Magda Stolarska, University of St. Thomas
Authors: Magdalena Stolarska, Aravind Rammohan
2022 AWM Research Symposium
Recent advances in Cell- and Tissue-Scale Mathematical Modeling of Cancer

Cell motility and spreading require large local deformations and stretch of the lipid bilayer that makes up the cell membrane. Membrane dynamics, namely unfolding of surface projections and exocytosis from intracellular reservoirs to the lipid bilayer, are necessary for these large changes in cell shape (Figard & Sokac, BioArchitecture, 2014). In addition, tension in the actin cortex underlying the lipid bilayer also produces cellular shape changes that aid in motility. This talk will primarily focus on membrane dynamics required for cell spreading. It has been well established that most cell types spread more on stiffer surfaces. Our work aims to show that membrane tension and focal adhesion modulated membrane unfolding and exocytosis are required to achieve the cell spread areas observed experimentally. To do this, we model the cell as viscous material surrounded by a viscoelastic, actively deforming membrane. The model also incorporates stress-dependent focal adhesion dynamics and their effect on actin polymerization and myosin contractility. Finite element analysis shows that membrane dynamics plays a critical role in modulating protrusive activity and actin retrograde flow, the balance of which controls the extent of cell spreading (Gianonne et al. Cell, 2004). We will also discuss preliminary work on a mathematical model that explores how active deformations of the actin cortex elicit tension gradients in the lipid bilayer. Numerical simulations show that such tension gradients lead to movement in attachment-free cells suspended in a viscous fluid. Together, these mathematical models confirm that the cell membrane is a control mechanism for cellular motility, which has large implications in various aspects of cancer, including metastasis, angiogenesis, and invasion.

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