Difference between revisions of "Team:ETH Zurich/Detector Module"
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<p><b>Figure 4:</b> 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, but other factors like linear range of the measurement device must be taken in account.</p> | <p><b>Figure 4:</b> 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, but other factors like linear range of the measurement device must be taken in account.</p> | ||
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| − | <div> | + | <div class="sec"> |
| − | + | <p>Figure 4 shows a simualtion of the GFP expression after induction by the candidate marker. Clearly the amount of expressed GFP increase linearly with the number of flipped promoters in the switch. This is shown also 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:</p> | |
| − | + | <p>\begin{align*} | |
| − | + | fluorescence_{SS}=k_{fl} \cdot \frac{k_{sfGFP}}{d_{sfGFP}} \cdot \frac{k_{mRNAsfgfp}}{d_{mRNAsfgfp}}\cdot P_{sfGFP} | |
| − | + | \end{align*}</p> | |
| − | + | <p>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 just looking at the amount of expressed GFP. Since our reporter is placed on a medium-low copy plasmid, we can assume that GFP expression is not too stressful for the cell and the computed relationship holds in practice.</p> | |
| − | + | <p>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 so that measurements fit into the linear range.</p> | |
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Revision as of 12:36, 19 October 2016
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 learning 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 been detected. 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.
GOALSGOALS
- 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 (for the system simulation) and stochastically (for the parameter estimations).
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. |
CHARACTERIZATION MODEL
The reporter has been characterized by placing the fluorescent proteins under an 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 aTc is the tetracycline variant used for induction, $l_{pTet}$ is the leakiness of the promoter, $n$ the sensitivity to aTc and $K_m$ the affinity.
MODEL 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 repression to be modeled in the sensor module and 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: Distributions of the parameters stochastically estimated from the experimental data. The leakiness ($l_{Ptet}=0.06$) and the cooperativity ($n=1.57$) of the tet promoter are well estimated, while $K_m$ (not shown, see next section) is badly identified. Production and degradation rates also have good quality estimates (see parameters), it's important to note that degradation rates include dilution as well.
EXPERIMENTAL DESIGN IMPROVEMENT
Parameter estimation for the tet promoter revealed that the half-occupation $K_m$ of the tet promoter is in the order of 9000 nM. This is about double the maximum aTc concentration we were using for induction (2000 ng/mL = 4320.6 nM) in the experiments, meaning we were not using the full range of the promoter.
Since cells die at higher aTc concentrations, we need to reduce the concentration of the TetR repressor in the cells. We suggested to the experimentalists to use a low (~5) copy plasmid for TetR expression instead of the medium-low (~15-20) copy plasmid originally used. We expect whis change to lower $K_m$ so that we can better induce the Tet promoter. This change improved the quality of the switch characterization.
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, but other factors like linear range of the measurement device must be taken in account.
Figure 4 shows a simualtion of the GFP expression after induction by the candidate marker. Clearly the amount of expressed GFP increase linearly with the number of flipped promoters in the switch. This is shown also 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 just looking at the amount of expressed GFP. Since our reporter is placed on a medium-low copy plasmid, we can assume that GFP expression is not too stressful for the cell and 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 so that measurements fit into the linear range.
Thanks to the sponsors that supported our project:
