Cell shape index: combined roundness and circularity

Epithelial cells display tension in their adherens junctions belts and subcortical actin rings, giving rise to straight lines. Besides, even in the absence of neighbor cells, they have quite sharp borders. In contrast, mesenchymal or mesenchymal-like cells have serrated, wavy junctions and an irregular outline due to the presence of filopodia and lamellipodia (which can be decorated with ruffles) (Innocenti, 2018). To be able to quantify and compare morphological changes, it was required to express these morphologies in terms of numbers. ImageJ offers measurements of Roundness and Circularity. While Roundness accounts for gross changes (from circular to ovoid or triangular), it is insensitive to straight vs. serrated or undulated borders. On the other hand, Circularity is very sensitive to such edge characteristics. Thus, we defined a Cell Shape Index (CShin) combining Roundness and Circularity.

Figure 1A depicts values of CShin associated to some geometric figures (on the left). CShin is sensitive to radial symmetry, being higher for a circle than for an ellipse or higher for a square than a rectangle. If the clean edge of each geometric form is substituted by a serrated or undulated border, CShin values show a sharp increase. As can be seen in Fig. 1A (right), CShin is very sensitive to the edge characteristics of the shape. For example, CShin = 1 for a perfect circle and CShin = 1.81 for a form that conserves the circular proportions but has an undulated edge.

(A) Roundness, circularity and their quotients were initially measured and calculated for geometric figures. Here are Cshin values for some geometric figures and the correspondent figures with wavy limits. (B) NMuMG cells are a well-known model to study a process through which an epithelial cell loses its epithelial characteristics and acquires mesenchymal characteristics. Such process is an epithelial to mesenchymal transition (EMT) and is induced by treatment with TGF-β. We induced that process and measured Cshin to validate the proposed index. ****p < 0.0001.

As a proof of concept, CShin was applied to a well-characterized cell model of an epithelial to mesenchymal transition (EMT). NMuMG (NAMRU Murine Mammary Gland) cells were measured untreated (when they have epithelial characteristics) or after treatment with TGF-β (when they have mesenchymal characteristics).

The Plotly Chart Studio online graph maker (https://chart-studio.plotly.com/create/box-plot/#/) was used to build box & whisker graphs, plus represent all the individual data points. Statistics were done using the free software available online at https://astatsa.com/, attributed to Vasavada (2016). As CShin statistical distribution is not normal, medians were compared using Mann-Whitney non-parametric test. Kruskall-Wallis non-parametric ANOVA followed by Conover test adjusted by Benjamini-Hochberg FDR method.

The shape change was evidenced as an increased CShin index (Fig. 1B). In this model, CShin mean and median were below 1 for epithelial cells and above 1 for mesenchymal cells, with a significant difference (p = 2.413887 × 10⁻⁸). Thus, the index proved to be useful to evidence the cell shape change from an epithelial to a mesenchymal cell.