Team:Heidelberg/Model/Mutagenesis Induction


Modeling
Mutagenesis Induction
{{{5}}}
\) can then be calculated using from the concentration of the arabinose solution with which the lagoon is supplied \(c_{A_{S}}\).

               $$
               \frac{\partial c_{A_{L}}(t)}{\partial t} = \Phi_{A} \cdot c_{A_{S}} - \Phi_{L} \cdot c_{A_{L}(t)}
               $$
               
               \(\Phi_{A}\) and \(\Phi_{L}\) are measured relative to the lagoon volume. For a steady state, the above equation results in 
               $$
               c_{A_{L}}(t) = \frac{\Phi_{A}}\{\Phi_{L}} \cdot c_{A_{S}}
               $$
               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) = \Phi_{A} \cdot c_{A_{S}} \cdot t - e^{-\Phi_{L} \cdot t}
               $$
           }}
       }}
   }}

References