Shape based kinetic outlier detection in real-time PCR

Abstract

Background: Real-time PCR has recently become the technique of choice for absolute and relative nucleic acid quantification. The gold standard quantification method in real-time PCR assumes that the compared samples have similar PCR efficiency. However, many factors present in biological samples affect PCR kinetic, confounding quantification analysis. In this work we propose a new strategy to detect outlier samples, called SOD.

Results: Richards function was fitted on fluorescence readings to parameterize the amplification curves. There was not a significant correlation between calculated amplification parameters (plateau, slope and y-coordinate of the inflection point) and the Log of input DNA demonstrating that this approach can be used to achieve a "fingerprint" for each amplification curve. To identify the outlier runs, the calculated parameters of each unknown sample were compared to those of the standard samples. When a significant underestimation of starting DNA molecules was found, due to the presence of biological inhibitors such as tannic acid, IgG or quercitin, SOD efficiently marked these amplification profiles as outliers. SOD was subsequently compared with KOD, the current approach based on PCR efficiency estimation. The data obtained showed that SOD was more sensitive than KOD, whereas SOD and KOD were equally specific.

Conclusion: Our results demonstrated, for the first time, that outlier detection can be based on amplification shape instead of PCR efficiency. SOD represents an improvement in real-time PCR analysis because it decreases the variance of data thus increasing the reliability of quantification.

Figure 1

Linear regression analysis of standard samples. The amplification profiles were produced by averaging the fluorescence readings of twelve replicate reactions (A). Linear regression obtained plotting Log input DNA versus Ct (B).

Figure 2

Efficiency and shape parameter values of standard curve samples. The plots of efficiency (A), Fmax (B), Yf (C) and m (D) were shown; we reported in abscisse the Log transformation of input DNA and in ordinate the parameter value. The square represents the median, the length of the box shows the interquartile range and the whiskers indicate the min-max values of the estimated parameters.

Figure 3

Effect of tannic acid inhibition on amplification curve shape. Left upper panel: amplification profiles obtained from samples with equal starting number of template molecules and increasing inhibitor concentrations. For each inhibitor concentration only an amplification curve was plotted (instead of all 6 replicates). Values over and under triangle indicator (at the upper right of the Fig.) show the lowest and the highest inhibitor concentration used (A). Right upper panel: effect of PCR inhibition on the ratio Log(N_ob/N_exp) in the presence of equal starting number of template molecules and increasing inhibitor concentration. The ratio Log(N_ob/N_exp) represents the residues obtained from linear regression of calibration curves where LogN_ob is the number of calculated molecules using Ct method and N_exp is the number of expected molecules. Each symbol represents a single run. The abscisse axis is the mean and the dotted lines are the 95% confidence interval of the Log(N_ob/N_exp) ratio calculated from standard curve runs (B). Left lower panel: variation of F_max, Y_f. and m versus increasing inhibitor concentration. The variation is expressed as Relative Error = ; where is the mean of parameter calculated for each inhibitor concentration; represents the mean of parameter value from standard curve samples (C). Right lower panel: asymmetry values versus increasing inhibitor concentration. Asymmetry was computed as the following ratio: (D).

Figure 4

Effect of IgG inhibition on amplification curve shape. For details refer to figure legend 3.

Figure 5

Effect of quercitin inhibition on amplification curve shape. For details refer to figure legend 3.

Figure 6

Values of KOD and SOD related of each amplification curve versus Log of inhibitor concentration. Symbols (squares and dots) represent the χ² values related to each amplification curve obtained in the presence of different inhibitor concentrations. The horizontal continuous lines are the critical values for detecting outliers (left panels: the KOD χ² critical value is 3.84; right panels: the SOD χ² critical value is 7.81; with α = 0.05). Different inhibitors were used: Tannic acid (A-B), IgG (C-D) and Quercitin (E-F). True outliers (represented by black symbols; squares for KOD and dots for SOD) are amplification curves with Log(N_ob/N_exp) ratio out of 95% confidence interval, while white symbols represent acceptable runs with Log(N_ob/N_exp) ratio included in 95% confidence interval. The 95% confidence interval has been obtained from the amplification curves of the standard samples. The black symbols, over the horizontal continuous line, are runs correctly detected as outliers. Conversely, black symbols under this line are undetected outliers.