Team:ETH Zurich/Modeling/AHL Module
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AHL Module
Introduction
Chemical species
Name | Description |
---|---|
AHL | Signaling protein, Acyl homoserine lactone (30C6-HSL) |
LuxR | Regulator protein, that can bind to AHL to form a complex |
LuxRAHL | Complex of LuxR and AHL, activates transcription of LuxI |
LuxI | Autoinducer synthase |
Aiia | AHL-lactonase, N-Acyl Homoserine Lactone Lactonase |
Equations
The equations are based on mass action kinetics and basic rate laws such as Hill equation.
Assumptions
- As LuxR is constitutively produced in this model, we considered that LuxR was constant. We used then the conservation of mass to derive the equations
- On the other hand, the binding and unbinding of LuxR to AHL is fast compared to the synthesis of LuxI. We used the quasi steady state approximation (QSSA)
- In this model we considered that no AHL diffuses out of the cell.
Simplified equations
\begin{align*} [LuxRAHL]&= \frac{[AHL]\cdot LuxR_\mathrm{tot}}{K_{\mathrm{d,LuxRAHL}}+[AHL]}\\ \frac{d[LuxI]}{dt}&=a_{\mathrm{LuxI}}k_{\mathrm{leaky}}(LuxR_\mathrm{tot}-[LuxRAHL])+\frac{a_{\mathrm{LuxI}}(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}{1+(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}-d_{\mathrm{LuxI}}[LuxI]\\ \frac{d[AHL]}{dt}&=a_{\mathrm{AHL}}[LuxI]-d_{\mathrm{AHL}}[AHL]-\frac{v_\mathrm{Aiia}\cdot [AHL]}{K_{\mathrm{M,AiiA}}+[AHL]}\\ \frac{d[GFP]}{dt}&=a_\mathrm{GFP}k_{\mathrm{leaky}}(LuxR_\mathrm{tot}-[LuxRAHL])+\frac{a_\mathrm{GFP}(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}{1+(\frac{[LuxRAHL]}{K_{\mathrm{a,LuxRAHL}}})^2}-d_{\mathrm{GFP}}[GFP]\\ K_\mathrm{d,LuxRAHL} &= \frac{k_\mathrm{-LuxRAHL}}{k_\mathrm{LuxRAHL}}\\ \end{align*}Simulations
We decided to simulate the single cell model in order to check the influence of AHL degradation by AiiA, and to confirm the sequential design.