Modeling - mutual repressor switch

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

C#Sim model of the mutual repressor 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.

With bistability we mean that even after the removal of inducer signals, the switch remained in the state it had achieved.

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 = 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.

For our first test, leaky expression of each gene was equal to 15 units (compared to active transcription rate of 200, that means leaking of 7,5%). Translation effectiveness, P_T, was 25%. All exponents were equal to 1.3. No bistability was exhibited for this scenario, as demonstrated in Figure 1. Increasing transcription factor exponents (n and m) to 3 still produced no bistability. Increasing translation effectiveness (to e.g. 85%) still resulted in no bistable behavior, nor did higher PIP:KRAB or E:KRAB production rate. Bistability was only exhibited for little or no leaky production, and even then only for relatively high non-linearity (exponent values of 2 or above). This suggested (as other models did) that leaky expression is highly problematic with the mutual repressor switch and causes it to lose bistable behavior past a certain threshold.

Figure 2 shows the mutual repressor switch exhibiting bistability when zero leaky production was present. Transcription factor exponents in this case were equal to 4. Translational effectiveness was 80%. While bistability was exhibited in this case, the reached expression levels could differ significantly between different stable states. Decreasing non-linearity to e.g. 2 lead to loss of bistable behavior.