Comprehensive Algorithm for Quantitative Real-Time Polymerase Chain Reaction

TLDR

Quantitative real‑time PCR (qRT‑PCR) is the preferred method for rapid, sensitive, quantitative measurement of RNA transcript abundance, but accurate mRNA quantification requires precise estimation of reaction efficiency and threshold cycle (CT), parameters that many existing algorithms approximate. This study presents an objective, curve‑free method that directly calculates efficiency and CT from individual PCR kinetics without relying on standard curves or subjective assumptions. The approach fits raw fluorescence data to a four‑parameter logistic model to locate the exponential phase, then applies a three‑parameter exponential model via iterative nonlinear regression, selecting candidate regressions by P‑value and averaging them to obtain efficiency, while CT is identified as the first positive second‑derivative maximum of the logistic fit. The resulting algorithm delivers a noise‑resistant, equipment‑independent quantification of qRT‑PCR results.

Abstract

Quantitative real-time polymerase chain reactions (qRT-PCR) have become the method of choice for rapid, sensitive, quantitative comparison of RNA transcript abundance. Useful data from this method depend on fitting data to theoretical curves that allow computation of mRNA levels. Calculating accurate mRNA levels requires important parameters such as reaction efficiency and the fractional cycle number at threshold (CT) to be used; however, many algorithms currently in use estimate these important parameters. Here we describe an objective method for quantifying qRT-PCR results using calculations based on the kinetics of individual PCR reactions without the need of the standard curve, independent of any assumptions or subjective judgments which allow direct calculation of efficiency and CT. We use a four-parameter logistic model to fit the raw fluorescence data as a function of PCR cycles to identify the exponential phase of the reaction. Next, we use a three-parameter simple exponent model to fit the exponential phase using an iterative nonlinear regression algorithm. Within the exponential portion of the curve, our technique automatically identifies candidate regression values using the P-value of regression and then uses a weighted average to compute a final efficiency for quantification. For CT determination, we chose the first positive second derivative maximum from the logistic model. This algorithm provides an objective and noise-resistant method for quantification of qRT-PCR results that is independent of the specific equipment used to perform PCR reactions.