Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: II. Parameter estimates for individual cells from experiments - PubMed (original) (raw)

Comparative Study

Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: II. Parameter estimates for individual cells from experiments

Ian C Schneider et al. Biophys J. 2004 Jan.

Abstract

Fibroblast migration is directed by gradients of platelet-derived growth factor (PDGF) during wound healing. As in other chemotactic systems, it has been shown recently that localized stimulation of intracellular phosphoinositide (PI) 3-kinase activity and production of 3' PI lipids in the plasma membrane are important events in the signaling of spatially biased motility processes. In turn, 3' PI localization depends on the effective diffusion coefficient, D, and turnover rate constant, k, of these lipids. Here we present a systematic and direct comparison of mathematical model calculations and experimental measurements to estimate the values of the effective 3' PI diffusion coefficient, D, turnover rate constant, k, and other parameters in individual fibroblasts stimulated uniformly with PDGF. In the context of our uniform stimulation model, the values of D and k in each cell were typically estimated within 10-20% or less, and the mean values across all of the cells analyzed were D = 0.37 +/- 0.25 microm2/s and k = 1.18 +/- 0.54 min(-1). In addition, we report that 3' PI turnover is not affected by PDGF receptor signaling in our cells, allowing us to focus our attention on the regulation of 3' PI production as this system is studied further.

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Figures

FIGURE 1

FIGURE 1

Association-dissociation experiments with TIRF excitation. (a) Total internal reflection fluorescence (TIRF) images of a representative GFP-AktPH-transfected NIH 3T3 fibroblast. Panel 1 shows the cell before treatment (scale bar = 10 _μ_m); the line scan used to generate the data is also shown. Panels 2, 3, and 4 were acquired 1, 2, and 7 min after addition of 10 nM PDGF-BB, over which time the fluorescence profile achieved a steady state. Panels 5 and 6 were acquired 0.5 and 10 min after addition of wortmannin, which rapidly blocks 3′ PI production. (b) Raw fluorescence profiles across the line scan are shown for each of the six images in a. (c) The line scan profiles at all time points, acquired every 10 s, were converted into normalized kinetic traces as described in Materials and Methods: open triangles, contact area periphery f(1,t); open inverted triangles, contact area center f(0,t); closed circles, contact area average formula image. Time zero corresponds to the addition of PDGF, and the arrow signifies the addition of wortmannin.

FIGURE 2

FIGURE 2

The apparent 3′ PI turnover rate constant is not altered by PDGF signaling. (a) Representative association-dissociation experiment with no PDGF added during the association phase, demonstrating that the decay of the basal 3′ PI level could be detected in our assay. Symbols are as in Fig. 1 c, and the arrow signifies the addition of wortmannin. (b) For each of 197 cells stimulated with various concentrations of PDGF-BB, the time course of the average fluorescence was fit to Eq. 3, and the apparent 3′ PI turnover rate constant, _k_app, was accepted if the fit exhibited an _R_2 value exceeding 0.95. Circle symbols are _k_app values for 168 individual cells, plotted as a function of the PDGF-BB concentration used in the association phase. The solid line connects the means at each PDGF-BB dose.

FIGURE 3

FIGURE 3

Fluorescence characteristics of individual cells subjected to the full model analysis. Of the cells imaged in association-dissociation experiments, 32 satisfied all criteria for comparison with model calculations. (a) The gradient depth of each cell, assessed through the steady-state center/average fluorescence ratio, formula image, is a function of cell size, measured as the radius of the line scan squared. (b) Correlation of the fluorescence dip at the center of the contact area, _f_min(0) (y axis), and the steady-state center/average fluorescence ratio, formula image (x axis). Two cells with relatively low formula image yet high _f_min(0) are indicated with arrows; these are referred to again in Fig. 5.

FIGURE 4

FIGURE 4

Model fits to individual cell fluorescence tracks. (a) Limiting cases of the model were used to constrain the parameter space. A histogram for the number of cases (up to 6) satisfied is shown, and the identities of the cases are indicated (see also Table 1). (b) The quantity _χ_2/n is used to assess quality of fit, where n is the number of data points considered. The _χ_2/n value for each cell, averaged over the applicable limiting cases, is plotted versus cell size, taken as the square of the line scan radius (_μ_m2); the error bars signify the range of _χ_2/n values obtained. The four cells indicated with open symbols yielded the least ideal model fits, with average _χ_2/n > 0.10. (c) Representative cell tracks exhibiting radial gradients of varying depth. The values of formula image are (left) 0.82, (middle) 0.53, and (right) 0.25. Symbols signify fluorescence measurements as in Fig. 1 c, and solid curves are the best-fit model calculations.

FIGURE 5

FIGURE 5

Estimates of the 3′ PI diffusion coefficient, turnover rate constant, and other parameters in individual cells. Circle symbols mark the mean parameter value averaged over the limiting model fits, and the error bars signify the range of parameter values for each cell. Open symbols signify the four cells that yielded less ideal model fits as described under Fig. 4. (a) The estimated diffusion coefficient D (_μ_m2/s) in each cell is plotted versus the square of the line scan radius (_μ_m2), demonstrating that the apparent lipid mobility is independent of cell size. The dotted line indicates the mean of the 32 cells (0.374 _μ_m2/s). (b) The average turnover rate constant, k, is correlated versus the associated _k_app, from a fit to Eq. 3, for each cell. The solid line is the best fit of the data to y = m*x, with m = 1.75; the dashed line is the y = x line. (c) The fluorescence gain, σ, the ratio of the cytosolic volume to the effective volume of TIRF excitation, is plotted versus the square of the line scan radius (_μ_m2). (d) The estimated values of basal/steady-state 3′ PI ratio, _X_0/_X_ss (x axis), and the steady-state probe-binding fraction, _p_ss (y axis), are shown.

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