Transcript Photopolarization in Fucoid Algae

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
 Study on adaptation
Photopolarization in Fucoid Algae
(Kropf et al. 1999)
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
Distribution of calcium
(Pu et al. 1998)
Model 1 : Diffusion - trapping of channels
Ca2+ channels
N
Blue light
N
N
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:
1) unbound : free to move
2) bound : static
1)
2)
CU
 2CU
 DC
 kU ( x)CB  k B ( x)CU
2
t
x
CB
 k B ( x)CU  kU ( x)CB
t
Rate of binding
Rate of unbinding
Model 1 : Calcium Diffusion
We assume that the cell is a cylinder.
C
 2C
2
 D 2  klossC  P( x)(Cbulk  C )
t
x
R
where:
P( x)  KCc ( x)
Channel concentration
Flux on the illuminated side:
D
C
x
Flux on the shaded side:
D
C
x
x 0
 P(0)(Cbulk  C (0))
xL
 P( L)(C ( L)  Cbulk )
Model 2 : Static Channels
The players involved are similar to the
ones in rod cells.
In rod cells:
Activated rhodopsin
Electrical
response of
the cell
activate
G protein
activate
Reduce the
probability of opening
of Ca++ channels
Cyclic nucleotide
phosphodiesterase
[cGMP] 
=> similar process in Fucoid Algae ?
Model 2 : Static Channels
C
 2C
2
 D 2  klossC  P( x)(Cbulk  C )
t
x
R
where:
P( x)  K ( x)Cc
 Channels are immobile
 Permeability decreases with closing of channels
K
t
 kC ( x) K
Model 1 - results
linear distribution of light
Unbound channels distribution
#
Bound channels distribution
#
10 hrs
10 hrs
Total channels distribution
#
Calcium distribution
#
10 hrs
10 hrs
Model 1 - results
logarithmic distribution of light
Unbound channels distribution
Total channels distribution
Bound channels distribution
Calcium distribution
Distribution of calcium
linear distribution of light
logarithmic distribution of light
Model 1
linear distribution of light
Model 2
logarithmic distribution of light
Flux of calcium
linear distribution of light
logarithmic distribution of light
shaded side
Model 1
illuminated side
time
linear distribution of light
time
logarithmic distribution of light
shaded side
Model 2
illuminated side
time
time
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
[Ca++]
[Ca++]
[Ca++]
position
10-4 s-1
[Ca++]
10-5 s-1
[Ca++]
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
Light vector
 Identify best light distribution to improve this 1D model
Previous experimental data
Calcium indicator (Calcium Crimson)
Ca2+-dependent
fluorescence emission
spectra of the Calcium
Crimson indicator
Experimental Setup
to verify models accuracy
Calcium-specific vibrating probe : Flux measurement
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
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
Adaptation
I ÷ IB = Weber fraction
Quantal effects
Acknowledgements
Professor Ken Robinson
Ali Khademhosseini
Professor Douglas Lauffenburger
Professor Paul Matsudaira
References
Pu, R., Wozniak, M., Robinson, K. R. (2000). Developmental Biology 222, 440-449
Robinson, K. R., Miller, B. J. (1997). Developmental Biology 187, 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). Planta 209, 414-423
Shaw, S. L., Quatrano, R. S. (1996). J. Cell Science 109, 335-342
Alessa, L., Kropf, D. L. (1999). Development 126, 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 Science 4(12), 490-494
Kuhtreiber, W. M., Jaffe, L. F. (1990). J. Cell Biology 110, 1565-1573
Fain, G. L., Matthews, H. R., Cornwall, M. C., Routalos, Y. (2001). Physiological Reviews
81(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 USA 97, 1932-1937
Torre, V., Ashmore, J. F., Lamb, T. D., Menini, A. (1995). Journal of Neuroscience 15, 77577768
Brawley, S. H., Robinson, K. R. (1985). J. Cell Biology 100, 1173-1184
Kropf, D. L. (1994). Developmental Biology 165 , 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