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 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