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A simpler model based on the bistable paper was developed that takes the combined, relative transcription/translation rates into account Media:tristable2007.txt.
Parameters in the Model
Repressor Production Rate
Repressor production rate is determined by two factors:
- Promoter Strength (Transcription)
- Ribosome Binding Strength (Translation)
In the model, the total repressor production rate = alpha
The promoter strength cannot be easily changed because this would require mutations in the promoter or a different promoter/repressor combo. However, RBSs have been well characterized and the alpha parameter can be modulated by inserting different strength RBSs as determined by the model and testing.
Repressor Strength
The strength of the repressors is determined by:
- The repressor concentration, [Repressor].
- The cooperativity of repression, Beta.
In the Model, the repressor strength = [Repressor]^Beta
The Beta value is characteristic of each repressor and represents a constant that cannot be changed.
Degradation
The degradation in the model is denoted by the term "-repressor," where the degradation constant is unity because the rates are relative, rather than absolute. The next iteration of the model will include degradation constants. Currently in the registry all of the repressors have strong degradation tags. Jason Kelly made a comment on one repressor and said he was suspicious of how strong of a repression would be able to be obtained from the repessors. We need strong repression for our system, so we may need to remove the tag our system to function.
The Model
- Beta = Repression Strength
- Alpha = Repressor Production Rate
- X = Repressor1
- Y = Repressor2
- Z = Repressor3
Stability
 Tri-Stable region solved in Matlab Blue points are stable combinations of repressor production rates, while red circles are unstable combinations of repressor production rates. This graph is for Beta = 2. The tristable region gets larger (i.e. more disparate alpha values will be able to constitute a tristable system) as beta gets larger. The tristable region disappears when Beta equals one or less.
An easy visual aid to seeing how increased beta values (cooperativity of repression) leads to a more stable system consider the following graph of rate of production of repressor1 vs. the repressor that inhibits the production of repressor1. dx/dt vs. [y]
The black arrow shows that there is a larger region for larger beta values where stray repessors will not significantly affect the rate of repressor production rate whereas in a system of beta = 1, stray repressors will significantly change the system, making it less robust.
Modeling
The first draft of the code started last year:
[http://parts2.mit.edu/wiki/index.php/Table_of_preliminary_model_constants Initial Table of Constants]
[http://parts2.mit.edu/wiki/index.php/Derivation_of_the_Model_Equations Derivation of Model Equations]
Media:tristable2006.txt This code proved to complicated to work with and a more simplified version was developed.
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