Kinetic models for chemotaxis: hydrodynamic limits and spatio-temporal mechanisms.
We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smooth chemoattractant density, the macroscopic limit is carried out rigorously. It leads to a drift equation with a chemotactic sensitivity depending on the time derivative of the chemoattractant density. As an application it is shown by numerical experiments that the new model can resolve the chemotactic wave paradox. For this purpose, the macroscopic equation is coupled to a simple activation-inhibition model for the chemoattractant which produces the chemoattractant waves typical for the slime mold Dictyostelium discoideum.
Dolak
Y
Y
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040 Linz, Austria. yasmin.dolak@oeaw.ac.at
Schmeiser
C
C
D000818:Animals; D002630:Chemotactic Factors / Q000502:physiology; D002633:Chemotaxis / Q000502:physiology*; D000242:Cyclic AMP / Q000502:physiology; D004023:Dictyostelium / Q000502:physiology; D007700:Kinetics; D008433:Mathematics; D008954:Models, Biological
D002630:Chemotactic Factors; D000242:Cyclic AMP