Team:INSA-UPS France/test
iGEM UPS-INSA Toulouse 2017
System of ODEs For fearless people, our complete mathematical model and demonstration can be found there! The behaviour of our microbial consortium is summed up to thirteen differential equations. These equations characterize the growth and death of the three microorganisms.
\begin{equation}
\frac{d[\textit{Vc}]_W}{dt} = V_{growth,Vc} - V_{death,Vc}
\end{equation}
\begin{equation}
\frac{d[\textit{Vh}]_D}{dt} = V_{growth,Vh} - V_{death,Vh}
\end{equation}
\begin{equation}
\frac{d[\textit{Pp}]_D}{dt} = V_{growth,Pp} - V_{death,Pp}
\end{equation}
Microorganisms death is impacted by antimicrobial peptides production, produced by translation of antimicrobial peptides mRNA.
\begin{equation}
\frac{dAMP_{RNA}}{dt}=V_{transcription,AMP} - V_{degradation,AMP RNA}
\end{equation}
\begin{equation}
\frac{dAMP_{peptide,Pp}}{dt}=V_{translation,AMP}
\end{equation}
These peptides need to be transfered from the device to water.
\begin{equation}
\frac{d[AMP]_D}{dt} = V_{diff,AMP,Pp\to D} - V_{degradation,AMP} + \frac{V_{diff,AMP,W \to D}}{\mathcal{V}_D}
\end{equation}
\begin{equation}
\frac{d[AMP]_W}{dt} = -V_{diff,AMP,W\to D}
\end{equation}
To have this peptides production, an activation by diacetyl is needed.
\begin{equation}
\frac{d[dac]_D}{dt}=V_{prod,dac}+\frac{V_{diff,dac,W \to D}}{\mathcal{V}_D}
\end{equation}
\begin{equation}
\frac{d[dac]_W}{dt}=- V_{diff,dac,W \to D}
\end{equation}
Diacetyl is produced by the acetolactate synthase, ALS, wich results from ALS mRNA translation.
\begin{equation}
\frac{dALS_{RNA}}{dt} = V_{transcription,ALS} - V_{degradation,ALS RNA}
\end{equation}
\begin{equation}
\frac{dALS_{enzyme}}{dt} = V_{translation,ALS} - V_{degradation,ALSenzyme}
\end{equation}
ALS production has to be activated by the quorum sensing molecule CAI-1, initially in water, wich has to diffuse into the device.
\begin{equation}
\frac{d[CAI\text{-}1]_D}{dt} = \frac{V_{diff,CAI\text{-}1,W\to D}}{\mathcal{V}_D}
\end{equation}
\begin{equation}
\frac{d[CAI\text{-}1]_W}{dt} = -V_{diff,CAI\text{-}1,W\to D}
\end{equation}
The system of ODEs was solved using Matlab R2017a, thanks to the free offer from iGEM.
You can freely re-use our code:
Equations
Data
Name
Notation
Unit
Value
Reference
Vibrio cholerae maximum growth rate
μMAX,Vc
s-1
3.10-4
BioNumbers 112369 (1)
Vibrio harveyi JMH626 maximum growth rate
μMAX,Vh
s-1
2.10-4
Experiment - 21/06/17
Pichia pastoris SMD1168 maximum growth rate
μMAX,Pp
s-1
4.10-5
Experiment - 21/06/17
Solver
References
