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An agent based model for plasto-elastic mechanical interactions between cells, basement membrane and extracellular matrix

Authors
Publisher
American Institute of Mathematical Sciences (AIMS)
Publication Date
Disciplines
  • Biology
  • Mathematics
  • Medicine

Abstract

The basement membrane (BM) and extracellular matrix (ECM) play critical roles in developmental and cancer biology, and have been of increasing interest in the mathematical biology community. In this paper, we introduce a model of mechanical cell-BM-ECM interactions that extends current elastic and viscoelastic models, and connects to recent agent-based cell models. We model the BM as a linked series of Hookean springs, each with time-varying length, thickness, and spring constant. Each BM spring node exchanges adhesive and repulsive forces with the cell agents using potential functions. We model elastic BM-ECM interactions by introducing additional ECM springs with analogous and time-dependent length, equilibrium length, and spring constant, directed normal to the basement membrane. We introduce a new model of plastic BM and ECM reorganization in response to prolonged strains. To better account for the molecular-scale impact of plastic reorganization, we introduce new constitutive relations between the spring constants, equilibrium lengths, and thicknesses. We find that the balance of BM and ECM spring constants can radically affect the spacing of nodes along cell boundaries, and hence resulting in a variable BM thickness. Further, over longer time periods, BM and ECM plasticity can help relieve strains arising from uneven BM node spacing. We also find that plasto-viscoelastic cell shape response is critical to relieving uneven stresses in the BM. Our results highlight the importance of rigorous modeling of cell-BM-ECM mechanical interactions, and are an important step towards quantitative, mechanistic modeling of progression from in situ to invasive carcinoma. The results also have implications for other biomedical applications where time-varying membrane properties couple with significant deformations, such as aneurysms

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