A mechanical model for the formation of vascular networks in vitro

Abstract

Endothelial cells, when cultured on gelled basement membrane matrix exert forces of tension through which they deform the matrix and at the same time they aggregate into clusters. The cells eventually form a network of cord-like structures connecting cell aggregates. In this network, almost all of the matrix has been pulled underneath the cell cords and cell clusters. This phenomenon has been proposed as a possible model for the growth and development of planar vascular systems in vitro. Our hypothesis is that the matrix is reorganized and the cellular networks form as a result of traction forces exerted by the cells on the matrix and the latter's elasticity. We construct and analyze a mathematical model based on this hypothesis and examine conditions necessary for the formation of the pattern. We show cell migration is not necessary for pattern formation and that isotropic, strain-stimulated traction is sufficient to form the observed patterns.

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

“…In a model based on the Murray-Oster mechanochemical theory, Manoussaki and coworkers [25] proposed that endothelial cells exert traction forces on the Matrigel ( Figure 3B). The cells thus drag the Matrigel towards them, together with the attached endothelial cells which passively move along with the Matrigel.…”

Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

“…Some of these models include feedback, while others do not. Historically, pattern formation has been a popular subject for modelers (Oster et al, 1983;Murray and Oster, 1984;Manoussaki et al, 1996;Namy et al, 2004;Taber, 2000). In fact, Belintsev et al (1987) proposed an HR-type model for pattern formation.…”

Computational modeling of morphogenesis regulated by mechanical feedback

“…The governing equations produce a reaction-diffusion type system similar to those studied extensively in biochemical models of pattern formation (Murray, 1993). Using this theory, Manoussaki et al (1996) and Namy et al (2004) studied two-dimensional models for vasculogenesis, while Barocas and Tranquillo (1997) extended the theory to model the development of cell-populated collagen gels.…”