Metabolic model

Overview

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.

Assumptions

Model Description

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:
 
We reduced this equation to:

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:

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.


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.

Parameters:

Name	Value	Unite	Description	Reference
p	0.1	min^-1	Permeability of cell wall	-
KfeFUR	0.01	M^-1.s^-1	Formation constant of FeFur complex	-
Dff	0.001	min^-1	-	-
Kp	0.5	min^-1	translation rate	-
KT	2.0	M.min^-1	transcription rate	-
milliNa	6.02.10^20	mol^-1	Avogadro's constant	[1]
V	6.5.10^-16	m^3	Volume of a call	-
Dmrna	0.001	min^-1	mRNA degradation rate	-
Denz	0.001	min^-1	Enzyme degradation rate	-
Kf	10^-4	min^-1	fixation rate of FeFUR	-

Enzymatic Parameters:

KcatA	5550	min^-1	-	-
KcatB	600	min^-1	-	-
KcatC	173	min^-1	-	-
KmA	300	M	-	-
KmB	14.7	M	-	-
KmC	14	M	-	-

Results

Conclusion

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