System-specific periodicity in quantitative real-time polymerase chain reaction data questions threshold-based quantitation

Abstract

Real-time quantitative polymerase chain reaction (qPCR) data are found to display periodic patterns in the fluorescence intensity as a function of sample number for fixed cycle number. This behavior is seen for technical replicate datasets recorded on several different commercial instruments; it occurs in the baseline region and typically increases with increasing cycle number in the growth and plateau regions. Autocorrelation analysis reveals periodicities of 12 for 96-well systems and 24 for a 384-well system, indicating a correlation with block architecture. Passive dye experiments show that the effect may be from optical detector bias. Importantly, the signal periodicity manifests as periodicity in quantification cycle (C_q) values when these are estimated by the widely applied fixed threshold approach, but not when scale-insensitive markers like first- and second-derivative maxima are used. Accordingly, any scale variability in the growth curves will lead to bias in constant-threshold-based C_qs, making it mandatory that workers should either use scale-insensitive C_qs or normalize their growth curves to constant amplitude before applying the constant threshold method.

Figure 1. Discovering periodicity in raw and baselined qPCR data.

(A) Plot of raw fluorescence values of the ‘380-replicates’ dataset from, color-coded by sample number. (B) Same as in (A), but raw fluorescence data baselined by a linear model obtained from the first 10 cycles. Black boxes mark cycles 10, 20 and 40. (C) Fluorescence values at cycle 10 from the raw data of (A) throughout all 379 samples. A Loess smoother line was superimposed on the data to visualize periodicity. (D),(E) and (F) Fluorescence values at cycles 10, 20, and 40 from the baselined data of (B), with Loess smoother lines added in each case.

Figure 2. Principle analysis pipeline as demonstrated on the ‘380-replicates’ dataset.

(A) Repetition of Fig. 1B, with selection of cycle 20 for periodicity analysis. (B) Cycle 20 data plotted against sample number and fitted to a quadratic model. (C) The residuals of the quadratic model are plotted against sample number, and a Loess curve is fitted to the data in order to visualize periodicity. A Runs test and a Ljung-Box test are performed to check for randomness and autocorrelated residuals, respectively. (D) The residuals from (B) are subjected to an autocorrelation function with lags 1…n, and the autocorrelations are plotted as a function of lag. Periodicities are estimated from the autocorrelation peaks by the findpeaks function.

Figure 3. Detection of periodicity in baselined qPCR data acquired by six different hardware systems.

Based on the analysis pipeline defined in Fig. 2, six different qPCR hardware systems (Bio-Rad CFX384, Biorad CFX96, Qiagen Rotorgene, Biorad iQ5, LifeSciences StepOne and Roche LC96) were analysed with respect to periodicity of fluorescence values for cycles early in the exponential region (red vertical line) using baselined data. Strong periodic patterns are evident for Biorad CFX384, Biorad CFX96 and LifeSciences StepOne while slight to almost negligible periodicity is visible for Qiagen Rotorgene, Biorad iQ5 and Roche LC96, as measured by Runs test and Ljung-Box test on the residuals. Omitted x-axis labels are those found for the different graphs types in Fig. 2. RFU: raw fluorescence units; RV: residual value; COR: autocorrelation.

Figure 4. Impact of periodicity on C_t and C_qSDM estimation and the effect of normalization.

(A) A five-parameter sigmoidal function was fitted to the baselined fluorescence values of the ‘380-replicates’ dataset and C_t values (red box) calculated at a threshold fluorescence of F_t = 500 by the inverse function. Autocorrelation analysis of these C_t values indicates strong and significant periodicity (right panel). (B) From the same fits as in (A), but C_q values estimated from SDM (C_qSDM). Autocorrelation analysis of these C_q values indicates removal of periodicity and random pattern with insignificant Runs test p-value (right panel). (C) Fluorescence values were normalized (rescaled) into the interval [0, 1], fitted with a five-parameter sigmoidal model and C_t values calculated at F_t = 0.1 (red box). Similar to (B), autocorrelation analysis of the C_t values indicates removal of periodicity and random pattern with insignificant Runs test p-value (right panel). Omitted x-axis labels are those found for the different graphs types in Fig. 2. RFU: raw fluorescence units; RV: residual value; COR: autocorrelation.

Figure 5. Non-amplification periodicity acquired by cycling a qPCR mastermix without template with three different fluorescent dyes.

ROX (A), SYBR Green (B) and a Cy5-labeled Oligo-dT₂₀ oligonucleotide (C) were subjected to 40 cycles. Shown are the fluorescence values at cycles 1 (red), 10 (green) and 20 (blue) throughout all 96 samples, obtained from the three different channels. Periodicity is evident for ROX and Cy5, and to a lesser extent for SYBR Green. (D) The EvaGreen-based fluorescence values at Cycle 20 (with periodicity) was normalized with the corresponding ROX-based fluorescence values (with periodicity), resulting in periodic data with significantly lower magnitude. RFU: raw fluorescence units; COR: autocorrelation.