Weekly Updates on the Tri-Stable Switch
Tri-stable Toggle SwitchThe Tri-stable Toggle Switch will be able to produce three distinct, continuous (stable) outputs for each of the three inputs. A chemical will induce the system to "lock into" one state while repressing the other two states. AraC represses pBAD, LacI represses pLac and TetR represses pTet. The three chemicals (arabinose, IPTG (Isopropyl β-D-1-thiogalactopyranoside) and Tetracycline, respectively), cause conformational changes in their respective repressor proteins 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.
AraC/BADThe gene AraC is one of several genes (AraA, AraB, AraD, etc) originally for the metabolism of arabinose. Bcl-2-associated death promoter, an apoptotic regulator in humans).
LacIIn nature, LacI represses pLac which promotes LacYZA genes that metabolize lactose, thus LacI represses pLac except in the presence of lactose (or lactose mimics, eg IPTG). 
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 which acts to pump tetracycline out of the cell, thus the pump is only activated in the presence of Tetracycline.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.
Tetracycline is highly diffusable through cell membrane (permeation coeficient or 5.6±1.9 * 10^-9 cm/s or half equilibrium time = 35 ± 15 min) and TetR shows a very high affinity for the molecule. The binding constant of TetR to [tc-Mg+] is Ka ~ 10^9 M^-1. When bound to tc, TetR has a low binding level to DNA of 10^5 M^-1. 
Brown iGEM 2006 Matlab model code Media:tristable2006.txt
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.
The combined transcription/translation rate of the repressor is the combined strength of the promoter and the RBS. In 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 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.
Naturally, we don't want to add more ligand than we need. If we wanted to change the state again by adding a different ligand, we wouldn't want other ligand floating around. Furthermore, tetracycline is an antibiotic and we don't want to add so much that we are compromising the activity of the cell.
Standardizing Repressor Characterization
Ultimately we would like to make a protocol by which all other repressors could be characterized that would be easy to construct, repeatable and useful to all applications. Hopefully, we will find the correct combination of cell concentration and growth phase, reporter readout, induction method, cell type and variables to test for so that this information can be useful to others.