Theoretical Modeling of a Biosensor Expressing Nitrate Concentration in 3-Tiered Color Scale

In recent years, methods like spectroscopy have emerged as a viable option to accurately measure underwater concentrations of nitrate. Excessive nitrate levels in bodies of water cause environmental concerns, such as eutrophication. As such, the role of accurate and responsive sensors became significant in artificially maintaining the optimal nitrate level. Conventional techniques are costly, so monitoring a wide region like a lake is impractical. To address the aforementioned issue, we propose a cost-effective nitrate biosensor utilizing synthetic biology. The sensor expresses nitrate concentrations in a 3-tiered color scale through fluorescent protein. This paper discusses the mathematical approach to modeling this nitrate biosensor prior to the experiments handling living cells. The ultimate goal is to transition from green to red fluorescence as nitrate gets more concentrated. The mechanism for this involves various processes that happen simultaneously, effectively divided into three groups that each represent a component of the biosensor. We present a set of differential equations with relevant variables that model the behaviors of components in response to a spike in nitrate level. The ideal values for respective variables are determined by initializing them with arbitrary values and fine-tuning them by plotting them in Matlab. In conclusion, the model demonstrates the potential of the biosensor to detect underwater nitrate concentrations robustly.