Dynamic Enterobactin model
The dynamic enterobactin model describes siderophore-mediated cross-feeding between E. coli and C. glutamicum, developed within the SFB MibiNet community to study how iron competition shapes synthetic microbial communities. Enterobactin is a catecholate siderophore produced only by E. coli under iron limitation; once secreted it chelates ferric iron and can be taken up by both species, so C. glutamicum exploits the iron captured by E. coli without paying the production cost — enterobactin therefore acts as a public good.
The model tracks four state variables — the two biomasses, a shared carbon substrate and extracellular enterobactin — with double-Monod growth kinetics that require both substrate and siderophore simultaneously.
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Model Details
Review and edit model structure, biological variables, and kinetic parameters.
| Name | Tex name | Initial value | Actions |
|---|---|---|---|
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Build an expression by selecting a node and replacing it with a MathML element, then adjust symbols to the allowed variable names.
Arithmetic
Functions
Trigonometry
Hyperbolic
Comparison
Logic
Tip: click any element to select it, then choose a MathML element above or adjust its value. Click the surrounding canvas to wrap the whole expression in a new element. Drag any element onto another to move it there; Ctrl+Z / Ctrl+Shift+Z undo and redo.
Generated LaTeX Code
\begin{align*}
\frac{d x1}{dt} &= x1 \cdot \frac{mu\_max1 \cdot p1 \cdot s1}{(K\_s1 + s1) \cdot (K\_s\_X1-P + p1)} \\
\frac{d x2}{dt} &= x2 \cdot \frac{mu\_max2 \cdot p1 \cdot s1}{(K\_s2 + s1) \cdot (K\_s\_X2-P + p1)} \\
\frac{d s1}{dt} &= - \frac{x1}{Y\_X1\_S} \cdot \frac{mu\_max1 \cdot p1 \cdot s1}{(K\_s1 + s1) \cdot (K\_s\_X1-P + p1)} \\
& - \frac{x2}{Y\_X2\_S} \cdot \frac{mu\_max2 \cdot p1 \cdot s1}{(K\_s2 + s1) \cdot (K\_s\_X2-P + p1)} \\
\frac{d p1}{dt} &= x1 \cdot \frac{mu1 \cdot q\_p1\_max}{mu\_max1} \\
& - x1 \cdot \frac{mu1 \cdot q\_up\_X1\_max}{mu\_max1} \\
& - x2 \cdot \frac{mu2 \cdot q\_up\_X2\_max}{mu\_max2}
\end{align*}