Estimation via "theoretical sigmoidal fit"  (all fluorescence data points)

Liu W & Saint DA (2002)
Validation of a quantitative method for real time PCR kinetics.
Biochem Biophys Res Commun. 2002 294(2): 347-353

Real time RT-PCR is the most sensitive method for quantitation of gene expression levels. The accuracy can be dependent on the mathematical model on which the quantitative methods are based. The generally accepted mathematical model assumes that amplification effciencies are equal at the exponential phase of the reactions for the same amplicon. However, no methods are available to test the assumptions regarding amplification effciency before one starts the real time PCR quantitation. Here we further develop and test the validity of a new mathematical model which dynamically its real time PCR data with good correlation (r2 = 0.9995, n = 50). The method is capable of measuring cycle-by-cycle PCR amplification effciencies and demonstrates that these hange dynamically. Validation of the method revealed the intrinsic relationship between the initial amount of gene transcript and kinetic parameters. A new quantitative method is proposed which represents a simple but accurate quantitative method.

Estimation via "experimental four parametric sigmoidal model fit"
(all fluorescence data points)

Improving quantitative real-time RT-PCR reproducibility by boosting primer-linked amplification efficiency.
Ales Tichopad, Anamarija Dzidic  &  Michael W. Pfaffl
Biotechnology Letters 24: 2053-2056 (2002)

Polymerase chain reaction amplification of product of reverse transcribed RNA is a modern approach to quantify gene expression. Several commercial platforms are in current use and much effort is made to enhance the precision of their quantitative outputs. Generally, optimization of polymerase performance and search for closer computing algorithms are two major ways to achieve it. Often, data show that selection of primers can alter the performance of polymerase chain reaction. To test how this affects reaction reproducibility, mathematical model was applied describing a full kinetic of the reactions where just primers were varied. Statistical consideration of parameters yielded by this model revealed, that reactions with higher amplification efficiency – primed by “good” primers – run with lower variability and they are therefore better suited for measurement purposes.

4 parametric sigmoidal model

Model is described by equation [1]. One fluorescence data set from this study was used as an example. In this model, y0 is the ground fluorescence, a is the difference between maximal fluorescence acquired in the run and the ground fluorescence,  x0 is the first derivative maximum of the function or the inflexion point of the curve and b describes the slope of curve.

equation [1]

Estimation via "experimental four parametric logistic model fit"
(all fluorescence data points)

Standardized determination of real-time PCR effciency from a single reaction set-up.
Ales Tichopad, Michael Dilger,  Gerhard Schwarz  &  Michael W. Pfaffl (2003)
  Nucleic Aids Research 31(20): e122  (2003)

The paper has been frequently cited by other researchers:  => 411 times until April 2016

We propose a computing method for the estimation of real-time PCR amplifcation effciency. It is based on a statistic delimitation of the beginning of exponentially behaving observations in real-time PCR kinetics. PCR ground fluorescence phase, nonexponential and plateau phase were excluded from the calculation process by separate mathematical algorithms. We validated the method on experimental data on multiple targets obtained on the LightCycler platform. The developed method yields results of higher accuracy than the currently used method of serial dilutions for amplification effciency estimation. The single reaction set-up estimation is sensitive to differences in starting concentrations of the target sequence in samples. Furthermore, it resists the subjective influence of researchers, and the estimation can therefore be fully instrumentalized.

Figure 1:    Plot of fluorescence observations from LightCycler (Roche Diagnostics). Forty observations give a sigmoid trajectory that can be described by full data fit (four parametric logistic model). Ground phase can be well linearly regressed (inlay). Following data of n > 7 are considered exponentially behaved and can be fitted by exponential model. Various model fits are designated in legend within figure. FDM and SDM denote position of first and second derivative maximum within full data fit.

Figure 2:    Flowchart of statistical estimation of the exponential phase beginning based on inspection of externally studentised residuals.  

ERRATUM  download PDF   tichopad-et-al-nar-2003-figure-2.pdf
ERRATUM  download PDF   tichopad-2003-erratum.pdf

A quantitative approach for polymerase chain reactions based on a hidden Markov model.
Lalam N.
J Math Biol. 2009 59(4): 517-533

Polymerase chain reaction (PCR) is a major DNA amplification technology from molecular biology. The quantitative analysis of PCR aims at determining the initial amount of the DNA molecules from the observation of typically several PCR amplifications curves. The mainstream observation scheme of the DNA amplification during PCR involves fluorescence intensity measurements. Under the classical assumption that the measured fluorescence intensity is proportional to the amount of present DNA molecules, and under the assumption that these measurements are corrupted by an additive Gaussian noise, we analyze a single amplification curve using a hidden Markov model (HMM). The unknown parameters of the HMM may be separated into two parts. On the one hand, the parameters from the amplification process are the initial number of the DNA molecules and the replication efficiency, which is the probability of one molecule to be duplicated. On the other hand, the parameters from the observational scheme are the scale parameter allowing to convert the fluorescence intensity into the number of DNA molecules and the mean and variance characterizing the Gaussian noise. We use the maximum likelihood estimation procedure to infer the unknown parameters of the model from the exponential phase of a single amplification curve, the main parameter of interest for quantitative PCR being the initial amount of the DNA molecules. An illustrative example is provided.

Inhibition of real-time RT–PCR quantification due to tissue-specific contaminants
Ales Tichopad, Andrea Didier, Michael W. Pfaffl (2004)  
Molecular and Cellular Probes (18): 45-50

Real-time reverse transcription–polymerase chain reaction (RT–PCR) is currently considered the most sensitive method to study low abundance gene expression. Since comparison of gene expression levels in various tissues is often the purpose of an experiment, we studied a tissue-linked effect on nucleic acid amplification. Based on the raw data generated by a LightCycler instrument, we propose a descriptive mathematical model of PCR amplification. This model allowed us to study amplification kinetics of four common housekeeping genes in total RNA samples derived from various bovine tissues. We observed that unknown tissue-specific factors can influence amplification kinetics but this affect can be ameliorated, in part, by appropriate primer selection.

Locked nucleic acid (LNA) single nucleotide polymorphism (SNP) genotype analysis and validation using real-time PCR.
Johnson MP, Haupt LM, Griffiths LR.
Nucleic Acids Res. 2004 Mar 26;32(6):e55.
Genomics Research Centre, School of Health Science, Griffith University Gold
Coast, PMB 50, Gold Coast Mail Centre, QLD 9726, Australia.
With an increased emphasis on genotyping of single nucleotide polymorphisms (SNPs) in disease association studies, the genotyping platform of choice is constantly evolving. In addition, the development of more specific SNP assays and appropriate genotype validation applications is becoming increasingly critical to elucidate ambiguous genotypes. In this study, we have used SNP specific Locked Nucleic Acid (LNA) hybridization probes on a real-time PCR platform to genotype an association cohort and propose three criteria to address ambiguous genotypes. Based on the kinetic properties of PCR amplification, the three criteria address PCR amplification efficiency, the net fluorescent difference between maximal and minimal fluorescent signals and the beginning of the exponential growth phase of the reaction. Initially observed SNP allelic discrimination curves were confirmed by DNA sequencing (n = 50) and application of our three genotype criteria corroborated both sequencing and observed real-time PCR results. In addition, the tested Caucasian association cohort was in Hardy-Weinberg equilibrium and observed allele frequencies were very similar to two independently tested Caucasian association cohorts for the same tested SNP. We present here a novel approach to effectively determine ambiguous genotypes generated from a real-time PCR platform. Application of our three novel criteria provides an easy to use semi-automated genotype confirmation protocol.

Sigmoidal curve-fitting redefines quantitative real-time PCR with the prospective of developing automated high-throughput applications.
Rutledge RG
Natural Resources Canada, 1055 du P.E.P.S, Sainte-Foy, Quebec, Canada G1V 4C7.
Nucleic Acids Res. 2004 32(22): e178.
Quantitative real-time PCR has revolutionized many aspects of genetic research, biomedical diagnostics and pathogen detection. Nevertheless, the full potential of this technology has yet to be realized, primarily due to the limitations of the threshold-based methodologies that are currently used for quantitative analysis. Prone to errors caused by variations in reaction preparation and amplification conditions, these approaches necessitate construction of standard curves for each target sequence, significantly limiting the development of high-throughput applications that demand substantive levels of reliability and automation. In this study, an alternative approach based upon fitting of fluorescence data to a four-parametric sigmoid function is shown to dramatically increase both the utility and reliability of quantitative real-time PCR. By mathematically modeling individual amplification reactions, quantification can be achieved without the use of standard curves and without prior knowledge of amplification efficiency. Combined with provision of quantitative scale via optical calibration, sigmoidal curve-fitting could confer the capability for fully automated quantification of nucleic acids with unparalleled accuracy and reliability.

Improved real-time RT-PCR method for high-throughput measurements using second derivative calculation and double correction.
Van Luu-The, Paquet N, Calvo E, Cumps J.
Molecular Endocrinology and Oncology Research Center, Laval University, Quebec, Canada.
Biotechniques. 2005 38(2): 287-293
Quantification of mRNA expression levels using real-time reverse transcription PCR (RT-PCR) is increasingly used to validate results of DNA microarrays or GeneChips. It requires an improved method that is more robust and more suitable for high-throughput measurements. In this report, we compare a user non-influent, second derivative method with that of a user influent, fit point method that is widely used in the literature. We also describe the advantage of using a double correction: one correction using the expression levels of a housekeeping gene of an experiment as an internal standard and a second using reference expression levels of the same housekeeping gene in the tissue or cells. The first correction permits one to decrease errors due to sample preparation and handling, while the second correction permits one to avoid the variation of the results with the variability of housekeeping in each tissue, especially in experiments using various treatments. The data indicate that the real-time PCR method is highly efficient with an efficiency coefficient close to the theoretical value of two. The results also show that the second derivative method is more accurate than the fit point method in quantifying low gene expression levels. Using triplicate experiments, we show that measurement variations using our method are low with a mean of variation coefficients of <1%.

Gene expression of HIF-1 α and XRCC4 measured in human samples by real-time RT-PCR
using the sigmoidal curve-fitting method.
Hao Qiu, Karine Durand, Hélène Rabinovitch-Chable, Michel Rigaud, Virgile Gazaille,
Pierre Clavère, and Franck G. Sturtz
BioTechniques 42:355-362 (March 2007)

Quantitative reverse transcription PCR (RT-PCR) has become an important tool for studying functional gene expression. However, the most often used cycle threshold (CT)-based method, primarily related to the required amplification efficiency determination via serial dilution, can call into question the level of quantitative reliability and accuracy that can be achieved, in addition to the impracticalities inherent to CT-based methodologies. In this study, an alternative method, named the sigmoidal curve-fitting (SCF) method, was compared with the classic CT method for two target genes (XRCC4 and HIF-1α) and a reference gene (HPRT). The PCR conditions were optimized for each gene on a LightCycler® apparatus. Fluorescence data were fitted to a four-parametric sigmoidal function, and the initial messenger RNA (mRNA) copy number was determined by a theoretical fluorescence (F0) value calculated from each fitting curve. The relative expression of the target gene versus that of the reference gene was calculated using an equation based upon these F0 values. The results show that the F0 value had a good linearity with the initial number of target genes between 107 and 101 copies. The reproducibility tests showed that the variations of initial target quantity were well reflected by F0 values. Relative expression of target gene calculated by the SCF method and by the CT method showed similar results. In our hands, the SCF method gave reliable results and a more precise error description of quantitative RT-PCR.

Model based analysis of real-time PCR data from DNA binding dye protocols.
Alvarez MJ, Vila-Ortiz GJ, Salibe MC, Podhajcer OL, Pitossi FJ.
Gentron Research Unit, Arenales Piso, Buenos Aires C1061AAO, Argentina.
BMC Bioinformatics. 2007 8:85.

BACKGROUND: Reverse transcription followed by real-time PCR is widely used for quantification of specific mRNA, and with the use of double-stranded DNA binding dyes it is becoming a standard for microarray data validation. Despite the kinetic information generated by real-time PCR, most popular analysis methods assume constant amplification efficiency among samples, introducing strong biases when amplification efficiencies are not the same.
RESULTS: We present here a new mathematical model based on the classic exponential description of the PCR, but modeling amplification efficiency as a sigmoidal function of the product yield. The model was validated with experimental results and used for the development of a new method for real-time PCR data analysis. This model based method for real-time PCR data analysis showed the best accuracy and precision compared with previous methods when used for quantification of in-silico generated and experimental real-time PCR results. Moreover, the method is suitable for the analyses of samples with similar or dissimilar amplification efficiency.
CONCLUSION: The presented method showed the best accuracy and precision. Moreover, it does not depend on calibration curves, making it ideal for fully automated high-throughput applications.

A kinetic-based sigmoidal model for the polymerase chain reaction and its application to high-capacity
absolute quantitative real-time PCR

Robert G Rutledge & Donald Stewart
BMC Biotechnology 2008, Published: 8 May 2008

Background:  Based upon defining a common reference point, current real-time quantitative PCR technologies compare relative differences in amplification profile position. As such, absolute quantification requires construction of target-specific standard curves that are highly resource intensive and prone to introducing quantitative errors. Sigmoidal modeling using nonlinear regression has previously demonstrated that absolute quantification can be accomplished without standard curves; however, quantitative errors caused by distortions within the plateau phase have impeded effective implementation of this alternative approach.
Results:  Recognition that amplification rate is linearly correlated to amplicon quantity led to the derivation of two sigmoid functions that allow target quantification via linear regression analysis. In addition to circumventing quantitative errors produced by plateau distortions, this approach allows the amplification efficiency within individual amplification reactions to be determined. Absolute quantification is accomplished by first converting individual fluorescence readings into target quantity expressed in fluorescence units, followed by conversion into the number of target molecules via optical calibration. Founded upon expressing reaction fluorescence in relation to amplicon DNA mass, a seminal element of this study was to implement optical calibration using lambda gDNA as a universal quantitative standard. Not only does this eliminate the need to prepare target-specific quantitative standards, it relegates establishment of quantitative scale to a single, highly defined entity. The quantitative competency of this approach was assessed by exploiting "limiting dilution assay" for absolute quantification, which provided an independent gold standard from which to verify quantitative accuracy. This yielded substantive corroborating evidence that absolute accuracies of +/-25% can be routinely achieved. Comparison with the LinReg and Miner automated qPCR data processing packages further demonstrated the superior performance of this kinetic-based methodology.
Conclusions:  Called "linear regression of efficiency" or LRE, this novel kinetic approach confers the ability to conduct high-capacity absolute quantification with unprecedented quality control capabilities. The computational simplicity and recursive nature of LRE quantification also makes it amenable to software implementation, as demonstrated by a prototypic Java program that automates data analysis. This in turn introduces the prospect of conducting absolute quantification with little additional effort beyond that required for the preparation of the amplification reactions.

A new real-time PCR method to overcome significant quantitative inaccuracy due to slight amplification inhibition.
BMC Bioinformatics 2008, 9:326
Michele Guescini, Davide Sisti, Marco BL Rocchi, Laura Stocchi, Vilberto Stocchi
Background: Real-time PCR  analysis  is  a  sensitive DNA quantification  technique  that  has  recently gained  considerable attention  in  biotechnology,  microbiology  and  molecular diagnostics. Although, the cycle-threshold (Ct) method is the present “gold standard”, it is  far  from  being  a  standard  assay. Uniform  reaction  efficiency  among  samples  is  the most  important  assumption  of  this method. Nevertheless,  some  authors  have  reported that it may not be correct and a slight PCR efficiency decrease of about 4% could result in an error of up to 400% using the Ct method. This reaction efficiency decrease may be caused by  inhibiting agents used during nucleic acid extraction or copurified  from  the biological sample. We propose a new method (Cy0) that does not require the assumption of equal reaction efficiency between unknowns and standard curve.
Results: The  Cy0 method  is  based  on  the  fit  of  Richards’  equation  to  real-time  PCR  data  by nonlinear  regression  in  order  to  obtain  the  best  fit  estimators  of  reaction  parameters. Subsequently, these parameters were used to calculate the Cy0 value that minimizes the dependence of its value on PCR kinetic. The Ct, second derivative (Cp), sigmoidal curve fitting method (SCF) and Cy0 methods were  compared  using  two  criteria:  precision  and  accuracy.  Our  results  demonstrated that,  in  optimal  amplification  conditions,  these  four methods  are  equally  precise  and
accurate. However, when PCR efficiency was slightly decreased, diluting amplification mix quantity or adding a biological inhibitor such as IgG, the SCF, Ct and Cp methods were markedly  impaired while  the Cy0 method  gave  significantly more  accurate  and precise results.
Conclusion: Our results demonstrate that Cy0 represents a significant improvement over the standard methods  for  obtaining  a  reliable  and  precise  nucleic  acid  quantification  even  in  suboptimal amplification  conditions  overcoming  the  underestimation  caused  by  the presence of some PCR inhibitors.

WEB INTERFACE - Cy0 is a new method in Real-time PCR analysis that does not require the assumption of equal efficiency between unknowns and standard curve (Michele Guescini, Davide Sisti, & Renato Panebianco, 2010)

Highly accurate sigmoidal fitting of real-time PCR data by introducing a parameter for asymmetry.
Andrej-Nikolai Spiess, Caroline Feig and Christian Ritz
BMC Bioinformatics 2008, 9:221
Background: Fitting four-parameter sigmoidal models is one of the methods established in the analysis of quantitative real-time PCR (qPCR) data. We had observed that these models are not optimal in the fitting outcome due to the inherent constraint of symmetry around the point of inflection. Thus, we found it necessary to employ a mathematical algorithm that circumvents this problem and which utilizes an additional parameter for accommodating asymmetrical structures insigmoidal qPCR data.
Results: The four-parameter models were compared to their five-parameter counterparts by means of nested F-tests based on the residual variance, thus acquiring a statistical measure for higher performance. For nearly all qPCR data we examined, five-parameter models resulted in a significantly better fit. Furthermore, accuracy and precision for the estimation of efficiencies and calculation of quantitative ratios were assessed with four independent dilution datasets and compared to the most commonly used quantification methods. It could be shown that the fiveparameter model exhibits an accuracy and precision more similar to the non-sigmoidal
quantification methods.
Conclusion: The five-parameter sigmoidal models outperform the established four-parameter model with high statistical significance. The estimation of essential PCR parameters such as PCR efficiency, threshold cycles and initial template fluorescence is more robust and has smaller variance. The model is implemented in the qpcR package for the freely available statistical R environment. The package can be downloaded from the author's homepage.

qPCR:  an R package for sigmoidal model selection
in quantitative real-time polymerase chain reaction analysis.
Christian Ritz and Andrej-Nikolai Spiess
BIOINFORMATICS APPLICATIONS NOTE Vol. 24 no. 13 2008, pages 1549–1551
Summary: The qpcR library is an add-on to the free R statistical environment performing sigmoidal model selection in realtime quantitative polymerase chain reaction (PCR) data analysis. Additionally, the package implements the most commonly used algorithms for real-time PCR data analysis and is capable of extensive statistical comparison for the selection and evaluation of the different models based on several measures of goodness of fit.

Supplementary Information:   Statistical evaluations of the implemented methods can be found at under ‘Supplemental Data’.

Critical evaluation of methods used to determine amplification efficiency refutes the exponential character of real-time PCR
Rutledge & Stewart 2008
BMC Molecular Biology 2008, 9:96

The challenge of determining amplification efficiency has long been a predominant aspect of implementing real-time qPCR, playing a critical role in the accuracy and reliability that can be achieved. Based upon analysis of amplification profile position, standard curves are currently the gold standard for amplification efficiency determination. However, in addition to being highly resource intensive, the efficacy of this approach is limited by the necessary assumption that all samples are amplified with the same efficiency as predicted by a standard curve. These limitations have driven efforts to develop methods for determining amplification efficiency by analyzing the fluorescence readings from individual amplification reactions. The most prominent approach is based on analysis of the "log-linear region", founded upon the presumption that amplification efficiency is constant within this region. Nevertheless, a recently developed sigmoidal model has provided new insights that challenge such historically held views, dictating that amplification efficiency is not only dynamic, but is linearly coupled to amplicon DNA quantity. Called "linear regression of efficiency" or LRE, this kinetic-based approach redefines amplification efficiency as the maximal efficiency (Emax) generated at the onset of thermocycling.
Assessing the performance capabilities of LRE-based assays for absolute quantitative real-time PCR.
Rutledge RG, Stewart D.
PLoS One. 2010 5(3):e9731.
BACKGROUND: Linear regression of efficiency or LRE introduced a new paradigm for conducting absolute quantification, which does not require standard curves, can generate absolute accuracies of +/-25% and has single molecule sensitivity. Derived from adapting the classic Boltzmann sigmoidal function to PCR, target quantity is calculated directly from the fluorescence readings within the central region of an amplification profile, generating 4-8 determinations from each amplification reaction.
FINDINGS: Based on generating a linear representation of PCR amplification, the highly visual nature of LRE analysis is illustrated by varying reaction volume and amplification efficiency, which also demonstrates how LRE can be used to model PCR. Examining the dynamic range of LRE further demonstrates that quantitative accuracy can be maintained down to a single target molecule, and that target quantification below ten molecules conforms to that predicted by Poisson distribution. Essential to the universality of optical calibration, the fluorescence intensity generated by SYBR Green I (FU/bp) is shown to be independent of GC content and amplicon size, further verifying that absolute scale can be established using a single quantitative standard. Two high-performance lambda amplicons are also introduced that in addition to producing highly precise optical calibrations, can be used as benchmarks for performance testing. The utility of limiting dilution assay for conducting platform-independent absolute quantification is also discussed, along with the utility of defining assay performance in terms of absolute accuracy.
CONCLUSIONS: Founded on the ability to exploit lambda gDNA as a universal quantitative standard, LRE provides the ability to conduct absolute quantification using few resources beyond those needed for sample preparation and amplification. Combined with the quantitative and quality control capabilities of LRE, this kinetic-based approach has the potential to fundamentally transform how real-time qPCR is conducted.

LRE Analyzer Hompage - Enabling large-scale absolute quantification
Installation files for the most current version of the LRE Analyzer are available on the LRE qPCR Open Source download page.

The LRE Analyzer is a fully featured desktop application that provides the automated analysis and data storage capabilities required by large-scale qPCR projects, wanting to exploit the many advantages of absolute quantification. Foremost is the universal perspective provided by absolute quantification, which among other attributes, provides the ability to directly compare quantitative data derived from diverse sources, such as from different assays, instruments and/or research groups. Furthermore, absolute quantification has important implications for gene expression profiling, in that it provides the foundation for comparing transcript quantities produced by any gene to any other gene, within and between any sample.

Based on the application of sigmoidal mathematics in combination with utilizing lambda gDNA as a universal quantitative standard, the LRE Analyzer provides the ability to conduct absolute quantification without construction of standard curves. In addition to enabling large-scale absolute quantification, the LRE Analyzer also expands the fundamental capabilities of qPCR, reflected in part by the quality control capabilities it provides that are not possible using conventional methods.

Getting Started
The LRE Analyzer has an extensive help set that provides an in-depth introduction to LRE, in addition to guidelines on how to implement LRE quantification. Demonstration database files are provided to help illustrate how the program functions. The Introduction to LRE page provides basic background information about how LRE quantification is conducted, with the LRE Video Overview page providing a three part video describing how LRE was conceived, along with a detailed overview of methods that were used to evaluate the accuracy and dynamic range of LRE quantification. The LRE Literature page provides links to LRE-related publications, in addition to two earlier qPCR studies that were instrumental in the development of LRE.

Improving qPCR efficiency in environmental samples by selective removal of humic acids with DAX-8.
Schriewer A, Wehlmann A, Wuertz S.
J Microbiol Methods. 2011 Jan
Quantitative PCR is becoming the method of choice for the detection of pathogenic microorganisms and other targets in the environment. A major obstacle when amplifying DNA is the presence of inhibiting substances like humic acids that decrease the efficiency of PCR. We combined the polymeric adsorbent Supelite™ Dax-8 with a large-volume (10mL) nucleic acid extraction method to decrease the humic acid content prior to qPCR quantification in water samples. The method was tested by spiking with humic acid standards and the bacterial surrogate Acinetobacter baylyi ADP1. Improvements in qPCR detection of ADP1 after application of Dax-8 resin (5 and 10w/v %) were compared with the effects of added bovine serum albumin (BSA) (50, 100 and 200ng/μL). Both additions improved detection of ADP1 by counteracting inhibitory effects. There were no changes in mean cycle threshold difference (ΔC(T)) after application of DAX-8 compared to the control despite some loss of DNA, whereas significant increases occurred for BSA, irrespective of BSA concentration applied. The use of DAX-8 leads to an increase in qPCR amplification efficiency in contrast to BSA. The commonly used method to calculate genomic sample concentrations by comparing measured CT values relative to standard curves is only valid if amplification efficiencies of both are sufficiently similar. Dax-8 can provide this efficiency by removing humic acids permanently from nucleic acid extracts and has the potential to significantly increase the reliability of reported non-detects and measured results obtained by qPCR in environmental monitoring.