# Team:Slovenia/ModelingMutualRepressorSwitch

### From 2012.igem.org

# Modeling - mutual repressor switch

**Deterministic model**- Stochastic model
- C#Sim model

# Deterministic model of the mutual repressor switch

Deterministic analysis demonstrated that while theoretical conditions under which the mutual repressor switch would exhibit bistability exist, they are unlikely to occur in a realistic experimental setting. This was because: - high transcription factor cooperativity of value 2 or above was required for high-level bistability;
- even for high cooperativity values, the switch was highly intolerant to even very low leaky gene expression, which is always present to a certain extent in an actual cellular environment.
Increase in cooperativity lead to more robust behavior – higher expression levels of stable states were reached and higher – but still low - tolerance to leaky expression was observed. Experimental results confirmed that the mutual repressor switch did not exhibit bistability. |

## 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; - [TAL-A:KRAB], [TAL-B: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:

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