Brief Intro to LRE qPCR

Linear regression of efficiency (LRE) originated from recognition that real-time qPCR could be greatly simplified through the application of sigmoidal modelling, that in turn allows absolute qPCR to be conducted without the need to construct standard curves. The following provides an overview of how LRE was developed based on the concepts introduced by Rutledge and Stewart (2008a).

Real-time qPCR was developed from the ability to monitor amplicon DNA quantity using some form of fluorescence chemistry. This in turn generates an "amplification profile" in which fluorescence is plotted against cycle number:

An Amplification Profile

Each cycle is thus defined by the fluorescence signal it generates (Fc), which when using the fluorescent dye SYBR Green I, is directly proportional to the amount amplicon DNA present at the end of the cycle. Conventional qPCR methods determine target quantity based on the relative position of a profile. A major limitation of this approach (among many others) is that absolute quantification requires construction of target-specific standard curves (Rutledge and Côté 2003).

LRE expands the capabilities of qPCR by extending data analysis beyond profile position. This was accomplished by first determining the amplification efficiency produced by each individual cycle within the central region of a profile, based on the increase in amplicon DNA relative to the amount present at the beginning of the cycle. This of course is the amount of amplicon present at the end of the previous cycle (FC-1):

This then generates a second parameter defining a cycle , which is the amplification efficiency it generated, referred to as "cycle efficiency" or EC. Importantly, contrary to the historically held belief that PCR amplification is an exponential process in which amplification efficiency is constant, this revealed that amplification efficiency progressively decreases as amplicon DNA increases, and that this decrease is linearly coupled to amplicon DNA mass (Rutledge and Stewart 2008b).

The core functionality of LRE was subsequently derived from the ability to view PCR amplification not as the increase in amplicon DNA, but rather as the loss in amplification efficiency. This is done by plotting the EC of each cycle against its FC, generating what is referred to as the "LRE Plot":

Although the mechanism of this linear coupling is unknown, this provided the ability to apply linear regression analysis to PCR amplification using  the equation:

Referred to as "linear regression of efficiency" or LRE, this generates values for amplification efficiency (Emax), determined from the Y-intercept, and the rate of loss in amplification efficiency (ΔE), determined from the slope. Note also that the plateau phase of a profile is defined as the maximal fluorescence (Fmax), which corresponds to the X-intercept within the LRE plot, and can be calculated using the equation:

The cycles included into the linear regression analysis are taken from the central region of a profile, which avoids distortions caused by low fluorescence generated during early cycles, in addition to aberrations associated with cycles within the upper region. This central region is referred as the "LRE window" as denoted by black and red circles within the LRE and FC plots, respectively:

LRE Analysis

The LRE Window

In addition to generating a linear representation of PCR amplification, adapting the classic Boltzmann sigmoid function to PCR generated a derivative that can be used to determine target quantity directly from a cycle's FC reading:

This generates the third parameter defining a cycle, which is the predicted target quantity expressed in fluorescence units (F0). This can be visually displayed in what is called the "F0 Plot", which displays the F0 generated by cycles within LRE window:

Target quantity is derived by averaging the LRE window F0 values, which as described below, can be converted into the number of target molecules by correlating fluorescence to DNA mass.

The fourth cycle parameter is the predicted FC, calculated using a second sigmoidal derivative:

When displayed in the FC plot as circles, this allows the general conformity of the profile to the LRE model to be assessed:

As described in the optical calibration video presented in the LRE Video Overview page, the final step is to convert the average F0 into the number of target molecules by first correlating fluorescence units to DNA mass. This is accomplished by amplifying a known quantity of lambda gDNA, from which an optical calibration factor (OCF =  FU / ng dsDNA) is determined, although alternative methods are also described within the help documentation.

Similar to a conventional fluorescence assay for quantifying DNA, F0 is converted into DNA mass (M0), which is then converted into the number of target molecules (N0) based on amplicon size (AS):

A subsequent study by Rutledge and Stewart (2010) investigated the performance capabilities of LRE quantification, in addition to describing the impact of Poisson distribution, which becomes a dominant factor for target quantities below 10 molecules. This study also demonstrated that quantitative accuracy can be maintained down to a single target molecule, and that amplification of a single target molecule provides independent support for the quantitative accuracy that can be achieved with LRE.

Finally, Rutledge 2011 describes development of the LRE Analyzer, a platform-independent desktop program that automates LRE qPCR, which provided the final component required for conducting large-scale qPCR projects.

In summarize, LRE introduced a new paradigm for real-time qPCR that is based on deriving the target quantity directly from the  fluorescence readings within the central region of an amplification profile. In combination with adopting lambda gDNA as a universal quantitative standard, the need to construct target-specific standard curves is eliminated, making it possible to conduct large-scale absolute quantification with few resources beyond that needed for target amplification.