Figure 1.
In panel A, product formation (green circles) is modeled to accumulate with a perfect, constant efficiency of 100% (blue diamonds) using equation 4 (Information S1). The simulated data was fit using non-linear regression using the same function (black line). Panel B, simulated data of a purely reagent-limited reaction is shown using equation 5 with a maximum product yield of 5×106 (also fit to its function). Panel C, simulated data is shown using the PCR equation 6 with a max value of 5×106 and a Kd value of 5×105. The efficiency terms at each cycle were extracted and plotted as blue diamonds. Panel D shows examples of real qPCR data fitted to equation 6 from amplifications using cDNA libraries generated from total E. coli RNA as templates. The resulting fitting values were: rpsO, max = 25.148, Kd = 1.6798, R2 = 0.99996; gapA, max = 19.56, Kd = 1.5753, R2 = 0.99998; lacZ, max = 16.29, Kd = 1.141, R2 = 0.99996.
Figure 2.
Simulated PCR and cycle threshold analysis.
In panel A, PCR product formation was modeled according to equation 6 with max = 5×106 and Kd = 5×105. Four data points are highlighted that depict the region when the signal reached 1% of the final maximum observed. The data was transformed into log2 and the same 4 points were fit using linear regression. The slope and intercept from that fit were used to construct a straight line that was overlaid onto the log2 plot (panel B, diamonds). Note that the line does not predict the true progression of product at earlier cycles. Also, the earlier a reliable signal can be observed, the more accurate the estimation of the trend is. Panel C, the derivative of the log2 data. A value of 1 means that the efficiency was 100 % and the product doubled during that cycle. The region fitted for the cycle threshold analysis is marked in red and each value is lower than all preceding cycles.
Figure 3.
The PCR equation 6 is fitted to experimental data with weighting for stronger signals by floating the values max and Kd. These values are then used to generate simulated data and a seed amount is computed that best superimposes the simulated data onto the experimental data. The relative values of seed correspond to the relative amounts of template DNA at that cycle.
Figure 4.
Using regression to determine relative abundance.
Panel A, 6 independently-mixed qPCR samples that amplified cDNA from the ompT gene were fitted to PCR equation 6 to obtain max and Kd values. These were then used in a spreadsheet to model synthetic data. The hypothetical DNA amount present as seeding doses in cycles 4, 9, 14, and 19 (arrows) were computationally floated to minimize the differences between the simulated and real data in cycles 5 plus through 20 plus respectively. The seed amounts present in cycles 4 and 19 differed by more than 3×104. Panel B, The calculated seed amounts are plotted as fractions of the mean (straight lines) with dotted lines connecting the data from two outliers to highlight the small variance when different cycles were used in the regressions of the same sample.
Figure 5.
Regression analysis is insensitive to reaction efficiency and template abundance.
Panel A, six qPCR mixtures targeting the E. coli gapA cDNA contained either 0, 0.01, 0.03, 0.12, 0.5, or 2 units of thermostable inorganic pyrophosphatase (New England Biolabs) added as 1 μL of a 20 μL reaction. The remaining volume was matched using the same storage buffer lacking enzyme. Fitting of the resulting amplification profiles with the PCR equation 6 (lines) yielded max and Kd values that were used to calculate relative abundance in cycle 14 (arrow). The same data was also analyzed using the Ct method for comparison (inset). Panel B, a series of cDNA libraries were used as templates for qPCR that had been generated from an experiment in which the gapA mRNA levels changed drastically over time (series A and B). For clarity, only the data fitting curves are shown for series B in which the template abundance changed more than 20-fold. Both regression (circles) and Ct (squares) analyses were performed on the same data and the relative abundance plotted as a function of time (inset). Note that the resulting values described the same relative changes and trends, but that the regression method yielded smoother data.