Using interconnected viscoelastic elements to investigate forces and the role of cell properties during cell migration

• Interconnected viscoelastic elements model a 3D migrating cell • Focal adhesions arise in a lamellipodia-like protrusion and connect with a substrate • A mathematical and computational model of cell migration is experimentally validated • A sensitivity analysis of elastic and other factors affecting cell migration is done We build a model of a general three-dimensional cell migrating across a flat substrate using an interconnected network of viscoelastic elements (damped springs). While the end goal is to use the model to investigate forces in migrating biological cells, the goal here is to demonstrate the model’s validity, practical feasibility, and capability. We first show qualitative agreement with experiment including reasonable shape and speed, higher protrusive forces correlating with higher focal adhesion forces, and higher adhesive forces near the cell’s front and back. We then show the model can produce estimates of deformation and stresses in migrating cells. We lastly perform a sensitivity analysis demonstrating that 1) cell length is increased by increasing driving force and focal adhesion attachment strength and by decreasing reference volume, 2) cell speed is increased by decreasing cell membrane-substrate interaction and increasing driving force, and 3) focal adhesion forces are increased by decreasing membrane elasticity and number of focal adhesions. Our results suggest that future model calibration will yield useful insights into how cell forces affect migration.