Mathematical Biology

MATHEMATICAL BIOLOGY: An overview of Alan Turing model.

-By Gaurish Loya

Mathematical biology is a mathematical approach to explain certain biological phenomena.

This tool has been unfolding from a centenary time and is one of the most reliable techniques adopted by scientists to answer biological analysis based problems.

One such problem was the unique development of a pattern in wild creator, like the stripes in the Tiger and zebrafish, the spots on leopards.

Alan Turing answered it using a mathematical model applying the partial differential equation.

As we all know that Skin toe appearance comes as an effect of melanin pigment production; Turing supposes out that there were two rather one chemical at work, so there is no uniformity of pigments, the two chemicals (morphogenesis) were an "activator" that generates a pigment and an "inhibitor" that hinders its effect.

Turing proposed that the two chemicals spread throughout a system much like gas atoms in a box two (with one crucial difference was, instead of diffusing evenly, the chemicals diffuse at "different rates").

Turing worked out a partial mathematical differential equation that revealed that when the activator and inhibitor diffused at different rates, they can generate an "exquisite variety" of patterns that we see in the animal world. Further, Turing bring-up the concept of "diffusion driven instability", which explains the reason for existence of stripes/ spots on the various animal species.

The beauty of this explanation is that it tells why tigers have unique stripes and how it changes as it grows.

These patterns/stripes are exhibited by non-stop interaction between the activator and inhibitor molecules.

Turing model is so mighty that it works in all animal classes.

References:

Turing research paper: https://pubmed.ncbi.nlm.nih.gov/25750229/

Laboratory confirmation of Turing's work: https://phys.org/news/2012-02-alan-turing-1950s-tiger-stripe.html

Basics of mathematical biology and model: Wikipedia and https://www.smb.org/

Book: J.D Murray for reaction diffusion system.