The analytical solution to the migration of an epithelial monolayer with a circular spreading front and its implications in the gap closure process

TL;DR

This paper presents an analytical model of epithelial monolayer migration with a circular gap, revealing key factors influencing gap closure and front stability, with implications for understanding wound healing processes.

Contribution

The work provides the first analytical solutions for epithelial sheet spreading with a circular gap, highlighting the roles of contractility and purse-string contraction in gap closure.

Findings

Two spreading modes identified through analytical solutions.

Purse-string contraction is crucial for gap closure.

Critical parameter values determine gap closure initiation.

Abstract

The coordinated behaviors of epithelial cells are widely observed in tissue development, such as re-epithelialization, tumor growth, and morphogenesis. In these processes, cells either migrate collectively or organize themselves into specific structures to serve certain purposes. In this work, we study a spreading epithelial monolayer whose migrating front encloses a circular gap in the monolayer center. Such tissue is usually used to mimic the wound healing process in Virto. We model the epithelial sheet as a layer of active viscous polar fluid. With an axisymmetric assumption, the model can be analytically solved under two special conditions, suggesting two possible spreading modes for the epithelial monolayer. Based on these two sets of analytical solutions, we assess the velocity of the spreading front affected by the gap size, the active intercellular contractility, and the purse-string contraction acting on the spreading edge. Several critical values exist in the model parameters for the initiation of the gap closure process, and the purse-string contraction plays a vital role in governing the gap closure kinetics. Finally, the instability of the morphology of the spreading front was studied. Numerical calculations show how the perturbated velocities and the growth rates vary with respect to different model parameters.