Table 1.

Summary of applications to date of different modelling approaches for epithelial tissue morphogenesis. CA, Cellular automata; CPM, cellular Potts model; IBM, immersed boundary method; SEM, subcellular element model.

modelling approach	example applications	strengths	limitations
continuum models	brain cortical folding [18] cephalic furrow formation [19] ventral furrow formation [20]	strong mathematical foundation; typically few parameters; well placed to study buckling and folding phenomena	difficult to incorporate cell-level heterogeneity or subcellular processes
lattice-based models (CA, CPM)	epiboly [23] branching morphogenesis [22]	computationally cheap; straightforward to simulate many cells	risk of lattice anisotropies and cell fragmentation; difficult to relate parameters to experimentally accessible quantities
off-lattice cell-centre models	C. elegans germ line [29]	more physically motivated and easily parametrized than lattice-based models	more computationally costly than lattice-based models Lack explicit description of cell shape dynamics
vertex models	tissue size regulation [30,31] germband extension [32,33]	explicitly incorporate cell neighbour rearrangements; straightforward to generate experimentally testable summary statistics	typically neglect cell–matrix adhesion, medial actomyosin contractility, active cytoskeletal remodelling
viscoelastic models	ventral furrow formation [34–36] cell sorting [37] germband retraction [38]	include active cytoskeletal remodelling	like vertex models, require cells to be in confluent tissues
‘multi-node’/curved edge models	gastrulation [39] cell sorting [40]	detailed description of cell shape dynamics	more computationally costly than vertex and ‘finite-element’ models
IBM	limb bud morphogenesis [41] Turing patterns [42]	do not require confluent tissues; allow detailed modelling of regulated growth and death processes; straightforward to incorporate subcellular structures	unclear how to estimate ‘fluid’ properties from biological data; require sophisticated numerical solvers to avoid fluid ‘leakage’
SEM	primitive streak formation [43]	allow detailed and emergent cell shape changes in response to mechanical stimuli	computationally intensive; difficult to associate interactions functions directly with particular cytoskeletal components