The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics

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Background: The biophysical characteristics of cells determinethe shape of individual cells and their packing within tissues. Cellscan form regular or irregular epithelial structures, round up andform clusters, or deform and attach to substrates. The acquired shapeof cells and tissues is a consequence of (i) internal cytoskeletalprocesses, such as actin polymerisation and cortical myosin contraction,(ii) adhesion molecules within the cell membrane that interact withsubstrates and neighbouring cells, and (iii) processes that regulatecell volume. Although these processes seem relatively simple, whencombined they unleash a rich variety of cellular behaviour that isnot readily understandable outside a theoretical framework.Results: Here we present a mathematical and computationalanalysis of a commonly used class of model formalisms that describecell surface mechanics using an energy-based approach. The analyticalstudy reveals the complete possible spectrum of single cell behaviourand tissue packing in both 2D and 3D, by taking the typical core elementsof cell surface mechanics into account: adhesion, cortical tensionand volume conservation. We show that from an energy-based description,forces and tensions can be derived, as well as the prediction of cellbehaviour and tissue packing, providing an intuitive and biologicallyrelevant mapping between modelling parameters and experiments. Thesepredictions are confirmed by the computational outcomes of cell-packinggeometries, both in a vertex-model and in 2D and 3D simulations ofthe Cellular Potts Model.Conclusions: The biological insights and qualitative cellularbehaviours agree with the this analytical study, even across differentmodel formalisms. This illustrates the generality of energy-basedapproaches for cell surface mechanics and highlights how meaningfuland quantitative comparisons between models can be established. Moreover,the mathematical analysis yields direct links between known biophysicalproperties and specific parameter settings within the Cellular PottsModel.