Team:BHSF/Model
Modeling
In order to find out the promoters with the most suitable intensity to construct the toggle switch, we created a model with the intensity of promoter as independent variable, and the concentration of two protein as dependent variable.
Principle of toggle switch
Promoter A (in red) and Promoter B (in yellow) are in charge of expressing Protein A (red) and Protein B (yellow) respectively in the circuit. The Protein A inhibits Promoter B, and vice versa.
Before we trigger the switch, the switch is kept at “off” state, where protein A gets to express, repressing expression of the gene of protein B nearly to the full extent.
After the gene of protein B starts expressing outside the switch, its over-expression triggers the switch to be turned on, and the expression of the other inhibitor protein A is rapidly shut down, leading to a drop in its concentration, and eventually, the transition of the switch from off to on state.
As different combination of promoter strengths gives different initial concentration of protein A, as well as different rate of protein B accumulation, the choice of promoters will decide the transition time of our toggle switch, i.e. the fermentation time of our timer yeast. To this end, we built the model as follows:
Our model
In our model, u is the concentration of repressor 1, v is the concentration of repressor 2, a1 is the effective rate of synthesis of repressor 1, a2 is the effective rate of synthesis of repressor 2, b is the cooperativity of repression of promoter 2 and g is the cooperativity of repression of promoter 1.
The model above is derived from a biochemical rate equation formulation of gene expression. [1-4]
The final form of the toggle equations retains the two most basic aspects of the network: cooperative repression of promoters that are transcribed constitutively (the first term in each equation), and degradation/dilution of the repressors (the second term in each equation).
In our project, we will randomly selected one or several pairs of promoters and test the transition time of each pair. Then, by plugging the experiment data, we will able to fix the formula and get a more precise relation between transition time and promoter strengths, therefore find appropriate combinations to meet different needs of fermentation time.
With this model, we will be able to reduce the amount of experiment needed for testing the promoter, and our workload and chance of failure greatly decreased.
Reference
1. Edelstein-Keshet, L. Mathematical Models in Biology (McGraw-Hill, New York, 1988).
2. Kaplan, D. & Glass, L. Understanding Nonlinear Dynamics (Springer, New York, 1995).
3. Yagil, E. & Yagil, G. On the relation between effector concentration and the rate of induced enzyme
synthesis. Biophys. J. 11, 11卤27 (1971).
4. Rubinow, S. I. Introduction to Mathematical Biology (Wiley, New York, 1975).
