Model hierarchies for cell aggregation by chemotaxis. (English) Zbl 1094.92009
Summary: We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finite-time blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.
MSC:
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35K57 | Reaction-diffusion equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
Keywords:
chemotaxis; Keller-Segel model; moment expansion; macroscopic limit; Fokker-Planck equationReferences:
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