Two Component System

The two components in the TCS in our case are SaeS and SaeR. SaeS senses the change in the concentration of zinc ions, which causes downstream phosphorylation of SaeR. Phosphorylated SaeR can act as a transcription factor for the promoter phla.Under phla, we express fluorescent protein, which is mCerulean in our case.

The change in the concentration of zinc ions alters the autophosphorylation rate of SaeS, which refers to the rate of SaeS gaining a phosphate group. After obtaining a phosphate group, SaeS would act as a kinase and transfer it to SaeR. Phosphorylated SaeR would dimerize and bind to DNA to regulate gene expression.

We studied the dynamics of the Sae system using a phla - mCerluean generator (BBa_K4822007) in the pSB1C3 backbone in a DH5α E. coli strain. We chose ordinary differential equations to illustrate the interaction between zinc ion concentrations and the Sae system, consequently influencing the expression of FP in the cells. The modeling process was conducted using MATLAB R2022b.

Assumption of the model

The parameters values are found in vitro experiment. However, experiments involving radioactivity are not allowed in our school.If there is a chance to conduct experiments to obtain these parameters in the future, modeling and simulating can be done in MATLAB. Some assumption of the model is as follows.

• In this model only one stimulus is under investigation and it represented as a fixed parameter.
• Phosphorylation of response regulator by alternative phosphor donor is ignored.
• The dephosphorylation of response regulator is solely dependent on sensor kinase and rate of dephosphorylation decay is taken into consideration.
• Non- specific binding of the response regulator to other DNA binding site is neglected in the model.
• Sensor kinase acts as an enzyme that de-phosphorylated phosphorylated response regulators.

Equations of the model

The basic reaction equations are as follows, which include the autophosphorylation of SaeS, dephosphorylation, phosphorus transfer between SaeS and SaeR, and free DNA binding to SaeR.

Based on the experimental results fitted with a logarithmic function for trend analysis, we can observe a correlation between standardized mCerulean intensity and the concentration of zinc ions. According to our empirical findings, it is only when the concentration of zinc ions exceeds 1 mM that we can observe the inhibition of fluorescent protein gene expression. In the future, we plan to continue increasing the dataset to enhance the reliability of the trend line and reduce errors.