Validation

To validate our heuristic method, we ran two experiments where we tried to stabilize the concentration of living cells in a bacterial culture during 5 consecutive hours. Both were successful, and we will report in more detail one of them.

Experiment

In the first part of the experiment, we first determined the parameters of the model that describe the behavior of our cell culture, according to the procedure described in the modeling part.

The first part of the experiment followed a protocol close to the other:

1.0-90 min : this first incubation was done in the dark to let the bacteria grow and produce KillerRed.

2. 90-330 min : a longer 4 hours period with illumination at maximal intensity. After that time, the effects of light were clear, and the parameters of the model were calculated to fit the observable kinetics.

3. 330-450 min : Then our model was used to calculate the light intensity that would stabilize the population of living cells : light was applied at 70% of its maximal intensity.

4. 450-720 min : After 2 hours, we noticed that the fluorescence and the absorbance were slowly drifting away from the predictions. Since the fluorescence was higher than expected and the OD was lower than expected, we reduced the illumination to 50% of its maximal intensity for 2 hours and then at 40% of its maximal intensity.

On the curves below:

$\bullet$ The red surface is the prediction of absorbance caused by dead bacteria ($D$, in $OD_{600}$) on the absorbance curve, and the prediction of fluorescence caused by KillerRed stored in dead bacteria ($K_D$, in $UF$) on the fluorescence curve.

$\bullet$ The yellow surface is the prediction of absorbance caused by living bacteria ($C$, in $OD_{600}$) on the absorbance curve, and the prediction of fluorescence caused by KillerRed stored in living bacteria ($K$, in $UF$) on the fluorescence curve.

$\bullet$ The blue line follows the collected datas.

Step 1: We ran the the experiment to be able to improve the fit of parameters (90 minutes in the dark, then 3 hours at maximal intensity). The predictions below were calculated with parameters of the previous experience, we see that on this one, bacteria are growing slower, and procuce less KillerRed.

Step 2 ($t=330min$):

$\diamond$ modification of parameters to improve the fit.

$\diamond$ creation of prediction with different light intensity.

$\diamond$ selfction of the intensity that will stabilise the bacterial population, here $I=70%$ of maximal intensity.

Step 3 ($t=330min$):

We observed that the fluorescence and the absorbance were too low compared to the prevision, so light intensity was decreased at $I=50%$ of maximal intensity.

Step 4 ($t=570min$):

The fluorescence and the absorbance were still too low copmpared to the prevision, light intensity was decreased at $I=40%$ of maximal intensity.

Step 5($t=660min$):

The absorbance as grown up at a steady we have just obtained a level of more than 5 hours

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