# Modeling

# Mathematically Modeling ChiSPY

To demonstrate and evaluate the specifications of the chitin biosensor, mathematical models of the ChiSPY system were constructed using MatLab. Because the *V. cholerae* one-component chitin-utilization program is a relatively uncharacterized system, our models will use parameters estimated from comparable systems and sensitivity analysis will be performed on them to better represent the kinetics of the system. The models aimed to answer the following questions:

*What concentration range of chitin will our biosensor detect?*

*What is the detection time of our biosensor?*

*What concentration ranges of GFP will be produced to indicate “x” amount of chitin detected?*

*What concentration ranges of GFP will be produced to indicate “x” amount of chitin detected?*

*What is the maximum level of GFP expression?*

#### Assumptions

The chitin sensing pathway from *V. cholerae* is a complex biological mechanism that necessitates simplification for modeling purposes.

*The amount of chitin in the periplasm remains constant (is not consumed)*

* Chitin binding protein (CBP) is in abundance and saturates ChiS*

*The amount of time it takes for chitin to enter the cell is negligible*

*Chitin binds to CBP only when CBP is bound to ChiS *

#### Determining Parameters

Once we conduct the plate reader experiments to read fluorescence output of our biosensor, sensitivity analysis will be performed on the parameters so that they best fit the data gathered and better represent the kinetics of our system.

#### Results & Conclusions

After plotting the ODEs listed above, the above graph shows us that when chitin fully saturates CBP_ChiS complexes, the biosensor takes between 200 and 300 seconds to reach maximum protein translation. Now that we can estimate the maximum level of sfGFP that gets translated, we can lower the amount of chitin oligos below the cell’s saturation point and observe the different levels of GFP production.

The above graph shows how the concentration of sfGFP translated changes with varying concentrations of chitin. As we can see, the maximum GFP translation is induced by 210 molecules of chitin and above.

### Sources

**[1]** Klancher, Catherine A., et al. “ChiS Is a Noncanonical DNA-Binding Hybrid SENSOR Kinase That DIRECTLY Regulates the CHITIN Utilization Program in Vibrio Cholerae.” PNAS, National Academy of Sciences, 18 Aug. 2020, www.pnas.org/content/117/33/20180.

**[2]** Martineau P, Szmelcman S, Spurlino JC, Quiocho FA, Hofnung M. Genetic approach to the role of tryptophan residues in the activities and fluorescence of a bacterial periplasmic maltose-binding protein. J Mol Biol. 1990 Jul 5 214(1):337-52.

**[3]**Wong P, Gladney S, Keasling JD. Mathematical model of the lac operon: inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose. Biotechnol Prog. 1997 Mar-Apr13(2):132-43.

**[4]** ETH_Zurich. Pavolv's Coli Parameters. (n.d.). Retrieved October 20, 2021, from https://2016.igem.org/Team:ETH_Zurich/Parameters