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
