Team:Aberdeen Scotland/Modeling

From 2010.igem.org

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<h3><a href="https://2010.igem.org/Team:Aberdeen_Scotland/Fixed_Points"><font color="blue">Fixed Points</font></a></h3>
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<p>We used fixed point analysis to predict the equilibrium state(s) of the ayeSwitch system for different parameters. Three or more fixed points will give us bistability and the possibility of switching.  </p>
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<p>We used fixed point analysis to predict the equilibrium state(s) of the ayeSwitch system for different parameters. Three or more equilibrium points will give us bistability and the possibility of switching.  </p>
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<h3><a href="https://2010.igem.org/Team:Aberdeen_Scotland/Bifurcation"><font color="blue">Bifurcation</font></a></h3>
<h3><a href="https://2010.igem.org/Team:Aberdeen_Scotland/Bifurcation"><font color="blue">Bifurcation</font></a></h3>

Revision as of 17:45, 24 October 2010

University of Aberdeen - ayeSwitch - iGEM 2010

Introduction to the Modelling of the ayeSwitch

This page is an introduction to the different equations and techniques that we used to design and predict the behaviour of the ayeSwitch.


Equations

In this section we describe the process of developing a basic mathematical model for the ayeSwitch based on the promotion and inhibition behaviour necessary for mutual repression. We developed a set of four differential equations, one to model each of the two mRNAs and two proteins that are the active components of our system.


Fixed Points

We used fixed point analysis to predict the equilibrium state(s) of the ayeSwitch system for different parameters. Three or more equilibrium points will give us bistability and the possibility of switching.


Bifurcation

Bifurcation analysis allows us to track the number and relative position of the equilibrium points of our system for different parameters. Parameters below a certain value may only give us one fixed point, but increasing the value of the parameter could give us a bifurcation point and then increasing the value more we can get three fixed points. The further apart the fixed points are from each other, the more difficult it will be to switch between them.

Stochastic Model

Stability

Parameter Variations

Probability

Directed Evolution