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

C#Sim model of the positive feedback loop switch, like other modeling approaches, showed that this switch was much more robust than the mutual repressor switch. The positive feedback loop switch would exhibit bistability even for low transcription factor exponent values, such as 1.1 - much lower than required for bistability of the mutual repressor switch. It again proved tolerant to leaky production of transcription factors and exhibited bistability even for low translation effectiveness (e.g. 25%). Decreasing translation effectiveness required a relatively slight increase in transcription factor exponent values for bistability to occur.

The model

The model was constructed in C# programming language by defining objects that represented the switch. 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.

Figure 1. The positive feedback loop switch transitioning between stable states for parameter values that did not result in bistability of the mutual repressor switch (here, transcription factor exponents were equal to 1.3 and leaky transcription rates were 15 units).

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%.

Figure 2. The positive feedback loop switch exhibited bistability for exponent values of 1.1 when translation effectiveness was 90%, despite leaky expression of 15 units for all genes.

Figure 3. The positive feedback loop switch exhibited bistability for exponent values of 1.3 when translation effectiveness was 40%.

Figure 4. The positive feedback loop switch exhibiting bistability for translation effectiveness of 100%.

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