Abstract
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 materialThe online version of this article (doi:10.1007/s10237-015-0697-6) contains supplementary material, which is available to authorized users.
Highlights
Demands on computational models are continuing to increase as they play a broader and more central role in the advancement of cell mechanics
The goal of this study is to describe the mathematical and computational foundations of that polyline model; to investigate contact angle, cell shape, and cell motion discrepancies between monoline and polyline models; and to determine whether these discrepancies are a direct result of the straightedge assumption
Ever since the first computational models of cell mechanics were constructed in the 1970s, straight edges have been considered a suitable approximation to the actual shapes of cell edges, appearing in many kinds of models, from cell lattice models to centric models to vertex models to finite element models (Brodland 2004)
Summary
Demands on computational models are continuing to increase as they play a broader and more central role in the advancement of cell mechanics. Since the detailed force information needed to test these inverse methods could not be obtained experimentally, synthetic data were generated by running computer simulations in which the driving forces could be arbitrarily specified and the resulting cell shapes known to many digits of accuracy (Brodland et al 2010b, 2014; Graner 1993; Ishihara et al 2013) As these force inference techniques were applied to increasingly challenging problems, data from straight-edge models no longer proved satisfactory. We aim to create a framework that will help modellers choose an appropriate model for studying specific scenarios
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