# Team:Bologna/Modeling

(Difference between revisions)
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- !align="center"|[[Team:Bologna|HOME]] + "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." - !align="center"|[[Team:Bologna/Project|PROJECT]] + - !align="center"|[[Team:Bologna/Team|TEAM]] +

- !align="center"|[[Team:Bologna/Software|SOFTWARE]] + A. Einstein - !align="center"|[[Team:Bologna/Modeling|MODELING]] +
- !align="center"|[[Team:Bologna/Wetlab|WET LAB]] +

- !align="center"|[[Team:Bologna/Notebook|LAB-BOOK]] + - !align="center"|[[Team:Bologna/Parts|SUBMITTED PARTS]] + = Introduction = - !align="center"|[[Team:Bologna/Biosafety|BIOSAFETY AND PROTOCOLS]] + + We developed a mathematical model to simulate the response of the testing circuit  (Fig. 1). + +

+ [[Image:circuit2OK.jpg|center|900px|thumb|
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 +
+ [[Image:Reazioniagg.jpg|center|940px|thumb|Figure 2: GFP transcription and GFP translation (left); LacI transcription, LacI translation and LacI dimerization (right) ]]
+ {|align="center" + |[[Image:Pag3.jpg|450px|thumb|Figure 3: Other Chemical Reactions]] + |[[Image:Trans-reactions2.jpg|450px|thumb|Figure 4. Trans-Reactions]] |} |} + Symbol definitions are listed in Table 1 + [[Image:Tabella.jpg|center|500px|thumb|Table 1. Legend]] +
+ =Differential Equations= + + The differential equations describing the above biochemical reaction are obtained appling the law of mass action. + [[Image:Differentialequations3.jpg|940px|thumb| Figure 5. Differential Equations]] + [[Image:Transequations2.jpg|center||540px|thumb| Figure 6. Differential Equations]] +
+ {|align="center" + |[[Image:Constants3.jpg|center|550px|thumb|Figure 7: Equilibrium Constants]] + |[[Image:Algebricalconstrain2.jpg|center|650px|thumb|Figure 8: Algebraic Constrains]] + |} +
+ [[Image:constantsvalue.jpg|center|800px|thumb|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). + [[Image:ModelSandro.png|center|750px|thumb|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. + [[Image:cistrans.jpg|center|750px|thumb|Figure 10: T-REX Device]] + + 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

"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 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).

## 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.