LuisM Turing Patterns with Stochastic π Calculus

A global Context from the iGEM Mexico team and Turing Patterns

One of the most important problems in developmental biology is the understanding of how structures emerge in living systems. Several mechanisms have been proposed, depending on the observed patterns. The so called Turing patterns are based on the interaction of two effects: diffusion of some chemicals, called morphogenes, and the chemical interaction between them. It has been highly controversial whether some patterns observed in several organisms are of this type. In particular, although some systems have been identified to be of activator-inhibitor type (the most popular Turing system proposed by Gierer and Meindhart), it is still questioned if pattern formation and more generally, the appearance of functional structures can be understood by means of Turing patterns or more broadly, reaction-diffusion mechanisms.

Talking about Patterns

After the last jamboree(Nov, 2007) some members of team started a quest with the objetive of generate turing patterns at the lab and since a theoretical way. A teammate Juan A. investigated the theoretical part to produce Turing, and in a nice afternoon of january he explained to Federico and me his results:

There are many ways to produce the patterns, but essentialy we need and autocatalizer and an inhibitor working together.

The catalizer does a positive feedback loop autoinducing itself and inducing the production of the inhibitor, wich will repress the catalizer untill the inhibitor signals degrade.

We need too that the signals of both get outside of the system and hose interact with the neighbors.

The model with Stochastic Pi Calculus