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 results to determine the required light induction pattern. Given the complexity of the system and the fact that many variables are not present in literature, we hypothesized intra-cellular concentrations of reporter protein and estimated the parameters from these hypothetic data. This might be used as a proof of concept.

Of course a better approach would be to obtain experimental data on the intracellular concentration of the reporter protein. We are in the process of improving the model.

The model

For simplicity, we did not model the entire circuit (that can be found in the datapage). Instead, the model is based on the BBa_K1065302 part, that 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 will simplify the retrieving of experimental data for parameter estimation.

Also, a couple of assumptions/approximations have been arranged to simplify the model even more:

• 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 does not include the dimerization reaction.
• in the light, YF1 has phosphatase net activity and so is responsible for FixJ-P de-phosphorylation. The model does not contain all the details of this reaction since they are not meaningful for our purpose.

Figure 1 shows the modeled pathway. You can download our model (COPASI) here. Figure 1: the image shows the model behavior in the light (right) and in the dark (left). Red arrows indicate degradation reactions. In the light YF1 acts both as kinase and phosphatase.

Some kinetic constants have been found in literature and used as center of an interval to estimate the variables of our model, other variables were estimated from hypothetical data within constraints of our choice:

• Starting DNA concentrations were estimated based on hypothetical data within the interval [1e-6;1e-2]
• FixJ phosphorylation and FixJ-P de-phosphorylation kinetics, k4 and k4b, were estimated based on hypothetical data within the interval [0;10] 1/s
• Transcription kinetic was taken from BIONUMBERS (k = 0.33 1/s) and estimated for each reaction inside the interval [1e-4;1e-1] 1/s
• RNA degradation kinetic was taken from BIONUMBERS (k = 0.011 1/s) and estimated for each reaction inside the interval [1e-3;1e-1] 1/s
• Protein degradation kinetic was taken from BIONUMBERS (k = 0.00083 1/s) and estimated for each reaction inside the interval [1e-3;1e-1] 1/s
• Protein translation kinetic was taken from BIONUMBERS (k = 22 1/s) and estimated within the interval [1e-2;1] 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)

The result of a time-course simulation of 2e+05 seconds with a 8e+04 dark exposure window is shown in Figure 2.

Figure 2: the image shows the protein (also in the phosphorylated form, x-P) concentration over time. AmilGFP is produced only during the window of dark exposure. 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, then we repeated the windows to make the enzyme production fluctuate into the desired interval.

Figure 3. Left panel shows the purpose of our model: keeping the concentration of the protein under pFixK2 inside a certain interval. Right panel shows windows of light/dark exposure. Windows of 4,8e+03 s of dark exposure are spaced out by windows of 1e+03 s of light exposure. Thus, certain patterns of light induction can be theoretically used to maintain EFE concentration (and consequently ethylene concentration) under control.

This represents a proof of concept, since we are now in the process of implementing the model with experimental data.