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Levande cellers matematik

Rybalko, Volodymyr
Start- och slutdatum
Beviljat belopp
2 000 000 kr
Förvaltande organisation
Chalmers University of Technology
Beräkningvetenskap och tillämpad matematik


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.

Populärvetenskaplig beskrivning

All living organisms consist of cells, which are minimal biological units. The aim of this project is to develop and study mathematical models that describe several bio- physical processes occurring on the cellular and multicellular (tissue) level. Namely, the project concerns modeling of (i) cell motility, (ii) tissue spreading and (iii) signal propagation in nerve cells. (i) Cell motility is the ability of a cell to move. A crucial role in the mechanics of cell motility plays cytoskeleton of the cell. It is a complex dynamical network of interlinking protein filaments present in the cytoplasm, and various components of cy- toskeleton are involved in cell motility. It is proposed to study a minimal 2D model, describing cell motion due to contraction of myosin (a motor protein). This myosin contraction mechanism dominates at the onset of motion. In mathematical terms, we will study a free boundary problem when the shape of the cell is one of the unknowns, modeling contraction driven cell motility. Another problem is to develop a mathemati- cal model of cell-substrate interaction. (ii) Tissue spreading is an example of collective rather than individual cell motion. We will study a recently introduced free boundary problem modeling spreading of epithelial tissue, and establish bifurcation of flat front solutions to finger like patterns. Various properties of these new solutions as, e.g., linear and nonlinear stability, will be investigated. Besides of purely mathematical novelty, the aforementioned problems can be applied for modeling of, e.g., wound healing and tumor growth. (iii) Signal propagation in nerve cells is typically modelled by an ordinary differen- tial equation, called cable equation. However, in the case of a bundle of axons this cable equation is no longer applicable since, as nowadays commonly accepted, ephaptic in- teractions between axons play an important role. We will obtain an effective continuous model out of complex 3D problem describing a bundle of many axons. This reduction will facilitate numerical simulations as well as qualitative analytical study.