Tristable

From 2007.igem.org

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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 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=====
=====The Model=====
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[[Image:model equations.png|left|Tri-Stable Mathematical Model]]
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[[Image:model equations.jpg|left|Tri-Stable Mathematical Model]]
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Revision as of 03:01, 24 October 2007

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Contents

Tri-stable Toggle Switch

The purpose of the Tri-stable Toggle Switch is to produce three distinct, continuous, 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 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 pBAD 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

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