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Real time PCR parameter CT

Real time PCR parameter CT


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When puting a real time PCR, parameter CT, which means threshold cycle, is used. What does it mean really? according to wikipedia "The number of cycles at which the fluorescence exceeds the threshold is called the threshold cycle (Ct)" could anyone put it in conext?


Realtime PCR uses a fluorescent dye which binds to double-stranded DNA and thus allows to measure the growing amount of DNA by each cycle. The DNA added to the reaction also binds the fluorescent dye and makes some part of the fluorescent background. When the PCR reaction starts, it takes a while until enough DNA is synthesized to go over the background and to be able to reliable distinguish the signal from the noise. I think this becomes clearer, when you look at the image below (from the NIH):

The Ct is the point where the signal can be distinguished from the background when it enters the exponential grwoth phase. The no template control stays below this threshold.


What is Real-Time PCR (qPCR)?

Nucleic acid amplification and detection techniques are among the most valuable tools in biological research today. Scientists in all areas of life science &mdash basic research, biotechnology, medicine, forensics, diagnostics, and more &mdash utilize these methods in a wide range of applications. For some applications, qualitative nucleic acid detection is sufficient. Other applications, however, demand a quantitative analysis. Real-time PCR can be used for both qualitative and quantitative analysis choosing the best method for your application requires a broad knowledge of this technology. This section provides an overview of real-time PCR, reverse-transcription quantitative PCR techniques, and the choice of instruments that Bio-Rad offers for these techniques. It also provides tips for steps in RNA isolation such as sample collection, RNA extraction, and analyzing the quality and quantity of RNA.

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Delta Delta Ct method for multiple reference genes? - (Jan/23/2011 )

I was wondering if anyone could tell me whether you can use the delta delta Ct method for qPCR data analysis with multiple reference genes and if anyone would know how to go about this?

You can use it but consider that delta-delta is only an aproximation method, since it doesn't take into account different efficiencies of different genes. More housekeepings are used to make the results more accurate, but at the same time you just throw away your accuracy with a delta-delta.

You can use this Pfaffl equation:

Where E is the efficiency of each gene. If you put "2" as E, it's the same as delta-delta. But if you do a dilution series for each gene and actualy calculate the efficiencies, you may get more accurate results.

Now how to normalise to multiple references - instead of single E^deltaCP for one gene you make a geometric mean of all of them. That means if you have two housekeepings, in the denominator you will multiply each E^deltaCP and then take square root of the result. (if three, than again, multiply and then take cube-root, and so on).

The final equation is from this paper Hellemans, Mortier, De Paepe, Speleman, Vandesompele (2007) (but I had to ask mathematicians to explain in, because it looks horrible).


Where is qPCR being used?

Due to its powerful advantages, qPCR has a wide range of applications. The method had been around long enough so that the research community proved its reliability and robustness. Similarly, manufacturers of qPCR cyclers developed reliable platforms, and that providers of liquid handling automation devices developed qPCR-compatible automation solutions (e.g. robots).

The most evident is the use of qPCR in molecular diagnostics, where it is slowly replacing conventional methods (Figure 3). It is used to detect, identify and quantify microorganisms that cause diseases (bacteria, viruses, and fungi). With qPCR manual labor is reduced and along with that concern over contamination and erroneous results. It also allows for large amounts of samples to be processed in less time (up to 384 or even 1536 reactions per run) and has thus proven to be an irreplaceable method in diagnostic laboratories. It has to be noted, though, that the method detects only the presence of DNA or RNA of a microorganism and does not report its viability. Consequently, conventional microbiological techniques are sometimes still required alongside it.

Figure 3: Shows a Rupestris stem pitting associated virus (RSPaV) as visualized by transmission electron microscope, one of the conventional detection techniques that are being replaced by RT-qPCR (photo: NIB).

qPCR is also used to detect and quantify genetically modified organisms or to perform genotyping. The latter means that different alleles of the same gene or single nucleotide polymorphisms (SNPs) can be detected which can be used as genetic diagnostic or prognostic markers for certain diseases.

A very important field of application is represented by gene expression studies that help us understand the biological processes in various fields of biology, microbiology, medicine, and other life sciences. A very useful, almost blockbuster combination is a genome-wide gene expression screening with DNA-microarrays followed by validation of results with qPCR. DNA microarrays are a very powerful method on its own, but they are less sensitive and still require validation.


3. Research vs Diagnostic Applications

Applications of qPCR technology can be broadly divided into research and diagnostic applications. Research applications usually analyze a wide range of targets with a fairly low throughput and many different sample types. The main parameters that need to be addressed relate to assay analytical sensitivity and specificity, which in this context refer to how many target copies the assay can detect and whether the no-template controls (NTCs) are reliably negative, respectively.

In contrast, diagnostic applications usually analyze a limited number of targets, but require high-throughput protocols that are targeted at only a few sample types. Although all of the considerations that apply to research applications also apply to diagnostic assays, clinical-diagnostic assays have a number of additional requirements that need to be considered. These requirements include information on analytical sensitivity and specificity that in this context refers to how often the assay returns a positive result when a target is present and how often it is negative in the absence of the target. Furthermore, the accuracy and precision within and between laboratories is often monitored by external QC programs. Additional clinical laboratory requirements include criteria for generating reportable results, whether repeated measurements are made on samples, data on the resolution of false-positive/false-negative data, and the similarity of results from multiple laboratories that use the same and different technologies. Thus far, only a couple of interlaboratory comparisons have been performed, and both of these studies emphasized the need for standardization of qPCR diagnostic assays( 44)( 45). Another interlaboratory exercise is planned within the European Framework 7 project: SPIDIA (Standardisation and Improvement of Generic Pre-analytical Tools and Procedures for In-Vitro Diagnostics http://www.spidia.eu).


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Livak KJ, Schmittgen TD (2001) Analysis of relative gene expression data using real-time quantitative PCR and the 2(−DeltaDelta C(T)) method. Methods 25:402–408. doi:10.1006/meth.2001.1262

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Luu-The V, Paquet N, Calvo E, Cumps J (2005) Improved real-time RT-PCR method for high-throughput measurements using second derivative calculation and double correction. Biotechniques 38:287–293. doi:10.2144/05382RR05

Higuchi R, Fockler C, Dollinger G et al (1993) Kinetic PCR analysis: real-time monitoring of DNA amplification reactions. Biotechnology 11:1026–1030. doi:10.1038/nbt0993-1026

Tichopad A, Dilger M, Schwarz G, Pfaffl MW (2003) Standardized determination of real-time PCR efficiency from a single reaction set-up. Nucleic Acids Res 31:e122. doi:10.1093/nar/gng122

Grace MB, Mcleland CB, Blakely WF (2002) Real-time quantitative RT-PCR assay of GADD45 gene expression changes as a biomarker for radiation biodosimetry. Int J Radiat Biol 78:1011–1021. doi:10.1080/09553000210158056

Suslov O, Steindler DA (2005) PCR inhibition by reverse transcriptase leads to an overestimation of amplification efficiency. Nucleic Acids Res 33:e181. doi:10.1093/nar/gni176


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.

Figures

Flow chart showing steps in…

Flow chart showing steps in implementing the algorithm described. The process of quantification…

Fitting the whole curve and…

Fitting the whole curve and determining the exponential phase. The fluorescent data from…

Comparison of linear regression versus…

Comparison of linear regression versus nonlinear regression. ( A ) Equations for linear…

Evaluation of noise-resistant regression. The…

Evaluation of noise-resistant regression. The same data in Table 5 were plotted. Note…

Comparison of methods for CT…

Comparison of methods for CT determination. ( A ) CT determination using FDM,…

Validation of real-time PCR Miner.…

Validation of real-time PCR Miner. Multiple internal control genes (actin, G3PDH, and 18S…


Cy0 - A new qPCR quantification method

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 sub-optimal amplification conditions overcoming the underestimation caused by the presence of some PCR inhibitors.

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In the last few years, the real-time polymerase chain reaction (PCR) has rapidly become the most widely used technique in modern molecular biology [1-4].
This technique relies on fluorescence-based detection of amplicon DNA and allows the kinetics of PCR amplification to be monitored in real time, making it possible to quantify nucleic acids with extraordinary ease and precision. With a large dynamic range (7-8 magnitudes) and a high degree of sensitivity (5-10 molecules), the real-time PCR addresses the evident requirement for quantitative data analysis in molecular medicine, biotechnology, microbiology and diagnostics [ 5, 6].
Although, the real-time PCR analysis has gained considerable attention in many fields of molecular biology, it is far from being a standard assay. One of the problems associated with this assay, which has a direct impact on its reliability, is inconsistent data analysis. At the present, real-time PCR analysis is highly subjective and, if carried out inappropriately, confuses the actual results [7].
Many different options for data processing are currently available. The basic choice in real time PCR calculations is between absolute quantification, based on standard curve, and relative quantification, based on PCR efficiency calculation. Using the software currently available, analysis of real-time PCR data is generally based on the "cycle-threshold " method. The cycle-threshold is defined as the fractional cycle number in the log-linear region of PCR amplification in which the reaction reaches fixed amounts of amplicon DNA. There are two methods for determining the cycle-threshold value one method, namely fit point, is performed by drawing a line parallel to the x-axis of the real-time fluorescence intensity curve (Ct) [8]. The second, namely second derivative, calculates the fractional cycle where the second derivative of the real-time fluorescence intensity curve reaches the maximum value (Cp) [9]. Standard curve method requires generating serial dilutions of a given sample and performing multiple PCR reactions on each dilution [10, 11], the threshold-cycle values are then plotted versus the log of the dilution and a linear regression is performed from which the mean efficiency can be derived. This approach is only valid if the threshold-cycle values are measured from the exponential phase of the PCR reaction and if the efficiency is identical between amplifications. Furthermore, this efficiency is assumed to be the same for all the standard dilutions, but some authors have reported that this assumption may be questionable [12].
It is well-recognized that template quality is one of the most important determinants of real-time PCR reliability and reproducibility [13], and numerous authors have shown the significant reduction in the sensitivity and kinetics of real-time PCR assays caused by inhibitory components frequently found in biological samples [14, 17].
The inhibiting agents may be reagents used during nucleic acid extraction or copurified components from the biological sample such as bile salts, urea, haeme, heparin, and immunoglobulin G. Inhibitors can generate strongly inaccurate quantitative results while, a high degree of inhibition may even create false-negative results.
The Ct method is the most widely used method even though its calculation is user-dependent. The Ct method is quite stable and straightforward but the accuracy of estimates is strongly impaired if efficiency is not equal in all reactions. Indeed, uniform reaction efficiency is the most important assumption of the Ct method.
An alternative approach, proposed by Liu and Saint [18], assumes a dynamic change in efficiency fitting PCR amplification with a sigmoid function (Sigmoidal curve fitting method, SCF). One of the advantages of this regression analysis is that it allows us to estimate the initial template amount directly from the non-linear regression, eliminating the need for a standard curve. These pioneering works showed that it was possible to obtain absolute quantification from real-time fluorescence curve shape. However, recent reports have demonstrated that, in an optimized assay, the Ct method remains the gold standard due to the inherent errors of the multiple estimates used in non-linear regression [19, 20].
We propose, in this report, a modified standard curve-based method (named Cy0) that does not require the assumption of uniform reaction efficiency between standards and unknown and does not involve any choice of threshold level by the user.
The aim of this work was also to compare the accuracy and precision of the SCF, Ct, Cp and Cy0 methods in presence of varying PCR kinetics. Our results clearly show that the proposed data processing procedure can effectively be applied in the quantification of samples characterized by slight amplification inhibition obtaining reliable and precise results.

The absolute quantification method relies on the comparison of distinct samples, such as the comparison of a biological sample with a standard curve of known initial concentration [21].
We wondered how accuracy and precision change when a standard curve is compared with unknown samples characterized by different efficiencies. A natural way of studying the effect of efficiency differences among samples on quantification would be to compare the amounts of a quantified gene.
A slight amplification inhibition in the quantitative real-time PCR experiments was obtained by using two systems: decreasing the amplification mix used in the reaction and adding varying amounts of IgG, a known PCR inhibitor.
For the first system, we amplified the MT-ND1 gene by real-time PCR in reactions having the same initial amount of DNA but different amounts of SYBR Green I Master mix. A standard curve was performed over a wide range of input DNA (3.14x10 7 -3.14x10 1 ) in the presence of optimal amplification conditions (100% amplification mix), while the unknowns were run in the presence of the same starting DNA amounts but with amplification mix quantities ranging from 60% to 100%. This produced different reaction kinetics, mimicking the amplification inhibition that often occurs in biological samples [17, 22].
Furthermore, quantitative real-time PCR quantifications were performed in the presence of an optimal amplification reaction mix added with serial dilutions of IgG (0.0625 - 2 µg/ml) thus acting as the inhibitory agent [23].
The reaction efficiency obtained was estimated by the LinReg method [24]. This approach identifies the exponential phase of the reaction by plotting the fluorescence on a log scale. A linear regression is then performed leading to the estimation of the efficiency of each PCR reaction.

Quantitative Real-Time PCR

The DNA standard consisted of a pGEM-T (Promega) plasmid containing a 104 bp fragment of the mitochondrial gene NADH dehydrogenase 1 (MT-ND1) as insert. This DNA fragment was produced by the ND1/ND2 primer pair (forward ND1: 5 ' -ACGCCATAAAACTCTTCACCAAAG-3 ' and reverse ND2: 5 ' -TAGTAGAAGAGCGATGGTGAGAGCTA-3 ' ). This plasmid was purified using the Plasmid Midi Kit (Qiagen) according to the manufacturer ' s instructions. The final concentration of the standard plasmid was estimated spectophotometrically by averaging three replicate A260 absorbance determinations.
Real time PCR amplifications were conducted using LightCycler ® 480 SYBR Green I Master (Roche) according to the manufacturer's instructions, with 500 nM primers and a variable amount of DNA standard in a 20µl final reaction volume. Thermocycling was conducted using a LightCycler ® 480 (Roche) initiated by a 10 min incubation at 95°C, followed by 40 cycles (95°C for 5 s 60°C for 5 s 72°C for 20 s) with a single fluorescent reading taken at the end of each cycle. Each reaction combination, namely starting DNA and amplification mix percentage, was conducted in triplicate and repeated in four separate amplification runs. All the runs were completed with a melt curve analysis to confirm the specificity of amplification and lack of primer dimers. Ct (fit point method) and Cp (second derivative method) values were determined by the LightCycler ® 480 software version 1.2 and exported into an MS Excel data sheet (Microsoft) for analysis after background subtraction (available as Additional file 1). For Ct (fit point method) evaluation a fluorescence threshold manually set to 0.5 was used for all runs.

Description of the SCF method

Fluorescence readings were used to fit the following 4-parameter sigmoid function using nonlinear regression analysis:

Eq. 1
where x is the cycle number, Fx is the reaction fluorescence at cycle x, Fmax is the maximal reaction fluorescence, c is the fractional cycle at which reaction fluorescence reaches half of Fmax, b is related to the slope of the curve and Fb is the background reaction fluorescence. Fmax quantifies the maximal fluorescence read by the instrument and does not necessarily indicate the amount of DNA molecules present at the end of the reaction. The fact that Fmax does not necessarily represent the final amount of DNA might be due to un-saturating dye concentration or to fluorescence quenching by inhibitors. For each run a nonlinear regression analysis was performed and these four parameters were evaluated. A simple derivative of Eq. 1 allowed us to estimate F0, when x = 0:
Eq. 2
where F0 represents the initial target quantity expressed in fluorescence units. Conversion of F0 to the number of target molecules was obtained by a calibration curve in which the log input DNA was related to the log of F0 [18]. Subsequently, this equation was used for quantification with log transformation of fluorescence data to increase goodness-of-fit as described in Goll et al. 2006 [19].

Description of the Cy0 method

The Cy0 value is the intersection point between the abscissa axis and tangent of the inflection point of the Richards curve obtained by the non-linear regression of raw data (Fig. 1).

Example of modelling PCR amplification with a 5-parameter Richards function Effectiveness of this model is illustrated by the predicted values generated by Eq. 3 (open circles) that agree with the observed fluorescence (dot and line). Curve-fitting of experimentally derived fluorescence dataset to Eq. 3 generates values for the kinetic parameters from which the inflection point (solid black rhombus) and the slope of the curve can be derived. The quantitative entity Cy0(solid black dot), used in the proposed method, shows the cross point between the x-axis and the tangent crossing the inflection point of real-time PCR fluorescence curve.

The Cy0 method was performed by nonlinear regression f itting of the Richards function [25], an extension of logistic growth curve, in order to fit fluorescence readings to the 5-parameter Richards function:
Eq. 3
where x is the cycle number, Fx is the reaction fluorescence at cycle x, Fmax is the maximal reaction fluorescence, x is the fractional cycle of the turning point of the curve, d represents the Richards coefficient, and Fb is the background reaction fluorescence. The inflection point coordinate (Flex) was calculated as follows (Additional file 2):
Eq. 4
and the tangent slope (m) was estimated as:
Eq. 5
When d = 1, the Richards equation becomes the logistic equation shown above. The five parameters that characterized each run were used to calculate the Cy0 value by the following equation:
Eq. 6
Although the Cy0 is a single quantitative entity, as is the Ct or Cp for threshold methodologies, it accounts for the reaction kinetic because it is calculated on the basis of the slope of the inflection point of fluorescence data.

Statistical data analysis

Nonlinear regressions (for 4-parameter sigmoid and 5-parameter Richards functions) were performed determining unweighted least squares estimates of parameters using the Levenberg-Marquardt method. Accuracy was calculated using the following equation: , where was the relative error, while and were the estimated and the true number of DNA molecules for each combination of input DNA (nDna) and amplification mix percentage (%mix) used in the PCR. Precision was calculated as:

, where was the coefficient of variation, and were the mean and the standard deviation for each combination of nDna and %mix. In order to verity that the Richards curves, obtained by nonlinear regression of fluorescence data, were not significantly different from the sigmoidal curves, the values of d parameter were compared to the expected value d= 1, using t test for one sample. For each combination of nDna, %mix, the t values were calculated as follow:

, where and were the mean and the standard error of d values for each combination of nDna and %mix, with p(t) < 0.05 for significance level. values were reported using 3-d scatterplot graphic, a complete second order polinomial regression function was shown to estimate the trend of accuracy values. where also reported using 3-d contour plots using third-order polynomials spline fitting. All elaborations and graphics were obtained using Excel (Microsoft), Statistica (Statsoft) and Sigmaplot 10 (Systat Software Inc.).

Experimental system 1: reduction of amplification mix percentage

With our experimental set up, the mean PCR reaction efficiency was 88% under optimal amplification conditions and slightly decreased in the presence of smaller amplification mix up to 84%. Moreover, for decreasing amplification mix amounts, the PCR reaction efficiencies showed higher dispersion levels than optimal conditions leading to increasing quantitative errors (Variation Interval, VI100%= 1.921-1.852 and VI60%= 1.903-1.776 Fig. 2). Subsequently, the fluorescence data obtained in these reactions were used to calculate the initial DNA amount using four different procedures: SCF, Ct, Cp and Cy0.

Precision and accuracy of the SCF method

Previous studies have shown that the SCF approach can lead to quantification without prior knowledge of amplification efficiency [18, 19, 26] therefore, we evaluated the performance of this method on our data set. To assess the effect of unequal efficiencies on accuracy, the calculated input DNA, expressed as molecular number, was compared to the expected value obtaining the relative error (RE). The precision was further evaluated measuring the variation coefficient (CV%) of the estimated initial DNA in the presence of different PCR efficiencies and input DNA.
In our experimental design, the SCF method showed a very poor precision (mean CV% = 594.74%) and low accuracy (mean RE = -5.05). The impact of amplification efficiency decline on accuracy was very strong resulting in an underestimate of samples of up to 500% (Additional file 3). The log transformation of fluorescence data before sigmoidal fitting significantly reduced the CV% and RE to 66.12% and -0.20, respectively however, the overall bias remained the same [19]. Finally, we also tested an improved SCF approach based on a previous study by Rutledge 2004 [26] without obtaining significant amelioration (Additional file 4).

Estimation of PCR efficiency using LinReg method Efficiency values were determined from 420 independent reactions using a combination of 3.14 x 10 7 x 3.14 x 10 1 DNA molecules as starting template and amplification mix quantities ranging from 60% to 100%. The graph shows the distribution of PCR efficiencies in relation to the percentage of amplification mix used in the reaction. The solid black squares (?) represent the mean of each distribution.

The SCF model assumes that the fluorescence signal is proportional to the amount of product, which is often the case for SYBR-Green I real-time PCR performed with saturing concentrations of dye. In such conditions, centrally symmetric amplification curves are expected. However, in our experience, we found several non-symmetric amplification curves shown to have good amplification efficiency using standard curve analysis (Additional file 1 and 3). In order to find a suitable mathematical representation of the complete PCR kinetic curve we compared the standard error of estimate obtained by several equations that generate S-shaped curves (Tab. 1). As shown in Figure 1, these results demonstrated that real-time PCR readouts can be effectively modelled using the 5-parameter Richards function (Eq. 3). The Richards equation is an extension of the sigmoidal growth curve specifically, when d coefficient is equal to 1, the sigmoidal and Richards curves are the same. Hence, we analysed the variation of the d coefficient in the presence of different input DNA and PCR efficiencies. Figure 3 shows that the d value is close to 1 at amplification mix percentages ranging from 100% to 90% while at lower amplification mix contents, where PCR efficiency decreases, the d coefficient was significantly higher than 1 regardless of the starting DNA content (Fig. 3 Tab. 2). These data demonstrate that sigmoidal fitting represents a good approximation of real-time PCR kinetic only in the presence of optimal amplification conditions while the Richards curve is more suited when PCR is inhibited. Since the Richards growth equation includes sigmoidal amplification curves, when d = 1, this nonlinear fitting was used in our method.

Distribution of Richards coefficients (d) estimated from PCR fluorescence curves using Eq. 3 in nonlinear fitting procedure. Richards coefficient values were determined from 420 independent PCR reactions. The data have been reported in Log10scale, and represented as mean and standard deviation.

Comparison of five S-shaped models to fit the PCR curve: Sigmoid, Richards, Gompertz, Hill and Chapman. In this table, f is the fluorescence at cycle x Fmaxrepresents the maximum fluorescence value Fbis the background reaction fluorescence b, c and d determine the shape of each curve. For each model the determination coefficient (R 2 ), the adjusted determination coefficient (Adj R 2 ) and the standard error of estimate have been calculated.

Name Equation Estimated Parameters R 2 Adj R 2 Standard Error of Estimate
Fmax b c Fb d
Sigmoid f = Fb+Fmax/(1+exp(-(x-c)/b)) 45.11 1.49 22.37 -0.03 1 1 0.1354
Richards f = Fb+(Fmax/(1+exp(-(1/b)*(x-c)))^d) 45.11 1.58 21.95 0.02 1.20 1 1 0.0926
Gompertz f = Fb+Fmax*exp(-exp(-(x-c)/b)) 45.19 2.15 21.45 0.29 0.9992 0.9992 0.6006
Hill f = Fb+Fmax*x^b/(d^b+x^b) 45.18 14.95 0.08 22.34 1 1 0.1351
Chapman f = Fb+Fmax*(1-exp(-b*x))^d 45.19 0.46 0.29 20615 0.9992 0.9992 0.6006

tstatistic values obtained for all variable combinations. When t < 0 the Richards coefficient is lower than 1, while for t > 0 the Richards coefficient is higher than 1.
Significance levels:
* 0.05 <p < 0.01
** p < 0.01.

Amplification mix percentage
Log10input DNA 100% 90% 80% 70% 60%
7.5 0.28348 1.15431 2.9303* 5.43493** 4.26067**
6.5 -3.0233* -0.5329 7.8552** 8.68609** 7.28178**
5.5 -2.2195* 2.70419* 4.7185** 8.61406** 4.60465**
4.5 0.97856 1.32162 2.34* 16.5192** 17.5903**
3.5 1.00647 -1.038 2.3307* 13.2572** 4.65683**
2.5 -1.731 -0.5995 5.8385** 6.90378** 6.13465**
1.5 0.14417 1.25452 -0.898 1.87978 3.69668**

Plot of fluorescence observations versus cycle number obtained from the same starting DNA but in presence of decreasing amounts of amplification mix. This slight PCR inhibition produces curves which are less steep than controls and shifted towards the right. When analysed by the threshold method, these curves showed higher Ct values with a CV% of 1.45% (A). An example of Cy0procedure has been reported for the same data set (B). In this method, the amplification reactions are described by the tangent crossing the inflection point of fluorescence curves. As shown in this figure, the straight-lines originating from PCRs, characterized by slightly different PCR efficiency and the same starting amounts, tend to cross into a common point near the x-axis leading to small variations in the Cy0values (CV% = 0.6%).

Precision and accuracy of the Ct, Cp and Cy0 methods.

The performance of the Ct, Cp and Cy0 methods was compared in terms of precision and accuracy over a wide range of input DNA concentrations and under different reaction efficiencies obtained by decreasing the amount of amplification mix as reported in Liu and Saint [18, 27]. As shown in Figure 5A, the Ct method is highly rigorous at maximum reaction efficiency regardless of the starting DNA template. However, the absolute value of RE increased almost linearly with the decrease of efficiency regardless of the template concentrations resulting in an underestimation of the unknown of about 50% at the lowest amplification efficiencies. The Cp was more accurate than the Ct method in the presence of different amounts of amplification mix. Indeed, the relative error in the presence of 100% amplification mix tended towards zero as it did using the Ct method. However, when the efficiency declined, the RE increased initially in the same manner at low and high input DNA concentrations, while at 60-70% of the amplification mix, this method markedly underestimated at low concentrations (mean RE60% mix = -0.58 Fig. 5C). Finally, the Cy0method was more accurate than the Cp method (mean RE -0.12 versus -0.18, respectively Fig. 5C, E), which in turn was better than the Ct method (mean RE = -0.31). Notably, at optimal amplification conditions (90-100% of the amplification mix) the Cp and Cy0 methods were equivalent, but at decreasing efficiencies, the Cy0 accuracy was more stable than that of the Cp in the concentration range from 3.14x10 7 to 3.14x10 5 molecules. At lower DNA concentrations, from 3.14x10 4 to 3.14x10 2 molecules, the RE proportionally increased with the efficiency decline, but this underestimate was less marked than that of the Cp method at the same starting DNA (Fig. 5C, E). Regarding the precision of the three methods, the variation coefficients were determined for each combination of initial template amount and amplification mix percentage. The random error of quantification achieved by the Cp and Cy0method was similar (mean CV% 21.8% and 22.5%, respectively), while the Ct procedure produced an overall CV% of about 39.7% (Tab. 3). When the CV was analysed in relation to PCR efficiency and input DNA, an area of low variation coefficients for the three methods was found between 3.14x10 4 and 3.14x10 7 molecules as starting material (Fig. 5B, D, F). With DNA amounts ranging from 3.14x10 3 to 3.14x10 2 molecules, the precision progressively decreased in each analysis procedure. These variations were not efficiency-dependent, but were related to initial DNA quantity as shown by the shapes of level curves reported in figure 5B, D and F, which were perpendicular to the input template amounts.

Comparison of the Ct, Cp and Cy0methods in terms of precision and accuracy. The accuracy of each method has been reported as Relative Error (RE = expected value ? estimated value) while the precision was evaluated measuring the variation coefficient (CV%). The 3D plots show the variation of relative error in relation to amplification mix percentage and log10 input DNA for the Ct (A), Cp (C) and Cy0(E) methods. The areas in the level curve graphs represent the CV% values obtained for each amplification mix percentage and Log10 input DNA combination using the Ct (B), Cp (D) and Cy0(F) methods.

Comparison of mean Relative Error and mean Variation Coefficient among the Ct, Cp, Cy0and SCF methods. The reported data were calculated on 420 PCRs except for a ) in which the reaction number was 210.

Ct Cp Cy0 SCF Log10SCF
Mean CV% 39.70% 21.80% 22.52% 594.74% a 66.12% a
Mean RE -0.318 -0.184 -0.128 -5.058 a -0.205 a

Experimental system 2: Real-time PCR quantification in the presence of the inhibitor IgG

The real-time amplification plot of 4.05x10 6 DNA molecules with increasing concentrations of IgG demonstrates the effects of PCR inhibition on amplification efficiency and accumulated fluorescence (Fig. 6A). As inhibitor concentrations increased, the amplification curves showed lower plateau fluorescence levels and a shift towards the right and the bottom of the inflection points, leading to amplification curves that were less steep and not as symmetric as those obtained in absence of the inhibitor agent (Fig. 6A). As shown in figure 6A the amplification curves inhibited by IgG showed a shape very similar to those resulting from the system of amplification mix reduction (system 1 Fig. 4A). Quantitative data analysis of these amplification plots showed that the estimated DNA quantities were systematically underestimated in the presence of IgG concentrations higher than 0.25 µg/ml and 1 µg/ml using Ct and Cp methods, respectively. However, the Cy0 method was able to adjust this bias minimizing the RE at high IgG concentrations (RE = 4.98% CV = 4.33% Fig. 6B). Furthermore, in presence of high IgG concentrations, the SCF approach, modified according to Rutledge 2004 [26], was inapplicable because it was impossible to minimize F0 value (Additional file 5).

Real-time PCR amplification plots obtained from the same starting DNA in the presence of IgG acting as reaction inhibitor This inhibition system produces curves which are progressively less steep than non-inhibited reactions with increasing IgG concentrations (A). When analysed by the Ct, Cp and Cy0methods these curves showed a RE% of -25.37%, -9.02% and 4.98% and a CV% of 25.62%, 10.66% and 4.33%%, respectively (B).

Real-time PCR analysis is becoming increasingly important in biomedical research because of its accuracy, sensitivity and high efficiency. Although, real-time PCR analysis has gained considerable attention, it is far from being a standard assay. The standard methods are quite stable and straightforward but the accuracy of estimates is strongly impaired if efficiency is not equal in all reactions. Furthermore, the assumption of uniform efficiency has been reported to be invalid in many cases regarding medical diagnostics. In fact, the biological samples may contain inhibitors that could lead to different amplification efficiencies among samples. We propose, in this report, a modified standard curve-based method, called Cy0, that does not require the assumption of uniform reaction efficiency between standards and unknown.
To the best of our knowledge, this is the first method in which the stability and reliability of a standard curve approach is combined with a fitting procedure to overcome the key problem of PCR efficiency determination in real-time PCR nucleic acid quantification. The data reported herein clearly show that the Cy0 method is a valid alternative to the standard method for obtaining reliable and precise nucleic acid quantification even in sub-optimal amplification conditions, such as those found in the presence of biological inhibitors like IgG.

List of abbreviations used

Cp: crossing point Ct: threshold cycle CV: coefficient of variation IgG: immunoglobulin G RE: relative error SCF: sigmoidal curve fitting.

MG and DS carried out the design of the study, participated in data analysis, developed the Cy0 method and drafted the manuscript. MBLR participated in data collection and analysis and critically revised the manuscript. LS carried out the real-time PCR. VS participated in the design of the study and critically revised the manuscript. All authors read and approved the final manuscript.

We thank Dr. Pasquale Tibollo for technical assistance and Dr. Giosué Annibalini for helpful comments on the manuscript.

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Additional file 2 -
Windows Word file containing first and second derivative of Richards equation and the mathematical formulas for obtaining the coordinate of the Cy0point. Additional file 4 -
Windows Excel file containing the results obtained with the SCF approach based on a previous study by Rutledge 2004. Additional file 5 -
Windows Excel file containing the results obtained with the SCF approach based on a previous study by Rutledge 2004 in presence of IgG.

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Watch the video: qPCR real-time PCR protocol explained (January 2023).