Team:Strasbourg/Model

iGEM

Modeling with GFP

Theoretical modeling is very useful in science, as it helps us to construct, evaluate and understand nature. It allows us to make predictions of a system in order to improve the results of our experiments as well as to try hypothetical conditions in order to determine the optimal setup for our experiments.
Our project for this year is to develop a future allergen detection kit, based on the triple hybrid system (BH3) implemented in E. coli and regulated by aptazymes, which in presence of its respective ligand, undergo to self-cleavage or not depending on the aptazyme. Importantly, their extremities are fused with PP7 and MS2 stem-loops RNA, and are used to recruit a hybrid RNA upstream of a lacZ promoter which triggers the production of β-galactosidase. This signal is strong and easy to measure, allowing us to know if the ligand is present or not.
The benefit of this approach is the flexibility provided by the aptazyme, which can be interchanged for specific allergens. The aptazyme is an RNA molecule whose price for synthesis is continuously decreasing with the breakthrough in molecular biology. Therefore, it allows the development of a cheap and easy-to-use test.
We were inspired by the diffusion model proposed by iGEM Oxford team 2015. Therefore, we decided to model the GFP expression based on arabinose induction in order to know which quantity of arabinose would be necessary to induce the pBAD promoter - which then induces the aptazyme transduction in one of our plasmids. We used ordinary differential equations (ODE) which involve functions of only one independent variable and one or more of their derivatives with respect to that variable. They are widespread formalism to model dynamical systems in science and engineering. In systems biology, many biological processes such as gene regulation and signal transduction can be modelled by reaction-rate equations expressing the rate of production of one species (e.g., protein, mRNA, metabolite, or small molecules) as a function of the concentration of other species in the system [1].
In order to predict the GFP expression in our system, we adapted the chemical equations proposed by iGEM Oxford team 2015 to our system:

Arabinose induces the transcription of our GFP gene. We will assume that the arabinose concentrations are constants. The rate constant, K from Michaelis-Menten enzyme kinetics model, is a proportionality constant which indicates the relationship between the molar concentration of reactants and the rate of a chemical reaction [2].
Using Michaelis-Menten kinetics, are described the next equations:

where arabinose means the concentration of arabinose used in the model and GPF represents the production of this protein.
The parameters used in this model are mentioned below:

In our BH3 system the arabinose induces the aptazyme transduction, so we decided to model the activity of our pBAD promoter with different inputs of arabinose concentrations, in order to know how much arabinose is needed for the optimal production of our aptazymes.
The code of our modeling was implemented in Wolfram Mathematica in which A represents the arabinose concentration:

The results of the modelling are presented below:

0.1% Arabinose concentration
0.2% Arabinose concentration

After having made several simulations with different arabinose concentrations, we decided to use a 0.2% arabinose concentration for the induction of the aptazyme production in our BH3 system. Due to this, it allowed us to have maximal fluorescence yields, as well as higher production of our protein compared with the 0.1% induction. Additionally, this concentration is not toxic for the bacteria. We corroborated our results with a paper from Morgan-Kiss et al., (2002) which proves by experimental procedures that the 0.2% concentration is optimal for the induction of pBAD promoter. Thanks to the implementation of this model, we were able to induce optimally the aptazyme production in our system.

References

  1. Wang, Y. 2014. Discussion on the Complicated Topological Dynamic System of Ordinary Differential Equation (ODE). Applied Mechanics and Materials 696, 30-37.
  2. Connors, K. 1990. Chemical Kinetics: The Study of Reaction Rates in Solution. John Wiley & Sons ISBN 978-0-471-72020-1.
  3. Proshkin, S., Rahmouni, A. R., Mironov, A., Nudler, E. 2010. Cooperation between translating ribosomes and RNA polymerase in transcription elongation. Science.
  4. Sourjik, V., Berg, H. C. 2004. Functional interactions between receptors in bacterial chemotaxis. Nature.
  5. Salto, R., Delgado, A., Michán, C., Marqués, S., Ramos, J. L. 1998. Modulation of the function of the signal receptor domain of XylR, a member of a family of prokaryotic enhancer-like positive regulators. J Bacteriol.
  6. Selinger, D. W., Saxena, R. M., Cheung, K. J., Church, G. M., Rosenow, C. 2003. Global RNA half-life analysis in Escherichia coli reveals positional patterns of transcript degradation. Genome Res.
  7. Andersen, J. B., Sternberg, C., Poulsen, L. K., Bjorn, S. P., Givskov, M., Molin, S. 1998. New Unstable Variants of Green Fluorescent Protein for Studies of Transient Gene Expression in Bacteria. Appl Environ Microbiol.
  8. Morgan-Kiss, R. M., Wadler, C., Cronan, J. E. 2002. Long-term and homogeneous regulation of the Escherichia coli araBAD promoter by use of a lactose transporter of relaxed specificity. Proceedings of the National Academy of Sciences of the United States of America.