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An algorithm to quantify correlated collective cell migration behavior
 
Benjamin Slater*1, Camila Londono*2, and Alison P. McGuigan1,2
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Supplementary Material


Figure 1.  Cell tracking visualization. (Click to enlarge)


Stream visualization and quantification

To assess the width of cellular streams, we imported the text files generated from the MetaXpress tracking algorithm into our analysis program. The text files contain information for individual cells over a series of time frames including the cells’ assigned object numbers, their positions and radii from a designated origin, and the angles that they are moving relative to the previous time frame. These variables are specifically used in the correlation algorithm to evaluate the correlated stream widths. While we used text files generated by MetaXpress, any method of cell tracking that gathers this coordinate data, including manual tracking, could be used with our algorithm with minor modifications to the code. For comparison, we also calculated the velocity correlation function using Equation 1 (16, 20-22). The resulting average of the velocity correlation function falls between zero and one (zero means no correlation between cell streams, and one means that all streams are moving in the same direction) (16, 18, 26).

The MetaXpress tracking algorithm also outputs an image file that allows the visualization of the moving streams (Figure 1B), but the color coding is random. To better visualize the coordination between cells in the stream, we wrote a Matlab (The MathWorks, Natick, MA, USA) program that specifically colors the moving cell streams based on the direction of motion from the text files (Figure 1, C and D). Using these latter images, we estimated the accuracy of our algorithm by comparing reported stream widths for specific cells with manual measurements for those cells from the angle-based colored images.

Algorithm design

An overview of the algorithm is shown in Figure 2. To evaluate the widths of the moving cell streams, the algorithm compares the angle of displacement for a given cell (the comparison cell) at a given time point with the angles of displacements of certain surrounding cells at that same time point. Specifically, the algorithm compares the angle of displacement of surrounding cells located within an 140° arc perpendicular (above and below) to the angle of displacement of the comparison cell (Figure 2A). We did this to avoid overestimating stream width due to correlated movement along the stream length (6). For each surrounding cell, the algorithm designates the cell as correlated with the comparison cell if it is moving within 10° relative to the direction of the comparison cell. This threshold angle can be changed if desired. Only objects in the same time frame are compared, because objects moving in the same direction as the comparisoncell at earlier or later time frames are not necessarily part of the same cellular stream.




Figure 2.  A step-by-step explanation as to how the algorithm functions. (Click to enlarge)


The algorithm assesses the correlation of surrounding cells at progressively increasing distances from the comparison cell and defines stream width as the distance at which correlation is lost. Specifically, the algorithm examines the cells in the defined arcs that are within a ring of 20 µm thickness (rin to rout in Figure 2) from the comparison cell, starting at an inner radius of 0 µm (Figure 2A). This ring thickness was chosen because ARPE-19 and BJ cells have widths that are within a 20 to 30 µm range (25.4 ± 6.4 µm and 25.7 ± 7.4 µm, respectively); this number should be altered if larger or smaller cell types are being assessed. Each successive ring is considered to be correlated if the number of correlated cells is greater or equal to the number of uncorrelated cells in either one or both arcs of the ring. If the algorithm detects the cells in a particular radius are correlated, the algorithm expands the inner radii by a further 20 µm (Figure 2B) and compares the number of uncorrelated and correlated cells in arcs in the new ring region. This comparison operation is continued until a ring is reached in which the number of uncorrelated cells is greater than the number of correlated cells (Figure 2B) in both 140° arc regions of that ring. The inner radius of this ring is defined as the stream width for that object (comparison cell) for that time frame. Since each 140° arc is defined separately, if one or both of the arcs do not contain any cells in a given time frame, the inner radius is increased until new objects are found. If objects are not found within 100 µm, the arc is declared done, and the inner radius where cells were last previously detected is logged as the stream width. This component of the algorithm is important in situations where cells are more spread out, at lower cell densities, at the boundaries of the image, or if a wound is present. To account for situations where the comparison cell being analyzed is in the center of a stream, the radius is doubled if both arcs finish at the same time. For a given comparison cell, the stream widths are analyzed for all of the time frames, and the average radius is calculated and recorded as the stream width. This is then repeated for all cells in the image. The algorithm therefore outputs a distribution of stream widths (one for each cell in the image).

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