# Team:Slovenia/ModelingPositiveFeedbackLoopSwitchStochastic

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# Modeling - positive feedback loop switch

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

## Stochastic model of the positive feedback loop switch

 Stochastic simulation, in agreement with the deterministic analysis, proved that the positive feedback loop switch was more robust than the mutual repressor switch. It exhibited bistability without cooperativity (i.e. cooperativity equal to 1) even for leaky expression that caused the mutual repressor switch to lose bistable behavior. Higher cooperativity further increased the robustness and leaky expression tolerance, allowing for higher expression levels to be reached.

## The model

The basis for the stochastic simulation of the positive feedback loop switch was the following set of reactions that describe the dynamics of the switch:

Here:

• Pro1 is construct 1 promoter (i.e. promoter 1 - minimal);
• Pro2 is construct 2 promoter (i.e. promoter 2 - minimal);
• Pro3 is construct 3 promoter (i.e. promoter 3 - constitutive);
• Pro4 is construct 4 promoter (i.e. promoter 4 - constitutive);
• Pro5 is construct 5 promoter (i.e. promoter 5 - constitutive);

It is implicitly assumed that when both activator (TAL:VP16) and repressor (TAL:KRAB) bind to the promoter, the effect of the repressor will be more significant.

See the mutual repressor switch stochastic model for additional description.

## Simulation results

The same assumptions apply as for the mutual repressor switch simulation. Detailed parameter values for each simulation can be found in the corresponding simulation files that can be found here.

Figure 1 shows the result of the first simulation, where zero leaky expression and no cooperativity were assumed. Bistability was exhibited, just like it was in the deterministic simulation. The state-switching scenario used was the same as for the mutual repressor switch:

• at time = 500, signal 2 was introduced, inducing stable state 2 (high mCitrine state);
• at time = 2500, signal 1 was introduced, inducing stable state 1 (high BFP state);
• at time = 4500, signal 2 was introduced, switching the system to stable state 2;
• at time = 6500, signal 1 was introduced, switching the system to stable state 1.

While the introduction of leaky expression of 0.03 for each gene caused the mutual repressor switch to stop exhibiting bistable behavior, this was not the case for the positive feedback loop switch. Here, while the stable-state levels dropped moderately, bistability was observed in such case – shown in Figure 2 - even with no cooperativity (i.e. cooperativity equal to 1). This was in agreement with the deterministic model.

The simulation showed that the constitutive promoters leakage was more detrimental to bistability than the minimal promoters leakage. The leaky expression tolerance depended on both production and degradation rates (with production to degradation rate ratios too high or too low resulting in no bistable behavior). Figure 3 shows the positive feedback switch exhibiting bistability without cooperativity for minimal promoters leaky expression of 10% and constitutive promoters leaky expression of 5%. The mutual repressor switch did not exhibit bistability for these parameters.

When leaky expression was above a certain threshold (depending on other parameter values), cooperativity was required for bistability. Figure 4 shows a case where leaky expression of 0.08 did not result in bistability loss if cooperativity was equal to 2. Increasing leaky expression resulted in lower stable-state levels. Higher cooperativity improved this, allowing high (maximal) levels to be reached. Cooperativity being too high, like for the mutual repressor switch, caused the loss of bistability.

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