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From 2011.igem.org

Brief overview of the model

The model of our system consists of two connected parts: the band detector and the toggle switch. The band detector produces green fluorescent protein upon a detection of a certain range (band) of acetaldehyde concentration. After acetaldehyde concentration passes a certain threshold the toggle switch turns the system red (red fluorescent protein is expressed).

Acetaldehyde from the smoke binds to AlcR and the formed complex then inhibits TetR. TetR inhibits LacI and CI. CI also inhibits LacI which inhibits GFP. This part of the circuit makes up the band detector. The Acetaldehyde-AlcR complex is considered as constant input to our system. By simulating with varying acetaldehyde concentrations we can see at which concentration is the band , i.e. at which concentrations GFP is produced. The connection to the switch is the LuxI inbition by CI. LuxI in turn produces AHL, which is described in our model as two states (AHL external and AHL internal). AHL diffuses in and out of the cell and after binding of AHL internal to LuxR, the complex R is created. In the model the LuxR concentration is taken as a parameter since it does not vary with time. Finally, RFP is inhibited by the complex R.

Our model has 9 states in total and 37 parameters, including the Acetaldehyde-AlcR input and LuxR. Basal expression is considered for none of the states and linear degradation is considered for all of them.

Band Detector

The band detector is an amplitude band-pass filter that gives a GFP output when acetaldehyde is in a certain concentration range. The filter is a feed-forward system with 2 branches – an amplitude low-pass filter and an amplitude high-pass filter – interconnected by a NOR gate.

The input of the system is acetaldehyde which binds to AlcR. After the complex TetR inhibition by the acetaldehyde-AlcR complex the systems splits into the 2 branches, the slow branch and the fast branch.

The fast branch is the amplitude low-pass filter. This means that it will repress the production of GFP when the acetaldehyde concentration goes above the high threshold.In other words, GFP is produced only at low acetaldehyde concentrations. High acetaldehyde concentration will repress TetR which will not be able to repress LacIm1, GFP production being thus inhibited.

The slow branch is the amplitude high-pass filter which represses GFP when acetaldehyde concentration falls below the low threshold or in other words GFP is produced only at high levels of acetaldehyde.

By combining these 2 filters, GFP is produced when neither LacIm1 or LacI represses it, which is region between the two thresholds. This region is the range of acetaldehyde concentration which can trigger the GFP pulse. The ODEs for the species involved in the band detector are given below.

We simulated the model for 5000s and for various concentrations of acetaldehyde. In the following figure you can see how the steady state concentration of GFP changes for different input concentrations of acetaldehyde. The band is formed when the acetaldehyde concentration is in the range of microMolars.

Toggle Switch