http://en.wikipedia.org/wiki/Chemotaxis
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 : 
.
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 : .
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