Team:Bologna/Modeling
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= Equibrium conditions = | = Equibrium conditions = | ||
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+ | If we assume that: | ||
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+ | # to be under conditions of equilibrium [[Image:f009.jpg]]; | ||
+ | # all the entries are void [[Image:f010.jpg]] | ||
+ | # [[Image:f011.jpg]] the affinity of the repressor for the operator site is high, [[Image:f012.jpg]] for as we have been defined it will surely be smaller of one so [[Image:f013.jpg]]; | ||
+ | # | ||
+ | # | ||
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 15:34, 16 October 2008
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Contents |
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 .
Posing:
The equations (1.1) and (1.2) can be written in adimensional form:
Equibrium conditions
If we assume that:
- 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 ;
Placing:
The dimensionless equations are:
Equibrium conditions
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: