Vertex models capturing subcellular scales in epithelial tissues
Fig 2
Spatiotemporal dependence of model parameters and alternative cell contractility models.
(A) Different models with spatiotemporally dependent coefficients aim to represent observed effects of (B) the complex recruitment dynamics of myosin to actin fibers in the cytoskeleton. (A) Stochastic models can describe spatial static inhomogeneity of myosin distribution. This can be expanded towards temporal stochastic processes (e.g., Ornstein-Uhlenbeck) where myosin abundance on an actin fiber varies over time. Deterministic models impose a specific condition for myosin distribution, e.g., with respect to an angle or a clock. These models are directly motivated to capture observations like convergent extension or active contractility. Some observed patterns are implemented model-free into vertex model parameters. A representative example is the contractile cable along the perimeter of the amnioserosa during dorsal closure of Drosophila embryo development. (C) The actomyosin contractility mode expressed in a vertex model with a perimeter contractility term [23] is sometimes called a purse-string mechanism; it represents a continuous actomyosin belt along the cell perimeter and generates uniform contractility. Apart from that, a series of non-uniform contractility models exist. The edge model assumes a discontinuous actomyosin belt and thus reduces coupling of the contractility structures [80]. The medial cytoskeleton observed in premature tissues has been modeled as isotropic radial fibers and anisotropic parallel fibers [35,81,82]. Parallel fibers carry a load and resist isotropic extension without introducing additional degrees of freedom [82].