RESULTS

STOCHASTIC PARAMETER ESTIMATION

We estimated the parameters for the reporter genes and the tet promoter stochastically using flow cytometry measurements. The simulated distribution was fitted to the measurements by Approximate Bayesian Computation (ABC) usign the INSIGHT tool.

The figure below shows the distributions of the estimated parameters. The parameters page reports the maximum a posteriori (MAP) estimates, which are used in the simulation and analysis of our system.

Figure 3: Parameter estimations from flow cytometry data using stochastic simulation. The leakiness ($l_{Ptet}=0.06$) and the cooperativity ($n=1.57$) of the tet promoter are well estimated, while the $K_m$ value was difficult to identify and showed a broad estimate of 4,000-10,000 nM (not shown, see next section for explanation). Production and degradation rates have been nicely estimated (see parameters). Note that the degradation rates include also the dilution due to cell division.

EXPERIMENTAL DESIGN IMPROVEMENT

The parmeter estimation for the deterministic model of the tet promoter revealed that the $K_m$ value is approximately 9000 nM. This is about double the maximum aTc concentration we were using for induction (2000 ng/mL = 4320.6 nM) in the experiments. This means, we were not measuring the full range of the promoter activation.

Because we observed that our cells die at higher aTc concentrations, we decided that we need to reduce the concentration of the TetR repressor. We suggested the experimentalists to use a low (~5) copy plasmid for TetR expression instead of the medium-low (~15-20) copy plasmid originally used. We expected that this would result in a lower $K_m$ value such that we can fully induce the Tet promoter with 2000 ng/ml aTc. This change was indeed effective and allowed us to properly induce the recombinase in our characterization experiment.

OUTPUT INTERPRETATION

Figure 4: Amount of GFP expression as a function of the state of the switch 2 hours after induction by the candidate marker. The relation is linear which enables to properly determine the concentration of the candidate marker. However, to enable a quantitative measurement, the fluorescence measurement device (for instance flow cytometer) must be adjusted to the linear detection range.

Figure 4 shows a simulation of the GFP expression after induction by the candidate marker. Clearly the amount of expressed GFP increases linearly with the number of flipped promoters in the switch. This is also shown by applying the analytical solution of the steady-state of a production-degradation system to our reporter. The relationship between the measured fluorescence and the switch state $P_{sfGFP}$ can be formulated as:

\begin{align*} fluorescence_{SS}=k_{fl} \cdot \frac{k_{sfGFP}}{d_{sfGFP}} \cdot \frac{k_{mRNAsfgfp}}{d_{mRNAsfgfp}}\cdot P_{sfGFP} \end{align*}

Where $k_{fl}$ is the device-dependent ratio between measured fluorescence and protein concentration. This is a nice property of the system, because it allows to compute the state of the switch easily by measuring the amount of expressed GFP. Since our reporter is expressed on a medium-low copy plasmid, we can assume that GFP expression is not too stressful for the cell and that the computed relationship holds in practice.

However, the relationship above is true only if samples are taken in the linear range of the measurement device. If this is not the case samples must be diluted such that fluorescence intensity lies in the linear range.