Model

Goal

We were asked about the sensitivity of the project by an expert during human practice, so we combined the data from the lab and aimed to find dissociation constants that measure the HBC dye and pepper aptamer.

In this model, we are going to use the Hill equation to measure the dissociation constant of HBC ligands with MALAT1-miRNA pepper constructs and therefore deduce the binding affinity of HBC and pepper aptamer.

Binding affinity is typically measured and reported by the equilibrium dissociation constant (KD), which is used to evaluate and rank order strengths of bimolecular interactions. The smaller the KD value, the greater the binding affinity of the ligand for its target. The larger the KD value, the more weakly the target molecule and ligand are attracted to and bind to one another.

Hypothesis

Pepper530 is monomeric with a very low dissociation constant for HBC (Kd≈3.5nM).[1] Using the hill equation dissociation rate and association rate can find pepper Kd. [2]

Assumption

Parameters affecting aptamer binding equilibrium such as Metal ions, pH, and temperature stay constant.

Method

Theoretically, we can know the concentration of pepper aptamer and MALAT1-miRNA complex from the brightness of gel electrophoresis [P0] . We assumed that all factors that will affect the binding affinity are constant, hence the concentration of microRNA145 is the total concentration of initially free aptamer concentration, which was 2ug shown in Table 1 (notebook).

In the experiment, we used HBC as a ligand to combine with pepper aptamer to see the fluorescence value to detect cervical cancer. Therefore, only when the pepper aptamer is combined with the HBC, the fluorescence value will be brightened. Figure 1: Using raw data distribution, we programmed those data on Python, and then we got interpolation data distribution which is shown in Figure 2. After that, we coded polynomial fitting on the data to deduce the corresponding fluorescence value of the pepper .

Therefore we substituted one of the fluorescence values (154871) at the miR-145 concentration is 2ug, so we could know the concentration of bound protein, which was 1.90ug.

Figure1. Raw data distribution

Figure 2. Interpolation data distribution

Figure 3. Fitting data distribution

In the experiment, we added 2 micro M of HBC dye to each well plate, so we could find the total ligand concentration according to the calculation.

n represents the Hill coefficient, it may describe cooperativity. According to the reference, in our model is equal to 1, which means the affinity of the enzyme for a ligand molecule is not dependent on whether or not other ligand molecules are already bound. [3]

Finally, according to the hill equation, we can calculate the dissociation constant of pepper and HBC, and hence the sensitivity.

Model and Results

Lis of notation

The Hill–Langmuir equation is a special case of a rectangular hyperbola and is commonly expressed in equation 1,

Conclusion

The model clearly shows that the fluorescence values can be used to calculate the concentration of bound protein, in this way, we can calculate the dissociation constant of HBC and pepper aptamer. With the model, we can also use the concentration of miRNA that was added to deduce the fluorescence values, and this method is important for early diagnosis of cervical cancer. Last, with the hill equation, the whole process of finding the dissociation constant is more straightforward and clear to be applied in a wide range.

Reference

[1] Chen, X., Zhang, D., Su, N., Bao, B., Xie, X., Zuo, F., ... & Yang, Y. (2019). Visualizing RNA dynamics in live cells with bright and stable fluorescent RNAs. Nature Biotechnology, 37(11), 1287-1293.ISO 690

[2] Goutelle, S., Maurin, M., Rougier, F., Barbaut, X., Bourguignon, L., Ducher, M., & Maire, P. (2008). The Hill equation: a review of its capabilities in pharmacological modeling. Fundamental & clinical pharmacology, 22(6), 633-648.ISO 690

[3] Rees, H. C. (2022). Crystal Structure-Driven Investigations of a Fluorogenic RNA Aptamer with Divalent Cation Dependence (Doctoral dissertation, The University of Chicago).