A Mathematical Model for Chemo-mechanically Induced Collective Cell Motility on Planar Elastic Substrates

Abstract

Cells interact with mechanical and chemical environmental cues, such as mechanical cues from other cells and chemical signals from growth factors. The current study aims to develop a mathematical model for combined chemically and mechanically induced collective cell motility on planar substrates. The mechanically induced cell motility is simulated using strain energy density gradients generated in an elastic substrate by cellular traction forces. For chemotaxis, Greens function and Duhamels principle are used to solve the diffusion equation that describes the distribution of a growth factor and to represent chemo-mechanically induced deterministic collective cell motility on planar elastic substrates. Chemically induced motility of cells towards a growth factor source is predicted for different growth factor production and diffusion rates. Chemo-mechanical cues with varying growth factor production and diffusion rates are explored for the motility of four cells and one motile cell in the presence of one stationary cell. The developed model describes the chemo-mechanically induced motility of individual cells on planar substrates. The model provides valuable information for in vivo or in vitro studies due to its suitability for extension to other chemical source shapes, mobilised sources, many sources, and soluble concentration gradients.