# User:Luis De Jesus Martinez

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## Welcome to Luis' page

Visitor, feel free to comment, ask or discuss anything about my work here

## Luis de Jesús Martínez Lomeli

- Undergraduate Mathematics Student at the University of Mexico (UNAM)
- Member of the UNAM-IPN iGEM team
- Member of the iGEM MEXICO UNAM-IPN team 2008

Contact:

luis27 AT ciencias DOT unam DOT mx

luis_de_jesus_27 AT hotmail DOT com

## Motivation

Biomathematics

My main interest in the field of the Synthetic Biology is based on the mathematical modeling of new biological systems that the synthetic biology can proporcionate. I am specially interested in the Stochastic π Calculus (SPi), a new tool which in first instance (the π-Calculus) was thought to resolve concurrent problems in computer science, but in this case the Stochastic π Calculus is implemented modeling biological systems. This formal language has some advantages against the deterministic models based on ODE's or ODP's; the stochastic component give a better grade of accuracy for create different types of models. Andrew Phillips and Luca Cardelli designed a simulation algorithm (Stochastic π-Machine, SPiM) [1] for the stochastic π-calculus based on standard theory of chemical kinetics [Gillespie 1977] where the probability of a reaction is proportional to the rate of the reaction times the number of reactants. In this simulator I have implemented my models and some of my results have give us an importat approach about how we will able to see the results at the lab(if the model was right).

The use of the SPi as a main tool to create my models has motivated myself because this formal language is not so known as the ODE's and I hope that some of my results could lead, at least in the iGEM, a different and very interesting new point of view since the most common ways of modeling.

## Projects

- iGEM México

A very very short history about my job in the team.

Since 2006 our team was focused in the formation of patterns, we are specially interested in the formation of Turing patterns, but the work was very slowly... fortunately the situation changed when new integrants to the team arrived in the middle of 2007, Federico my teammate and me between them. Since there we started to investigated what is the basic way to form patterns with the help of the synthetic biology; and finally after some time in which many many problems emeged each time we was close to solve the problem, Fede showed me a beta version of an oscillator. Then my objective was model it theroretically some teachers recommended me the use of Stochstic Pi Calculus and I started learning it by myself. Just before the Jamboree i got the results from our oscillator... Actually and whith the results from the oscillator model I have started now addressing the problem of the Turing patterns formation.

A link to the theoretically description of the iGEM MEXICO 2007 oscillator.

My work in the team is focus in the modeling of biological processes, for the last jamboree I fulfil my task and i got a model that was done in Stochastic Pi Calculus(SPi)and implemented in the Stochastic Pi Machine(SPiM)

The results of the simulation gave us an idea about how we should expect to see the GFP and RFP be expressed in the lab.

- Turing Patterns

This kind of patterns were first proposed by A. Turing in 1952 in his classical work "The Chemical basis of Morphogenesis". He proposed, in few words, that the emergence of spatial-temporal structures in the early stages of an embrion corresponds to the interaction of two or more chemicals around the mass of cells which spread around the cells. Actually the idea of the existance of those chemicals (morphogens) is not completely accepted by the biologysts despite there are some papers that have demostrated the existance of those chemicals.

The mechanisms that produce the turing patterns are called Reaction-Difussion systems (RDS) and in chemestry there are some phenomena that belong to this type like the Belousov-Zhavotinsky reactions which have been well studied and is well documented how the system produce patterns. Another "simple classical mechanism" is the Activator-Inhibitor, it is based on a system with the interaction of two components, an autocatalizer and an inhibitor interacting with each other. We can think that this system is inside a cell but the signals of the system will afect neighbor cells. And by this patterns are produced.

Since a biological approach, the use of synthetic biology is a powerfool tool that give us a way to create and implement a synthetic system which can be identified with some proposed by Turing and be able to produce the necessary chemicals that will play the role of morphogens. Our first approaches was based on designed a synthetic oscillator which could leed us to obtain oscillatory structures in the population of bacteria but we had problems with the diffusion and degradation of the chemicals. My teammate Federico in his personal page explained some of our problems with the synthetic oscillator.

My personal goal is to model the Turing patterns since different approaches. One of them is use Stochastic Pi Calculus on the Activator-Inhibitor(AI) system and modeling an array of cells with this AI inside but communicating with his neighbors.

In this link, I explained all my work addresing the goal of modeling Turing Patterns with Stochastic Pi Calculus.

Last updated November/24/2008