Kellermodellen
Kellermodellen, usually referred to in English as the Keller–Segel model, is a mathematical framework used to describe chemotaxis, the directed movement of cells in response to chemical signals. It was introduced by Evelyn Keller and Leo Segel in the 1970s to explain how cells such as Dictyostelium discoideum aggregate in response to chemoattractants. In its classical form the model describes the evolution of a cell density n(x,t) and a chemical concentration c(x,t) on a spatial domain Ω with boundary conditions.
The standard form consists of a coupled system of partial differential equations. A common parabolic form is:
Key features include the possibility of cell aggregation and pattern formation, and, in two dimensions, a threshold
Variants of Kellermodellen incorporate logistic growth, volume-filling effects, multiple chemicals, or more complex kinetics. The model
See also: Keller–Segel equations, chemotaxis, mathematical biology. References: Keller and Segel (1970) JTB; reviews in mathematical