Enhanced analysis of real-time PCR data by using a variable efficiency model: FPK-PCR

Abstract

Current methodology in real-time Polymerase chain reaction (PCR) analysis performs well provided PCR efficiency remains constant over reactions. Yet, small changes in efficiency can lead to large quantification errors. Particularly in biological samples, the possible presence of inhibitors forms a challenge. We present a new approach to single reaction efficiency calculation, called Full Process Kinetics-PCR (FPK-PCR). It combines a kinetically more realistic model with flexible adaptation to the full range of data. By reconstructing the entire chain of cycle efficiencies, rather than restricting the focus on a 'window of application', one extracts additional information and loses a level of arbitrariness. The maximal efficiency estimates returned by the model are comparable in accuracy and precision to both the golden standard of serial dilution and other single reaction efficiency methods. The cycle-to-cycle changes in efficiency, as described by the FPK-PCR procedure, stay considerably closer to the data than those from other S-shaped models. The assessment of individual cycle efficiencies returns more information than other single efficiency methods. It allows in-depth interpretation of real-time PCR data and reconstruction of the fluorescence data, providing quality control. Finally, by implementing a global efficiency model, reproducibility is improved as the selection of a window of application is avoided.

Figure 1.

The Linear Regression of Efficiency (LRE) approach. Cycle efficiency is regressed against cycle fluorescence. The window of application for the linear regression is designated by circles. The y-intercept of the regression line then yields the maximal efficiency estimate (Emax).

Figure 2.

Fold changes in baseline subtracted fluorescence per cycle for a single PCR reaction (soybean, le1 target, approximately 103600 initial copies) using the flat baseline model (open circle), the slanted baseline model (cross symbol) and the baseline protocol proposed by (12) (asterisk, carried out by the LinReg PCR program v12.11). Neither model displays an extended phase of true constant efficiency. Note the differences in cycle efficiency between the models during the ‘exponential phase’ (centered around cycle 21).

Figure 3.

Linear regression of the log transformed baseline subtracted fluorescence data for a single PCR reaction (soybean, le1 target approximately 103 600 initial copies) using three different approaches to determine the exponential phase [short dashed (blue), dotted (red) and long dashed (black) lines representing Equations 3, 4 and 5, respectively]. In (A) the flat baseline model was used, in (B) the slanted model was used, in (C) the baseline protocol proposed by (12) was used (carried out by the LinReg PCR program v12.11).

Figure 4.

The double log of the reaction efficiency is plotted against the fluorescence values for two soybean reactions with le1 target: in (A) approximately 103 600 initial targets were used and in (B) approximately 150 initial targets. Both panels demonstrate the application of the kinetic demarcations: data on the left hand side of the 5% line are considered to be part of the ‘ground phase’ of the reaction, the phase change is situated between the 85% and the 95% lines.

Figure 5.

FPK-PCR model fitted efficiency to a single soybean reaction with le1 target at approximately 103 600 initial copies. (A) displays the bilinear model fit (ln²E_n plotted versus ) whereas (B) plots the untransformed efficiencies, calculated from the bilinear model, against their respective cycles (E_n versus n).

Figure 6.

Comparison of the FPK-PCR efficiency model to other models used in the field of real-time PCR analysis. The different models are: the four parameter logistic model (4PLM, see Equation 6), the five parameter logistic model (5PLM, see Equation 1 and the sigmoid model [Sigmoid, as used in (19)]. Both panels (A) and (B) represent the cycle efficiency of the same reaction (soybean Le1 target, approximately 103 600 initial copies) once after double log transform, plotted against the cycle fluorescence (A), and once untransformed, plotted against the cycle number (B). In the latter panel, the mark on the right hand side of the vertical axis represents the efficiency estimate returned by the golden standard of serial dilution. To improve comparison between both panels cycles 10, 20, 30, and so on, have been marked with solid dots.

Figure 7.

Detailed comparison of the FPK-PCR efficiency model and other models fitted to a single PCR reaction (soybean Le1 target, approximately 103 600 initial copies). Fluorescence measurements are plotted versus their respective cycle number in three plots each containing a subset of the reaction data. In (A) cycles 1–15 are shown, illustrating the ground phase of the reaction. In (B) cycles 12–25 are shown, illustrating fluorescence emergence from the ground phase. In (C) cycles 30–45 are shown, detailing the gradual decrease in fluorescence growth and the onset of the plateau phase.

Figure 8.

Illustration of the effect of truncated data on two empirical model fits. In (A) the Four parameter logistic model is used. In (B) the Sigmoid model is used. In both cases the blue line represents the fit to the full reaction profile (60 cycles), whereas the red line represents the fit to the truncated dataset (40 cycles). Data truncation affects all model parameters both for the 4PLM (parameters: n_flex = 36.3, F₀ = 86.0, F_max = 5817 and b = −17.7 for the 40 cycle fit; n_flex = 38.1, F₀ = 52.4, F_max = 7633 and b = −12.2 for the 60 cycle fit) and for the sigmoid model (parameters: n_flex = 36.2, F₀ = 83.1, F_max = 5553 and k = 1.93 for the 40 cycle fit; n_flex = 38.1, F₀ = 29.7, F_max = 7561 and k = 3.05 for the 60 cycle fit). Note that in case of truncation the plateau is placed directly after the truncation, hence the cycle in which 95% of the total fluorescence is reached, is found within the available cycle range.

Figure 9.

Box and whisker plots for the results of the FPK-PCR approach on three soybean (le1 target) datasets: uninhibited (blue), containing tannic acid (orange) and containing isopropanol (red). For each dataset 5 initial target concentrations are shown, each dilution point contains approximately the same number of target copies for each dataset. (A) contains the efficiency estimates (E_max), (B) contains the initial target fluorescence estimates (α · i₀).