Team:Mexico-UNAM-CINVESTAV/Human Practices/Collaboration

From 2010.igem.org

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== [http://2010.igem.org/Team:UNAM-Genomics_Mexico/Collaboration UNAM Genomics Mexico] ==
== [http://2010.igem.org/Team:UNAM-Genomics_Mexico/Collaboration UNAM Genomics Mexico] ==
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Collaboration
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===Collaboration===
The system our countrymen asked us to model was a three element positive feedback loop. They expected us to find an oscillatory  behaviour in time between the concentration of the three substances.  
The system our countrymen asked us to model was a three element positive feedback loop. They expected us to find an oscillatory  behaviour in time between the concentration of the three substances.  
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img(ciclo d genomicos)
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[[Image:Cliclo_Genomicas.png|center]]
*Cycle
*Cycle
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*Kind of Repressilator system
*Kind of Repressilator system
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Linear model
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===Linear model===
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In these images we observe that the system only posses an stable equilibrium point.
In these images we observe that the system only posses an stable equilibrium point.
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Non Linear Model
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===Non Linear Model===
By making the model a little more realistic we added another form of dependance of the substance concentration change in time. We also added a saturation term and a degradation term.
By making the model a little more realistic we added another form of dependance of the substance concentration change in time. We also added a saturation term and a degradation term.
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|  [[Image:Figura1_nolineal.jpg|425px|none|thumb|123]]  ||  [[Image:Figura2_nolineal.jpg|425px|none|thumb|123]]  
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|  [[Image:Figura1_nolineal.jpg|425px|none|thumb| k1=k2=k3=0.5;  M1=M2=M3=2;  σ=-0.1045]]  ||  [[Image:Figura2_nolineal.jpg|425px|none|thumb| k1=k2=k3=0.5;  M1=M2=M3=2;  σ=-0.1045]]  
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|  [[Image:Figura3_nolineal.jpg|425px|none|thumb|123]]    ||     
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|  [[Image:Figura3_nolineal.jpg|425px|none|thumb| k1=k2=k3=0.5;  M1=M2=M3=2;  σ=-0.1045]]    ||     
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Extension
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===Extension===
With the two approaches above we did not obtained an oscillatory behavior as expected. Nevertheless, an idea emerged from the team. There could be an use for the dynamics we encountered. The idea was to 'reset' the system every certain amount of time. This 'pacemaker' system looks like this:
With the two approaches above we did not obtained an oscillatory behavior as expected. Nevertheless, an idea emerged from the team. There could be an use for the dynamics we encountered. The idea was to 'reset' the system every certain amount of time. This 'pacemaker' system looks like this:

Revision as of 05:23, 27 October 2010


This year we think was the most collaborative one. there were plenty of surveys, meetings and intense information exchange. Next we describe all the

Our team participated in different surveys:

  • Warsaw Team
  • METU_Turkey_Software Team
  • University of Edimburg iGEM Team

We also made a contribution to the UNAM Genomics Team modeling, by proposing a mathematical model of their three component positive feedback network.

Contents

UNAM Genomics Mexico

Collaboration

The system our countrymen asked us to model was a three element positive feedback loop. They expected us to find an oscillatory behaviour in time between the concentration of the three substances.

Cliclo Genomicas.png
  • Cycle
  • Positive Feedback
  • Kind of Repressilator system

Linear model

We proposed a linear model thinking in a first approach to solve the problem. For each of the rate of change of the concentration in time there is a dependance with the substance itself and with one of the other substances. These dependances are cyclic.

Sistema LinealT1.png

Sistema Lineal1.png

The resulting dynamics of these equations are represented in the following images.


y1(0)=1.5, y2(0)=1, y3(0)=1
y1(0)=0, y2(0)=3, y3(0)=10
y1(0)=1, y2(0)=10, y3(0)=1
y1(0)=2.5, y2(0)=0.1, y3(0)=0.5

Sistema LinealT2.png

Sistema Lineal2.png


The resulting dynamics of these equations are represented in the following images.


r1=1 r2=1 z=4; y1 = y2 = y3 = 1; d1=3, d2=19, d3=17; u1(t)=39, u2(t)=-1, u3(t)=-1; y1(0)=0.1, y2(0)=0.2, y3(0)=0.8
r1=1, r2=1, z=2; y1 = y2 = y3 = 1; d1=3, d2=4, d3=2; u1(t)=9, u2(t)=-1, u3(t)=-1; y1(0)=0.1, y2(0)=0.2, y3(0)=0.8
r1=1 r2=1 z=2; y1 = y2 = y3 = 1; d1=3, d2=7, d3=5; u1(t)=15, u2(t)=-1, u3(t)=-1; y1(0)=0.1, y2(0)=0.2, y3(0)=0.8

In these images we observe that the system only posses an stable equilibrium point.

Non Linear Model

By making the model a little more realistic we added another form of dependance of the substance concentration change in time. We also added a saturation term and a degradation term.

Sistema No LinealT.png


center‎


Non Linear Simulation


In the following images we appreciate that there is a bifurcation point such that we obtain two different dynamics, one in which the system saturates and other in which the substances concentration reaches the zero value.

k1=k2=k3=0.5; M1=M2=M3=2; σ=-0.1045
k1=k2=k3=0.5; M1=M2=M3=2; σ=-0.1045
k1=k2=k3=0.5; M1=M2=M3=2; σ=-0.1045


Extension

With the two approaches above we did not obtained an oscillatory behavior as expected. Nevertheless, an idea emerged from the team. There could be an use for the dynamics we encountered. The idea was to 'reset' the system every certain amount of time. This 'pacemaker' system looks like this:

Pacemaker

Pacemaker1.jpg


We want to thank all the team members that answered our own survey which was about intellectual property.

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