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Mathematical modelling page

Mathematical modelling plays nowadays a central role in Synthetic Biology, due to its ability to serve as a crucial link between the concept and realization of a biological circuit. According to this, after a brief overview about the advantages that modelling engineered circuits can bring, we deeply analyze the system of equation formulas, underlining the role and the function of the parameters involved.
Then, experimental procedures for parameters estimation are presented and, finally, different types of circuit are discussed and their simulations performed, using ODE's with MATLAB and explainig the difference between a closed-loop model and an open one.

The importance of the mathematical model

Several motivations are strong enough to accept the idea that mathematical model is very useful in this study.

• Firstly in the initial steps of the project, beacuse of its capability to predict the kinetics of the enzymes (aiiA, Luxi) and HSL involved in our gene network, well realizing the a-priori identification in silico in order to understand if the complex circuit's structure and functioning could be achievable.

• Secondly, for the parametric identification. Using the lsqnonlin function of MATLAB it was possible to get all the parameters involved in the model and consequently to know, for example, the shape of the activation curve of the promoters (Plux, Ptet), according to the a-posteriori identification.

• Thirdly, the reproducibility. Studing and characterizing simple subparts can allow us not only to predict the behavior of the final circuit, but also it can be useful in other studies, facing with the same basic modules.