Modeling Nonlinear Dynamics of Cells in Confinement

During physiological processes like tissue development and metastasis, migrating cells navigate various constrictions that affect their behaviors. Recent work on the confined migration of cancerous MDA-MB-231 cells in two-state adhesive micropatterns suggests their motion can be described by a limit cycle, i.e., persistently hopping from side to side, while they remain stationary on average in rectangular confinements [1]. Moreover, cells in two-state geometry have a nonlinear acceleration-velocity relationship. By contrast, healthy MCF10A cells plated on two-state micropattern can be described as bistable, with only noise-induced hopping between the two states [1]. Can we explain these different behaviors with a single model of cell-extracellular matrix interaction? What cell properties determine whether cells limit-cycle or are bistable? To investigate these questions, we build a computational model within the phase field framework. Our model incorporates a simple cell-micropattern coupling where cells decrease their polarity when they leave the micropattern. We also include stochastic dynamics of cell protrusions. We can recapitulate, depending on cell parameters and the geometry of the micropattern, limit cycle, bistable, or simple linear behavior. Our model predicts that larger cells and cells with lower tension are more likely to develop a limit cycle, while smaller and stiffer cells are more likely to be bistable. Other key factors affecting cell migration are the time between protrusions and the level of noise in protrusion amplitude.

[1] David Bruckner, et. al, Nature Physics, 15, 595-601 (2019)