Team:Heidelberg/Model/Mutagenesis Induction
Modeling
Mutagenesis Induction
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$$
\frac{\partial c_{A_{L} }(t)}{\partial t} = \Phi_{S} \cdot c_{A_{S} } - \Phi_{L} \cdot c_{A_{L}(t)}
$$
\(\Phi_{S}\) and \(\Phi_{L}\) are measured relative to the lagoon volume.
The arabinose concentration in the lagoon \(c_{A_{L} }\) can then be calculated using the concentration of the arabinose solution with which the lagoon is supplied \(c_{A_{S} }\).
$$
c_{A_{L}} = \frac{\Phi_{S}}{\Phi_{L}} \cdot c_{A_{S}}
$$
However, in some cases it may be relevant to estimate when a given percentage of the equilibrium concentration is reached. To make statements about that, the differential equation is solved to
$$
c_{A_{L} }(t) = \frac{c_{A_{L}} \Phi_{S} + c_{A_{L}}(t_{0}) e^{-\frac{\Phi_{L}}{t}}
$$
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References
