Stepwise kinetic equilibrium models of quantitative polymerase chain reaction

Gary Cobbs

doi:10.1186/1471-2105-13-203

Abstract

BackgroundNumerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented.ResultsTwo models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of initial target concentration. Model 1 was found to be slightly more robust than model 2 giving better estimates of initial target concentration when estimation of parameters was done for qPCR curves with very different initial target concentration. Both models may be used to estimate the initial absolute concentration of target sequence when a standard curve is not available.ConclusionsIt is argued that the kinetic approach to modeling and interpreting quantitative PCR data has the potential to give more precise estimates of the true initial target concentrations than other methods currently used for analysis of qPCR data. The two models presented here give a unified model of the qPCR process in that they explain the shape of the qPCR curve for a wide variety of initial target concentrations.

Highlights

Numerous models for use in interpreting quantitative PCR data are present in recent literature
A value of MSresidual was computed for every quantitative PCR (qPCR) curve for each model and for each estimation method
The lack of fit of model 0 to qPCR curves seen in Figures 4, 5 and 6 is likely to be due to the same cause as the variation in k values pointed out by Boggy and Woolf (2010) [14]

Summary

Introduction

Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. During early cycles of the amplification, the concentration of target is too small to produce measurable fluorescence and is called the lag phase (Figure 1). When target is present in quantities sufficient to be measured, the increase in fluorescence is approximately exponential over a number of successive cycles and the reaction is said to be in the exponential phase (Figure 1). Fluorescence values during the exponential phase may be used to estimate E and most models of qPCR use only this part of the curve to estimate E and assume the estimated value applies throughout the lag phase as well. The reaction enters stationary phase, during which E approaches zero and increases in fluorescence are minimal (Figure 1)

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Discussion

Conclusion