Team:Bologna/Modeling

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HOME TEAM PROJECT SOFTWARE MODELING WET LAB PARTS HUMAN PRACTICE JUDGING CRITERIA


"The theory is when you know everything and nothing works. Practice is when everything works and nobody knows why. We have put together the theory and practice: there is nothing that works ... and nobody knows why."

A. Einstein


Contents

Introduction

We developed a mathematical model to simulate the response of the testing circuit (Fig. 1):

Figure 1 - Genetic Circuit to test CIS and TRANS' mRNA functionality



Mathematical Model


The mathematical model is based on the law of mass action, and the transcription and translation process, are considered similar to enzymathic reactions.
In this context, RNA polymerase and ribosome perform enzymes' role, while gene promoter and RBS sequence act as substrates.
The interaction between enzyme and substrate leads to the formation of a complex, yielding to the final product: mRNA for the polymerase-promoter complex and protein for ribosome-RBS complex.


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Reactions

Here below (Fig. 1, Fig. 2 and Fig. 2) are listed all the reactions included in the model of the testing circuit.

Figure 1: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right)

Figure 2: Other Chemical Reactions
Figure 3. Trans-Reactions

Symbol definitions are listed in Table 1

Table 1. Legend

Differential Equations

Differential equations, that describes the project, are obtained appling the law of mass action at the reactions above.

Figure 3. Differential Equations
Figure 4. Differential Equations
Table 2. Model constants; some of them was taken from the literature other obtained from experimantal data
Figure 5: Equilibrium Constants
Figure 6: Algebraic Constrains

Simulations

We realized the below Simulink model with the differential equations in figure 3 and 4.

Figure 8: Simulink Model