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.
We can observe that for small amount of LuxR consitutively produced, we have a difference in the activation time between the system including AiiA degradation and the system without degradation.
Expected limitations
Our system should respond to the colocalization of the e-coli cells on the mammalian cell surface. The different concentrations of e-coli in the bulk and around the mammalian cells will determine the response of the sensor. However, we anticipate the following problems:
- If the concentration of the protein LuxR is too high, the leakiness of the promoter might self activate the sensor too quickly.
- If AHL diffuses in the nano well plate too fast, the fluctuations in the concentration of e coli cells might not be detected by the quorum sensing module.
The reaction-diffusion model is meant to answer these questions.