Abstract
A non-conservative Lagrangian is used to derive a dynamic beam equation in a moving reference frame to describe the motility of Listeria monocytogenes. Bending, stretching, and frictional forces are incorporated to describe the kinematics of the moving actin filament network. Adapted boundary conditions are able to simulate the influence of the bacterium on the tail as well as the polymerization process. A semi-implicit numerical operator splitting method has been developed to solve the nonlinear equations in the plane. The model has been validated on existing force-velocity relationships and measurements for realistic physical model parameters. In particular, the fictional losses due to substrate-tail adhesion have been analyzed by a linear and a nonlinear approach. Numerical simulations are performed for varying polymerization speeds, friction, and bending parameters. Complex trajectories of the actin tail are found by adjusting the bending properties of the attaching actin filament cluster. The results reveal that the present model is able to predict and reproduce actin-based motions observed in experiments.
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