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From 2012.igem.org

Auxin detection

Overview

Now that we’ve managed to model auxin creation and transport, you may be asking yourself ; great, those guys have done all those models, but how can we link it to what we see ? That’s the aim of this model that will link the quantity of auxin transported into the cell to GFP degradation that we can observe in our tadpole’s cells. As for us, this model will also help our biologists to find the conditions upon which the reception can work and the help them guess the reasons of possible dysfunction in the auxin reception. Very schematically, this is what's happening during auxin detection:

Figure 1. Kinetic squeme depicting the auxin detection model in the cell.

Once TIR and GFP are produced and auxin has entered the cell, it binds with TIR and then this complex degrades GFP. This is what we're going to model.

Assumptions

In these reactions, we assimilate the complex Auxin-TIR to an enzyme that is able to degrade the GFP. Auxin would then be its activator.
The degradation rate of GFP is negligible; indeed a molecule of GFP takes 72 hours to degrade normally, whereas during auxin detection the complex auxin-TIR degrades it in less than an hour.
The Tir protein is continuously produced and degraded in the cell,

Model Description

Chemical equations:
After adding to these equations the creation rate of GFP and desintegration rate of auxin whe obtain the system of equations: Where:

• [A] stands for auxin concentration
• [AT] stands for the complex auxin-TIR concentration
• [ATG] stands for the complex auxin-TIR-GFP concentration
• [G] stands for GFP concentration
• [T₀] stands for TIR concentration, that we assume to be constant
• k_cat is the turnover number. Thus k_cat[T₀] corresponds to V_max of the Michaelis-Menten equation.
• Ɣ is the strength of the promoter used to create GFP
• f_eaux(t) is the quantity of auxin that enters in the cell at time t
• V is the volume of the cell.
• K_A is the reaction constant of the creation of the auxin-TIR1 complex
• K_G is the reaction constant of the degradation of GFP
• δ is the degradation rate of auxin
• P_G are the proteins left after degradation of GFP.