A fixed-point algorithm for estimating amplification efficiency from a polymerase chain reaction dilution series
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Background The polymerase chain reaction amplifies and quantifies small amounts of DNA. It is a cyclic process, during each cycle of which each strand of template DNA is copied with probability approaching one: the amount of DNA approximately doubles and this amount can be estimated fluorimetrically each cycle, producing a set of fluorescence values hereafter referred to as the amplification curve. Commonly the biological question of relevance is one of the ratio of DNA concentrations in two samples: a ratio that is deduced by comparing the two amplification curves, usually by way of a plot of fluorescence against cycle number. Central to this analysis is measuring the extent to which one amplification curve is shifted relative to the other, a measurement often accomplished by defining a threshold or quantification cycle, Cq, for each curve: the fractional cycle number at which fluorescence reaches some threshold or at which some other criterion (maximum slope, maximum rate of change of slope) is satisfied. We propose an alternative where position is measured relative to a reference curve; position equates to the cycle shift which maximizes the correlation between the reference and the observed fluorescence sequence. A key parameter of the reference curve is obtained by fixed-point convergence. Results We consider the analysis of dilution series constructed for the estimation of qPCR amplification efficiency. The estimate of amplification efficiency is based on the slope of the regression line when the Cq is plotted against the logarithm of dilution. We compare the approach to three commonly used methods for determining Cq; each is applied to publicly accessible calibration data sets, and to ten from our own laboratory. As in the established literature we judge their relative merits both from the standard deviation of the slope of the calibration curve, and from the variance in Cq for replicate fluorescence curves. Conclusions The approach does not require modification of experimental protocols, and can be applied retrospectively to existing data. We recommend that it be added to the methodological toolkit with which laboratories interpret their real-time PCR data. Keywords: qPCR; Fixed-point; Amplification efficiency
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