• PCR inhibition by reverse transcriptase leads to an overestimation of amplification efficiency.
    Suslov O, Steindler DA.    download PDF
  • Overview article - Comprehensive Algorithm for Quantitative Real-Time Polymerase Chain Reaction
  • Sheng Zhao and Russell D. Fernald     download PDF
  • Relative quantification of mRNA: comparison of methods currently used for real-time PCR data analysis.
  • Cikos S, Bukovská A, Koppel J., 2007      download PDF
  • Enhancing the efficiency of a PCR using gold nanoparticles.
    Li M, Lin YC, Wu CC, Liu HS.  2006   
    download PDF
  • Technical Note - Evaluation of Real-Time PCR Amplification Efficiencies to Detect PCR Inhibitors
    Elias J. Kontanis and Floyd A. Reed, 2005   
    download PDF
  • Estimation of the reaction efficiency in polymerase chain reaction
    Nadia Lalam, 2006     download PDF  
  • Molelling the PCR amplification process by a size-dependent branching process and estimation of the efficiency
    Lalam et al., 2004
       download PDF
  • Statistical Inference for Quantitative Polymerase Chain Reaction Using a Hidden Markov Model: A Bayesian Approach       Lalam, 2007    download PDF
  • Evaluation of absolute quantitation by nonlinear regression in probe-based real-time PCR
    Goll et al., 2006   download PDF
  • Mathematical Model of Real-Time PCR Kinetics
  • Gevertz et al., 2005    download PDF

PCR inhibition by reverse transcriptase leads to an overestimation of amplification efficiency.
Suslov O, Steindler DA.
McKnight Brain Institute of the University of Florida, FL, USA.
Nucleic Acids Res. 2005 Nov 27;33(20):e181.
This study addresses the problem of PCR inhibition by reverse transcriptase. It has been shown that the inhibition occurs mostly when a small amount of RNA is taken for RT reaction, and it is more visible for rarely expressed transcripts. We show here that the inhibition takes place regardless of what amount of template is utilized for RT. The inhibition possesses a global nature, i.e. the amplification of any given transcript may be compromised with different levels of inhibition. The process of inhibition also explains wrongfully derived PCR amplification efficiencies, sometimes more than 100%, when the sequential dilutions of unpurified RT sample are utilized to build the calibration curve. The RT influences PCR not only by inhibiting it. When microgram(s) of RNA are taken for RT reaction, reverse transcriptase may cause overamplification of some transcripts under certain PCR conditions. The possible mechanism of RT influence on PCR is presented, and a purification method is implemented to remove the effects of RT on PCR.

Absolute and relative real-time PCR in the quantification of tst gene expression among methicillin-resistant Staphylococcus aureus: evaluation by two mathematical models.
Chini V, Foka A, Dimitracopoulos G, Spiliopoulou I.
Lett Appl Microbiol. 2007 Nov;45(5):479-84.
Department of Microbiology, School of Medicine, University of Patras, Patras, Greece.
AIM: Absolute and relative quantitative real-time reverse transcriptase polymerase chain reaction (RT-PCR) by the use of two mathematical models were applied in order to study the expression of tst gene encoding the toxic shock syndrome toxin-1 (TSST-1), among methicillin-resistant Staphylococcus aureus (MRSA).
METHODS AND RESULTS: Thirteen epidemic MRSA belonging to different clones and carrying a variety of toxin genes were selected. tst gene expression was achieved by using absolute and relative quantitative real-time RT-PCR and the SYBR Green I. Absolute RT-PCR showed a statistically significant higher level of  tst expression among strains isolated from soft tissue infections. Relative quantification was performed in relation to 23S rRNA expression by the application of two mathematical models, the 2(-DeltaDeltaCt) and the Pfaffl analysis methods.
CONCLUSIONS: tst gene expression was best calculated by the relative real-time RT-PCR analysis applying the Pfaffl analysis method, taking into account the reactions' efficiencies. Level of tst expression was related to patients' infection and did not depend on the MRSA genetic profile.
SIGNIFICANCE AND IMPACT OF THE STUDY: The results indicate that the application of the Pfaffl analysis method in the evaluation of relative real-time RT-PCR is more adequate.

Comprehensive Algorithm for Quantitative Real-Time Polymerase Chain Reaction

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.

Relative quantification of mRNA: comparison of methods currently used for real-time PCR data analysis.
Cikos S, Bukovská A, Koppel J.
BMC Mol Biol. 2007 Dec 20;8:113.
Institute of Animal Physiology, Slovak Academy of Sciences, Soltésovej 4, 04001 Kosice, Slovakia.
BACKGROUND: Fluorescent data obtained from real-time PCR must be processed by some method of data analysis to obtain the relative quantity of target mRNA. The method chosen for data analysis can strongly influence results of the quantification.
RESULTS: To compare the performance of six techniques which are currently used for analysing fluorescent data in real-time PCR relative quantification, we quantified four cytokine transcripts (IL-1beta, IL-6 TNF-alpha, and GM-CSF) in an in vivo model of colonic inflammation. Accuracy of the methods was tested by quantification on samples with known relative amounts of target mRNAs. Reproducibility of the methods was estimated by the determination of the intra-assay and inter-assay variability. Cytokine expression normalized to the expression of three reference genes (ACTB, HPRT, SDHA) was then determined using the six methods for data analysis. The best results were obtained with the relative standard curve method, comparative Ct method and with DART-PCR, LinRegPCR and Liu & Saint exponential methods when average amplification efficiency was used. The use of individual amplification efficiencies in DART-PCR, LinRegPCR and Liu & Saint exponential methods significantly impaired the results. The sigmoid curve-fitting (SCF) method produced medium performance; the results indicate that the use of appropriate type of fluorescence data and in some instances manual selection of the number of amplification cycles included in the analysis is necessary when the SCF method is applied. We also compared amplification efficiencies (E) and found that although the E values determined by different methods of analysis were not identical, all the methods were capable to identify two genes whose E values significantly differed from other genes.
CONCLUSION: Our results show that all the tested methods can provide quantitative values reflecting the amounts of measured mRNA in samples, but they differ in their accuracy and reproducibility. Selection of the appropriate method can also depend on the design of a particular experiment. The advantages and disadvantages of the methods in different applications are discussed.

Enhancing the efficiency of a PCR using gold nanoparticles.
Li M, Lin YC, Wu CC, Liu HS.
Nucleic Acids Res. 2005 Nov 27;33(21):e184.
Erratum in:  Nucleic Acids Res. 2006;34(1):396.
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan, Republic of China.

We found that the PCR could be dramatically enhanced by Au nanoparticles. With the addition of 0.7 nM of 13 nm Au nanoparticles into the PCR reagent, the PCR efficiency was increased. Especially when maintaining the same or higher amplification yields, the reaction time could be shortened, and the heating/cooling rates could be increased. The excellent heat transfer property of the nanoparticles should be the major factor in improving the PCR efficiency.
Different PCR systems, DNA polymerases, DNA sizes and complex samples were compared in this study. Our results demonstrated that Au nanoparticles increase the sensitivity of PCR detection 5- to 10-fold in a slower PCR system (i.e. conventional PCR) and at least 10(4)-fold in a quicker PCR system (i.e. real-time PCR). After the PCR time was shortened by half, the 100 copies/microl DNA were detectable in real-time PCR with gold colloid added, however, at least 10(6) copies/microl of DNA were needed to reach a detectable signal level using the PCR reagent without gold colloid. This innovation could improve the PCR efficiency using non-expensive polymerases, and general PCR reagent. It is a new viewpoint in PCR, that nanoparticles can be used to enhance PCR efficiency and shorten reaction times.

Evaluation of Real-Time PCR Amplification Efficiencies to Detect PCR Inhibitors
Elias J. Kontanis and Floyd A. Reed.
J Forensic Sci, July 2006, Vol. 51, No. 4
Real-time PCR analysis is a sensitive template DNA quantitation strategy that has recently gained considerable attention in the forensic community. However, the utility of real-time PCR methods extends beyond quantitation and allows for simultaneous evaluation of template DNA extraction quality. This study presents a computational method that allows analysts to identify problematic samples with statistical reliability by comparing the amplification efficiencies of unknown template DNA samples with clean standards. In this study, assays with varying concentrations of tannic acid are used to evaluate and adjust sample-specific amplification efficiency calculation methods in order to optimize their inhibitor detection capabilities. Kinetic outlier detection and prediction boundaries are calculated to identify amplification efficiency outliers. Sample-specific amplification efficiencies calculated over a four-cycle interval starting at the threshold cycle can be used to detect reliably the presence of 0.4 ng of tannic acid in a 25 mL PCR reaction. This approach provides analysts with a precise measure of inhibition severity when template samples are compromised. Early detection of problematic samples allows analysts the opportunity to consider inhibitor mitigation strategies prior to genotype or DNA sequence analysis, thereby facilitating sample processing in high-throughput forensic operations.

Estimation of the reaction efficiency in polymerase chain reaction.
Nadia Lalam
Journal of Theoretical Biology
EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Polymerase chain reaction (PCR) is largely used in molecular biology for increasing the copy number of a specific DNA fragment. The succession of 20 replication cycles makes it possible to multiply the quantity of the fragment of interest by a factor of 1 million. The PCR technique has revolutionized genomics research. Several quantification methodologies are available to determine the DNA replication efficiency of the reaction which is the probability of replication of a DNA molecule at a replication cycle. We elaborate a quantification procedure based on the exponential phase and the early saturation phase of PCR. The reaction efficiency is supposed to be constant in the exponential phase, and decreasing in the saturation phase. We propose to model the PCR amplification process by a branching process which starts as a Galton–Watson branching process followed by a size-dependent process. Using this stochastic modelling and the conditional least-squares estimation method, we infer the reaction efficiency from a single PCR trajectory.

Molelling the PCR amplification process by a size-dependent branching process and estimation of the efficiency.
Lalam N, Jacob C. and Jagers P.
Adv. Appl. Prob. (2004) 36: 601-612
We propose a stochastic modelling of the PCR amplification process by a size dependent branching process starting as a supercritical Bienayme-Galton-Watson transient phase and then having a saturation near-critical size-dependent phase. This model allows us to estimate the probability of the replication of the DNA molecule at each cycle of a single PCR trajectory with a very good accuracy.

Statistical Inference for Quantitative Polymerase Chain Reaction Using a Hidden Markov Model:
A Bayesian Approach

Nadia Lalam, Chalmers University of Technology, Sweden
Statistical Applications in Genetics and Molecular Biology: Vol. 6  : Iss. 1, Article 10.
Quantitative Polymerase Chain Reaction (Q-PCR) aims at determining the initial quantity of specific nucleic acids from the observation of the number of amplified DNA molecules. The most widely used technology to monitor the number of DNA molecules as they replicate is based on fluorescence chemistry. Considering this measurement technique, the observation of DNA amplification by PCR contains intrinsically two kinds of variability. On the one hand, the number of replicated DNA molecules is random, and on the other hand, the measurement of the fluorescence emitted by the DNA molecules is collected with some random error. Relying on a stochastic model of these two types of variability, we aim at providing estimators of the parameters arising in the proposed model, and, more specifically, of the initial amount of molecules. The theory of branching processes is classically used to model the evolution of the number of DNA molecules at each replication cycle. The model is a binary splitting Galton-Watson branching process. Its unknown parameters are the initial number of DNA molecules and the reaction efficiency of PCR, which is defined as the probability of replication of a DNA molecule. The number of DNA molecules is indirectly observed through noisy fluorescence measurements resulting in a so-called Hidden Markov Model. We aim at inference of the parameters of the underlying branching process, and the parameters of the noise from the fluorescence measurements in a Bayesian framework. Using simulations and experimental data, we investigate the performance of the Bayesian estimators obtained by Markov Chain Monte Carlo methods.

Mathematical Model of Real-Time PCR Kinetics.
Jana L. Gevertz,1 Stanley M. Dunn,1 Charles M. Roth1,2
1Department of Biomedical Engineering, Rutgers University, Piscataway, New Jersey
2Department of Chemical & Biochemical Engineering, Rutgers University,
98 Brett Road, Piscataway, New Jersey 08854

Biotechnol Bioeng. 2005 Nov 5;92(3):346-55.

Abstract: Several real-time PCR (rtPCR) quantification techniques are currently used to determine the expression levels of individual genes from rtPCR data in the form of fluorescence intensities. In most of these quantification techniques, it is assumed that the efficiency of rtPCR is constant. Our analysis of rtPCR data shows, however, that even during the exponential phase of rtPCR, the efficiency of the reaction is not constant, but is instead a function of cycle number. In order to understand better the mechanisms belying this behavior, we have developed a mathematical model of the annealing and extension phases of the PCR process. Using the model, we can simulate the PCR process over a series of reaction cycles. The model thus allows us to predict the efficiency of rtPCR at any cycle number, given a set of initial conditions and parameter values, which can mostly be estimated from biophysical data. The model predicts a precipitous decrease in cycle efficiency when the product concentration reaches a sufficient level for template–template reannealing to compete with primer-template annealing; this behavior is consistent with available experimental data. The quantitative understanding of rtPCR provided by this model can allow us to develop more accurate methods to quantify gene expression levels from rtPCR data.

Evaluation of absolute quantitation by nonlinear regression in probe-based real-time PCR.
Rasmus Goll, Trine Olsen, Guanglin Cui and Jon Florholmen
  Institute of Clinical Medicine, University of Tromso, Tromso, Norway
Department of gastroenterology, University hospital of Northern Norway, Tromso, Norway
BMC Bioinformatics 2006, 7:107 doi:10.1186/1471-2105-7-107

In real-time PCR data analysis, the cycle threshold (CT) method is currently the gold standard. This method is based on an assumption of equal PCR efficiency in all reactions, and precision may suffer if this condition is not met. Nonlinear regressionanalysis (NLR) or curve fitting has therefore been suggested as an alternative to the cycle threshold method for absolute quantitation. The advantages of NLR are that the individual sample efficiency is simulated by the model and that absolute quantitation is possible without a standard curve, releasing reaction wells for unknown samples. However, the calculation method has not been evaluated systematically and has not previously been applied to a TaqMan platform. Aim: To develop and evaluate an automated NLR algorithm capable of generating batch production regression analysis.Total RNA samples extracted from human gastric mucosa were reverse transcribed and analysed for TNFA, IL18 and ACTB by TaqMan real-time PCR. Fluorescence data were analysed by the regular CT method with a standard curve, and by NLR with a positive control for conversion of fluorescence intensity to copy number, and for this purpose an automated algorithm was written in SPSS syntax. Eleven separate regression models were tested, and the output data was subjected to Altman-Bland analysis. The Altman-Bland analysis showed that the best regression model yielded quantitative data with an intra-assay variation of 58% vs. 24% for the CT derived copy numbers, and with a mean inter-method deviation of x0.8. NLR can be automated for batch production analysis, but the CT method is more precise for absolute quantitation in the present setting. The observed inter-method deviation is an indication that assessment of the fluorescence conversion factor used in the regression method can be improved. However, the versatility depends on the level of precision required, and in some settings the increased cost effectiveness of NLR may justify the lower precision.

Quantitative real-time RT-PCR based transcriptomics: Improvement of evaluation methods.
PhD. Thesis - Ales Tichopad
Lehrstuhl für Physiologie, Fakultät Wissenschaftszentrum Weihenstephan, Technische Universität München, Germany.
Quantitative real-time polymerase chain reaction (qRT-PCR) is a new method for reliable quantification of low-abundance mRNA in biological samples. Since the strength of the fluorescence signal emitted by the report dye should be proportional to the produced DNA amount, the fluorescence monitoring enables visualisation of the full reaction trajectory. The reaction trajectory can be then extrapolated back to an input concentration.
RNA extraction can introduce unwanted contaminants into the sample, inhibiting the reverse transcription (RT) as well as the PCR reaction. These inhibitions cause then the reaction to precede sample-specific. In addition, the amplification efficiency varies not only between samples, but also along the recorded amplification trajectory of a single sample. Consequently, a correct determination of each probe’s PCR efficiency as well as a good standardization of the raw expression estimators is of great importance for a correct interpretation of results.
To find a solution to above problems a series of biological experiments with RNA extracted from various ovine and bovine tissues and from cultured leukocytes was carried out. Constant amount of RNA was then reverse–transcribed to cDNA. All PCR runs were performed on a LightCycler instrument and Fluorescence data was saved in the LightCycler software.
Based on this data, mathematical models together with statistical procedures were developed and validated. These can investigate the optimal quantification range and exactly determine its real-time PCR efficiency. Additionally, methods were developed to disclose heterogeneity between probes. All these procedures contribute to better quality of results obtained. Resulting from these standardisations, a decision algorithm for a proper analysis of the qRT-PCR data was designed.

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