# Physical Simulation-Based Calibration for Quantitative Real-Time PCR
## 4 On-Machine Test  
### Standard Curve Simulation  
First, a series of diluted standard substances were used to calibrate the sample linearity of the ABI 7500 qPCR instrument, in order to obtain a basic standard curve for simulation and comparative analysis. The standard substance used was the EGFR-1 (18-, 19-, 20-, 21-) gene mutation standard substance, which includes seven different dilution concentrations, as detailed in Table 4. The standard substance was placed into the 7500 qPCR instrument as depicted in Figure 10a. We set the fluorescence reporter to FAM and the thermal-cycling run method as follows: 50 \({}^{\circ}\)C for 2 min once, 95 \({}^{\circ}\)C for 10 min once, 95 \({}^{\circ}\)C for 30 s, 60 \({}^{\circ}\)C for 1 min \(\times\) 40 cycles, acquisition is performed in the 60 \({}^{\circ}\)C for 1 min step. The amplification results of the standard substances are shown in Figure 11, and the results are presented in Table 5. A standard curve for standard substances is plotted with the logarithm of the concentrations of the standard substances as the x-axis and the Ct values corresponding to each standard substance as the y-axis, as shown in Figure 12, which was automatically generated by the 7500 qPCR instrument. The regression coefficient representing sample linearity was calculated according to Equation (3). The linear correlation obtained was r = \(-\)0.9975 (R\({}^{2}\) = 0.995). Sample linearity characterizes how closely the regression line of a standard curve fits with Ct values of standards, indicating a \begin{table}
\begin{tabular}{c c c} \hline
**Name** & **Sample Type** & **Concentration** \\ \hline S1 & Standard & 1.04 \(\times\) 10\({}^{7}\) copies/uL \\ S2 & Standard & 1.06 \(\times\) 10\({}^{6}\) copies/uL \\ S3 & Standard & 1.06 \(\times\) 10\({}^{5}\) copies/uL \\ S4 & Standard & 1.07 \(\times\) 10\({}^{4}\) copies/uL \\ S5 & Standard & 1.12 \(\times\) 10\({}^{3}\) copies/uL \\ S6 & Standard & 1.10 \(\times\) 10\({}^{2}\) copies/uL \\ S7 & Standard & 1.11 \(\times\) 10\({}^{1}\) copies/uL \\ NTC & Negative control & 0 \\ \hline \end{tabular}
\end{table} 
Table 4: Reference material details. Figure 9: Measured luminance results when the relative luminance of a probe is 100%. high degree of fit between them; when r = 1, it indicates a perfect fit between the regression line and the data points [13]. \[r=\frac{\sum_{i=1}^{n}\left(Ct_{i}-\overline{Ct}\right)\left(lnc_{i}-\overline{ lnc}\right)}{\sum_{i=1}^{n}\left(Ct_{i}-\overline{Ct}\right)^{2}\sum_{i=1}^{n} \left(lnc_{i}-\overline{lnc}\right)^{2}} \tag{3}\]  
where the \(r\) represents the linear correlation coefficient; \(Ct_{i}\) denotes the \(i\)-th measured Ct value of serially diluted standard substances; \(\overline{Ct}\) is the mean measured Ct value of serially diluted standard substances; \(lnc_{i}\) stands for the logarithm of concentration values for the i-th dilution of standard substances; and \(\overline{lnc}\) represents the average logarithm of concentration values for serially diluted standard substances. Figure 11: Measured amplification curves of serially diluted standard substances. Figure 10: On-machine test scene. (**a**) On-machine test of standard substances. (**b**) On-machine test of calibration device. Since the calibration device relies on the variation in fluorescence intensity at the end of each cycle to simulate the fluorescence changes, Ct values can only be simulated as integers. Based on the distribution of Ct values of the standard substances, simulated Ct values and initial sample concentrations can be estimated. The calibration device has eight probes, which can simulate standard samples with eight different initial concentrations. Taking S1 as an example, the simulated logarithm of concentration value is 7 and the Ct value is 15; for S8, the simulated logarithm of concentration value is 0 and the Ct value is 36. The linear equation for drawing a standard curve with r = 1 would be: \(y=-3x+36\). The simulated logarithm of concentration values and Ct values for each probe can be calculated accordingly.