Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell–to–cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell–to–cell adhesion, despite the fact that cell–to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell–to–cell adhesion strength, q, and cell proliferation rate, λ, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and λ. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell–to–cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D=161−243μm2hour−1, q=0.3−0.5 (low to moderate strength) and λ=0.0305−0.0398hour−1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell–to–cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.


Estimating the diameter of the cell nucleus
High magnification images of MM127 cells were used to obtain an estimate of the mean diameter of the cell nucleus. Images were acquired using a Nikon TI Eclipse microscope fitted with a Nikon digital camera. ImageJ was used to measure the diameter of the cell nucleus in the images (Figure 1). These measurements are reported in Table 1, and indicate that the mean diameter of the MM127 cell nucleus is approximately 18 µm. 21  Image analysis software was used to detect the location of the leading edge of the expanding MM127 cell colonies. All measurements of the location of the leading edge were converted to an equivalent circular radius R.  Table 2: Experimental radius measurements of the entire expanding cell colonies for all experiments performed. Image processing was used to determine the area of the expanding colony for each experiment with and without Mitomycin-C pretreatment at t = 0, t = 24 and t = 48 hours for both initial densities. The area of the expanding colony was converted into an equivalent circle from which we estimated the radius R = √ A/π. Each data point was replicated three times to give the mean radius and standard deviation.

Data type 2: Cell density profiles
Cell density profiles were extracted from Propidium Iodide stained images which show the location of the nucleus of individual cells throughout the entire colony. Cell density profiles for each experiment were averaged over three experimental replicates as described in the main manuscript [see section Data 2: Cell density profiles]. Figure 2 compares the cell density profiles extracted from three replicate experiments with the final averaged cell density profile for experiments initialised with 20, 000 and 30, 000 cells both with and without Mitomycin-C pretreatment. For all experiments, the averaged cell density profile appears to be an appropriate approximation given that the variation between the three replicate cell density profiles is minimal.

Data type 3: Degree of cell clustering
The degree of cell clustering in the MM127 cell colonies was measured by counting the number of isolated cells in Propidium Iodide images showing the location of the nucleus of individual cells throughout the entire colony. Table 3 summarises the proportion of isolated cells compared to total number of cells in six subregions in the middle of the colony as described in the main manuscript.  Table 3: Proportion of isolated cells in the MM127 cell colonies with Mitomycin-C pretreatment. Image processing was used to identify the number of isolated cells and the total number of cells in the expanding colony for each experiment with Mitomycin-C pretreatment at t = 0, t = 24 and t = 48 hours. The proportion of isolated cells in the expanding colony was converted into a percentage. Each data point was replicated six times to give the mean and standard deviation.

Data type 4: Cell density counts
The rate of cell proliferation in the cell population was quantified by counting the number of cells in four subregions located in the centre of the cell colonies for each experiment and at each time point. Results in Table 4 Table 4: Experimental measurements of the non-dimensional cell density, c(t). Image processing was used to count the total number of cells in four subregions located in the centre of the cell colonies for each set of experiments, with and without Mitomycin-C pretreatment. The number of cells was converted into a non-dimensional cell density. Each data point was replicated four times to give the mean non-dimensional cell density and standard deviation.

A. B.
Proliferation rate  6 Predicting the spatial expansion of a MM127 melanoma cell colony Table 5 summarises the estimates of the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, λ, obtained from the analysis described in the main manuscript.

Image acquisition and analysis
Detecting the location of the leading edge of the cell colony Customised image processing software was written in MATLAB's image processing toolbox. The same software was used to detect the location of the leading edge in both the experimental cell colonies and the simulated cell colonies. Each colour image was imported (imread ) and converted to greyscale (rgbtogray). A binary gradient mask containing the segmented cell colony was obtained by applying the Sobel operator (edge(Original Image, 'Sobel'), edge (I,'sobel',threshold ) to enhance lines of high contrast. To show the outline of the object, the lines in the binary gradient mask were dilated (strel, imdilate).
Remaining holes in the images were filled (imfill ) and objects disconnected from the edge were removed (imclearborder ).
The image was smoothed and filtered to remove small objects detected in the previous steps (imerode, medfilt2 ). The resulting image contains both a large object (corresponding to the expanding cell colony) and smaller objects. The smaller objects were removed (regionprops, bwareopen) to leave the edge of the cell colony. An outline of the detected edge was superimposed back onto the original image (bwperim) to verify the accuracy of the procedure. The area (regionprops) of the detected object was estimated and converted into an equivalent circular radius.

Detecting individual cells in the cell colony
To count the number of cells in the various subregions, we used a combination of customised image processing software, written using the MATLAB image processing toolbox, and manual counting where necessary. Each colour image was imported (imread ), converted to greyscale (rgbtogray) and enhanced (imadjust) to provide sufficient contrast between each cell and the background of the image. The image was converted to black and white based on a threshold (graythresh, im2bw ). To reduce noise, objects less than 30 pixels were removed (bwareaopen). Remaining holes in the image were filled (strel, imfill, Bwboundaries), using a similar method as in the leading edge software. The centre of each detected region (which we assume to be an individual cell) was identified (regionprops(image,'Centroid')) and superimposed back on the original image to test the accuracy of the detection method. The number of cells detected by the automated software was recorded. All remaining cells not automatically identified were manually included in the total cell count.

Identifying isolated cells in the cell colony
In addition to counting individual cells, we identified isolated cells that did not share a circular region, of radius 18 µm, with other cells. To do this, we repeated the same image processing procedure to identify the total number of cells in the colony. For each identified region corresponding to a cell, we recorded the physical location of each identified cell using (regionprops). Each identified cell was checked to determine whether the cell was isolated by comparing the location of the identified cell with the locations of all other cells. For example, to check if cell A, located at (x 1 , y 1 ), and cell B, located at (x 2 , x 2 ) share the same circular region of radius 18 µm, we calculated the physical distance between the two cells using W = √ (x 2 − x 1 ) 2 + (y 2 − y 1 ) 2 . If W > 18 µm, this indicates that cell B does not share the same circular region of radius 18 µm around cell A and vice versa. This was repeated systematically for all cells to identify which cells were completely isolated in the cell colony. To test the accuracy of the detection method, we superimposed the locations of each isolated cell back onto the original image and overlaid a square grid of size 18 µm. The image was visually checked to make sure all identified isolated cells were correctly detected and that the image processing had identified all isolated cells. In some cases, a small number of identified cells were incorrectly identified and were deleted. Similarly, a small number of isolated cells were not identified and had to be manually added.