Team:Bologna/Modeling

From 2009.igem.org

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= Introduction =
= Introduction =
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In order to test and characterize our T-REX device, we developed the following genetic circuit (Fig. 1):
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We developed a mathematical model to simulate the response of the testing circuit (Fig. 1).
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= Mathematical Model =
= Mathematical Model =
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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.<br>
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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.  
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In this context, RNA polymerase and ribosome perform enzymes' role, while gene promoter and RBS sequence act as substrates.
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<br> 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=
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All the biochemical reactions occurring in the testing circuit are listed in Fig. 2, Fig. 3 and Fig. 4
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==Reactions==
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Here below are shown all the reactions occurring the circuit (Fig. 1 and Fig. 2).
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[[Image:Modello1.png|center|940px||thumb|Figure 1: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right) ]]<br>
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[[Image:Reazioniagg.jpg|center|940px|thumb|Figure 2: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right) ]]<br>
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|[[Image:Pag3.jpg|450px|thumb|Figure 2: Other Chemical Reactions]]
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|[[Image:Pag3.jpg|450px|thumb|Figure 3: Other Chemical Reactions]]
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|[[Image:Trans-reactions2.jpg|450px|thumb|Figure 3. Trans-Reactions]]
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|[[Image:Trans-reactions2.jpg|450px|thumb|Figure 4. Trans-Reactions]]
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Symbol definitions are listed in Table 1
Symbol definitions are listed in Table 1
[[Image:Tabella.jpg|center|500px|thumb|Table 1. Legend]]
[[Image:Tabella.jpg|center|500px|thumb|Table 1. Legend]]
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==Differential Equations==
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=Differential Equations=
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Differential equations, that describes the project, are obtained appling the law of mass action at the reactions above.  
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[[Image:Differentialequations3.jpg|940px||thumb| Figure 3. Differential Equations]]
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The differential equations describing the above biochemical reaction are obtained appling the law of mass action.  
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[[Image:Transequations2.jpg|center||540px||thumb| Figure 4. Differential Equations]]
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[[Image:Differentialequations3.jpg|940px|thumb| Figure 5. Differential Equations]]
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[[Image:constantsvalue.jpg|center|1000px|thumb|Table 2.  ]]
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[[Image:Transequations2.jpg|center||540px|thumb| Figure 6. Differential Equations]]
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[[Image:Constants3.jpg|center|500px||thumb|Figure 5: Equilibrium Constants]]
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[[Image:Algebricalconstrain2.jpg|center|650px||thumb|Figure 6: Algebraic Constrains]]
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|[[Image:Constants3.jpg|center|550px|thumb|Figure 7: Equilibrium Constants]]
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|[[Image:Algebricalconstrain2.jpg|center|650px|thumb|Figure 8: Algebraic Constrains]]
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[[Image:constantsvalue.jpg|center|800px|thumb|Table 2. Model parameters; Value of parameter was taken from the literature or obtained from experimantal data]]
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=Simulations=
=Simulations=
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[[Image:ModelSandro.png|center|650px||thumb|Figure 8: Simulink Model]]
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To simulate the model we implemented the equation in Simulink (Figure 3 and Figure 4). 
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[[Image:ModelSandro.png|center|750px|thumb|Figure 9: Simulink Model]]
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==T-REX device==
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In the below figure there's the T-REX device behaviour simulated with the mathematical model. In particular the figure number 10 outlines how the affinity between CIS and TRANS influences the production of GFP.
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[[Image:cistrans.jpg|center|750px|thumb|Figure 10: T-REX Device]] 
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Results of the model simulations are shown in the wet lab parts [https://2009.igem.org/Team:Bologna/Characterization characterization].

Latest revision as of 03:46, 22 October 2009

ProvaBol2.png
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

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 device


In the below figure there's the T-REX device behaviour simulated with the mathematical model. In particular the figure number 10 outlines how the affinity between CIS and TRANS influences the production of GFP.

Figure 10: T-REX Device

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

Retrieved from "http://2009.igem.org/Team:Bologna/Modeling"