Chemical and mechanical signaling in epithelial spreading

Abstract

We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanically induced strain, or both. The model is based on chemo-mechanical interactions including a chemical effect of strain, chemically induced polarization and active traction, and interaction between polarized cells. The results, showing kinase concentration distribution and cell displacement, velocity, and stress fields, allow us to reproduce qualitatively available experimental data and distinguish between distinct dynamical patterns observed under conditions of injury or unconstraining.

Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue

“…We adopt a two-dimensional mechanical model of the epithelial layer along the lines of an earlier study of wound healing [21]. The cells always remain attached to each other forming a continuous two-dimensional epithelial surface (Fig.…”

“…2a). In order to minimize the growing disorder in the distribution of nodes in the process of cell division, the probability to divide was connected to the number of vertices of the polygon n j according to the following formula (see [21] for more detail):…”

“…Another mechanism that increases the liquidity of the tissue and excludes the severe deformation of some cells is intercalation [21,46]. We introduce here a special parameter l 0 , which determines the moment when the intercalation can occur.…”

“…Here, the reactions of dimerization and dedimerization are given by (19) and (20); the dynamics of operator-sites during binding/unbinding of dimers are described by (21) and (22); the time-delayed synthesis of proteins is given by (23); the linear and non-linear degradations are described by (24) and (25), respectively. Assuming that reactions of dimerization and binding/unbinding are fast compared to the processes of production and degradation of proteins, so that they quickly reach a local equilibrium, we obtain two delay differential equations (in fact, the procedure of derivation is similar to those for Circadian model I):…”

“…The main idea of this work is that tumor occurrence is induced by a local disruption of the circadian rhythm in the epithelial tissue when the control of the peripheral circadian oscillators by the suprachiasmatic nuclei weakens or vanishes completely. We supplemented the mechanical epithelium model that was developed earlier [21] by two simple models of circadian rhythms suggested in our previous papers [22][23][24], where the crucial element of the mechanism of oscillations is a delay of protein synthesis during the process of gene regulation. These constitutive parts are supplemented by a simple phenomenological model of the cell transformation into the cancerous state leading to modification of its physical properties.…”