Editing Chemotaxis (section)

==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|amoeboid]] 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 <math> \varphi</math> the spatially non-uniform concentration of the chemo-attractant and <math>\nabla \varphi</math> as its gradient. Then the chemotactic cellular flow (also called current) <math> {\bf J} </math> that is generated by the chemotaxis is linked to the above gradient by the law:<ref name=":2">{{Cite book | vauthors = Murray JD |url=https://www.ucl.ac.uk/~rmjbale/3307/Reading_Chemotaxis1.pdf |archive-url=https://web.archive.org/web/20220506024008/https://www.ucl.ac.uk/~rmjbale/3307/Reading_Chemotaxis1.pdf |archive-date=2022-05-06 |url-status=live |title=Mathematical Biology I: An Introduction |publisher=Springer |year=2002 |isbn=978-0-387-95223-9 |edition=3rd |series=Interdisciplinary Applied Mathematics |volume=17 |location=New York |pages=395–417 |language= |doi=10.1007/b98868}}</ref>{{Equation box 1|cellpadding|border|indent=:|equation=<math> {\bf J} = C \chi(\varphi) \nabla\varphi </math>|border colour=#0073CF|background colour=#F5FFFA}}where <math> C </math> is the spatial density of the cells and <math> \chi </math> is the so-called 'Chemotactic coefficient' - <math>\chi</math> is often not constant, but a decreasing function of the chemo-attractant. For some quantity <math>\rho</math> that is subject to total flux <math>{\bf J}</math> and generation/destruction term <math>S</math>, it is possible to formulate a [[continuity equation]]:

:<math> {\partial \rho\over{\partial t}} + \nabla \cdot {\bf J} = S </math>

where <math>\nabla \cdot ()</math> is the [[divergence]]. This general equation applies to both the cell density and the chemo-attractant. Therefore, incorporating a diffusion flux into the total flux term, the interactions between these quantities are governed by a set of coupled [[Reaction–diffusion system|reaction-diffusion]] [[partial differential equation]]s describing the change in <math>C</math> and <math>\varphi</math>:<ref name=":2" />{{Equation box 1|cellpadding|border|indent=:|equation=<math> \begin{aligned}
{\partial C\over{\partial t}} &= f(C) + \nabla\cdot \left[D_{C}\nabla C - C\chi(\varphi)\nabla\varphi \right ] \\
{\partial \varphi\over{\partial t}} &= g(\varphi,C) + \nabla \cdot (D_{\varphi}\nabla\varphi)
\end{aligned} </math>|border colour=#0073CF|background colour=#F5FFFA}}where <math>f(C)</math> describes the growth in cell density, <math>g(\varphi,C)</math> is the kinetics/source term for the chemo-attractant, and the diffusion coefficients for cell density and the chemo-attractant are respectively <math>D_{C}</math> and <math>D_{\varphi}</math>.

[[Spatial ecology]] of soil microorganisms is a function of their chemotactic sensitivities towards substrate and fellow organisms.<ref name="Gharasoo2014">{{cite journal|doi=10.1016/j.soilbio.2013.11.019|title=How the chemotactic characteristics of bacteria can determine their population patterns|journal=Soil Biology and Biochemistry |volume=69 |pages=346–358 |year=2014 | vauthors = Gharasoo M, Centler F, Fetzer I, Thullner M |bibcode=2014SBiBi..69..346G }}</ref>{{primary source inline|date=March 2017}}{{primary source inline|date=March 2017}} The chemotactic behavior of the bacteria was proven to lead to non-trivial population patterns even in the absence of environmental heterogeneities. The presence of structural pore scale heterogeneities has an extra impact on the emerging bacterial patterns.