Our algorithm assesses the average stream width for a given cell at only selected time frames (frames 1, 4, 8, 12, 16, 20, and 24). This decision was made because examining every frame resulted in odd computations due to any random “wiggle” effects from non-straight movement of the cells. By eliminating frames, the cell movement was approximated to be more linear (see increase in straightness of path in skipped frame image compared with nonskipped frame image in Figure 1, C and D). Also, the 140° arcs are subdivided into two halves (four sections total). This prevents the algorithm from terminating early in cases where rings contain neighboring streams moving in different orientation. This was not an issue at small assessment radii but became a problem after the size of the arcs was increased to find more objects in the same frame.
Results and discussion
As expected, our live cell imaging demonstrated that both cell types we tested reorganize within the confluent cell sheet. Our Matlab recoloring tool, as has been seen previously (15), allows cells moving in the same direction to be more easily visualized (Supplementary Figure S3). Using our algorithm, we characterized the cell streams for one epithelial (ARPE-19) and one fibroblast (BJ) cell line, as shown in histograms in Figure 3, A and B. We selected these cell types because we expected them to show differing migratory behavior due to differences in the extent to which each cell type interacts with neighboring cells within the sheet: epithelial cells form stronger and more junctions between neighboring cells than fibroblasts. Surprisingly, both cell types showed similar behavior: a large number of the cells did not participate in streams, as evidenced by the peak at <20 µm in Figure 3, A and B, while for cells moving within streams, we observed a range of stream widths, with a peak at 40 µm, corresponding to a stream width of approximately two cells. Our analysis highlights the non-normal variation in stream widths for different cells within the sheet, suggesting a population average measurement is not necessarily an accurate representation of the behavior of all cells within the sheet.
We also quantified the size of the streams using the standard velocity correlation function method (shown in Figure 3, C and D). Figure 3, C and D, show data averaged for all cells and suggest that the radii at which cells become noncorrelated (in which the inverse cosine of the function levels off at ~π/2) are ~200 and ~250 µm for ARPE-19 and BJ cells, respectively. To allow easier comparison with our nonaveraged data, we also quantified for each cell the radius at which the velocity correlation function approached 0 (specifically when it fell below 0.273 or θ = π/1.7). This was selected to account for a nonperfect drop to exactly 0 in the function when cells become noncorrelated. Figure 3, E and F, show the distribution of “stream widths” defined using this method. The distribution of stream widths calculated using the velocity correlation function method was wider than that found using our algorithm, and peaked at ~100 µm for both cell types as seen in Figure 3, E and F, as opposed to the peak of stream width around 40 µm predicted by our algorithm as seen in Figure 3, A and B. We attribute this difference to the impact of correlation along the stream length and the error this introduces depending on where a cell lies within the stream. The value returned by the velocity correlation function is a combined measure of both the length and width of the stream. Our algorithm, on the other hand, provides a novel method to quantify stream width specifically.
We also used our algorithm to quantify stream width in ARPE-19 cell sheets in the presence of a wound (Supplementary Figure S2 and Supplementary Movie S2) and with cells expressing GFP-N-cadherin. Figure 3, G and H, show the stream width distribution for each situation. In the wound healing situation, the number of cells not participating in streams decreases, and an increase in the number of cells participating in streams of 40 µm were observed. These observations are consistent with the initiation of directed collective migration on introduction of the wound. Peak stream width does not appear to significantly increase in contrast to what the track images suggest. This illusion is due to the directed motion of the cell in different streams following similar paths, but at different time points. Interestingly, in cells expressing GFP-N-cadherin, where we expected increased cell-cell interactions, the distribution of stream widths shifted to lower values. This observation could be due to reduced cell motion in response to increased adhesiveness, and further studies are currently underway to probe this effect and identify the key cellular parameters that determine stream width within a sheet of cells. Beyond the wound and confluent sheet examples shown here, we believe our algorithm will also be useful in the future for defining the impact on stream width of cells moving within confined spaces (19).