Interplay between activator–inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning

Abstract

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This "agent-oriented" model represents cells by points on a lattice that obey rules motivated by experimental findings. The "cells" follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor ("activator," corresponding to TGF-beta) that stimulates production of the SAM, and another diffusible factor ("inhibitor") that suppresses the activity of the activator. We implemented the cellular automaton on a two-dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development.

Spots and stripes: Pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation

“…Further support comes from the diffuse presence of the dermal condensation marker NCAM (Jiang and Chuong, 1992) in ERK-suppressed specimens. This parallels the involvement of growth factors in regulating adhesion molecules during limb morphogenesis (Hentschel et al, 2004; Kiskowski et al, 2004). Using a localized bead source, we showed that FGF4 can specifically induce phosphorylation of ERK.…”

“…Mechanisms involving the reaction and diffusion of chemical substances and the chemotactic response of cells to such chemicals have been proposed for a number of biological phenomena including the pattern forming behavior of the slime mold, Dictyostelium discoidium (Vasiev, 1994) and the bacterium E. coli (Zorzano, 2005), patterns on the integument of snakes and fish (Myerscough, 1991; Painter, 1999), in the induction of hairs and feathers (Nagorcka and Mooney, 1992; Jung et al, 1998) and feather branching (Harris et al, 2005; Yu et al, 2005). These principles also have been used to explain skeletal patterning in the limb bud (Hentschel et al, 2004; Kiskowski et al, 2004; Miura and Maini, 2004). However, much remains to be learned about how molecular pathway and cellular events are coupled to the patterning process at the tissue / organ level.…”

Patterns of Mesenchymal Condensation in a Multiscale, Discrete Stochastic Model

“…Those that undergo condensation round up, reducing their surface area, but do not move away from adjacent noncondensing cells. Therefore, unlike the situation in the model of Kiskowski et al [26], mesenchymal condensation in micromass culture does not involve accumulation of cells at particular sites with concomitant depletion of cells in surrounding zones. (2) The representation of cells, morphogens, and ECM on a common grid is physically unrealistic.…”

“…In a previous study [26] we presented a discrete “biological lattice gas” model for high-density cultures of precartilage mesenchymal cells derived from the embryonic vertebrate limb. This model, which was based on the physical notion of a lattice gas, in which individual particles are free to move from point to point on a lattice at discrete time-steps, accurately simulated the formation of patterns of mesenchymal condensations observed in high-density micromass cultures of such cells.…”

“…The ability of the model of Kiskowski et al [26] to simulate both qualitative and quantitative aspects of precartilage condensation formation and distribution suggested that the core genetic network–cell behavioral mechanism that underlies this biological lattice gas might be sufficient to account for pattern formation in the limb cell micromass system and corresponding features of in vivo limb development. However, the model deviated from biological reality in several important ways.…”