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

Transcription and translation processes are considered similar to a second order kinetics like an enzymatic reaction: RNA polymerase and ribosome perform enzymes' role, while gene promoter and RBS sequence act as substrates. The binding 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 the ribosome-RBS complex.

Reactions

All the biochemical reactions occurring in the testing circuit are listed in Fig. 2, Fig. 3 and Fig. 4

Figure 2: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right)

Figure 3: Other Chemical Reactions

Figure 4. Trans-Reactions

Symbol definitions are listed in Table 1

Table 1. Legend

Differential Equations

The differential equations describing the above biochemical reaction are obtained appling the law of mass action.

Figure 5. Differential Equations

Figure 6. Differential Equations

Figure 7: Equilibrium Constants

Figure 8: Algebraic Constrains

Table 2. Model parameters; Value of parameter was taken from the literature or obtained from experimantal data

Simulations

To simulate the model we implemented the equation in Simulink (Figure 3 and Figure 4).

Figure 9: Simulink Model

T-REX system

In the graph above is shown the T-REX system behaviour predicted by the mathematical model. In particular figure 10 shows how the affinity influence the production of GFP.

Results of the other model simulations are shown in the wet lab parts characterization.

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