Difference between revisions of "Team:ETH Zurich/Modeling/AHL Module"
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[LuxRAHL]&= \frac{[AHL]\cdot LuxR_\mathrm{tot}}{K_{\mathrm{d,LuxRAHL}}+[AHL]}\\ | [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[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{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]\\ | \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}}\\ | K_\mathrm{d,LuxRAHL} &= \frac{k_\mathrm{-LuxRAHL}}{k_\mathrm{LuxRAHL}}\\ |
Revision as of 15:36, 20 August 2015
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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 |
Reactions
\begin{align*} \varnothing&\mathop{\xrightarrow{\hspace{4em}}}^{a_{\mathrm{LuxR}}} \text{LuxR}\\ \text{AHL} + \text{LuxR} &\mathop{\mathop{\xrightarrow{\hspace{4em}}}^{\xleftarrow{\hspace{4em}}}}_{k_{\mathrm{LuxRAHL}}}^{k_{\mathrm{-LuxRAHL}}} \text{LuxRAHL}\\ &\mathop{\xrightarrow{\hspace{4em}}}^{\displaystyle\mathop{\downarrow}^{\text{LuxRAHL}}} \text{LuxI}\\ \text{LuxI}&\mathop{\xrightarrow{\hspace{4em}}}^{a_{\mathrm{AHL}}}\text{AHL}+\text{LuxI}\\ \text{LuxR}&\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{LuxR}}}\varnothing\\ \text{AHL}&\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{AHL}}}\varnothing\\ \text{LuxRAHL}&\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{LuxRAHL}}}\varnothing\\ \text{LuxI}&\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{LuxI}}}\varnothing\\ \text{Aiia}+\text{AHL}&\mathop{\xrightarrow{\hspace{4em}}}^{K_{\mathrm{M}},v_{\mathrm{Aiia}}}\text{Aiia}\\ \end{align*}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)