Team:ETH Zurich/modeling/qs

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(Difference between revisions)
(Differential Equations)
(Differential Equations)
Line 78: Line 78:
Applying mass action kinetic laws, we obtain the following set of differential equations.
Applying mass action kinetic laws, we obtain the following set of differential equations.
$$\begin{align*}
$$\begin{align*}
-
\frac{d[Lux-AHL]}{dt} = k_{-RLux}[R_{Lux}]-k_{RLux}[Lux-AHL][LuxR]-d_{Lux-AHL}[Lux-AHL]\\
+
\frac{d[Lux-AHL]}{dt} &= k_{-RLux}[R_{Lux}]-k_{RLux}[Lux-AHL][LuxR]-d_{Lux-AHL}[Lux-AHL]\\
-
\frac{d[LuxR]}{dt} = \alpha_{LuxR} -k_{RLux}[Lux-AHL][LuxR] + k_{-RLux}[RLux] - d_{LuxR}[LuxR] \\
+
\frac{d[LuxR]}{dt} &= \alpha_{LuxR} -k_{RLux}[Lux-AHL][LuxR] + k_{-RLux}[RLux] - d_{LuxR}[LuxR] \\
-
\frac{d[RLux]}{dt} =  k_{RLux}[Lux-AHL][LuxR] - k_{-RLux}[RLux]  - 2 k_{DRLux} [RLux]^2 + 2 k_{-DRLux} [DRLux] - d_{RLux} [RLux] \\  
+
\frac{d[RLux]}{dt} &=  k_{RLux}[Lux-AHL][LuxR] - k_{-RLux}[RLux]  - 2 k_{DRLux} [RLux]^2 + 2 k_{-DRLux} [DRLux] - d_{RLux} [RLux] \\  
-
\frac{d[DRLux]}{dt} = k_{DRLux} [RLux]^2 - k_{-DRLux} [DRLux] - d_{DRLux} [DRLux] \\
+
\frac{d[DRLux]}{dt} &= k_{DRLux} [RLux]^2 - k_{-DRLux} [DRLux] - d_{DRLux} [DRLux] \\
-
\frac{d[P_{LuxON}]}{dt} = k_{P_{LuxON}} [P_{LuxOFF}][DRLux] - k_{-P_{LuxON}} [P_{LuxON}]\\
+
\frac{d[P_{LuxON}]}{dt} &= k_{P_{LuxON}} [P_{LuxOFF}][DRLux] - k_{-P_{LuxON}} [P_{LuxON}]\\
\end{align*}$$
\end{align*}$$

Revision as of 19:24, 11 October 2014

iGEM ETH Zurich 2014