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Experiments Meet Modeling
Thanks to the excellent cooperation between our wetlab biologists and our modellers, we successfully characterized our lactate promoter library, as well as the effect of the AHLdegrading enzyme AiiA.
 Investigate the biological mechanism of LldR, after finding that literature on the system is incomplete. During the course of this project, we first made a model based on an assumption on its functioning. We evaluated it against the results, and found that the model could not explain the data. We then studied the results and established an improved model.
 Characterize the influence of our AHLdegrading enzyme AiiA construct.
Goals
Understanding the biological mechanism of LldR
Nerd:
To model our system we need to have parameters from the lldR system?
Lab rat:
Let's have a closer look at the mechanism of LldR!
After a few days in the lab ...
Lab rat:
Here are your parameters:
Experiment 1): Characterization of lldR sytem in LB
Equations
Because, we consider that only diffusion is happening, then we have
\begin{align*} \frac{d[GFP]}{dt}&=\frac{a_\mathrm{GFP} \cdot \left(\frac{[Lact_{in}]}{K_\mathrm{A,Lact}}\right)^{n_1}}{1+\left(\frac{[Lact_{in}]}{K_\mathrm{A,Lact}}\right)^{n_1}}d_\mathrm{GFP}[GFP]\\ \end{align*}Parameter Fitting
We fitted our model using the Least Absolute Residual method, using the fitting toolbox of Matlab. We designed different constructs of the LldR responsive promoters.We were thus able to compare all the promoters thanks to their ON/OFF ratio and K_{M} values. For a more detailed description of the experiment and the characterization, go to the registry, by clicking on the different links provided below.
Promoter  Promoter Strength  ON/OFF ratio  K_{M} (μM) 

K822000  unknown (natural)  10.35  955 
K1847008  162  15.26  1075 
K1847009  1429  1.56  977.5 
K1847007  2547  1.34  697.7 
We can observe that our construct K1847008 has the best ON/OFF compared to the other synthetic promoters which are very leaky. Also, during all these experiments, the levels of LldR inside the cell were kept constant. The two binding sites of LldR were also conserved (same distance to the promoter and same sequences). It is therefore nice to see that the K_{M} values do not vary a lot depending on the construct.
Lab rat:
Have you seen lldR does not only act as an repressor it also activates gene expression?!
After looking at puzzling results, we realized that our first model of the mechanism of action of LldR was not realistic. Searching literature, we finally found a compatible explanation, depicted in Figure 1. In the paper by Aguilera et al. (2008), they suggest that LldR may be required for the transcription machinery. Hence, instead of having only repression by LldR, LldR might play a dual role as a repressor and an activator. It suggests that when lactate is present, it destabilizes the DNA loop and induces a conformational change of LldR.This results in the transcription of the gene of interest (goi). This mechanism is consistent with our results. In the following, we will describe the mathematical equations corresponding to this mechanism.
Nerd:
Therefore we have to update our model, let's include a activation term?
Reactions
\begin{align} \label{eq:1} \varnothing&\mathop{\xrightarrow{\hspace{4em}}}^{a_{\mathrm{LldR}}} \text{LldR}\\ 2 \cdot \text{LldR} &\mathop{\mathop{\xrightarrow{\hspace{4em}}}^{\xleftarrow{\hspace{4em}}}}^{K_{\mathrm{d,1}}} \text{LldR}_2\\ 2 \cdot \text{Lact}+\text{LldR}_2 &\mathop{\mathop{\xrightarrow{\hspace{4em}}}^{\xleftarrow{\hspace{4em}}}}^{K_{\mathrm{d,2}}}2 \cdot \text{LactLldR} \hspace{2em}\\ \text{LldR} &\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{lldR}}} \varnothing\\ \text{LldR}_2 &\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{lldR_2}}} \varnothing\\ \text{LactLldR} &\mathop{\xrightarrow{\hspace{4em}}}^{d_{\mathrm{LactLldR}}} \varnothing\\ \end{align} 

Mathematical model
According to the previous description, the gene of interest is activated by LactLldR and repressed by LldR dimer. Hence, if gfp is the gene of interest, we get the following ODE:
\begin{align*} \frac{d[GFP]}{dt}&=\frac{a_{GFP}}{1+\left(\frac{[LldR_2]}{K_R}\right)^{n_r}}\cdot \frac{\left(\frac{[LactLldR]}{K_A}\right)^{n_a}}{1+\left(\frac{[LactLldR]}{K_A}\right)^{n_a}}d_\mathrm{GFP}[GFP] \end{align*}Assuming mass conservation for LldR, the total amount of LldR is given by:
\begin{align*} \text{LldR}_{tot}&=[LldR]+[LactLldR]+2 \cdot [LldR_2] \end{align*}Simplification
This equation is unidentifiable and we simplified the system by approximating the transcription of gfp by an Hill activation function:
\begin{align*} \frac{d[GFP]}{dt}&=\frac{a_\mathrm{GFP} \cdot \left(\frac{[Lact]}{K_\mathrm{A,Lact}}\right)^{n}}{1+\left(\frac{[Lact]}{K_\mathrm{A,Lact}}\right)^{n}}d_\mathrm{GFP}[GFP]\\ \end{align*}Nerd:
We have a problem, the model predicts that the sensitivity of the lldR system is to low. Can we change sensitivity?
After digging into literature...
Lab rat:
Maybe there is a solution, we could add a lactate importer to increase internal lactate concentration...
Characterization of the lactate importer in LB
To the extent of our knowledge, no characterization of the lldPRD operon is available in literature, nor in the iGEM registry. We characterized our synthetic promoters and the natural promoter in two lactate titration experiments: one with overexpressed LldP, and one with the natural expression of LldP. For a further description of this experiment, click here. However, we encountered several problems. In this setup, the lldPRD operon is not knocked out in our E. coli strains. Thus, we don't know how much LldP is expressed by the E. coli . We only know that the natural promoter is weak. Therefore, we assumed that when LldP is not overexpressed, there is no active transport of lactate by the permease. As the lactate molecule is small, we consider lactate passes through the E. coli only thanks to diffusion mechanisms, and then: \([Lact_{in}]=[Lact_{out}]\). When LldP is overexpressed, we consider that the lactate concentration is higher inside the E. coli than in the extracellular space.
To see the details about the characterization, click here.
Experiment 2): Overexpressed LldP in LB
We then designed other constructs including the symporter LldP. We expected an increase in lactate import such that the E. coli cells became more sensitive. However, the designed promoters show completely different LldR levels compared to the previous experiments. That is why we can not extract the parameters for LldP symporter using both experiments, because the data sets are not comparable. We will therefore use the same fitting function as before. Below, the promoter levels computed with a RBS calculator and the registry are indicated.
Construct  Expression of LldR(A. U.)  Expression of LldP(A. U.) 

LldR  51100  
High LldP lldR  664  8400 
Low LldP lldR  12  23.4 
Parameter Fitting
We then fitted our model as explained before,and we obtained the following values for ON/OFF ratio and K_{M} values.
Promoter  Promoter Strength  ON/OFF ratio  K_{M} (μM) 

K822000  unknown (natural)  1.16  720.2 
K1847008  162  1.42  337.7 
K1847009  1429  0.96  459.8 
K1847007  2547  1.29  1337 
Promoter  Promoter Strength  ON/OFF ratio  K_{M} (μM) 

K822000  unknown (natural)  8.04  1930 
K1847008  162  23.96  1751 
K1847009  1429  24.34  2361 
K1847007  2547  3.85  1977 
Observations
It is difficult to make a correct explanation here, since, both the levels of LldP and lldR change. However, in the first construct, we can clearly see that the leakiness is increased for small amounts of LldP/LldR. Consistent with our model, it is probably due to the insufficient levels of LldR. Since LldR is thought to repress the transcription, this could explain the leakiness.
Nerd:
The lldP helps to have a more sensitive system but it is not enough.
Lab rat:
Maybe it is just the LB interfering with our system, let's try M9 media or better try our mammalian cell media!
Characterization of the lactate responsive promoter in mammalian medium
Below is displayed the response of one synthetic promoter in RPMI serum free medium. The promoter harboring the permease and LldR displays a much higher sensitivity than the one only harboring LldR. In the following, these parameters are going to be used to simulate the foldchange sensor.

Figure 3: Characterization of the low engineered promoter
Nerd:
Cool this works much better!
Lab rat:
Yeah, we also cocultured E.coli with cancer cells and they responded to the lactate produced by the cancer cells!
Nerd:
We can detect CTCs by their lactate production!
Geometry of the chip and design of the microfluidic chip
Nerd:
But how should we set up our final system? It has to be compact and easy to handle, but still needs to allow single cell analysis...
Lab rat:
I have an idea for that!
Singlecell analysis is a prerequisite for our cancer detection system. Circulating tumor cells are really scarce in the blood compared to healthy cells. Implementing a microfluidic chip was then the ideal solution because it enables highthroughput singlecell analysis. However, having small reaction volumes was very challenging. Indeed, the natural quorum sensing system is meant to work on large length scales, as proven by the last year’s ETHZ IGEM team. The signalling molecule AHL diffuses then almost instantaneously in the chip. Biologically, we thought first that including AiiA degradation in the design or tightening the leakiness of the P_{Lux } promoter would solve the problem. It turned out that implementing a foldchange sensor solved the problem, since a pulse of LuxR will limit overactivation of the system.
Nerd:
Very elegant, congratulations!
Characterization of the effect of AiiA
Lab rat:
So in the end, is AHL degradation beneficial for our system or not?
Nerd:
Hm, we need more date to estimate that...
To characterize the effect of AiiA on our system, we ran two experiments. In one of them, AiiA was constituvely produced and in the other one, AiiA was not present. Below we compare both responses. The first visible thing is that AiiA drastically shifts the curve until lower sensitivities. As AiiA degrades AHL, this phenomenon is expected. In addition, since AiiA is on a medium copy plasmid and under the control of a strong constitutive promoter, the large effect seen in our experiments is expected.
Nerd:
Ok, that should help us decide.
From the parameters, we know AiiA acts with Michaelis Menten Kinetics. The K_{M } value and turnover number are already known from literature, see parameters. However, for our model, we need to know how much AiiA is produced by the cell in order to characterize the behaviour of the system.
Dose response curves and apparent K_{ M } values
Here we compared the fitted curves of AiiA and the K


Figure 4: Experimental and fitted curves for the plasmid: A) Without AiiA, B) With expressed AiiA.
Concentration of AiiA inside the E. coli
Below we fitted two ordinary differential equations thanks to MEIGO toolbox. The equations are below.
Equations
Here, AHL is the input. There is no amplification by LuxI.
\begin{align*} \frac{d[AHL]}{dt}&= \frac{v_{AiiA} \cdot [AHL]}{K_{M,AiiA}+[AHL]} \\ \frac{d[GFP]}{dt}&=\frac{a_\mathrm{GFP} \cdot \left(\frac{[AHL]}{K_\mathrm{Lux}}\right)^{n_1}}{1+\left(\frac{[AHL]}{K_\mathrm{Lux}}\right)^{n_1}}d_\mathrm{GFP}[GFP]\\ \end{align*}Parameter fitting
Due to the practical identifiability problem, we could not estimate a value for K
We find:
\begin{align*} v_{AiiA}= 9.46 \cdot 10^4 nM min^{1} \\ \end{align*}Lab rat:
Ok, but just to be clear now...
Can AiiA be used in our system?
As already mentioned, AiiA shifts the active curve until lower sensitivities. This means that higher concentrations of AHL will be required to activate the construct. In our case, the leakiness is necessary to initiate the signal. The amount of AiiA present here, will prevent any form of activation. We will therefore, not use AiiA in our final design.