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Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae BE.400 December 12, 2002 Wilson Mok Marie-Eve Aubin Outline Biological background Model 1 : Diffusion – trapping of channels Model 2 : Static channels Model results Experimental setup Study on adaptation Photopolarization in Fucoid Algae (Kropf et al. 1999) 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 Distribution of calcium (Pu et al. 1998) Model 1 : Diffusion - trapping of channels Ca2+ channels N Blue light N N 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) Model 1 : Bound & Unbound Channels light We model one slice of the cell Reduce the system to 1D Divide the channels in two subpopulations: 1) unbound : free to move 2) bound : static 1) 2) CU 2CU DC kU ( x)CB k B ( x)CU 2 t x CB k B ( x)CU kU ( x)CB t Rate of binding Rate of unbinding Model 1 : Calcium Diffusion We assume that the cell is a cylinder. C 2C 2 D 2 klossC P( x)(Cbulk C ) t x R where: P( x) KCc ( x) Channel concentration Flux on the illuminated side: D C x Flux on the shaded side: D C x x 0 P(0)(Cbulk C (0)) xL P( L)(C ( L) Cbulk ) Model 2 : Static Channels The players involved are similar to the ones in rod cells. In rod cells: Activated rhodopsin Electrical response of the cell activate G protein activate Reduce the probability of opening of Ca++ channels Cyclic nucleotide phosphodiesterase [cGMP] => similar process in Fucoid Algae ? Model 2 : Static Channels C 2C 2 D 2 klossC P( x)(Cbulk C ) t x R where: P( x) K ( x)Cc Channels are immobile Permeability decreases with closing of channels K t kC ( x) K Model 1 - results linear distribution of light Unbound channels distribution # Bound channels distribution # 10 hrs 10 hrs Total channels distribution # Calcium distribution # 10 hrs 10 hrs Model 1 - results logarithmic distribution of light Unbound channels distribution Total channels distribution Bound channels distribution Calcium distribution Distribution of calcium linear distribution of light logarithmic distribution of light Model 1 linear distribution of light Model 2 logarithmic distribution of light Flux of calcium linear distribution of light logarithmic distribution of light shaded side Model 1 illuminated side time linear distribution of light time logarithmic distribution of light shaded side Model 2 illuminated side time time 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 [Ca++] [Ca++] [Ca++] position 10-4 s-1 [Ca++] 10-5 s-1 [Ca++] 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 Light vector Identify best light distribution to improve this 1D model Previous experimental data Calcium indicator (Calcium Crimson) Ca2+-dependent fluorescence emission spectra of the Calcium Crimson indicator Experimental Setup to verify models accuracy Calcium-specific vibrating probe : Flux measurement 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 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 Adaptation I ÷ IB = Weber fraction Quantal effects Acknowledgements Professor Ken Robinson Ali Khademhosseini Professor Douglas Lauffenburger Professor Paul Matsudaira References Pu, R., Wozniak, M., Robinson, K. 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