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Team:Heidelberg/Templates/Modelling/Ind-Production
From 2013.igem.org
Challenge
A challenge we had to face during the characterization and optimization of indC was to identify the production kinetics of Indigoidine. In order to disentangle the underlying mechanisms of bacterial growth and peptide synthesis, we decided to set up a mathematical model based on coupled ordinary differential equations (ODEs). Calibrated with our experimental time-resolved data, the mathematical model could potentially not only elucidate how Indigoidine production influences growth of bacteria but also provide a more quantitative understanding of the synthesis efficiency of the different T domains and PPTases that were tested.Mathematical modelling allows for
Approach
The ODE system determining the time evolution of the dynamical variables is given by the following four equations:$$ \mathrm{d}\mathrm{[Bac]}/\mathrm{d}t = -\frac{\mathrm{[Bac]} \cdot \left(\mathrm{[Bac]} - \mathrm{Bacmax\_native\_svp}\right) \cdot \left(\mathrm{beta\_native\_svp} - \mathrm{[Ind]} \cdot \mathrm{ki\_native\_svp}\right)}{\mathrm{Bacmax\_native\_svp}} $$ $$\mathrm{d}\mathrm{[Glu]}/\mathrm{d}t = - \mathrm{[Bac]} \cdot \mathrm{[Glu]} \cdot \mathrm{ksyn\_native\_svp} $$ $$\mathrm{d}\mathrm{[cGlu]}/\mathrm{d}t = - \mathrm{kdim\_native\_svp} \cdot {\mathrm{[cGlu]}}^2 - \mathrm{kdegg\_native\_svp} \cdot \mathrm{[cGlu]} + \mathrm{[Bac]} \cdot \mathrm{[Glu]} \cdot \mathrm{ksyn\_native\_svp} $$ $$\mathrm{d}\mathrm{[Ind]}/\mathrm{d}t = {\mathrm{[cGlu]}}^2 \cdot \mathrm{kdim\_native\_svp} - \mathrm{[Ind]} \cdot \mathrm{kdegi\_native\_svp} $$
