title: The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics.
abstract: BACKGROUND
  The biophysical characteristics of cells determine their shape in isolation and when packed within tissues. Cells can form regular or irregular epithelial structures, round up and form clusters, or deform and attach to substrates. The acquired shape of cells and tissues is a consequence of (i) internal cytoskeletal processes, such as actin polymerisation and cortical myosin contraction, (ii) adhesion molecules within the cell membrane that interact with substrates and neighbouring cells, and (iii) processes that regulate cell volume. Although these processes seem relatively simple, when combined they unleash a rich variety of cellular behaviour that is not readily understandable outside a theoretical framework.
  
  
  METHODS
  We perform a mathematical analysis of a commonly used class of model formalisms that describe cell surface mechanics using an energy-based approach. Predictions are then confirmed through comparison with the computational outcomes of a Vertex model and 2D and 3D simulations of the Cellular Potts model.
  
  
  RESULTS
  The analytical study reveals the complete possible spectrum of single cell behaviour and tissue packing in both 2D and 3D, by taking the typical core elements of cell surface mechanics into account: adhesion, cortical tension and volume conservation. We show that from an energy-based description, forces and tensions can be derived, as well as the prediction of cell behaviour and tissue packing, providing an intuitive and biologically relevant mapping between modelling parameters and experiments.
  
  
  CONCLUSIONS
  The quantitative cellular behaviours and biological insights agree between the analytical study and the diverse computational model formalisms, including the Cellular Potts model. This illustrates the generality of energy-based approaches for cell surface mechanics and highlights how meaningful and quantitative comparisons between models can be established. Moreover, the mathematical analysis reveals direct links between known biophysical properties and specific parameter settings within the Cellular Potts model.
authors.affiliation: Theoretical Biology/Bioinformatics, Dept. of Biology, Utrecht University, Padualaan 83584 CH, Utrecht, Netherlands ; Computational and Systems Biology, John Innes Centre,, Norwich Research Park, NR4 7UH, Norwich, UK.
authors.forename: Ramiro
authors.initials: R
authors.lastname: Magno
authors.affiliation: Computational and Systems Biology, John Innes Centre,, Norwich Research Park, NR4 7UH, Norwich, UK.
authors.forename: Verônica A
authors.initials: VA
authors.lastname: Grieneisen
authors.affiliation: Computational and Systems Biology, John Innes Centre,, Norwich Research Park, NR4 7UH, Norwich, UK.
authors.forename: Athanasius Fm
authors.initials: AF
authors.lastname: Marée
keywords: 3D modelling; Adhesion; Cell shape; Cell sorting; Cell surface mechanics; Cellular Potts model; Cellular dynamics; Cellular vertex-models; Cortical tension; Grid anisotropy; Membrane tension; Tissue packing