Viscoelastic gel-strip model for the simulation of migrating cells

Migrating tumor cells can exhibit both mesenchymal- and amoeboid-type behaviors. Recent studies have shown that both cellular and extracellular structural and mechanical variables control the transition of tumor cells from one mode to the other and provide them with morphological plasticity. The mesenchymal-mode migration is characterized by strong adhesion and proteolytic machinery to navigate through complex extracellular matrices. The amoeboid-mode migration is characterized by little or no adhesion and strong actomyosin contraction to squeeze through the matrices. While adhesion dependent migration has been computationally and experimentally studied in both 2D and 3D environments, quantitative models of amoeboid motion in native environments are lacking. In order to address this major gap in our understanding and to probe the mesenchymal to amoeboid transitions quantitatively and comprehensively, we have developed an axisymmetric viscoelastic gel-strip model of a single cell to investigate a cell migrating in native-like environments. In this model, cell migration and morphology are governed by internal stresses as well as external forces. The internal stresses are controlled by F-actin density distribution, protrusion strength, and contraction strength. The external forces are controlled by adhesion strength and steric resistance from the extracellular matrix. Our model predicts that the transition of the cell migration mode from mesenchymal- to amoeboid-type, and vice versa, is closely related to the loss of adhesion as well as increased contraction strength of the cells. Our results indicate that amoeboid migration is more suited for low-resistance environment while mesenchymal migration is preferred in high-resistance environment, which would explain the versatile behaviors of tumor cells in complex environments.