Team:ZJUT China B/Model
Modeling
Fluorescence bleaching kinetics
For a certain concentration of target and Cas proteins, they will combine to generate a certain concentration of complex. Assuming that the cleavage of the reporter by the Cas protein conforms to the Michaelis-Menten equation, the photodegradation effect of fluorescein is proportional to the concentration of fluorescein. Assuming that in the case of excess Cas protein, a complex with the same concentration as the target can be generated, and we have the following equation(Figure 1-2):
Figure 1. Visualized mathematical model in MATLAB-Simbiology
Equation 1. Main equation
FQ：reporter
F: Free fluorescein {Here F is RFU (Relative Fluorescence Unit), which is proportional to the amount of free fluorescein}
complex: Activated Cas13 protein, Cas (pre-combined crRNA) and target polymer
r: Fluorescence degradation reaction
cleavage: The reaction of Cas protein and reporter
This equation reflects the effect of enzyme activity on the fluorescence intensity-time curve.
Figure 2. Parameter sensitivity analysis
Figure 3. Data diagram obtained according to the assumed parameters
Through parameter sensitivity analysis (Figure 2), we found that kr has the greatest influence on the curve, but it depends on the nature of fluorescein which we can not control. In addition, cleavage. k is the most influential parameter. Therefore, we performed a scan on k and plotted the different values of k separately. We found that if the actual fluorescence bleaching effect is considered, the activity of the protein is critical. The higher the activity of the protein, the shorter the time to reach the maximum fluorescence and the greater the fluorescence value. And if the activity of the protein decreases (the most notable feature is the decreasing of k value), the time required for the fluorescence intensity to reach the maximum value becomes longer and the maximum value decreases. Therefore, it is very important to improve the activity of cas protein. While improving the detection sensitivity, the detection time is shortened (Figure 3).
At the CCiC exchange meeting, we were fortunate to meet a high school team from Tsinghua High School. They use Tardigrade intrinsically disordered proteins (TDPs) to reduce the influence that the protein freeze-drying has on the protein activity. We are cooperating with Tsinghua Middle School on the project, hoping to reduce the detection sensitivity of Cas protein due to freeze-drying, thereby improving our detection effect.
Parameter fitting
In the later stage of the experiment, we used the successfully expressed Cas13 Lwa protein for testing. Add a small amount of sample to the 384-well plate, blank control group: no reporter, containing Cas protein 4. 5 E 10-8 mol/L and target 2. 25E-8 mol/L; negative control group: containing Cas protein and reporter 125 nmol /L, no target; positive experimental group: contains Cas protein and reporter 125 nmol/L, target 2. 25E-8 mol/L. Four parallels are set respectively. Start timing from adding target, count every 5 minutes, and draw a kinetic curve of fluorescein intensity with a microplate reader, the unit is RFU (Relative Fluorescence Unit). In the post-processing, the average value was taken and the blank control value was subtracted (Figure 4).
Figure 4. Lwa dynamic curve
Figure 5. Curve of parameter fitting
Figure 6. Comparison of prediction and true value
We fitted the data with the mathematical model and found a higher degree of fit (Figure 5-6) This proves that the construction of our model is correct, and it also proves the rationality of the experimental data.
Figure 7. Scan re-made based on the fitted data
Data from the laboratory
We used the same method to experiment with Cas13 Lwa protein lyophilization. The data returned from the laboratory (Figure 8) can also reflect the correctness of our model. Under the condition of one hour of reaction, the fluorescence signal produced by the freeze-dried protein is indeed much lower.
Figure 8. Data from the laboratory
References
[1]Kellner MJ, Koob JG, Gootenberg JS, Abudayyeh OO, Zhang F. SHERLOCK: nucleic acid detection with CRISPR nucleases. Nat Protoc. 2019 Oct;14(10):2986-3012. doi: 10. 1038/s41596-019-0210-2. Epub 2019 Sep 23. Erratum in: Nat Protoc. 2020 Mar;15(3):1311. PMID: 31548639; PMCID: PMC6956564.
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