Team:UNITN-Trento/Modeling

Modeling

B. fruity exploits bacterial ethylene to ripen fruit. Given ethylene dangerous characteristics (flammable, asphyxiating, explosive) it is even more important to maintain ethylene concentration under a certain threshold or, even better, inside a certain interval.

For this purpose, we planned to model our light-regulated system and use the result to determine the required light induction pattern.

The model

For simplicity, we did not model the entire circuit (that you can find in the datapage). Instead, the model is based on the BBa_K1065302 part, which consists of YF1 and FixJ under R0010 followed by the amilGFP reporter gene under pFixK2. YF1 is the photo-sensor, FixJ is the response regulator (phosphorylated by YF1) and pFixK2 is the target of FixJ-P.

The main differences with the complete circuit are:

1. the inverter, which adds complexity, is not included in the model;
2. instead of EFE, the model contains the amilGFP reporter gene, which simplifies the retrieving of experimental data for parameter estimation.

Also, a couple of assumptions/approximations have been performed to simplify the model:

• the LOV domain is responsible for YF1 autodimerization. From literature it appears that YF1 has kinase net activity in the dark and phosphatase net activity in the light. It is not clear whether YF1 is able to phosphorylate FixJ only if dimerized, so the model do not include the dimerization reaction.
• in the light, YF1 has phosphatase net activity and so is responsible for FixJ-P dephosphorylation. The model does not contain the details of this reaction since they are not meaningful for our porpuse. The following Figure 1 shows our model, which can be found here.

Figure 1: the image shows the model behavior in the light (right) and in the dark (right). Red arrows indicate degradation reactions. In the light YF1 acts both as kinase and phosphatase.

Some kinetic constant have been found in literature and used as they were, other were estimated as an interval centered on the literature value and other were estimated from experimental data:

• Transcription kinetic was taken from BIONUMBERS (k = 0.33 1/s) and estimated for each reaction inside the interval I[0.1;1] 1/s
• RNA degradation kinetic was taken from BIONUMBERS, k = 0.011 1/s
• Protein degradation kinetic was taken from BIONUMBERS (k = 0.00083 1/s) and estimated for each reaction inside the interval I[1e-5;1e-3] 1/s
• Protein translation kinetic was taken from BIONUMBERS, k = 22 1/s
• The autophosphorylation kinetics in the light and in the dark, k3 and k3b, were taken from (Möglich A, J MOL BIOL, 2009, 385(5):1433-44)
• FixJ phosphorylation and FixJ-P de-phosphorylation kinetics, k4 and k4b, were estimated based on experimental data.
• Starting DNA concentration were estimated based on experimental data.

NEB10β cells transformed with BBa_K1065302, were grown in absolute darkness. When the colture arrived at an O.D.600 of 0.5, after nearly seven hours, a volume of 20ml was collected and analysed at the fluorimeter. The data retrieved from the fluorimetric analysis (Figure 2) have been used for parameter estimation.

Figure 2:

The result of a time-course simulation of 3e+6 seconds of our model is shown in Figure 3.

Figure 3: The light induction pattern

We added windows of “dark" and “light" exposure into the model. At first we simply added single windows of “dark" of various length (Figure 4), then we repeated the windows to make the enzyme production fluctuate into the desired interval (Figure 5).

Figure 4: a time-course simulation of 3e+05 seconds. The upper plot shows the amilGFP protein molar concentration while the lower shows the window of dark exposure (of 5e+03 seconds). IMMAGINE Figure 5:

This represent a proof of concept, since we do not have yet enough data on EFE production and on the EFE-ethylene relationship to model them.