Team:Slovenia/ModelingPositiveFeedbackLoopSwitch

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Modeling - positive feedback loop switch

1. Deterministic model
2. Stochastic model
3. C#Sim model

The model

We can describe the relations for the mutual repressor switch by the following equations. Fractional occupancies of promoters are:

where:
• f1, f2, f3 and f4 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;
• [TAL-A:KRAB], [TAL-B:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations at a given time;
• k1, k2, k3 and k4 are association constants;
• n1, n2, n3 and n4 are exponents representing the degree of functional cooperativity;
• Kr 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], [TAL-A:KRAB], [TAL-B:KRAB], [PIP:KRAB] and [E:KRAB] are protein concentrations;
• kBFP is BFP production rate from construct 1 (i.e. production rate when construct 1 promoter is active);
• kbBFP is basal BFP production rate from construct 1 (i.e. production rate when construct 1 promoter is inactive);
• degBFP is BFP degradation rate;
• kcit is mCitrine production rate from construct 2 (i.e. production rate when construct 2 promoter is active);
• kbcit is basal mCitrine production rate from construct 2 (i.e. production rate when construct 2 promoter in inactive);
• degcit is mCitrine degradation rate;
• k2AKR is TAL-A:KRAB production rate from construct 2;
• kb2AKR is basal TAL-A:KRAB production rate from construct 2;
• k4AKR is TAL-A:KRAB production rate from construct 4;
• kb4AKR is basal TAL-A:KRAB production rate from construct 4;
• degAKR is TAL-A:KRAB degradation rate;
• k1BKR is TAL-B:KRAB production rate from construct 1;
• kb1BKR Is basal TAL-B:KRAB production rate from construct 1;
• k3BKR is TAL-B:KRAB production rate from construct 3;
• kb3BKR is basal TAL-B:KRAB production rate from construct 3;
• degBKR is TAL-B:KRAB degradation rate;
• kPIP is PIP:KRAB production rate;
• degPIP is PIP:KRAB degradation rate;
• kE is E:KRAB production rate;
• degE is E:KRAB degradation rate.

See model derivation for details.

Simulation results

Next: Stochastic model of the positive feedback loop switch >>