The assumed geometry of the contact area affects the estimation of Da, which compares the rates of 3′ PI turnover and diffusion. (a) Estimated values of Da (Eq. 1), from fits to the two-sided disk and true contact area models, are correlated for 33 cells. (b) The corresponding correlation of the estimated spatial ranges (Eq. 2) from the two models is also shown. (c) The Da values estimated using the disk model may be adjusted, using 2 × area/perimeter as the relevant length scale, to closely approximate the true contact area model estimate. In each plot, the solid line is y = x.

Characteristic response kinetics of hot and transient cold spots. TIRF images and time courses of representative hot (a and c) and cold (b and d) spots (denoted by the asterisks in a and b) in association-dissociation experiments. (a) The images were taken, from left to right: before PDGF addition; after PDGF stimulation, with the cell body at pseudo-steady state but the hot spot still increasing in intensity; at steady-state; after wortmannin addition, with the cell body more or less uniform but the hot spot decay lagging; and after complete fluorescence decay. Scale bar = 20 μm. (b) The images were taken, from left to right: before PDGF addition; after stimulation, when the cold spot is apparent; at steady state; after wortmannin addition, with the cold spot and the rest of the cell body uniform; and after complete fluorescence decay. Scale bar = 20 μm. (c) Hot spot kinetics. The center, average, and periphery fluorescence, associated with the line scan in a, are shown as a function of time (black curves) as in Fig. 1, along with the fluorescence time course of the hot spot (red curve). (d) Transient cold spot kinetics. The center, average, and periphery fluorescence, associated with the line scan in b, are shown as a function of time (black curves) as in Fig. 1, along with the fluorescence time course of the cold spot (blue curve).

Analysis of mechanisms that give rise to hot spots. (a–c) The images depict model calculations of a hypothetical association-dissociation experiment and correspond to roughly the same times depicted in Fig. 4 a, with τ = kt = 0, 2, 7 (just before PI 3-kinase inhibition), 8, and 14 from left to right. Model parameters in the cell body are Da = 6, σ = 10, x₀ = 0.05, ν = 0, κ = 2, and μ = 5. For simplicity, a single hot spot with different kinetic properties was placed at the tip of the right pseudopod (in both the contact area and nonadherent membrane), representing ∼4% of the total membrane area (asterisk). In a, the hot spot has enhanced PI 3-kinase activation (υ_b = υ_t = 1.5). The hot spot in b has enhanced PI 3-kinase activation (υ_b = υ_t = 1) and no 3′ PI flux between the hot spot and the rest of the membrane (constrained diffusion). In c, the 3′ PI turnover rate in the hot spot was reduced to zero, but otherwise the region is normal. (d–f) The center, average, and periphery fluorescence for the line scans in a–c are shown as a function of time (black curves), along with the hot spot fluorescence assuming different parameters (red curves). In d and e, the hot spot has different 3′ PI insertion rates relative to the top of the cell body (1, 1.5, and 2 in the direction of the arrows); in e, the hot spot is also subject to constrained diffusion as in b. In f, the hot spot has a different 3′ PI turnover rate constant relative to the cell body (0.8, 0.6, 0.4, 0.2, and 0 in the direction of the arrow). (g) The hot spots depicted in d (enhanced PI 3-kinase, circles), e (enhanced PI 3-kinase with constrained diffusion, squares), and f (slow turnover, triangles) were subjected to the same analysis as in Fig. 5 for comparison.

Calculated 3′ PI lipid profiles in response to PDGF stimulation using true contact area geometries. (a) Cell geometries considered in our past and present models. From left to right: hemisphere; two-sided disk; true contact area. (b) The top row of the montage shows TIRF images of a representative GFP-AktPH-transfected fibroblast in an association-dissociation experiment, whereas the bottom row shows virtual images assembled from corresponding finite-element modeling calculations. The images were taken, from left to right: before stimulation; 2 min after PDGF addition; 7 min after PDGF addition (steady state); 0.5 min after subsequent PI 3-kinase inhibition (5 μM wortmannin); and 10 min after inhibition (cytosolic fluorescence only). The line in the bottom left panel indicates the fluorescence profile used for model fitting. Scale bar = 20 μm. (c) Fit of the two-sided disk model (dashed curves) and true contact area model (solid curves) for the cell depicted in b. Dimensionless model parameters Da, σ, x₀, and p_ss were estimated for the disk model (7.30, 19.3, 0.0668, and 0.270, respectively) from four fluorescence metrics associated with the center and average fluorescence, taken from the line scan as described under Materials and Methods. Based on previous experience, it was assumed that 3′ PI is in excess (μ = 5) and that PI 3-kinase is completely recruited to the top of the cell (ν = 0). Da, σ, and x₀ were adjusted to give adequate agreement for the true contact area model (Da = 6.25, σ = 21.5, x₀ = 0.0591). For illustrative purposes, the fit to the entire time course is shown, with a 3′ PI turnover rate constant of k = 0.72 min⁻¹ in the association phase and a lag time of t_lag = 40 s.

Hot and cold spots of 3′ PI signaling. Hot/cold spots are defined as localized regions in the contact area of a GFP-AktPH-transfected cell with noticeably higher/lower fluorescence than adjacent regions. (a) Histogram of the number of hot (solid bars) and cold (open bars) spots per cell, recorded for 49 cells. (b) Contact area morphology alone cannot account for hot or cold spots. Each row of the montage depicts the steady-state response to PDGF stimulation of a different representative cell. The first column shows the TIRF image, averaged over the time interval used to calculate the steady-state metrics, and the second column shows the virtual image obtained from model calculations as described under Fig. 1; these images use the same pseudo-color scale. The third column is the result of subtracting the virtual image from the TIRF image, and the fourth column is the result of subtracting the TIRF image from the virtual image. Scale bars are 20 μm.

Quantitative analysis of hot spot kinetics. This plot shows quantitative metrics that characterize the fluorescence decay during the dissociation phase in each of the periphery hot spots analyzed (n = 119). In each cell, a reference region at the periphery of the cell body contact area (not a hot or cold spot) was chosen, and the time at which its fluorescence had decayed by 50% (t_1/2) was estimated (Eq. 3). At this time, the normalized fluorescence value and rate of decay for the reference region and all hot spots in that cell were estimated by linear regression over a 1-min interval spanning the t_1/2 (seven time points, with the midpoint time being the closest to t_1/2). A hot spot's value ratio is defined as its fluorescence at the t_1/2 divided by that of the reference region, whereas its decay ratio is defined as the specific rate of decay (−slope/value) of the hot spot divided by that of the reference region. A decay ratio ≤1, together with a value ratio >1, indicates that the hot spot and reference fluorescence intensities have neither converged nor are in the process of doing so. The error bars were determined by propagation of standard errors. The closed circles indicate hot spots that displayed at least a 20% slower (higher) time constant in the association phase, whereas the open circles indicate hot spots that did not meet this criterion.