Team:ETH Zurich/Detector Module
REPORTER MODULE
OVERVIEW
Figure 1: Schematic of the reporter of our circuit. Only if the switch is turned on and the same marker that activated the switch is detected, the reporter circuit expresses GFP.
After the conditioning phase in which the switch is turned on if nitric oxide and AHL (or lactate) are detected at the same time, we have to identify the state of the switch and which one of the markers has triggered the switch. The reporter is the component of the circuit that enables such a readout in the lab. The state of the switch is displayed by two different fluorescent proteins: sfGFP is expressed by the promoter that has been switched, while the promoter that didn't switch expresses mNectarine.
To allow multiplexing, the reporter proteins are expressed only if they are induced by the same candidate marker that triggered the switch earlier during the learning phase.
The model shows that at steady-state of GFP our system has a linear dose-response relationship between the number of switched promoters and expressed GFP, which is crucial to enable a quantitative detection of the candidate markers.
GOALS
- To characterize the relationship between switch state and reporter expression.
- Estimate parameters necessary for characterizing sensor and switch.
MODEL
Our reporter system consists of two fluorescent proteins that report the state of the switch. In the non-switched state (OFF state), the plasmid expresses mNectarine, while after activation, the switched plasmid expresses GFP (ON state).
The model is based on mass-action kinectics and can be simulated both deterministically and stochastically.
Figure 2: Biological implementation of the integrase reporter. The figure shows both the switched and non-switched state. Expression of the reporter proteins is repressed by default and induced in presence of the candidate marker.
The following section describes the species and reactions of the ODE model:
REACTIONS
\begin{align*} 1) && P_{mNect} & \rightarrow P_{mNect} + mRNA_{mNect} \\ 2) && P_{sfGFP} & \rightarrow P_{sfGFP} + mRNA_{sfGFP} \\ 3) && mRNA_{mNect} & \rightarrow mRNA_{mNect} + mNect \\ 4) && mRNA_{sfGFP} & \rightarrow mRNA_{sfGFP} + sfGFP \\ 5) && mRNA_{mNect} & \rightarrow \\ 6) && mRNA_{sfGFP} & \rightarrow \\ 7) && mNect & \rightarrow \\ 8) && sfGFP & \rightarrow \\ \end{align*}
SPECIES
| Name | Description |
|---|---|
| $P_{mNect}$ | Non switched promoter, facing the mNectarine gene. |
| $P_{sfGFP}$ | Switched promoter, facing the sfGFP gene. |
| $mRNA_{mNect}$ | mRNA of the mNectarine protein. |
| $mRNA_{sfGFP}$ | mRNA of the sfGFP protein. |
| $mNect$ | mNectarine fluorescent protein. |
| $sfGFP$ | Superfolder GFP protein. |
STOCHASTIC REACTION RATES
\begin{align*} 1) \quad & k_{mRNAmnect} \cdot P_{mNect} \cdot p_{activity} \\ 2) \quad & k_{mRNAsfgfp} \cdot P_{sfGFP} \cdot p_{activity} \\ 3) \quad & k_{mNect} \cdot mRNA_{mNect} \\ 4) \quad & k_{sfGFP} \cdot mRNA_{sfGFP} \\ 5) \quad & d_{mRNAmnect} \cdot mRNA_{mNect} \\ 6) \quad & d_{mRNAsfgfp} \cdot mRNA_{sfGFP} \\ 7) \quad & d_{mNect} \cdot mNect \\ 8) \quad & d_{sfGFP} \cdot sfGFP \\ \end{align*}
PARAMETERS
| Name | Description |
|---|---|
| $p_{activity}$ | Fraction of the maximal activity of the promoter. This value is computed in the sensor module. |
| $k_{mRNAmnect}$ | mNectarine mRNA transcription rate. |
| $k_{mRNAsfgfp}$ | sfGFP mRNA transcription rate. |
| $k_{mNect}$ | mNectarine translation rate. |
| $k_{sfGFP}$ | sfGFP translation rate. |
| $d_{mRNAmnect}$ | mNectarine mRNA degradation rate. |
| $d_{mRNAsfgfp}$ | sfGFP mRNA degradation rate. |
| $d_{mNect}$ | mNectarine degradation rate. |
| $d_{sfGFP}$ | sfGFP degradation rate. |
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For parameter values, please check PARAMETERS
CHARACTERIZATION
The reporter has been characterized by placing the fluorescent proteins sfGFP and mNectarine under an anhydrotetracycline (aTc-inducible promoter. In this case the activity of the promoter is modeled as:
\begin{align*} p_{activity}=l_{pTet}+(1-l_{pTet})\cdot\frac{[aTc]^{n}}{K_m^n+[aTc]^{n}} \end{align*}
Where $l_{pTet}$ is the leakiness of the promoter, $n$ the steepness of the aTc-dependent activation and $K_m$ the concentration of aTc at which 50% of aTc-induced promoter activity is observed.
ASSUMPTIONS
- Conservation of the total number of promoters inside a cell: $P_{sfGFP}+P_{mNect}=P_{tot}$
- Independency between switching and repression of the promoters. This allows to model the repression in the sensor module and the switching in the switch module.
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
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 sfGFP 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 or the samples must be adjusted/diluted to the linear detection range.
Figure 4 shows a simulation of the sfGFP 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 can also be shown by analytically solving the equations at the steady-state of sfGFP. The relationship between the measured fluorescence and the switch state $P_{sfGFP}$ can be formulated as:
\begin{align*} fluoresc_{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 nice linear property is a key feature of our system, because it allows to compute the state of the switch easily by measuring the amount of expressed sfGFP. Since our reporter is expressed on a medium-low copy plasmid, we can assume that the sfGFP expression is not too stressful for the cell and that the computed relationship holds in practice.
However, a proper quantitative measurement is only possible if the fluorescence is measured 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.
Thanks to the sponsors that supported our project:
