— Assumptions —

1. Our GFPs’ degradation rate is approximately 25 hours.
2. Calcium in the cytosol is unable to activate our reporter genes mNeonGreen and sfGFP.
3. Calcium binds to Calmodulin and all the calcium-bound Calmodulin will bind to Calcineurin to make activated Calcineurin.
4. Activated Calcineurin will dephosphorylate Crz1p.
5. Dephosphorylated Crz1p will interact with PMC1 promoter to enable mNeonGreen and sfGFP expression.
6. Dephosphorylated Crz1p diffuses into the nucleus.
7.mNeonGreen and sfGFP’s degradation rates are similar to the degradation rate of GFP.

We modified Johns Hopkins’s 2010 iGEM model to show our gene reporter concentration curves at different levels of initial calcium concentration levels. Our constants for the model are:

— Setting System of Differential Equations of our Reporter Genes,
mNeonGreen & sfGFP, and Crz1p concentration curves: —

From this graph, our GFP expressions grow to detectable levels after approximately 2 days. The difference in our GFP concentration curves is dependent on the initial calcium concentration from the environment. Since we assume our reporter gene mNeonGreen and sfGFP’s degradation rates are similar to that of GFP, we only need one GFP concentration curves.

From this graph, we can see the proportional relationship between Crz1p and Calcium concentration. Our dephosphorylated Crz1p concentration curves returns to the initial condition, which is set to be zero, after approximately 40 minutes.

Our model helps us choose PMC1 as our promoter because PMC1 has low calcium sensitivity, i.e. PMC1 only activates at high level of Calcium, and is exclusively activated by Calcium.

— References —

[1] Jiangjun Cui, Jaap A. Kaandorp, Mathematical modeling of calcium homeostasis in yeast cells, In Cell Calcium, Volume 39, Issue 4, 2006, Pages 337-348, ISSN 0143-4160,
[2] Brian P. Ingalls, Mathematical Modeling in System Biology: an Introduction, The MIT Press, 2013.
[3] Weijiu Liu, Introduction to Modeling Biological Cellular Control Systems: Modeling, Simulation & Applications, Springer, 2012.
[4] James B. Riggs, Programming with MATLAB for Engineers , Ferret Publishing, 2014
[5] Stormy Attaway, MATLAB A Practical Introduction to Programming and Trouble Solving Fourth Edition, Butterworth-Heinemann, 2017