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"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

Introduction

In order to test and characterize our T-REX device, we developed the following genetic 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 processes involved in gene expression, that is transcription and translation, 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 RNA polymerase - promoter complex and ribosome - RBS sequence complex.

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Reactions

Here below are shown all the reactions occurring the circuit (Fig. 1 and Fig. 2).

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.

Figure 5: Equilibrium Constants

Figure 6: Algebraic Constrains

Simulations

Figure 8: Simulink Model

@@ Line 44: / Line 44: @@
 [[Image:Differentialequations3.jpg|940px||thumb| Figure 3. Differential Equations]]
 [[Image:Transequations2.jpg|center||540px||thumb| Figure 4. Differential Equations]]
-[[Image:constantsvalue.jpg|center|1000px|thumb|Table 2.  ]]
+[[Image:constantsvalue.jpg|center|800px|thumb|Table 2.  ]]
 [[Image:Constants3.jpg|center|500px||thumb|Figure 5: Equilibrium Constants]]
 [[Image:Algebricalconstrain2.jpg|center|650px||thumb|Figure 6: Algebraic Constrains]]

Team:Bologna/Modeling

From 2009.igem.org