Patterns of Mesenchymal Condensation in a Multiscale, Discrete Stochastic Model

Abstract

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.

Modeling Morphogenesisin silicoandin vitro: Towards Quantitative, Predictive, Cell-based Modeling

“…For example, both reaction-diffusion mechanisms [10,23] and a haptotactic mechanism [60] plausibly reproduce in vitro chondrogenesis micromass cultures, while a multitude of mechanisms, including those involving chemotaxis, mechanical traction or preferential adhesion to elongated structures, correctly reproduce in vitro blood vessel growth.…”

“…In the same way, eliminating the inhibitor, which the authors hypothesize is secreted by the nodules, also yielded cartilage monolayers both in silico and in vitro. Christley and coworkers refined the initial model of chondrogenesis [10], accommodating a number of new experimental observations. In contrast to the observations of Kiskowski and coworkers, 1) cell tracking measurements indicated that chondrocytes do not slow down in cartilage condensations, and 2) cell density in chondrocyte micromass cultures is constant and nodules do not deplete cells in their surroundings; cells only round up in nodules.…”

“…The mechanisms proposed by Kiskowski et al [23] and Christley et al [10] require a locally self-enhancing "activator" and a long-range "inhibitor", and indeed patterning in these models is due to a classic Turing-Gierer-Meinhardt mechanism. Although both papers propose plausible candidates for an activator and an inhibitor, their role has not been definitely pinned down.…”

Cell-Biomaterial Interactions Reproducing a Niche

“…Cadherin-mediated adhesion was in fact linked to GTPase-cytoskeleton signalling (Delanoe-Ayari, Al Kurdi et al 2004). Interestingly this process presents similarities with the self-organizing condensing mesenchymal cells that drive the growth of the pre-cartilagineous anlage in limb bud development through growth factor diffusion-processes and aptotaxis, although contribution from the latter seems relative (Christley, Alber et al 2007). In vitro chondrogenesis of MSC offers additional cues to dissect the pathways involved in cell shape-mediated commitment to differentiation.…”

Advances in Regenerative Medicine

“…Cadherin-mediated adhesion was in fact linked to GTPase-cytoskeleton signalling (Delanoe-Ayari, Al Kurdi et al 2004). Interestingly this process presents similarities with the self-organizing condensing mesenchymal cells that drive the growth of the pre-cartilagineous anlage in limb bud development through growth factor diffusion-processes and aptotaxis, although contribution from the latter seems relative (Christley, Alber et al 2007). …”