Team:ETH Zurich/modeling/int

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== Characterization ==
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== Characterization: K<sub>SABxb1</sub>==
=== Data ===
=== Data ===
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The parameter fitting is based on [[File:ETH Zurich Bonnet Amplifying Genetic Logic Gates 2013.pdf Bonnet's paper]. Their experimental setup is different from ours. However, they experimentally retrieve a transfer function between aTc and Bxb1 switching rate. Here is the figure of interest in our case.
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[[File:ETH Zurich Bonnet S4.jpg|center|800px|thumb|Transfer function from aTc to Bxb1. The experimental data corresponds to the points. They fitted this data with their own model. Supplementary figure S4 of Bonnet's paper ''Amplifying Genetic Logic Gates'']]
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To use their experimental data, we have to model their induction mechanism using aTc. We use a simplify version of it proposed by the [https://2013.igem.org/Team:UCSF/Modeling 2013 iGEM team UCSF]. They modeled the induction with aTc as a leaky Hill function. We then obtain the following set of differential equations:
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\begin{align*}
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\frac{d[Bxb1]}{dt} &= a_{F2}*(A_L + B_L * \frac{[aTc]^n}{[aTc]^n+K_L^n})- 2 k_{DBxb1}*[Bxb1]^2 + 2k_{-DBxb1}*[DBxb1] - d_{I}*[Bxb1] \\
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\frac{d[DBxb1]}{dt} &= k_{DBxb1}*[Bxb1]^2 - k_{-DBxb1}*[DBxb1] - k_{SABxb1}*[DBxb1]*[SI_{Bxb1}] + k_{-SABxb1}*[SA_{Bxb1}] - d_J*[DBxb1] \\
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\frac{d[SA_{Bxb1}]}{dt} &= k_{SABxb1}*[DBxb1]*[SI_{Bxb1}] - k_{-SABxb1}*[SA_{Bxb1}]
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\end{align*}
=== Assumptions ===
=== Assumptions ===

Revision as of 10:19, 12 October 2014

iGEM ETH Zurich 2014