Workshop on Biomechanics and Chemotaxis, Mon, 10 Dec, 2007
Speaker: Dietmar Ölz
Abstract
I deal with the lamellipodia of living cells. They are made up of a mesh-work of actin filaments that grow at the front and depolymerise at the rear, in a tread-milling mode. A model is developed to describe the structure and the turnover of this network and to relate it to the amoeboid movement of the cell.
The model will be introduced in a step-by-step way, first referring to a very simple model of gradient flow type, then presenting the curve-straightening flow of planar open curves as an example of a gradient flow describing the evolution of elastic rods.
The model for the Actin cytoskeleton finally will be developed as a far reaching extension of this model.
Most notably I will present the modelling of the life-cycle of chemical bonds with transport-decay model, so called "age-structured" models and the passage to a zero-lifetime limit of these chemical bonds where the aforementioned gradient flow model is obtained.
The steepest descent time step approximation scheme will be formulated and used to construct solutions analytically and present a typical numerical solution based on this scheme.
The model thus obtained already allows to simulate pushing experiments of cells. We present typical numerical solutions that illustrate the change in shape and position of the cell as a reaction to the pushing force.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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