Mathematical modeling to resolve the photopolarization mechanism in fucoid algae
Download
1 / 23

Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae - PowerPoint PPT Presentation


  • 93 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae' - nasya


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Outline Mechanism in Fucoid Algae

  • Biological background

  • Model 1 : Diffusion – trapping of channels

  • Model 2 : Static channels

  • Model results

  • Experimental setup

  • Study on adaptation


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Photopolarization in Fucoid Algae Mechanism in Fucoid Algae

(Kropf et al. 1999)


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Signal Transduction Mechanism in Fucoid Algae

  • Light

  • Photoreceptor: rhodopsin-like protein

  • cGMP

  • Ca++

  • Calcium channels

  • F-actin

  • Signal transduction pathway unknown

  • The mechanism of calcium gradient formation is still unresolved


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Distribution of calcium Mechanism in Fucoid Algae

(Pu et al. 1998)


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Blue light Mechanism in Fucoid Algae

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)


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Model 1 : Bound & Unbound Channels Mechanism in Fucoid Algae

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)


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Model 1 : Calcium Diffusion Mechanism in Fucoid Algae

We assume that the cell is a cylinder.

where:

Channel concentration

Flux on the illuminated side:

Flux on the shaded side:


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Model 2 : Static Channels Mechanism in Fucoid Algae

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 ?


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Model 2 : Static Channels Mechanism in Fucoid Algae

where:

  • Channels are immobile

  • Permeability decreases with closing of channels


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

# Mechanism in Fucoid Algae

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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Model 1 - results Mechanism in Fucoid Algae

logarithmic distribution of light

Unbound channels distribution

Bound channels distribution

Total channels distribution

Calcium distribution


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Distribution of calcium Mechanism in Fucoid Algae

linear distribution of light

logarithmic distribution of light

Model 1

linear distribution of light

logarithmic distribution of light

Model 2


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Flux of calcium Mechanism in Fucoid Algae

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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

[Ca Mechanism in Fucoid Algae++]

[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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Light vector Mechanism in Fucoid Algae

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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Previous experimental data Mechanism in Fucoid Algae

Calcium indicator (Calcium Crimson)

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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Experimental Setup Mechanism in Fucoid Algaeto verify models accuracy

Calcium-specific vibrating probe : Flux measurement


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Concluding remarks Mechanism in Fucoid Algae

  • 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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Necessity for Adaptation Mechanism in Fucoid Algae

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


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Adaptation Mechanism in Fucoid Algae

I ÷ IB = Weber fraction

Quantal effects


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

Acknowledgements Mechanism in Fucoid Algae

Professor Ken Robinson

Ali Khademhosseini

Professor Douglas Lauffenburger

Professor Paul Matsudaira


Mathematical modeling to resolve the photopolarization mechanism in fucoid algae

References Mechanism in Fucoid Algae

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

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

Berger, F., Brownlee, C. (1994). Plant Physiol.105, 519-527

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

Love, J., Brownlee, C., Trewavas, A. J. (1997). Plant Physiol.115, 249-261

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

Kropf, D. L., Bisgrove, S. R., Hable, W. E. (1999). Trends in Plant Science4(12), 490-494

Kuhtreiber, W. M., Jaffe, L. F. (1990). J. Cell Biology110, 1565-1573

Fain, G. L., Matthews, H. R., Cornwall, M. C., Routalos, Y. (2001). Physiological Reviews81(1), 117-151

Hofer, T., Politi, A., Heinrich, R. (2001). Biophysical Journal(80), 75-87

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

Torre, V., Ashmore, J. F., Lamb, T. D., Menini, A. (1995). Journal of Neuroscience15, 7757-7768

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