Team:ETH Zurich/labblog/20140818mod

Fitting quorum sensing Hill functions parameters

Wednesday, August 18th

The plasmids for quorum sensing experiments concerning the Lux system are made and operational to be used for experiments. We have three different plasmids:

• Lux promoter folowed by GFP gene
• Lux promoter followed by cisRNA and then by GFP
• Lux promoter controlling the expression of taRNA and cisRNA. The cisRNA coding gene is followed by GFP.

The third plasmid corresponds to a riboregulating system. The second plasmid allowed us to validate the crucial role of taRNA in this riboregulating system.

On the modeling point of view, we only tried to fit the data coming from experiments done with plasmid one (with no riboregulating system) and plasmid three (with an effective riboregulating system). They were the only one to show an answer to a change of input that was not on the noise level.

The experimental setting was to inject different concentration of the signaling molecule AHL at the same time point into different bacterial colonies. The factor that we want to observe is the strength of the activation of the Lux promoter. The read-out is made by the fluorescence. The data was gathered over several time points in order to be able to observe the dynamic behavior. More precisely, the read-out of the promoter activation is made by the relative fluorescence, which corresponds to the ratio of the absolute fluorescence over the Optical Density (OD). We consider that the concentration in GFP per cell is proportional to the relative fluorescence. As we try to avoid fitting the saturation events, we chose to normalize with respect to the highest value before a certain amount of time, which corresponds for each experiment to the apparition of the saturation.

As a first approach, we only try to fit the steady state value. As the signaling molecule is inducing the production of GFP, we chose to use an Hill function to fit the function [GFP] = f([AHL]) at steady state.

If Hill functions fit these two curves good, the parameters used are surprising. For our system, we suppose that AHL binds to the regulator protein LuxR. This complex called Rlux dimerizes before binding to the promoter to induce its expression. Thus, the dimerization event makes cooperativity emerge from AHL molecules. It is translated for a Hill function by n > 1. In this particular case, one could expect to find n=2 (as it is a dimerization event). Nevertheless, the n found are on the order of magnitude of 1 (0.89 for the non-riboregulated promoter plasmid and 1.22 for the ribo-regulated promoter plasmid). The data points were collected in triplicates and this allow us to have a look at the variability (namely standard deviation) around each value. Where the switch happens, the variability is higher (it is expected because the output GFP is more sensitive to variation of the input [AHL] around the switching point). Therefore, the inflexion points could need some improvment, by taking more points around this identified sensitive region. Moreover, this critical concentration of AHL was the one that was expected given the litterature and our system. We observe that it needs a higher [AHL] for the riboregulated system to be activated than for the non-riboregulated system.

We modeled leakiness as an offset in the Hill function : [GFP] = g([AHL]) = f([AHL]) + aLeakiness. We obtain the expected information that the signal over noise ratio is greater by one order of magnitude for the riboregulated system than for the non-riboregulated system. A drawback from the riboregulated system is that the amplitude of the signal corresponds to the amplitude of the noise in the non-riboregulated system.

The experimental design also allowed us to detect eventual cross-talk with other signaling molecules, the one corresponding to the las system and the one corresponding to the rhl system. No cross-talk was observed with the signaling molecule of the rhl system. However, the las system signaling molecule activated the Lux promoter. We chose to model this cross-talk, which corresponds to the induction of a promoter, by an Hill function. This fitting allowed us to verify that the Hill function was adapted to describe a cross-talk phenomena. The derived parameters indicated that the concentration in the las signaling molecule had to be high in order to have an effect on our system (It was two orders of magnitude away from the needed concentration of AHL to activate the system). Nevertheless, once activated, the effects of these crosstalk are not to be neglected. Check the following article for more information on the experimental setting.

These results are promising and we look forward to fit the dynamic data of this system.