From 2009.igem.org

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

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