Team:Valencia Biocampus/Modeling

Mathematical modeling: Introduction

Mathematical modeling plays a central role in Synthetic Biology, one of its mayor abilities: to predict the behavior of a biological circuit and then is an important bridge between the ideas and concepts, and biological experiments.

The main idea is to interact with the experimental part of the project in two ways. In one hand to characterize the constructed biobricks and identify parameters of the models allowing to a better understanding of the biology behind and on the other hand to direct the way in which experiments are performed to verify a prediction from the modeling.

The first step with a little knowledge was to develop a mathematical model based on a system of differential equations and then implemented using a set of reasonable values of model parameters from literature, to validate the feasibility of the project. Here, one of the main characters of the play came into the "cheaters". We saw the “cheaters” could appear from an original population of “normal” microorganism. This instruct us to perform several experiment to see the metabolic burden that arises when cells carrying a synthetic plasmid want to effectively synthetize the desired protein in comparison with cell that are NOT producing the protein. This could lead to increase the fitness of the “cheaters”.
Then we started the characterization of each part created in the lab, some of the mathematical model parameters were estimated thanks to several experiments we performed within the project (others were derived from literature) and they were used to predict the final behavior of each construction.
Experimental procedures for parameter estimation are discussed and simulation experiments performed, using ODEs with MATLAB and Global optimization algorithm for MINLP's based on Scatter Search (SSm by Process Engineering Group IIM-CSIC). == '''Mathematical modeling: Introduction''' == Here we modeled several of the Bacteria constructions. == '''Mathematical modeling: Introduction''' == For the case of the Heat Shock promoter, we decided to model the static transfer function of the Fluorescent Intensity as a result of the Temperature with the folow equation: