Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb

Abstract

A central question in developmental biology is how cells interact to organize into tissues? In this paper, we study the role of mesenchyme-ectoderm interaction in the growing chick limb bud using Glazier and Graner's cellular Potts model, a grid-based stochastic framework designed to simulate cell interactions and movement. We simulate cellular mechanisms including cell adhesion, growth, and division and diffusion of morphogens, to show that differential adhesion between the cells, diffusion of growth factors through the extracellular matrix, and the elastic properties of the apical ectodermal ridge together can produce the proper shape of the limb bud.

Coordinated Action of N-CAM, N-cadherin, EphA4, and ephrinB2 Translates Genetic Prepatterns into Structure during Somitogenesis in Chick

“…Extensive comparisons between experiments and GGH simulations have validated GGH methods (Mareé and Hogeweg, 2001;Zeng et al, 2004;Chaturvedi et al, 2005;Poplawski et al, 2007; for multicell morphogenesis modeling.…”

Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment

“…GGH applications include models of Hydra vulgaris regeneration, cell motility [62], cell deformation [72], chick embryo mesenchymal chondrogenesis [17,44], growth [71] and cell motility [63], tumor growth [47,77], embryonic convergent extension [86], vasculogenesis [57], avascular tumor growth [27], cancer invasion [79,80], aggregation, slug behavior and culmination in Dictyostelium discoideum [46,53,54,55,74], the liquid-like behavior of chick-cell aggregates [10], chick limb growth [71], engineering biological structures using self-assembly [45,65], directional sorting of chemotactic cells [49], evolutionary mechanisms [40,41,42], foams [48,73], and viscous flow [22]. Figure 1 Interaction descriptions and dynamics define how the various objects behave both biologically and physically.…”

“…We simulate growth of cells by increasing their V t by a function f which typically depends on the local concentrations of chemicals C that induce growth and the internal state of the cell [71]: (12) If a cell reaches a given doubling volume, it divides and splits along a random axis (with no splitting orientation) into two cells with equal target volumes of one half the parent-cell volume (we can easily add oriented cell division, but it is not included in the PLH model [66,67]). Adding constraints to the effective energy can describe many other cell properties, including osmotic pressure and membrane area [17,44], the average shape of the cells [57,86], chemotaxis [40,54], viscosity and advective diffusion [22], rigid-body motion [6], and cell compartments for the simulation of polarized cells, e.g., in epithelia [11].…”

Budding behaviors: Growth of the limb as a model of morphogenesis

“…Dillon and Othmer (1999) created the first realistic twodimensional finite element model (FEM) of limb development, in which mesenchymal growth rates were controlled by a molecule diffusing from the distal tip (Dillon and Othmer, 1999). Poplawski et al (2007) incorporated the gradient hypothesis within a Cellular Potts framework, and concluded that distally restricted growth was indeed important for bud elongation (Poplawski et al, 2007), while Morishita and Iwasa (2008) used a cell-based 2D spring lattice to demonstrate a similar result (Morishita and Iwasa, 2008).…”