Estimation of the reaction efficiency in polymerase chain reaction

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.     

Validation of real-time RT-PCR assays for mRNA quantification in baboons

Real-time RT-PCR has been used widely, both in fundamental research and in clinical diagnostics, for instance for quantification of RNA levels in human tissues and tissue biopsies. In the present study we provide a strategy to validate primers/probes for real-time RT-PCR quantification of baboon samples. The method is based on the TaqMan system and uses primers/probes that have been designed and validated for human real-time RT-PCR. A prerequisite for the accuracy of this strategy is a similar amplification efficiency between human and baboon PCR reactions. We propose two different methods, i.e. by calculating PCR efficiencies from the slope of a dilution curve or by using the linear regression method, to compare the amplification efficiency between human and baboon samples. In conclusion, by performing a simple validation experiment, real-time PCR assays based on human sequences, which are easily available, can be applied for analysis of baboon samples.     

A new method for robust quantitative and qualitative analysis of real-time PCR

An automated data analysis method for real-time PCR needs to exhibit robustness to the factors that routinely impact the measurement and analysis of real-time PCR data. Robust analysis is paramount to providing the same interpretation for results regardless of the skill of the operator performing or reviewing the work. We present a new method for analysis of real-time PCR data, the maxRatio method, which identifies a consistent point within or very near the exponential region of the PCR signal without requiring user intervention. Compared to other analytical techniques that generate only a cycle number, maxRatio generates several measurements of amplification including cycle numbers and relative measures of amplification efficiency and curve shape. By using these values, the maxRatio method can make highly reliable reactive/nonreactive determination along with quantitative evaluation. Application of the maxRatio method to the analysis of quantitative and qualitative real-time PCR assays is shown along with examples of method robustness to, and detection of, amplification response anomalies.     

Statistical methods for efficiency adjusted real-time PCR quantification

The statistical treatment for hypothesis testing using real-time PCR data is a challenge for quantification of gene expression. One has to consider two key factors in precise statistical analysis of real-time PCR data: a well-defined statistical model and the integration of amplification efficiency (AE) into the model. Previous publications in real-time PCR data analysis often fall short in integrating the AE into the model. Novel, user-friendly, and universal AE-integrated statistical methods were developed for real-time PCR data analysis with four goals. First, we addressed the definition of AE, introduced the concept of efficiency-adjusted Delta Delta Ct, and developed a general mathematical method for its calculation. Second, we developed several linear combination approaches for the estimation of efficiency adjusted Delta Delta Ct and statistical significance for hypothesis testing based on different mathematical formulae and experimental designs. Statistical methods were also adopted to estimate the AE and its equivalence among the samples. A weighted Delta Delta Ct method was introduced to analyze the data with multiple internal controls. Third, we implemented the linear models with SAS programs and analyzed a set of data for each model. In order to allow other researchers to use and compare different approaches, SAS programs are included in the Supporting Information. Fourth, the results from analysis of different statistical models were compared and discussed. Our results underline the differences between the efficiency adjusted Delta Delta Ct methods and previously published methods, thereby better identifying and controlling the source of errors introduced by real-time PCR data analysis.     

Potential influence of the first PCR cycles in real-time comparative gene quantifications

There is an underlying assumption in real-time PCR that the amplification efficiency is equal from the first cycles until a signal can be detected. In this study, we evaluated this assumption by analyzing genes with known gene copy number using real-time PCR comparative gene quantifications. Listeria monocytogenes has six 23S rRNA gene copies and one copy of the hlyA gene. We determined 23S rRNA gene copy numbers between 0.9 and 1.6 relative to hlyA when applying the comparative gene quantification approach. This paper focuses on the first cycles of PCR to explain the difference between known and determined gene copy numbers. Both theoretical and experimental evaluations were done. There are three different products (types 1-3) dominating in the first cycles. Type 1 is the original target, type 2 are undefined long products, while type 3 are products that accumulate during PCR. We evaluated the effects of type 1 and 2 products during the first cycles by cutting the target DNA with a restriction enzyme that cuts outside the boundaries of the PCR products. The digestion resulted in a presumed increased amplification efficiency for type 1 and 2 products. Differences in the amplification efficiencies between type 1, 2, and 3 products may explain part of the error in the gene copy number determinations using real-time PCR comparative gene quantifications. Future applications of real-time PCR quantifications should account for the effect of the first few PCR cycles on the conclusions drawn.     

Kinetic Outlier Detection (KOD) in real-time PCR

Real-time PCR is becoming the method of choice for precise quantification of minute amounts of nucleic acids. For proper comparison of samples, almost all quantification methods assume similar PCR efficiencies in the exponential phase of the reaction. However, inhibition of PCR is common when working with biological samples and may invalidate the assumed similarity of PCR efficiencies. Here we present a statistical method, Kinetic Outlier Detection (KOD), to detect samples with dissimilar efficiencies. KOD is based on a comparison of PCR efficiency, estimated from the amplification curve of a test sample, with the mean PCR efficiency of samples in a training set. KOD is demonstrated and validated on samples with the same initial number of template molecules, where PCR is inhibited to various degrees by elevated concentrations of dNTP; and in detection of cDNA samples with an aberrant ratio of two genes. Translating the dissimilarity in efficiency to quantity, KOD identifies outliers that differ by 1.3–1.9-fold in their quantity from normal samples with a P-value of 0.05. This precision is higher than the minimal 2-fold difference in number of DNA molecules that real-time PCR usually aims to detect. Thus, KOD may be a useful tool for outlier detection in real-time PCR.     

Experimental analysis of gene assembly with TopDown one-step real-time gene synthesis

Herein we present a simple, cost-effective TopDown (TD) gene synthesis method that eliminates the interference between the polymerase chain reactions (PCR) assembly and amplification in one-step gene synthesis. The method involves two key steps: (i) design of outer primers and assembly oligonucleotide set with a melting temperature difference of >10°C and (ii) utilization of annealing temperatures to selectively control the efficiencies of oligonucleotide assembly and full-length template amplification. In addition, we have combined the proposed method with real-time PCR to analyze the step-wise efficiency and the kinetics of the gene synthesis process. Gel electrophoresis results are compared with real-time fluorescence signals to investigate the effects of oligonucleotide concentration, outer primer concentration, stringency of annealing temperature, and number of PCR cycles. Analysis of the experimental results has led to insights into the gene synthesis process. We further discuss the conditions for preventing the formation of spurious DNA products. The TD real-time gene synthesis method provides a simple and efficient method for assembling fairly long DNA sequence, and aids in optimizing gene synthesis conditions. To our knowledge, this is the first report that utilizes real-time PCR for gene synthesis.     

Real-time PCR method for detection of pathogenic Yersinia enterocolitica in food

The current methods for the detection of pathogenic Yersinia enterocolitica bacteria in food are time consuming and inefficient. Therefore, we have developed and evaluated in-house a TaqMan probe-based real-time PCR method for the detection of this pathogen. The complete method comprises overnight enrichment, DNA extraction, and real-time PCR amplification. Also included in the method is an internal amplification control. The selected primer-probe set was designed to use a 163-bp amplicon from the chromosomally located gene ail (attachment and invasion locus). The selectivity of the PCR method was tested with a diverse range (n = 152) of related and unrelated strains, and no false-negative or false-positive PCR results were obtained. The sensitivity of the PCR amplification was 85 fg purified genomic DNA, equivalent to 10 cells per PCR tube. Following the enrichment of 10 g of various food samples (milk, minced beef, cold-smoked sausage, fish, and carrots), the sensitivity ranged from 0.5 to 55 CFU Y. enterocolitica. Good precision, robustness, and efficiency of the PCR amplification were also established. In addition, the method was tested on naturally contaminated food; in all, 18 out of 125 samples were positive for the ail gene. Since no conventional culture method could be used as a reference method, the PCR products amplified from these samples were positively verified by using conventional PCR and sequencing of the amplicons. A rapid and specific real-time PCR method for the detection of pathogenic Y. enterocolitica bacteria in food, as presented here, provides a superior alternative to the currently available detection methods and makes it possible to identify the foods at risk for Y. enterocolitica contamination.     

Real-time quantitative PCR for enteric adenovirus serotype 40 in environmental waters

Adenoviruses 40 and 41 have been recognized as important etiological agents of gastroenteritis in children. A real-time PCR method (TaqMan assay) was developed for rapid quantification of adenovirus 40 (Ad40) by amplifying an 88 bp sequence from the hexon gene. To establish a quantification standard curve, a 1090 bp hexon region of Ad40 was amplified and cloned into the pGEM-T Vector. A direct correlation was observed between the fluorescence threshold cycle number (Ct) and the starting quantity of Ad40 hexon gene. The quantification was linear over 6-log units and the amplification efficiency averaged greater than 95%. Seeding studies using various environmental matrices (including sterile water, creek water, brackish estuarine water, ocean water, and secondary sewage effluent) suggest that this method is applicable to environmental samples. However, real-time PCR was sensitive to inhibitors present in the environmental samples. Lower efficiency of PCR amplification was found in secondary sewage effluent and creek waters. Application of the method to fecal contaminated waters successfully quantified the presence of Ad40. The sensitivity of the real-time PCR is comparable to the traditional nested PCR assay for environmental samples. In addition, the real-time PCR assay offers the advantage of speed and insensitivity to contamination during PCR set up. The real-time PCR assay developed in this study is suitable for quantitative determination of Ad40 in environmental samples and represents a considerable advancement in pathogen quantification in aquatic environments.     

Locked nucleic acid (LNA) single nucleotide polymorphism (SNP) genotype analysis and validation using real-time PCR

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.     

Real-time PCR quantification using a variable reaction efficiency model

The quantitative real-time polymerase chain reaction (PCR) remains a cornerstone technique in gene expression analysis and sequence characterization. Despite the importance of the approach to experimental biology, the confident assignment of reaction efficiency to the early cycles of real-time PCR reactions remains problematic. Considerable noise may be generated when few cycles in the amplification are available to estimate peak efficiency. An alternate approach that uses data from beyond the log–linear amplification phase is explored in this article with the aim of reducing noise and adding confidence to efficiency estimates. PCR reaction efficiency is regressed to estimate the per-cycle profile of an asymptotically departed peak efficiency even when this is not closely approximated in the measurable cycles. The process can be repeated over replicates to develop a robust estimate of peak reaction efficiency. This leads to an estimate of the maximum reaction efficiency that may be considered primer design specific. Using a series of biological scenarios, we demonstrate that this approach can provide an accurate estimate of initial template concentration.     

Direct detection of Shigella flexneri and Salmonella typhimurium in human feces by real-time PCR

We have established a SYBR Green-based realtime PCR method using AnyDirect solution, which enhances PCR from whole blood, for direct amplification of the virA gene of Shigella flexneri and the invA gene of Salmonella typhimurium from human feces without prior DNA purification. When we compared the efficiency of conventional or realtime PCR amplification of the virA and invA genes from the supernatant of boiled feces supplemented with S. flexneri and S. typhimurium in the presence or absence of AnyDirect solution, amplification products were detected only in reactions to which AnyDirect solution had been added. The detection limit of real-time PCR was 1 x 10(4) CFU/g feces for S. flexneri and 2 x 10(4) CFU/g feces for S. typhimurium this sensitivity level was comparable to other studies. Our real-time PCR assay with AnyDirect solution is simple, rapid, sensitive, and specific, and allows simultaneous detection of S. flexneri and S. typhimurium directly from fecal samples without prior DNA purification.     

Antisense PCR: A simple and robust method for performing nested single-tube PCR

To overcome the disadvantages of two-round nested PCR, we developed a simple and robust closed single-tube nested PCR method (antisense PCR). The method uses antisense oligonucleotides that carry a 5′ tag and that can potentially hybridize to the 3′ ends of the outer primers, depending on the annealing temperature. During initial cycles, which are performed at a high annealing temperature, the antisense oligonucleotides do not hybridize and amplification is directed by the outer primers. During later cycles, for which the annealing temperature is decreased, the outer primers hybridize to the antisense oligonucleotides, extend to produce sequences that are mismatched to the amplicon templates, and consequently become inactivated, whereas the inner primers hybridize to the amplicon templates and continue amplification. Antisense quantitative PCR (qPCR) was compared with one-round qPCR for real-time amplification of four PCR targets (BCR, APC, N-RAS, and a rearranged IGH gene). It had equal amplification efficiency but produced much less nonspecific amplification. Antisense PCR enables both endpoint detection and real-time quantification. It can substitute for two-round nested PCRs but may also be applicable to instances of one-round PCR in which nonspecificity is a problem.     

The allele-specific probe and primer amplification assay, a new real-time PCR method for fine quantification of single-nucleotide polymorphisms in pooled DNA

The evolution of fungicide resistance within populations of plant pathogens must be monitored to develop management strategies. Such monitoring often is based on microbiological tests, such as microtiter plate assays. Molecular monitoring methods can be considered if the mutations responsible for resistance have been identified. Allele-specific real-time PCR approaches, such as amplification refractory mutation system (ARMS) PCR and mismatch amplification mutation assay (MAMA) PCR, are, despite their moderate efficacy, among the most precise methods for refining SNP quantification. We describe here a new real-time PCR method, the allele-specific probe and primer amplification assay (ASPPAA PCR). This method makes use of mixtures of allele-specific minor groove binder (MGB) TaqMan probes and allele-specific primers for the fine quantification of SNPs from a pool of DNA extracted from a mixture of conidia. It was developed for a single-nucleotide polymorphism (SNP) that is responsible for resistance to the sterol biosynthesis inhibitor fungicide fenhexamid, resulting in the replacement of the phenylalanine residue (encoded by the TTC codon) in position 412 of the enzymatic target (3-ketoreductase) by a serine (TCC), valine (GTC), or isoleucine (ATC) residue. The levels of nonspecific amplification with the ASPPAA PCR were reduced at least four times below the level of currently available allele-specific real-time PCR approaches due to strong allele specificity in amplification cycles, including two allele selectors. This new method can be used to quantify a complex quadriallelic SNP in a DNA pool with a false discovery rate of less than 1%.     

Quantitative PCR in the diagnosis of Leishmania

Polymerase chain reaction (PCR) is a sensitive and rapid method for the diagnosis of canine Leishmania infection and can be performed on a variety of biological samples, including peripheral blood, lymph node, bone marrow and skin. Standard PCR requires electrophoretic analysis of the amplification products and is usually not suitable for quantification of the template DNA (unless competitor-based or other methods are developed), being of reduced usefulness when accurate monitoring of target DNA is required. Quantitative real-time PCR allows the continuous monitoring of the accumulation of PCR products during the amplification reaction. This allows the identification of the cycle of near-logarithmic PCR product generation (threshold cycle) and, by inference, the relative quantification of the template DNA present at the start of the reaction. Since the amplification product are monitored in "real-time" as they form cycle-by-cycle, no post-amplification handling is required. The absolute quantification is performed according either to an internal standard co-amplified with the sample DNA, or to an external standard curve obtained by parallel amplification of serial known concentrations of a reference DNA sequence. From the quantification of the template DNA, an estimation of the relative load of parasites in the different samples can be obtained. The advantages compared to standard and semi-quantitative PCR techniques are reduction of the assay's time and contamination risks, and improved sensitivity. As for standard PCR, the minimal components of the quantitative PCR reaction mixture are the DNA target of the amplification, an oligonucleotide primer pair flanking the target sequence, a suitable DNA polymerase, deoxynucleotides, buffer and salts. Different technologies have been set up for the monitoring of amplification products, generally based on the use of fluorescent probes. For instance, SYBR Green technology is a non-specific detection system based on a fluorescent dsDNA intercalator and it is applicable to all potential targets. TaqMan technology is more specific since performs the direct assessment of the amount of amplified DNA using a fluorescent probe specific for the target sequence flanked by the primer pair. This probe is an oligonucleotide labelled with a reporter dye (fluorescent) and a quencher (which absorbs the fluorescent signal generated by the reporter). The thermic protocol of amplification allows the binding of the fluorescent probe to the target sequence before the binding of the primers and the starting of the polymerization by Taq polymerase. During polymerization, 5'-3' exonuclease activity of Taq polymerase digests the probe and in this way the reporter dye is released from the probe and a fluorescent signal is detected. The intensity of the signal accumulates at the end of each cycle and is related to the amount of the amplification product. In recent years, quantitative PCR methods based either on SYBR Green or TaqMan technology have been set up for the quantification of Leishmania in mouse liver, mouse skin and human peripheral blood, targeting either single-copy chromosomal or multi-copy minicircle sequences with high sensitivity and reproducibility. In particular, real-time PCR seems to be a reliable, rapid and noninvasive method for the diagnosis and follow up of visceral leishmaniasis in humans. At present, the application of real-time PCR for research and clinical diagnosis of Leishmania infection in dogs is still foreseable. As for standard PCR, the high sensitivity of real-time PCR could allow the use of blood sampling that is less invasive and easily performed for monitoring the status of the dogs. The development of a real-time PCR assay for Leishmania infantum infection in dogs could support the standard and optimized serological and PCR methods currenly in use for the diagnosis and follow-up of canine leishmaniasis, and perhaps prediction of recurrences associated with tissue loads of residual pathogens after treatment. At this regard, a TaqMan Real Time PCR method developed for the quantification of Leishmania infantum minicircle DNA in peripheral blood of naturally infected dogs sampled before and at different time points after the beginning of a standard antileishmanial therapy will be illustrated.     

A quantitative approach for polymerase chain reactions based on a hidden Markov model

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. This research was financed by the Swedish foundation for Strategic Research through the Gothenburg Mathematical Modelling Centre.     

Experimental validation of novel and conventional approaches to quantitative real-time PCR data analysis

Real-time PCR is being used increasingly as the method of choice for mRNA quantification, allowing rapid analysis of gene expression from low quantities of starting template. Despite a wide range of approaches, the same principles underlie all data analysis, with standard approaches broadly classified as either absolute or relative. In this study we use a variety of absolute and relative approaches of data analysis to investigate nocturnal c-fos expression in wild-type and retinally degenerate mice. In addition, we apply a simple algorithm to calculate the amplification efficiency of every sample from its amplification profile. We confirm that nocturnal c-fos expression in the rodent eye originates from the photoreceptor layer, with around a 5-fold reduction in nocturnal c-fos expression in mice lacking rods and cones. Furthermore, we illustrate that differences in the results obtained from absolute and relative approaches are underpinned by differences in the calculated PCR efficiency. By calculating the amplification efficiency from the samples under analysis, comparable results may be obtained without the need for standard curves. We have automated this method to provide a means of streamlining the real-time PCR process, enabling analysis of experimental samples based upon their own reaction kinetics rather than those of artificial standards.     

Single nucleotide polymorphism (SNP) allele frequency estimation in DNA pools using Pyrosequencing

Identifying the genetic variation underlying complex disease requires analysis of many single nucleotide polymorphisms (SNPs) in a large number of samples. Several high-throughput SNP genotyping techniques are available; however, their cost promotes the use of association screening with pooled DNA. This protocol describes the estimation of SNP allele frequencies in pools of DNA using the quantitative sequencing method Pyrosequencing (PSQ). PSQ is a relatively recently described high-throughput method for genotyping, allele frequency estimation and DNA methylation analysis based on the detection of real-time pyrophosphate release during synthesis of the complementary strand to a PCR product. The protocol involves the following steps: (i) quantity and quality assessment of individual DNA samples; (ii) DNA pooling, which may be undertaken at the pre- or post-PCR stage; (iii) PCR amplification of PSQ template containing the variable sequence region of interest; and (iv) PSQ to determine the frequency of alleles at a particular SNP site. Once the quantity and quality of individual DNA samples has been assessed, the protocol usually requires a few days for setting up pre-PCR pools, depending on sample number. After PCR amplification, preparation and analysis of PCR amplicon by PSQ takes 1 h per plate.