Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae

1. Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae BE.400 December 12, 2002 Wilson Mok Marie-Eve Aubin

2. Outline • Biological background • Model 1 : Diffusion – trapping of channels • Model 2 : Static channels • Model results • Experimental setup • Study on adaptation

3. Photopolarization in Fucoid Algae (Kropf et al. 1999)

4. Signal Transduction • Light • Photoreceptor: rhodopsin-like protein • cGMP • Ca++ • Calcium channels • F-actin • Signal transduction pathway unknown • The mechanism of calcium gradient formation is still unresolved

5. Distribution of calcium (Pu et al. 1998)

6. Blue light N N N Model 1 : Diffusion - trapping of channels Ca2+ channels Actin patch Actin patch: Involvement of microfilaments in cell polarization as been shown Model of Ca++ channel diffusion suggested (Brawley & Robinson 1985) (Kropf et al. 1999)

7. Model 1 : Bound & Unbound Channels light • We model one slice of the cell • Reduce the system to 1D • Divide the channels in two subpopulations: • unbound : free to move • bound : static 1) Rate of binding Rate of unbinding 2)

8. Model 1 : Calcium Diffusion We assume that the cell is a cylinder. where: Channel concentration Flux on the illuminated side: Flux on the shaded side:

9. Model 2 : Static Channels The players involved are similar to the ones in rod cells. In rod cells: activate activate Cyclic nucleotide phosphodiesterase G protein Activated rhodopsin Reduce the probability of opening of Ca++ channels Electrical response of the cell [cGMP]  => similar process in Fucoid Algae ?

10. Model 2 : Static Channels where: • Channels are immobile • Permeability decreases with closing of channels

11. # 10 hrs time position Model 1 - results linear distribution of light Unbound channels distribution Bound channels distribution # # 10 hrs 10 hrs time time position position Total channels distribution Calcium distribution # 10 hrs time position

12. Model 1 - results logarithmic distribution of light Unbound channels distribution Bound channels distribution Total channels distribution Calcium distribution

13. Distribution of calcium linear distribution of light logarithmic distribution of light Model 1 linear distribution of light logarithmic distribution of light Model 2

14. Flux of calcium linear distribution of light logarithmic distribution of light shaded side Model 1 illuminated side time time linear distribution of light logarithmic distribution of light shaded side Model 2 illuminated side time time

15. [Ca++] [Ca++] [Ca++] [Ca++] [Ca++] Model 1 :Rate of unbinding sensitivity analysis (linear distribution of light) Maximum Kunbind : 10-1 s-1 10-2 s-1 10-3 s-1 position 10-4 s-1 10-5 s-1

16. Light vector Light distribution measurements • Isolate 1 cell • Attach it to a surface • Use a high sensitive photodiode (e.g. Nano Photodetector from EGK holdings) with pixels on both sides what is coated with a previously deposited thin transparent layer of insulating polymer (e.g. parylene) • Rotate the light vector • Identify best light distribution to improve this 1D model

17. Previous experimental data Calcium indicator (Calcium Crimson) Ca2+-dependent fluorescence emission spectra of the Calcium Crimson indicator

18. Experimental Setupto verify models accuracy Calcium-specific vibrating probe : Flux measurement

19. Concluding remarks • 2 mathematical models which predict a successful photopolarization were proposed: • Diffusion-Trapping Channels Model • Static Channels Model  Generate more than quantitative predictions: give insights on an unresolved mechanism The experimental setup proposed would also elucidate the adaptation of this sensory mechanism

20. Necessity for Adaptation Sensitivity = increase of response per unit of intensity of the stimulus(S = dr/dI) Adaptation : change of sensitivity depending on the level of stimulation Dynamic range of photoresponse: sunlight: 150 watts / m2 moonlight: 0.5 x 10-3 watts / m2

21. Adaptation I ÷ IB = Weber fraction Quantal effects

22. Acknowledgements Professor Ken Robinson Ali Khademhosseini Professor Douglas Lauffenburger Professor Paul Matsudaira

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