Difference between revisions of "Team:Stockholm/Modeling"

Modeling

Our main goal was to estimate how the osmolarity in the cell's environment correlates with the signal from GFP production. For that we decided to divide our system into four main models:

Parts 1 & 2: OmpR phosphorylation and OmpC translation

We wanted to insert the EnvZ receptor into a bacterial cell to activate a signal cascade including four main parts (OmpR production, OmpC translation, quorum sensing and GFP expression). For the first two parts, OmpR and OmpC production, we used already published research to find equations describing the main reactions and their rate constants . We designed those models with the help of SimBiology software, a plug-in installed in MatLab. The designing was done by drawing them qualitatively, choosing the kinetics and adding all the constants. We then put the two parts together. Finally, we designed the OmpC production-reduction EnvZ switch depending on the osmolarity level.

The way to design a model is to define each compartment, in this case the cell membrane and the cytoplasm. Each reactant is a chemical entity that is connected to another reactant by a corresponding chemical reaction. Each reaction has a specific kinetic rate. The kinetic law Mass Action is selected if the kinetics is unknown.

Since we wanted our final product to be OmpC or OmpF (depending on the surrounding osmolarity), we chose to make two models for each scenario. This was done in order to get a better understanding of how the osmolarity changes the endpoint. In our case, it was the osmolarity-dependent GFP expression.

After the model was designed and a simulation created, we could change the initial data and study how each component is codependent.

Part 3: release of quorum sensing (QS) molecules

At first we decided to use the same procedure as with the previous parts. But, after a lot of trial and error, we contacted the Modeling Representative from the Technion 2014 iGEM, Ittai Rubinstein, and got several tips on how to proceed. One of them was to use MatLab instead of SimBiology. This could be done by deriving our own equations from the SimBiology model. Most of the biological systems can be easily converted into a series of Ordinary Differential Equations (ODEs). A steady state solution of those ODEs is the simplest model that can be produced. For the time dependency and feedback loop inclusion, which is present in our model, we actually needed to find a numerical solution for the ODEs, since a steady state is not sufficient to reflect the biological environment. Generally, the variant of the Euler’s method could be adequate, especially for ODEs of higher degrees.

To estimate the degree of error approximated and time-dependent Fokker-Plank Partial Differential Equation was used (Fokker-Plank PDE). Eventually, quorum-sensing signaling could also be modeled by the use of averaging effect that is separated from the intracellular modeling. This would let us demonstrate the ability of the system to reduce the noise.

Our team got all the ideas and procedures involving mathematical concepts and Generalized Promoter Binding from the representation of the iGEM Technion 2014. The file with detailed description of the mathematical concepts prepared by this team can be found in the following file:

Nevertheless, as a team, we decided to follow the SimBiology modeling that is represented in the next part of the modeling part of the project. We designed the Part 3 of the modeling using the BHL and LuxR quorum sensing systems.

Part 4: GFP expression

The GFP production is the last part of our model. With the help of measuring the GFP production we would hopefully, in theory, be able to estimate the EnvZ concentration by looking at their correlation.

Conclusion

Using previous publications on modeling and doing a research on general kinetic constants that could be implemented to our model we managed to simulate that obtained data in the MatLab plug-in called SimBiology and predict the outcome of our system depending on the starting concentrations. This, in turn, let us to optimize the system for a given substantial input and successfully predict ensuing alterations in the cellular compounds’ concentrations over time.

Appendix: Equations for SimBiology

Model 1: EnvZ to OmpC (high osmolarity)

Model 2: EnvZ to OmpF (low osmolarity)

Model 3: quorum sensing for BHL molecule

Model 4: quorum sensing for LuxR molecule

The rate constant in each model is not related to one from another model.

References