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Team:Bologna/Modeling
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The equations (1.1) and (1.2) can be written in adimensional form: | The equations (1.1) and (1.2) can be written in adimensional form: | ||
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Knowing that [[Image:f1aa.jpg|center]] and the law of mass action [[Image:f2a.jpg|center]] is possible write [[Image:f3.jpg|center]] where we can replace [[Image:f4.jpg|center]] represents the entry of IPTG inside the cell. | Knowing that [[Image:f1aa.jpg|center]] and the law of mass action [[Image:f2a.jpg|center]] is possible write [[Image:f3.jpg|center]] where we can replace [[Image:f4.jpg|center]] represents the entry of IPTG inside the cell. | ||
Revision as of 15:26, 16 October 2008
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Mathematical Model
Let us pose: 
The genetic circuit in Figure 1 can be modeled with the following equations:
Where:
In the model we distinguish between LacI protein binded to repressor IPTG 
and protein free 
.
Since 
and considering the law of mass action 
we can write 
.
Posing:
The equations (1.1) and (1.2) can be written in adimensional form:
Placing:
The dimensionless equations are:
Hypothesizing: to be under conditions of equilibrium;
all the entries are void (); the affinity of the repressor for the operator site is high, for as we have been defined it will surely be smaller of one so ;the cooperativity is the same both for the LacI and for TetR and it is worth 2; the equations become:
