Modeling - positive feedback loop switch

1. Deterministic model
2. Stochastic model
3. C#Sim model
• Summary
• The model
• Simulation results

C#Sim model of the positive feedback loop switch

The model

The model was constructed in C# programming language by defining objects that represented the switch. See source code for complete implementation details. See modeling methods for algorithm description.

Simulation results

State-switching was achieved by introducing state-inducing signals for a certain duration of time. Each signal was modeled as a step function. Each binding site had a capacity equal to 10, to represent 10 binding site repeats. Active transcription rates (k) of all promoters were equal to 200 units. mRNA degradation percentage per simulation step was 0.25 and protein degradation percentage was 0.1.

Simulation results show reached protein levels (i.e. the amount of protein entities in the system) as a function of time.

In our first test, the following state-switching scenario was used:

• signal 2 was introduced at time = 0 to induce stable state 2 (high mCitrine) and removed at time = 100;
• signal 1 was introduced at time = 200 to induce stable state 1 (high BFP) and removed at time = 300;
• signal 2 was again introduced at time = 400 and removed at time = 500;
• signal 1 was again introduced at time = 600 and removed at time = 700.

Leaky expression (b) of each gene was equal to 15 units (compared to active transcription rate of 200, that means leaking of 7,5%). Exponent values (m and n - see Modeling methods for description) were equal to 1.3. Translation effectiveness was 25%. While the mutual repressor switch didn't exhibit bistability for this parameter values, the positive feedback loop switch did, as shown in figure 1.

For our next tests, the following state-switching scenario was used:

• signal 2 was introduced at time = 0 (with time here we mean simulation step number) to induce stable state 2 (high mCitrine) and removed at
  time = 100;
• signal 1 was introduced at time = 400 to induce stable state 1 (high BFP) and removed at time = 500;
• signal 2 was again introduced at time = 800 and removed at time = 900;
• signal 1 was again introduced at time = 1200 and removed at time = 1300.

Exponents were equal to 1.1. Leaky production rate of all proteins was again 15 units. Translation effectiveness was 90%. Bistability was exhibited, as shown in figure 2. Decreasing translation effectiveness required a slight increase in exponent values for bistability to occur. Figure 3 shows that bistability was exhibited fo exponent values of 1.3 when translation effectiveness was reduced to 40%. Figure 4 shows the switch exhibiting bistability for exponent values equal to 1.3 with leaky transcription rate equal to 15 units and translation effectiveness equal to 100%.