Team:CIDEB-UANL Mexico/Math/Overview

Math model Team: Rubén Navarro Castillo and José Eric Ortiz Castillo

We’ve decided to use a deterministic math model for our circuit because we considered that this is more appropriate for this circuit.

We’ve been using the traditional differential equations for the description of the production of proteins and mRNA that are described here: d[xmRNA]/dt = k1*f(yreg)-γ1 [xmRNA] y d[xprotein]/dt = k2*[xmRNA]-γ2 [xprotein] ]-f(post) *[xprotein].

To get the maximum transcription and maximum translation rates we used the ecuations recommended by iGEM Beijing 2009 that are:

Maximum Transcription Rate = Transcription Speed(nt/min)/Gene Length(bp)

Translation Rate = RBS * Translation Speed(Aa/min)/Protein Length(Aa)

As our circuit is inside a E. Coli we’ve decided to use the speed of transcription and traduction as: 70 nt/s y 40Aa/s respectively.

For the description of the binding of araC and arabinose in order to switch on the promoter pBAD, we’ve followed the recommendations of Cambridge 2009: as a way of repressing the promoter pBAD and it is showed in the section of differential equations.

You can find out the entire system described with differential equations in the page of equations and the parameters in the page of parameters.