Metabolism model

Overview

Assumptions

Model Description

Results

Conclusion

Enzymes regulation:
This regulation is based on two consecutives inhibitions, which, in the end, is an activator with a certain delay. The model will follow this principle.

Variables:

[Fe] : Iron concentration inside the bacteria [Fur] : FUR concentration inside the bacteria [FeFur] : Iron-FUR complex concentration inside the bacteria LacI : Number of inhibited LacI LacO : Number of non-inhibited LacO [mRNA]: mRNA (from LacO) concentration [Enz] : Enzyme concentration : EntA,-B,-C,-D,-E,-F All those concentrations are expressed in mmol/L

Parameters table:

Fe, FUR and FeFUR:
The iron-FUR complex is simply formed that way:

2Fur + 2Fe → Fur2Fer2 We reduced this equation to:

Fur + Fe → FeFur : Kfur Which is not annoying, since we just have to divide our [FeFur] by to to get the real complex concentration.
We can easily write down both the formation (v) and the dissociation (v') speed:

v = Kfur[Fur][Fe] v' = dff[FeFur] We chose to model the iron input in the bacteria using a linear function of the external iron concentration Ferext, the factor p being the cell-wall permeability for iron.
The FUR on the other hand, is produced by the bacteria. It's evolution can also be considered linerar, using a mean production rate Fur0.

d[Fer]/dt = p*Ferext – Kfur[Fur][Fer] + dff [FeFur] d[Fur]/dt = Pfur*Fur0 – Kfur[Fur][Fer] + dff[FeFur] In this model, we only track the free Fe-FUR and not those which are attached to a FUR Binding Site. As LacI is the number of inhibited LacI, we can use this number to express how much Fe-FUR does bind to a FBS per unit of time.
d[FeFur]/dt = Kfur*[Fur][Fer] – dff*[FeFur] – 1/(Na*V)*dLacI/dt