Random walk and directed movement: Comparison between inert particles and self-organized molecular machines

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Abstract
The differences and similarities between the behavior of inert particles exposed to force fields and of biological cells exposed to guiding fields are shown. Cell migration can be characterized by two independent variables: the speed v which is controlled by a steering device and the migration angle, cphi, which is controlled by an automatic pilot. Each variable is described by a stochastic differential equation. The cellular behavior can be obtained by solving the corresponding Fokker-Planck equations. The predicted dose-response curve (the dose is the guiding field as electric field or concentration gradient, the response is the polar order parameter) fits quite well the experimental data obtained for different cell types. The predicted field dependence of the first eigenvalue is in accordance with the measured ones. The limitation of the model is discussed.