Macroscopic PI3K signaling vector as a predictor of cell movement. (a) TIRF montage depicting signaling and migration vectors during random migration; the time relative to the start of image acquisition is indicated. Scale bar, 20 μm. (b) Migration path of the centroid for the cell shown in a, measured at 12-min intervals (circles). The direction of the signaling vector is indicated by a short line emanating from each centroid point. (c) Correlation of PI3K signaling and centroid velocity vectors. The time lag is the interval between measurements of signaling and migration vectors, and the correlation coefficient means (circles) and 95% confidence intervals (gray regions) are shown for n = 28 cells. (d) Correlation coefficients for individual cells at zero time lag, ranked in descending order. (e and f) The persistence of cell movement is consistent with that of the macroscopic PI3K signaling vector. The two vector quantities were autocorrelated, and the resulting correlation coefficients were averaged for the 28 cells and fit to an exponential distribution, exp(−t/τ), where t is the time lag and τ is the apparent time constant of change.

Productive movements of individual hot spots depend on their PI3K signaling levels. (a) Hot-spot paths were tracked from birth to death using μ-SVA. The schematic illustrates the determination of the net distance traveled (dashed line) and lifetime (number of segments in the path, converted to minutes). (b–d) The hot spots were binned into three, equal-sized groups (n = 465) based on their normalized, time-averaged fluorescence volume (see the main text for details) (b), from which was determined their net distance traveled from birth to death (c) and their net distance traveled divided by lifetime (d). Each hot-spot path is represented by a dot, and the black bars indicate mean values.

Stochasticity of PI3K signaling during random cell migration. (a) Hot-spot fluorescence kinetics exhibit dynamic, counteracting fluctuations. A representative cell was analyzed using μ-SVA, and the normalized fluorescence volume of each of its hot spots () is plotted as a function of time (in number of image planes, time interval = 2 min). The dynamics of each hot spot is assigned a unique color based on when it appeared, and the circle symbols indicate the recorded birth and death events. (Inset) Ranked plot of correlation coefficients (mean = −0.23, n = 22), where the normalized fluorescence volume of each unique hot-spot subpath was correlated against the sum of all others present at the same time; time intervals during which there was only one hot-spot subpath (i.e., when no others were present) were discarded from the analysis, and only those subpaths with five or more values to correlate were included. (b) Simple model of signaling pattern fragility. A stochastic model (Materials and Methods) was implemented using the Next Reaction Method, and the concentration of the integrator, I_j, is plotted as a function of time for each of five regions (subcompartments). The excitability of the model is caused by competition for a limiting component and positive feedback. The dotted, horizontal line on the plot illustrates that there is a level below which the signal could not be distinguished from noise.

Illustration of SVA. (a) Constructing the macroscopic signaling vector for M-SVA. (Upper) A representative TIRF image of a GFP-AktPH-expressing fibroblast's contact area is shown in pseudocolor (left) and after segmentation (middle) using the k-means algorithm (k = 4). Pixels in the highest intensity bin (hot spots) are shown in black, and other pixels assigned to the cell (bins 2 and 3) are shown in gray. Construction of the resultant macroscopic signaling vector is shown at right. Scale bar, 20 μm. (Lower) A cartoon illustrates our scheme for averaging signaling vectors (S_R) over time periods appropriate for tracking cell migration (C); it is noted that the time interval for cell tracking was 6Δt = 12 min, not 3Δt as shown (see Materials and Methods). (b) Tracking hot-spot dynamics and fates (μ-SVA). The plot shown indicates the (x,y) positions of each fluorescent hot-spot centroid from birth to death, accounting also for hot-spot branching and merging events, for a representative cell (see also Fig. 2, a and b). Each hot spot's path is connected by lines, color-coded from cool to warm according to advancing time (time interval, 2 min). This sequence is animated, alongside a pseudocolor TIRF movie of the migrating cell, in Movie S2.

PI3K signaling hot spots tend to be localized in regions of membrane protrusion. (a) TIRF images, separated by 12-min intervals, are compared so as to determine the protruded and retracted areas. Pixels in the protruded area are associated with the cell contact area in the more recent image but were in the background in the earlier image; conversely, pixels in the retracted area were in the contact area in the earlier image but are in the background in the more recent image. Scale bar, 20 μm. (b) The enrichment, E, of a region is defined as the fraction of its pixels belonging to hot spots, compared to that of the whole-cell contact area. Circles indicate the time-averaged mean values of E in the protruded and retracted areas for each of 28 cells (see main text for further description). An E value >1 indicates that the region of interest has, on average, a higher percentage of hot-spot pixels than the entire contact area.

Hot-spot birth and death events are positively coupled. Individual PI3K signaling hot spots were tracked using μ-SVA, and waiting-time distributions were determined for intervals between births, between deaths, and between death-birth and birth-death events. (a) Aggregate (pooled data for 28 cells) distributions of birth-birth and death-birth waiting times. (b) Aggregate distributions of death-death and birth-death waiting times. (c) Scatter plot showing the mean birth-birth and death-birth waiting times (in minutes) for each cell. (d) Scatter plot showing the mean death-death and birth-death waiting times (in minutes) for each cell.