Levande cellers matematik

Research Project, 2022 – 2024

The principal goal of this project is to study such functional activities of living cells as individual and collective cell motion, and signal propagation in nerve cells via the investigation of mathematical models. It is expected that this study will result in development of new analytical techniques which could be applied for modeling of such complex processes as wound healing, tumor growth, and the reponse of biological cells on electric stimulation. Based on the previously obtained results on existence and properties of traveling wave solutions to the 2D free-boundary problem modeling contraction driven cell motility, the question of stability will be addressed in the nonlinear setting. This stability analysis is important in predicting long time behavior of individual cells. We will study a free boundary problem modeling spreading of epithelial tissue, and establish bifurcation of flat front solutions to finger like patterns. Linear and nonlinear stability of these solutions will be investigated. To model cell-substrate interaction and durotaxis phenomenon recently introduced stochastic discrete models of focal adhesion will be studied in the limit of large adhesion cites. It is expected to obtain effective continuous models that are more amenable for numerical simulations as well as qualitative analytical study. Mathematical homogenization techniques will also be applied to model ephaptic interactions in nerve cells.