Simple cell model equations

Model.md

Internal HIF dynamics:

$$ hif\_production = k\_HIF\_production\_basal + k\_HIF\_production\_max * hif\_in^2 / (k\_HIF\_pos\_feedback + hif\_in^2) $$

$$ hif\_degradation = k\_HIF\_deg\_basal * hif\_in * oxygen\_ex + k\_HIF\_deg\_lactate * hif\_in * lactate\_in $$

Finally

$$ \begin{split} \frac{d (hif\_in) }{d t} = k\_HIF\_production\_basal + k\_HIF\_production\_max * hif\_in^2 / (k\_HIF\_pos\_feedback + hif\_in^2) - \\ k\_HIF\_deg\_basal * hif\_in * oxygen\_ex + k\_HIF\_deg\_lactate * hif\_in * lactate\_in \end{split} $$

Lactate:

$$ lactate\_production = k\_lactate\_production * hif\_in^2 / (k\_lactate\_production\_reg + hif\_in^2) $$

$$ lactate\_degradation = k\_lactate\_deg\_basal * lactate\_in $$

$$ lactate_transport = (k\_MCT1 * lactate\_ex - k\_MCT4 * lactate\_in) $$

Finally

$$ \begin{split} \frac{d (lactate) }{d t} =k\_lactate\_production * hif\_in^2 / (k\_lactate\_production\_reg + hif\_in^2) - \\ k\_lactate\_deg\_basal * lactate\_in + \\ (k\_MCT1 * lactate\_ex - k\_MCT4 * lactate\_in) \end{split} $$

GFP

$$ \begin{split} \frac{d (GFP) }{d t} =k\_GFP\_production\_constantFP\_production * hif\_in^3 / (k\_GFP\_production\_constant + hif\_in^3) - \\ k\_GFP\_deg * gfp\_in \end{split} $$

Oxygen

$$ \frac{d (Oxygen\_ext) }{d t} = - k\_min\_o2\_deg - k\_max\_o2\_deg / ((hif\_in / HIF\_threshold)^{hill\_coeff\_o2\_deg} + 1) $$