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Computational models of cell–cell mechanical interactions typically simulate sorting and certain other motions well, but as demands on these models continue to grow, discrepancies between the cell shapes, contact angles and behaviours they predict and those that occur in real cells have come under increased scrutiny. To investigate whether these discrepancies are a direct result of the straight cell–cell edges generally assumed in these models, we developed a finite element model that approximates cell boundaries using polylines with an arbitrary number of segments. We then compared the predictions of otherwise identical polyline and monoline (straight-edge) models in a variety of scenarios, including annealing, single- and multi-cell engulfment, sorting, and two forms of mixing—invasion and checkerboard pattern formation. Keeping cell–cell edges straight influences cell motion, cell shape, contact angle, and boundary length, especially in cases where one cell type is pulled between or around cells of a different type, as in engulfment or invasion. These differences arise because monoline cells have restricted deformation modes. Polyline cells do not face these restrictions, and with as few as three segments per edge yielded realistic edge shapes and contact angle errors one-tenth of those produced by monoline models, making them considerably more suitable for situations where angles and shapes matter, such as validation of cellular force–inference techniques. The findings suggest that non-straight cell edges are important both in modelling and in nature. Electronic supplementary material The online version of this article (doi:10.1007/s10237-015-0697-6) contains supplementary material, which is available to authorized users.

Cell populations in multicellular organisms show genetic and non-genetic heterogeneity, even in undifferentiated tissues of multipotent cells during development and tumorigenesis. The heterogeneity causes difference of mechanical properties, such as, cell bond tension or adhesion, at the cell–cell interface, which determine the shape of clonal population boundaries via cell sorting or mixing. The boundary shape could alter the degree of cell–cell contacts and thus influence the physiological consequences of sorting or mixing at the boundary (e.g., tumor suppression or progression), suggesting that the cell mechanics could help clarify the physiology of heterogeneous tissues. While precise inference of mechanical tension loaded at each cell–cell contacts has been extensively developed, there has been little progress on how to distinguish the population-boundary geometry and identify the cause of geometry in heterogeneous tissues. We developed a pipeline by combining multivariate analysis of clone shape with tissue mechanical simulations. We examined clones with four different genotypes within Drosophila wing imaginal discs: wild-type, tartan (trn) overexpression, hibris (hbs) overexpression, and Eph RNAi. Although the clones were previously known to exhibit smoothed or convoluted morphologies, their mechanical properties were unknown. By applying a multivariate analysis to multiple criteria used to quantify the clone shapes based on individual cell shapes, we found the optimal criteria to distinguish not only among the four genotypes, but also non-genetic heterogeneity from genetic one. The efficient segregation of clone shape enabled us to quantitatively compare experimental data with tissue mechanical simulations. As a result, we identified the mechanical basis contributed to clone shape of distinct genotypes. The present pipeline will promote the understanding of the functions of mechanical interactions in heterogeneous tissue in a non-invasive manner.