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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

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mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae

BE.400

December 12, 2002

Wilson Mok

Marie-Eve Aubin

slide2

Outline

  • Biological background
  • Model 1 : Diffusion – trapping of channels
  • Model 2 : Static channels
  • Model results
  • Experimental setup
  • Study on adaptation
slide4

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
slide5

Distribution of calcium

(Pu et al. 1998)

slide6

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)

slide7

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)

slide8

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:

slide9

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 ?

slide10

Model 2 : Static Channels

where:

  • Channels are immobile
  • Permeability decreases with closing of channels
slide11

#

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

slide12

Model 1 - results

logarithmic distribution of light

Unbound channels distribution

Bound channels distribution

Total channels distribution

Calcium distribution

slide13

Distribution of calcium

linear distribution of light

logarithmic distribution of light

Model 1

linear distribution of light

logarithmic distribution of light

Model 2

slide14

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

slide15

[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

slide16

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
slide17

Previous experimental data

Calcium indicator (Calcium Crimson)

Ca2+-dependent fluorescence emission spectra of the Calcium Crimson indicator

slide18

Experimental Setupto verify models accuracy

Calcium-specific vibrating probe : Flux measurement

slide19

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

slide20

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

slide21

Adaptation

I ÷ IB = Weber fraction

Quantal effects

slide22

Acknowledgements

Professor Ken Robinson

Ali Khademhosseini

Professor Douglas Lauffenburger

Professor Paul Matsudaira

slide23

References

Pu, R., Wozniak, M., Robinson, K. R. (2000). Developmental Biology222, 440-449

Robinson, K. R., Miller, B. J. (1997). Developmental Biology187, 125-130

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Robinson, K. R., Gualtieri, P. (2002). Photochemistry and Photobiology 75(1), 76-78

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Braun, M., Richter, P. (1999). Planta209, 414-423

Shaw, S. L., Quatrano, R. S. (1996). J. Cell Science109, 335-342

Alessa, L., Kropf, D. L. (1999). Development126, 201-209

Robinson, K. R., Wozniak, M., Pu, R., Messerli, M. (1999). “Current Topics in Developmental Biology” 44, 101-126

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Brownlee, C., Bouget, F. (1998). Cell & Developmental Biology(9), 179-185

Brownlee, C., Bouget, F., Corellou, F. (2001). Cell & Developmental Biology(12), 345-351

Goddard, H., Manison, N.F.H. Tomos, D., Brownlee, C. (2000). Proceedings of the National Academy of Sciences USA97, 1932-1937

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Brawley, S. H., Robinson, K. R. (1985). J. Cell Biology100, 1173-1184

Kropf, D. L. (1994). Developmental Biology165 , 361-371

Malho R. et al.1995, Calcium channel activity during pollen tube growth. Plant J 5:331-341

Meske V et al. 1996 Protoplasma 192:189-198

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