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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

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 of testing circuit, are considered similar to a second oder 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.

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Reactions

All the reactions occurring in the testing circuit are listed in Fig. 1, Fig. 2 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

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

Figure 3. Differential Equations

Figure 4. Differential Equations

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

Figure 5: Equilibrium Constants

Figure 6: Algebraic Constrains

Simulations

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

Figure 8: Simulink Model

@@ Line 21: / Line 21: @@
 = Mathematical Model =
 <br><font size="4">
-The mathematical model is based on the law of mass action, and the transcription and translation process, are considered similar to enzymathic reactions.<br>
+Transcription and translation processes  of testing circuit, are considered similar to a second oder 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.
-In this context, RNA polymerase and ribosome perform enzymes' role, while gene promoter and RBS sequence act as substrates.
-<br> 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.
 </font>
 <br><br>
@@ Line 30: / Line 28: @@
 <br><br><br>
 ==Reactions==
-Here below (Fig. 1, Fig. 2 and Fig. 2) are listed all the reactions included in the model of  the testing circuit.
+All the reactions occurring in the testing circuit are listed in Fig. 1, Fig. 2 and Fig. 2
 <br>
 [[Image:Modello1.png|center|940px|thumb|Figure 1: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right) ]]<br>
@@ Line 41: / Line 39: @@
 ==Differential Equations==
-Differential equations, that describes the project, are obtained appling the law of mass action at the reactions above.
+The differential equations describing the above biochemical reaction are obtained appling the law of mass action.
 [[Image:Differentialequations3.jpg|940px|thumb| Figure 3. Differential Equations]]
 [[Image:Transequations2.jpg|center||540px|thumb| Figure 4. Differential Equations]]
-[[Image:constantsvalue.jpg|center|800px|thumb|Table 2. Model constants; some of them was taken from the literature other obtained from experimantal data]]
+[[Image:constantsvalue.jpg|center|800px|thumb|Table 2. Model parameters; Value of parameter was taken from the literature or obtained from experimantal data]]
 {|align="center"
 |[[Image:Constants3.jpg|center|550px|thumb|Figure 5: Equilibrium Constants]]
@@ Line 51: / Line 49: @@
 =Simulations=
-We realized the below Simulink model with the differential equations in figure 3 and 4.
+To simulate the model we implemented the equation in Simulink (Figure 3 and Figure 4).
 [[Image:ModelSandro.png|center|750px|thumb|Figure 8: Simulink Model]]

Team:Bologna/Modeling

From 2009.igem.org