Mathematical Models
Several mathematical models of chemotaxis were developed depending on the type of
- migration (e.g. basic differences of bacterial swimming, movement of unicellular eukaryotes with cilia/flagellum and ameboid migration);
- physico-chemical characteristics of the chemicals (e.g. diffusion) working as ligands;
- biological characteristics of the ligands (attractant, neutral and repellent molecules;
- assay systems applied to evaluate chemotaxis (see incubation times, development and stability of concentration gradients);
- other environmental effects possessing direct or indirect influence on the migration (lighting, temperature, magnetic fields etc.)
Although interactions of the factors listed above make the behavior of the solutions of mathematical models of chemotaxis rather complex, it is possible to describe the basic phenomenon of chemotaxis-driven motion in a straightforward way. Indeed, let us denote with the spatially non-uniform concentration of the chemo-attractant and with its gradient. Then the chemotactic cellular flow (also called current) that is generated by the chemotaxis is linked to the above gradient by the law:, where is the spatial density of the cells and is the so-called ’Chemotactic coefficient’. However, note that in many cases is not constant: it is, instead, a decreasing function of the concentration of the chemo-attractant : .
Read more about this topic: Chemotaxis
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