Tristable

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Contents

Tri-Stable Toggle Switch

Tri-Stable Model

Testing Constructs

Appendix

Tri-stable Toggle Switch

The Tri-Stable switch three distinct and stable outputs in response to three distinct inputs. These three inputs are three separate chemicals which will each induce one state of the switch.
The Tri-stable Toggle Switch Architecture
In order to achieve this goal, we are constructing three constructs, each of which consists of a repressible, constitutively-on promoter attached to two repressors. Specifically, our three constructs are:

pBAD->LacI->TetR,

pLacI->AraC->TetR and

pTet->AraC->LacI,

where [http://en.wikipedia.org/wiki/L-arabinose_operon AraC] represses pAraC/BAD, [http://en.wikipedia.org/wiki/Lac_repressor LacI] represses pLac and [http://en.wikipedia.org/wiki/Tetracycline_controlled_transcriptional_activation TetR] represses pTet.


Each of the three repressors are inactivated by one of three chemicals, the three inducer chemicals mentioned earlier. These three([http://en.wikipedia.org/wiki/Arabinose arabinose], [http://en.wikipedia.org/wiki/IPTG IPTG] (Isopropyl β-D-1-thiogalactopyranoside) and [http://en.wikipedia.org/wiki/Tetracycline Tetracycline], respectively), cause conformational changes in their respective repressor proteins which keeps them from binding to DNA in an inhibitory manner which leads to gene expression. For example, in the presence of arabinose, AraC cannot repress pAraC/BAD so LacI and TetR are produced which in turn repress pTet and pLac and the pAraC/BAD construct is turned on.


AraC/BAD

The gene AraC, one of several genes (AraA, AraB, AraD, etc) originally for the metabolism of arabinose.[http://www.mun.ca/biochem/courses/3107/Topics/Ara_operon.html]

Dimer structure with arabinose on the left (yellow)
The left image shows the araC dimer repressing transcription, while the right conformation enables transcription
The protein forms a dimer with and without arabinose but the structural change activates or represses the pAraC/BAD.





LacI

In nature, LacI represses pLac which promotes the LacYZA genes that metabolize lactose. Thus LacI represses pLac except in the presence of lactose (or lactose mimics, eg IPTG).
Image[http://www.mun.ca/biochem/courses/3107/Topics/Lac_genetics.html]. LacI forms a tetramer and represses pLac. However, an inducer, such as IPTG, causes a conformation change that removes LacI from the operator site.
Lactose causes a conformational change which inhibits LacI from binding to the operator site of pLac. Four LacI proteins form a tetramer to inhibit pLac and four inducer molecules are required to cause the full conformational change in the repressor.[http://www.mun.ca/biochem/courses/3107/Topics/Lac_genetics.html]





TetR

TetR represses the constitutive promoter pTet. In the presence of tetracycline, an antibiotic, a conformational change in TetR inhibits the protein from binding to the operator region. In nature, pTet promotes TetR and TetA. The latter of which acts to pump tetracycline out of the cell, thus the pump is only activated in the presence of Tetracycline.[http://en.wikipedia.org/wiki/Tetracycline_controlled_transcriptional_activation] The TetR, as it turns out is a very tight repressor and a range of 0 to 1 ug/ml has been shown to cause a 5 order of magnitude change in luciferase production.[http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=1319065&query_hl=1&itool=pubmed_docsum]

A tetracycline molecule binds to each of the two TetR monomers to form a dimer

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.

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:

  1. Promoter Strength (Transcription)
  2. 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:

  1. The repressor concentration, [Repressor].
  2. 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

Tri-Stable Mathematical 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]

Comparison of different beta values

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.

Testing Constructs

There are two methods we could follow in designing the Switch. We could randomly try different RBSs, hope it works and if not try again without having much of an understanding of why our cnostructs didn't work. Or we can test our repressors, promoters and inducers and have a systematic approach to anaylizing our system so that when something works or doesn't work we will know why. Thus we have designed a few tests which should give us relative and absolute values of our system that we can then plug into the model.

We decided to to test for three values. The combined transcription/translation rate of each repressor, the cooperativity of each repressor and the concentration of ligand needed to deactivate each repressor. We managed to design three tests all using the same constructs so as to minimize ligations. These tests should determine our variables independantly, i.e. changing synthesis rate should not change cooperativity of repression.

Synthesis Rate

The combined transcription/translation rate of the repressor is the combined strength of the promoter and the RBS. In
The Alpha test Architecture
our model this is the alpha value. Our model predicts that the alpha values for each repressor should be fairly comparable (the stable region is along the 1 to 1 to 1 line in 3D). Since we can't change the promoter strength very easily, we will change the RBS strength to obtain similar alpha values for all repressors.






Cooperativity of Repression

The cooperativity describes an inherent characteristic of a repressor's repression. In our system we want to know how
The Beta test Architecture
much increased repressor concentration will increase repression. In our model, cooperativity is an exponent, beta, so that the repressor concentration is raised to the beta ([repressor]^beta = total repression). For beta = 1, repression increases linearly with repressor concentration. With twice as much repressor there is twice the repression. For beta = 2, repression increases with the square of the concetration. Twce as much repressor leads to four times the repression. Our model predicts that our system will be more robust with greater alpha values and the tri stable region (in the graph) will be larger. Beta must be larger than one for the system to be stable.



Ligand Concentration

Naturally, we don't want to add more ligand than we need. In what ever application the project might find, if we wanted to change the state again by adding a different
The Ligand test Architecture
ligand, we wouldn't want excessive amounts of the first ligand floating around.








Appendix

Schedule of Construction

We have a schedule of ligations and transformations that we keep on googledocs to easily access information about the dna and cells in our freezer and fridge. This also organizes what ligations we plan to do in the future. In all there are about 40 ligations we want to do to construct the test constructs and first tristable system and based on the results of the tests, we will need to do as many as 20 more ligations.

Brown iGEM transformation database on googledocs
Brown iGEM ligation database on googledocs









Other Predicted Obstacles

  1. Other iGEM teams (info via Patrick King) have found that the araC gene contains a promoter region. Grown in TOP10 cells the construct araC>RBS>GFP>Terminator was observed to give a strong florescent output. In our system, this would give a florescent output for one FP even if that construct was not on.
  2. AraC exhibits all or none gene expression in the presents of arabinose because the natural transporter, when induced, causes that cell to transport arabinose, depleting the culture. This may be overcome by adding a saturating level of arabinose. In the arabinose construct already made, we were not able to observe FP output even though there was a high level of arabinose. We used XL1Blue cells.
  3. The degradation tags on the repressors may not give a long enough protein life time to yield strong repression. Thus, the tags may need to be removed to have a working device.

Email Correspondances about Tri-Stable Switch

Media:emailwithJasonLohmueller.txt

Media:emailwithNicolaNeretti.txt

Media:emailwithPatrickKing.txt

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