Mechanical Cell Interactions on Curved Interfaces

• DOI: 10.1007/s11538-024-01406-w
• Publication Date: 2025-01-07T13:46:13Z
• Authors: Pascal R. Buenzli; Shahak Kuba; Ryan J. Murphy; Matthew J. Simpson
• Keywords: Cellular Automata and Lattice Gases (nlin.CG); FOS: Biological sciences; Cell Behavior (q-bio.CB); Quantitative Biology - Cell Behavior; FOS: Physical sciences; Quantitative Biology - Tissues and Organs; Original Article; Tissues and Organs (q-bio.TO); Nonlinear Sciences - Cellular Automata and Lattice Gases

Abstract We propose a simple mathematical model to describe the mechanical relaxation of cells within curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This generalises previous one-dimensional models flat epithelia investigate influence curvature for relaxation. represent mechanics cell body either straight springs, or springs that follow curve’s shape. To understand collective dynamics cells, we devise appropriate continuum limit which number and length substrate are constant but tends infinity. In this limit, density is governed diffusion equation arc coordinates, where may be linear nonlinear depending on choice spring restoring force law. Our results have important implications about modelling geometries: (i) can lead different when there finite they both converge quadratically equation; (ii) does not affect nor their tangential stress; (iii) cell’s normal stress depends due surface tension induced forces. Normal enables sense at scales much larger than body, could induce dependences experiments.