Mathematical Modeling to Resolve the Photopolarization Mechanism in Fucoid Algae

BE.400BE.400

December 12, 2002December 12, 2002

Wilson MokWilson Mok

Marie-Eve AubinMarie-Eve Aubin

Mathematical Modeling to Resolve Mathematical Modeling to Resolve the Photopolarization Mechanism in the Photopolarization Mechanism in

Fucoid AlgaeFucoid Algae

OutlineOutline

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

(Kropf et al. 1999)

Photopolarization in Fucoid AlgaePhotopolarization in Fucoid Algae

Signal TransductionSignal 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

(Pu et al. 1998)

Distribution of calciumDistribution of calcium

Blue light

N N N

Model 1 : Diffusion - trapping of channelsModel 1 : Diffusion - trapping of channels

Involvement of microfilaments in cell polarization as been shown

(Kropf et al. 1999)

Actin patch:

Ca2+ channels

Actin patch

Model of Ca++ channel diffusion suggested (Brawley & Robinson 1985)

Model 1 : Bound & Unbound ChannelsModel 1 : Bound & Unbound Channels

UBBUU

CU CxkCxk

x

CD

t

C)()(

2

2

BUUBB CxkCxk

t

C)()(

We model one slice of the cell Reduce the system to 1D Divide the channels in two subpopulations:

1) unbound : free to move2) bound : static

light

1)

2)Rate of binding

Rate of unbinding

))((2

2

2

CCxPR

Ckx

CD

t

Cbulkloss

)()( xKCxP c

))0()(0(0 CCPx

CD bulkx

))()(( bulkLx CLCLPx

CD

Model 1 : Calcium DiffusionModel 1 : Calcium Diffusion

We assume that the cell is a cylinder.

Flux on the illuminated side:

Flux on the shaded side:

where:

Channel concentration

The players involved are similar to the ones in rod cells.

In rod cells:

Model 2 : Static ChannelsModel 2 : Static Channels

=> similar process in Fucoid Algae ?

Activated rhodopsin G proteinactivate activate Cyclic nucleotide

phosphodiesterase

[cGMP] Reduce the

probability of opening of Ca++ channels

Electrical response of

the cell

Model 2 : Static ChannelsModel 2 : Static Channels

))((2

2

2

CCxPR

Ckx

CD

t

Cbulkloss

Kxkt

KC )(

cCxKxP )()( where:

Channels are immobile Permeability decreases with closing of channels

linear distribution of lightModel 1 - resultsModel 1 - results

Unbound channels distribution Bound channels distribution

Total channels distribution Calcium distribution

positiontime

10 hrs

#

positiontime

10 hrs

#

positiontime

10 hrs

#

positiontime

10 hrs

#

logarithmic distribution of lightModel 1 - resultsModel 1 - results

Unbound channels distribution Bound channels distribution

Total channels distribution Calcium distribution

Model 1

linear distribution of light logarithmic distribution of light

Model 2

linear distribution of light logarithmic distribution of light

Distribution of calciumDistribution of calcium

Model 1

linear distribution of light logarithmic distribution of light

Model 2

linear distribution of light logarithmic distribution of light

Flux of calciumFlux of calcium

illuminated side

illuminated side

shaded side

shaded side

time time

time time

Maximum Kunbind : 10-1 s-110-2 s-1

Model 1 :Model 1 : Rate of unbinding sensitivity analysisRate of unbinding sensitivity analysis(linear distribution of light)(linear distribution of light)

10-3 s-1

10-4 s-1 10-5 s-1

position

[Ca++] [Ca++]

[Ca++]

[Ca++]

[Ca++]

Identify best light distribution to improve this 1D model

Light distribution measurementsLight distribution measurements

Light vector

• 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

Previous experimental dataPrevious experimental data

Calcium indicator (Calcium Crimson)

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

Calcium-specific vibrating probe : Flux measurement

Experimental SetupExperimental Setupto verify models accuracyto verify models accuracy

Concluding remarksConcluding 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

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

Necessity for AdaptationNecessity for Adaptation

Quantal effects

I ÷ IB = Weber fraction

AdaptationAdaptation

AcknowledgementsAcknowledgements

Professor Ken Robinson

Ali Khademhosseini

Professor Douglas Lauffenburger

Professor Paul Matsudaira

ReferencesReferencesPu, R., Wozniak, M., Robinson, K. R. (2000). Developmental Biology 222, 440-449Robinson, K. R., Miller, B. J. (1997). Developmental Biology 187, 125-130Berger, F., Brownlee, C. (1994). Plant Physiol. 105, 519-527Robinson, K. R., Gualtieri, P. (2002). Photochemistry and Photobiology 75(1), 76-78Love, J., Brownlee, C., Trewavas, A. J. (1997). Plant Physiol. 115, 249-261Braun, M., Richter, P. (1999). Planta 209, 414-423Shaw, S. L., Quatrano, R. S. (1996). J. Cell Science 109, 335-342Alessa, L., Kropf, D. L. (1999). Development 126, 201-209Robinson, K. R., Wozniak, M., Pu, R., Messerli, M. (1999). “Current Topics in Developmental Biology” 44, 101-126Kropf, D. L., Bisgrove, S. R., Hable, W. E. (1999). Trends in Plant Science 4(12), 490-494Kuhtreiber, W. M., Jaffe, L. F. (1990). J. Cell Biology 110, 1565-1573Fain, G. L., Matthews, H. R., Cornwall, M. C., Routalos, Y. (2001). Physiological Reviews 81(1), 117-151Hofer, T., Politi, A., Heinrich, R. (2001). Biophysical Journal (80), 75-87Brownlee, C., Bouget, F. (1998). Cell & Developmental Biology (9), 179-185Brownlee, C., Bouget, F., Corellou, F. (2001). Cell & Developmental Biology (12), 345-351Goddard, H., Manison, N.F.H. Tomos, D., Brownlee, C. (2000). Proceedings of the National Academy of Sciences USA 97, 1932-1937Torre, V., Ashmore, J. F., Lamb, T. D., Menini, A. (1995). Journal of Neuroscience 15, 7757-7768Brawley, S. H., Robinson, K. R. (1985). J. Cell Biology 100, 1173-1184Kropf, D. L. (1994). Developmental Biology 165 , 361-371Malho R. et al.1995, Calcium channel activity during pollen tube growth. Plant J 5:331-341Meske V et al. 1996 Protoplasma 192:189-198