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PNAS 103 (31): 11549-11554

Copyright © 2006 by the National Academy of Sciences.

Cellular asymmetry and individuality in directional sensing

Azadeh Samadani, Jerome Mettetal, and Alexander van Oudenaarden*

Department of Physics and G. R. Harrison Spectroscopy Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139


Figure 1
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  		Fig. 1. Dynamic translocation of CRAC–GFP at the plasma membrane after stimulation with a 2-s pulse of cAMP. (a) The UV uncaging location is positioned a distance r away from the cell center. The angle {theta} defines the coordinate along the cell’s periphery, where {theta} = 0 defines the position at the membrane that is closest to the uncaging location. (b) Unprocessed epifluorescence images displaying CRAC–GFP as a function of time. The scale bar denotes 10 µm and r = 70 µm. (c) Subtracted images illustrate the relative change of CRAC–GFP concentration in the membrane with respect to the prestimulus level (t = –2 s). (d) Response function R({theta},t) as a function of time for the images in c.

 

Figure 2
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  		Fig. 2. Definition of localization, L, polarization, P, and polarization angle, {varphi}, and a comparison between the time dependence of these parameters for a single cell (which is stimulated 10 times) and a population of 40 cells (which are stimulated once). (a) The response function R({theta}, Tmax) (open circles) and the fitting function Rfit({theta}, Tmax) (red line). (b) Time dependence of L for a single cell. (c) Time dependence of the average L for a population. (d) Time dependence of P for a single cell. (e) Time dependence of the average P for a population. (f) Time dependence of {varphi} for a single cell. The two dashed red lines indicate the dynamics of {varphi} for two other single cells. {varphi} is very reproducible from pulse to pulse, even when {varphi} != 0. (g) Time dependence of the average {varphi} for a population of 40 cells, which averages to zero. Error bars denote standard deviations.

 

Figure 3
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  		Fig. 3. Comparison between single cell and population response. (a and b) R({theta}, Tmax) for a single cell that is stimulated 10 times (a) and a population of 40 cells that are stimulated once (b). (c and d) Polar plot of the polarization at Tmax for three single cells (c) and a population of 100 cells (d). In these representations, one data point represents data from a single cell at Tmax. The distance from a data point to the origin of the polar plot equals the polarization, P(Tmax). The angle between the x axis and the line that connects the data point to the origin of the polar plot is the polarization angle, {varphi}(Tmax). (e) Population probability distribution of |{varphi}(Tmax)|, illustrating the fraction of cells displaying a particular polarization angle at Tmax. (f) Average of L(Tmax) and P(Tmax) (left ordinate) and the ratio of P(Tmax)/L(Tmax) (right ordinate) as a function of |{varphi}(Tmax)|. (e and f) Solid lines are predictions of the geometric model.

 

Figure 4
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  		Fig. 4. Schematic illustration of the geometric model. (a and b) The effective signal (black line), which is a combination of the intracellular signal (blue line) and the extracellular signal (red line), shown for a uniform cAMP stimulus (a) and for a directed pulse of cAMP (b). (c and d) Graphical representation of the geometric model and the polarization angle, {varphi}, when cells are stimulated with a uniform pulse of cAMP and for a directed pulse of cAMP (d). The effective polarization angle strongly depends on the direction of the intracellular signal, {varphi}{varepsilon}. (e and f) Experimentally measured polar plots, as defined in Fig. 3 c and d, for a uniform pulse of cAMP (e) and a directed pulse of cAMP (f).

 

Figure 5
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  		Fig. 5. Experimentally measured relation between the polarization angle, {varphi}(Tmax), and the extracellular signal, {theta}s, when the direction of the extracellular signal is varied relative to the intracellular signal, {varphi}{varepsilon} and comparison to the geometric model. (a) Schematic illustration of the geometric model in the frame of reference of a cell with a fixed {varphi}{varepsilon}. (b) The difference image for a cell with a small {alpha} (<<1). Red dots on the images indicate the direction of extracellular stimulation. (c) {varphi}(Tmax) versus {theta}s for a cell with small {alpha} (<<1). The triangles and circles denote two independent experiments, demonstrating the reproducibility of this assay. (d and e) {varphi}(Tmax) versus {theta}s for a cell with an intermediate {alpha} ({approx}1) (d) and a large {alpha} (>>1) (e). The red lines represent fits to the geometric model with fitting parameters {alpha} and {varphi}{varepsilon}.

 

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