"
Team:Heidelberg/Templates/Modelling/Ind-Production
From 2013.igem.org
(Difference between revisions)
| Line 27: | Line 27: | ||
This system contains 4 dynamic variables: Bacteria (Bac), Glutamine (Glu), cyclized Glutamine (cGlu) and Indigoidine (Ind) that change with time t. | This system contains 4 dynamic variables: Bacteria (Bac), Glutamine (Glu), cyclized Glutamine (cGlu) and Indigoidine (Ind) that change with time t. | ||
Bacteria and Indigoidine was experimentally measured, we thus call Bac and Ind observables of our system. | Bacteria and Indigoidine was experimentally measured, we thus call Bac and Ind observables of our system. | ||
| - | The equations are described by | + | The equations are described by 7 parameters: |
<li> Bacmax: maximum capacity for bacterial growth | <li> Bacmax: maximum capacity for bacterial growth | ||
| - | <li> beta: | + | <li> beta: maximum attainable growth rate |
| + | <li> ki: inhibition coefficient of Indigoidine on bacterial growth | ||
| + | <li> ksyn: synthesis rate of cyclized Glutamine from Glutamine | ||
| + | <li> kdim: dimerization rate of two cyclized Glutamines to an Indigoidine dimer | ||
| + | <li> kdegg: degradation rate Glutamine | ||
| + | <li> kdegi: degradation rate Indigoidine | ||
| + | |||
| + | Additionally, error was estimated as well as initial concentration of bacteria. Data was normalized between 0 and 1, thus no scaling and offset parameters were required. | ||
<h3 id="D2D">Framework</h3> | <h3 id="D2D">Framework</h3> | ||
Revision as of 16:02, 27 October 2013
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.Approach
First, we set up a mind model based on the fact that the functional Indigoidine dimer is produced from two Glutamine (Glu) that are each cyclized (cGlu)Since we had already established our quantitative Indigoidine production assay (see Tag-Optimization) in a time-dependent manner, we wanted to further exploit these experimental data via quantitative dynamic modeling. The change of bacteria and Indigoidine with time was measured via optical density of the liquid cultures in a 96-well plate of a TECAN reader and can be described in ordinary differential equations (ODEs). Such ODEs contain parameters that characterize e.g. growth or synthesis rates for bacteria or Indigoidine, respectively.
Ordinary Differential Equations (ODEs)
But how to find proper equations for bacterial growth and indigoidine synthesis? From our mind model (Fig. 1), we derived ODEs based on mass-action kinetics$$ \mathrm{d}\mathrm{[Bac]}/\mathrm{d}t = -\frac{\mathrm{[Bac]} \cdot \left(\mathrm{[Bac]} - \mathrm{Bacmax}\right) \cdot \left(\mathrm{beta} - \mathrm{[Ind]} \cdot \mathrm{ki}\right)}{\mathrm{Bacmax}} $$ $$\mathrm{d}\mathrm{[Glu]}/\mathrm{d}t = - \mathrm{[Bac]} \cdot \mathrm{[Glu]} \cdot \mathrm{ksyn} $$ $$\mathrm{d}\mathrm{[cGlu]}/\mathrm{d}t = - \mathrm{kdim} \cdot {\mathrm{[cGlu]}}^2 - \mathrm{kdegg} \cdot \mathrm{[cGlu]} + \mathrm{[Bac]} \cdot \mathrm{[Glu]} \cdot \mathrm{ksyn} $$ $$\mathrm{d}\mathrm{[Ind]}/\mathrm{d}t = {\mathrm{[cGlu]}}^2 \cdot \mathrm{kdim} - \mathrm{[Ind]} \cdot \mathrm{kdegi} $$
This system contains 4 dynamic variables: Bacteria (Bac), Glutamine (Glu), cyclized Glutamine (cGlu) and Indigoidine (Ind) that change with time t. Bacteria and Indigoidine was experimentally measured, we thus call Bac and Ind observables of our system. The equations are described by 7 parameters:
