1. Or Spatiotemporal Stochastic Resonance in a Subexcitable Chemical System Sandor Kadar, Ph.D. & Carla Field When Noise Is a Blessing and Not an Annoyance

2. What is Stochastic Resonance (SR)? SR is a mechanism through which a weak otherwise undetectable periodic signal becomes detectable SR is a mechanism through which a weak otherwise undetectable periodic signal becomes detectable Spatial excitation patterns in an extended medium display resonance-type dependence on the noise-variance with the patterns being optimal at intermediate noise level What is Spatiotemporal Stochastic Resonance (STSR)?

3. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Chemical reactions Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

4. Periodic signal Threshold Noise + Signal Events Frequency of signal

6. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Demonstration Chemical reactions Chemical reactions Mechanism (Oregonator Model) Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

7. Paddlefish: Examples of SR Cricket: Passive receptor Passive receptor Detects electric signal emitted by zooplankton Detects electric signal emitted by zooplankton By applying noise food capture rate increased up to 50% By applying noise food capture rate increased up to 50% Cercal system Cercal system Detects 80-150Hz signal Detects 80-150Hz signal Senses predator (wasp) Senses predator (wasp)

8. Crayfish: Mechano-receptor (hair cell) Mechano-receptor (hair cell) Detects electric signal emitted by approaching predator Detects electric signal emitted by approaching predator Detects 8-25Hz signal Detects 8-25Hz signal

9. Enrico Simonotto Improve visual perception Improve visual perception Improve physiological functions Improve physiological functions Disorders of the nervous system are caused by increased sensory threshold which in turns resulted in reduced firing rate Disorders of the nervous system are caused by increased sensory threshold which in turns resulted in reduced firing rate Electrical/mechanical noise is used to enhance the ability of humans to detect subthreshold mechanical cutaneous stimuli. Electrical/mechanical noise is used to enhance the ability of humans to detect subthreshold mechanical cutaneous stimuli.

10. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Demonstration Chemical reactions Chemical reactions Mechanism (Oregonator Model) Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

11. Photosensitive Belousov-Zhabotinsky- reaction Components: NaBrO 3NaBrO 3 H 2 SO 4H 2 SO 4 Malonic acid (MA)/Bromomalonic acid (BrMA)Malonic acid (MA)/Bromomalonic acid (BrMA) Ru(Bpy) 3 2+ catalystRu(Bpy) 3 2+ catalyst Key intermediates: HBrO 2HBrO 2 Br -Br - Activator Inhibitor BrMA Br - Ru(Bpy) 3 2 Ru(Bpy) 3 2 + = 460 nm

13. Belousov-Zhabotinsky Reaction Bulk configuration

14. Belousov-Zhabotinsky Reaction Spatially extended configuration

15. Excitability Light intensity Photosensitive BZ-reaction Steady state (perturbation dies) Excitable (perturbation travels across the system) Oscillatory (perturbation causes sustained activity) More light Less light More Br - Less HBrO 2 Less Br - More HBrO 2

16. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Demonstration Chemical reactions Chemical reactions Mechanism (Oregonator Model) Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

18. high excitability (dark) sub-excitable low excitability - no wave support (bright) Excitability 0 255 100% noise 100% noise

19. Experimental setup

20. Experimental Results – single wave, colored noise Noise level = 0 Noise level = 0 Noise level = 30% Noise level = 30% Noise level = 60% Noise level = 60% Noise level = 100% Noise level = 100%

21. SNR as a function of cluster size

22. Model of the Belousov-Zhabotinsky Reaction (modified to account for photosensitivity)  Components: H 2 SO 4, Malonic acid, Bromomalonic acid, NaBrO 3,Ru(bpy) 3 2+ u  [HBrO 2 ], v  [Ru(bpy) 3 2+ ], w  [Br - ]

23. Numerical Results – single wave, colored noise Noise level = 30% Noise level = 30% Noise level = 60% Noise level = 60% Noise level = 100% Noise level = 100% Noise level = 0 Noise level = 0

24. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Demonstration Chemical reactions Chemical reactions Mechanism (Oregonator Model) Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

25. 0.2 0.5 0.9 0.7 0.0 Noise level Numerical Results – single wave, white noise

26. Surface plot showing multi-resonance in signal enhancement Signal enhancement as a function of noise level (cell size: 15) Noise level Cell size

27. General introduction to SR Demonstration Demonstration Examples Examples Demonstration Demonstration Chemical reactions Chemical reactions Mechanism (Oregonator Model) Mechanism (Oregonator Model) Simplified mechanism (Tyson-Fife scaling) Simplified mechanism (Tyson-Fife scaling) The Chemical System – Belousov Zhabotinsky Reaction Results STSR with colored noise – single wave STSR with colored noise – single wave STSR with white noise – single wave STSR with white noise – single wave STSR with white noise – wave trains STSR with white noise – wave trainsOutline

28. Events (waves passing threshold in the wave train configuration) Fourier transformation of events

29. Wave activity along the threshold line

30. Conclusions Addition of white noise results inAddition of white noise results in two optimal noise levels (stochastic multi-resonance) at different spatial correlations (cell sizes). Wave-train configuration exhibits SR as wellWave-train configuration exhibits SR as well Let’s see the experiments!Let’s see the experiments!

31. Acknowledgements Jichang WangJichang Wang Carla FieldCarla Field Marianna OldalMarianna Oldal BRIN Pilot Grant ProgramBRIN Pilot Grant Program Salve Regina University Small Grant ProgramSalve Regina University Small Grant Program