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Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae

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### Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae

BE.400

December 12, 2002

Wilson Mok

Marie-Eve Aubin

- 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)

- Light
- Photoreceptor: rhodopsin-like protein
- cGMP
- Ca++
- Calcium channels
- F-actin

- Signal transduction pathway unknown
- The mechanism of calcium gradient formation is still unresolved

(Pu et al. 1998)

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)

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)

We assume that the cell is a cylinder.

where:

Channel concentration

Flux on the illuminated side:

Flux on the shaded side:

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 ?

where:

- Channels are immobile
- Permeability decreases with closing of channels

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

logarithmic distribution of light

Unbound channels distribution

Bound channels distribution

Total channels distribution

Calcium distribution

linear distribution of light

logarithmic distribution of light

Model 1

linear distribution of light

logarithmic distribution of light

Model 2

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

[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

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

Calcium indicator (Calcium Crimson)

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

Experimental Setupto verify models accuracy

Calcium-specific vibrating probe : Flux measurement

- 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

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

Professor Ken Robinson

Ali Khademhosseini

Professor Douglas Lauffenburger

Professor Paul Matsudaira

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