What are these graphs and where did they come from?

Using the bacterial fluorescence models we have built, we predicted the steady-state fluorescence levels of the system in varying levels of DCM and ATC by solving the system of differential equations we produced during the characterization section. The results are illustrated in the 3-dimensional surface plot below. (which system?)

The two 2-dimensional graphs are slices taken from the 3-D plot. In each of these 'slices' we are effectively holding one variable constant (either DCM or ATC) while varying the other.

Producing the 3-dimensional plot was produced by plotting the final fluorescence value from lots of different possible combinations of the two inputs (ATC and DCM). The top graph shows the variation in final fluorescence when DCM is held constant and ATC is varied, the second graph is vice versa.

It is important to understand that these graphs represent the expected steady state level of fluorescence of thousands of different simulations. From this we can select the DCM and ATC concentrations for a specific fluorescence response.

How much of each input should we use to test the biosensor?

An ideal biosensor must be:

• Robust- it must be able to cope with variations in ATC concentration without radically altering the behaviour of the system. This is crucial because we cannot ensure that ATC concentrations throughout all the cells will be uniform in the real system.

The top graph demonstrates this nicely. Beyond a certain threshold value of ATC, there is little change in the fluorescence response predicted - it saturates and maintains a constant level. Practically, this means we have to ensure that the ATC concentrations present in our final system must comfortably exceed this threshold ATC value.

• Sensitive- it must change significantly in low concentrations of DCM. This is vital in order to achieve a response that is as close to binary as possible. The ideal system will have a very sharp decline in fluorescence at a predefined, very low value of DCM. This will ensure that the sensor will clearly indicate when the DCM mixture can be safely disposed of.

From our initial system characterization, we have established that when DCM is not present in the system, there will be no fluorescence response aside from that due to the basal transcription rate. However, the model predicts that when even a small amount of DCM is added and the transient behaviour has stabilized, the fluorescence expressed in the system quickly reaches its saturation value. This corresponds to a highly sensitive biosensor which can effectively only express two fluorescence levels- zero or a predefined maximum. The transition from zero to the maximum saturation value occurs at very low concentrations of DCM.

To summarise, we have established that the inputs to our biosensor should be a constant medium concentration of ATC and a varying concentration of DCM as it is degraded. We should note that the ATC concentration will not value without external influence because the system does not consume ATC and its rate of degradation is negligible.

We ran the deterministic model whilst varying the activation rate (see 'where did these equations come from?') of the sfGFP. The response is shown here:

What does this tell us?

As you can see from this graph, increasing the RBS strength only changes the amplitude of the systems response without affecting the response time of the system. This is highly beneficial for the system.

-->Therefore we will aim for as high an RBS strength as possible in our initial design.

We ran the deterministic model whilst varying the degradation rate (see 'where did these equations come from?') of the sfGFP. The response is shown here:

What does this tell us?

Changing the degradation rate of the protein is more of a trade-off. As you can see, a higher degradation rate gives a faster response but with a much lower steady state responses

-->We should aim for a low degradation rate to begin with so that we can ensure a detectable level of fluorescence, and then gradually increase the degradation rate to get a faster response.