Team:Bologna/Modeling
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In the model we distinguish between LacI protein binded to repressor IPTG ([[Image:f01.jpg]]) and protein free ([[Image:f02.jpg]]). | In the model we distinguish between LacI protein binded to repressor IPTG ([[Image:f01.jpg]]) and protein free ([[Image:f02.jpg]]). | ||
- | Since [[Image:f03.jpg]] and considering the law of mass action | + | Since [[Image:f03.jpg]] and considering the law of mass action [[Image:f2.jpg]] we can write I^F=I/(1+(IPTG/K_i )^γ ) . |
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. | ||
The same thing can be done even for LexA obtaining [[Image:f5.jpg|center]] where [[Image:f6.jpg|center]] represents the UV radiation. | The same thing can be done even for LexA obtaining [[Image:f5.jpg|center]] where [[Image:f6.jpg|center]] represents the UV radiation. |
Revision as of 13:03, 16 October 2008
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Mathematical Model
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 I^F=I/(1+(IPTG/K_i )^γ ) .
Knowing that and the law of mass action is possible write where we can replace represents the entry of IPTG inside the cell. The same thing can be done even for LexA obtaining where represents the UV radiation.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: