterministic equation • Mesoscopic Level: Stochastic, Discrete Master Equation

  9. New: Noise Induced Oscillation • A model system: The Brusselator Stochastic Deterministic FFT Noisy Oscillation

  10. Optimal System Size Best performance Optimal System size for mesoscopic chemical oscillation Z. Hou, H. Xin. ChemPhysChem 5, 407(2004)

  11. New features In the literature (Two important papers): Hu Gang, ... (PRL 1993)  External noise + Saddle Node Pikovsky/Kurths (PRL 1997)  External noise + Excitability In our work:  Internal noise + Supercritical Hopf Internal noise coherence resonance (INCR) Also: System Size Resonance (SSR)

  12. Seems to be common … • Internal Noise Stochastic Resonance in a Circadian Clock SystemJ.Chem.Phys.119, 11508(2003) ? Common mechanism • System size bi-resonance for intracellularcalcium signaling ChemPhysChem 5, 1041(2004) • Double-System-Size resonance for spiking activity of coupledHHneurons ChemPhysChem 5, 1602(2004) • Optimal Particle Size for Rate Oscillation in COOxidationonNanometer-SizedPalladium(Pd) Particles J.Phys.Chem.B 108, 17796(2004) • Effects of Internal Noise for rate oscillations during CO oxidation on platinum(Pt) surfaces J.Chem.Phys.122, 134708(2005) Analytical Study • Internal Noise Stochastic Resonance of syntheticgenenetwork Chem.Phys.Lett. 401,307(2005)

  13. Analytical study • Main idea Fact: all happens close to the HB Question: common features near HB? Answer: normal form on center manifold

  14. Analytical study • Stochastic Normal Form

  15. Analytical study • Stochastic Averaging (...) Time scale separation

  16. Analytical study(…) • Probability distribution of r Fokker-Planck equation Stationary distribution Most probable radius Noise induced oscillation

  17. Analytical study(…) • Auto-correlation function

  18. Analytical study(…) • Power spectrum and SNR Optimal system size:

  19. Analytical study(…) Universal near HB System Dependent ChemPhysChem 7, 1520(July 2006) ; J. Phys.Chem.A 111, 11500(Nov. 2007); New J. Phys. 9, 403(Nov. 2007) ;

  20. Applications of the theory • Extension to general reaction networks • Control CR via noise modulation • Multiple Noise: External and Internal • Entropy Production: Scaling Law

  21. General Reaction Network CLE:

  22. Control CR: Noise Modulation • What really matters:

  23. Example: Colored Noise • Model system: Brusselator Type 1: Ornstein-Uhlenbeck (OU) Type 2: Power-Limited (PL)

  24. Example: Colored Noise OU PL

  25. Multiple Noise: External+Internal • Model system: CO Oxidation Internal noise: External noise:

  26. The Interplay External Noise Internal Noise Too much internal noise, no CR with external noise: SR as a collective behavior of ion-channel clusters

  27. Entropy Production? • Macroscopic Level: Nonequilibrium Statistical Thermodynamics I. Prigogine 1970s

  28. Entropy Production? • Mesoscopic Level: Stochastic Thermodynamics Luo,Nicolis 1984; P.Gaspard 2004

  29. Entropy Production? • Single Trajectory Level: Dynamic Irreversibity A Random Trajectory Trajectory Entropy Total Entropy Change U. Seifert, PRL 2005

  30. Fluctuation Theorems ! • Integrate FT • Detailed FT(NESS)

  31. Brusselator • FT holds

  32. Scaling law • System Size Dependence Simulation SNF Theory

  33. Conclusion • Noise Induced Oscillation  Stochastic Modeling is important • Optimal System Size: Internal Noise Coherence Resonance  Intrinsic behavior • Stochastic Normal Form Theory  Universality + Underlying mechanism  Prediction: Control CR  Nonequilibrium Thermodynamics: FT

  34. Acknowledgements Supported by: National science foundation (NSF) Thank you

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