Team:Slovenia/ModelingPositiveFeedbackLoopSwitch
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Modeling  positive feedback loop switch
 Deterministic model
 Stochastic model
 C#Sim model
Deterministic model of the positive feedback loop switch

The model
We can describe the relations for the mutual repressor switch by the following equations. Fractional occupancies of promoters are:
where: f_{1}, f_{2}, f_{3} and f_{4} are probabilities of promoters 1 (construct 1), 2 (construct 2), 3 (construct 3) and 4 (construct 4), respectively, being in an active state, resulting in gene expression;
 [TALA:KRAB], [TALB:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations at a given time;
 k_{1}, k_{2}, k_{3} and k_{4} are association constants;
 n_{1}, n_{2}, n_{3} and n_{4} are exponents representing the degree of functional cooperativity;
 K_{r} is the amount of repressor required for 50% repression of constitutive promoter (equal to 1 in our simulations);
ODEs representing protein production are described by a set of equations:
where: [BFP], [mCitrine], [TALA:KRAB], [TALB:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations;
 k_{BFP} is BFP production rate from construct 1 (i.e. production rate when construct 1 promoter is active);
 kb_{BFP} is basal BFP production rate from construct 1 (i.e. production rate when construct 1 promoter is inactive);
 deg_{BFP} is BFP degradation rate;
 k_{cit} is mCitrine production rate from construct 2 (i.e. production rate when construct 2 promoter is active);
 kb_{cit} is basal mCitrine production rate from construct 2 (i.e. production rate when construct 2 promoter in inactive);
 deg_{cit} is mCitrine degradation rate;
 k_{2AKR} is TALA:KRAB production rate from construct 2;
 kb_{2AKR} is basal TALA:KRAB production rate from construct 2;
 k_{4AKR} is TALA:KRAB production rate from construct 4;
 kb_{4AKR} is basal TALA:KRAB production rate from construct 4;
 deg_{AKR} is TALA:KRAB degradation rate;
 k_{1BKR} is TALB:KRAB production rate from construct 1;
 kb_{1BKR} Is basal TALB:KRAB production rate from construct 1;
 k_{3BKR} is TALB:KRAB production rate from construct 3;
 kb_{3BKR} is basal TALB:KRAB production rate from construct 3;
 deg_{BKR} is TALB:KRAB degradation rate;
 k_{PIP} is PIP:KRAB production rate;
 deg_{PIP} is PIP:KRAB degradation rate;
 k_{E} is E:KRAB production rate;
 deg_{E} is E:KRAB degradation rate.
See model derivation for details.
Simulation results
Figure 2. Degraded bistability of the mutual repressor toggle switch for cooperativity of 1.15. In comparison to Figure 1  the same stateswitching scenario applies  bistability was exhibited, but very low difference between the states was achieved when cooperativity was set to 1.15 (other parameters were identical to parameters of Figure 1 ) and no leaky transcription was present. Increasing the the production rate of E:KRAB and PIP:KRAB slightly increased the levels, but even a 100fold increase in E:KRAB and PIP:KRAB production rate compared to other protein production rates did not produce significantly higher stablestate levels. Introducing residual TAL expression of as little as 1% resulted in the loss of bistability for the cooperativity of 1.15. 
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