| Nucleic Acids Research | Pages |
Single-tube nested competitive PCR with homologous competitor for quantitation of DNA target sequences: theoretical description of heteroduplex formation, evaluation of sensitivity, precision and linear range of the method
Introduction
Materials And Methods
Construction of the internal competitor sequence
PCR amplification
Analysis of competitive PCR experiments
Calculation of the unknown target sequence copy number from single point measurements
Results
Description of a model for variable formation of heteroduplices
Determination of target sequence copy number in the double cut mode
Determination of the target copy number using the single cut mode
Evaluation of the effect of heteroduplex formation on single-tube quantitation using the double cut mode of analysis
Experimental evaluation of the effect of heteroduplex formation on single-tube quantitations using the single cut mode of analysis
Evaluation of the linear range of single-tube competitive PCR quantitation using double cut analysis
Linear range of the single-tube competitive PCR using the single cut analysis
Intraassay precision of the single-tube competitive PCR
Discussion
Acknowledgements
References
Single-tube nested competitive PCR with homologous competitor for quantitation of DNA target sequences: theoretical description of heteroduplex formation, evaluation of sensitivity, precision and linear range of the method
ABSTRACT
INTRODUCTION
Competitive quantitative PCR using homologous mutated sequences as internal standards represents a highly sensitive technique for the quantitation of DNA and mRNA (1,2). The basic principle of the method consists of the co-amplification of a target sequence together with an internal standard, the competitor sequence. Using a titration-like experiment with varying but known amounts of the competitor sequence, the unknown copy number of the target sequence can be determined. One essential requirement for the accuracy of competitive PCR is that amplification efficiencies of both the competitor and target sequences are identical. Only when this condition is fulfilled do the ratio of target and competitor sequence remain constant over the process of amplification independent of the number of cycles and of other external factors. That amplification efficiencies are identical can best be ensured by using homologous mutated competitor sequences which allow specific identification by a unique restriction site. According to signal analysis, two main types of the experimental set-up can be distinguished: the single cut mode in which the competitor is cleaved specifically (2) and the double cut mode which requires specific cleavage of both sequences (3). In most cases, the application of mutated or other homologous competitors is impeded by the fact that, dependent on the number of PCR cycles, the formation of heteroduplex molecules occurs (4-6). As a result, the identification of the equivalence point may become cycle-dependent due to digestion-resistant heteroduplices which co-migrate together with either the competitor or target sequence in gel electrophoretic analysis (6). In contrast, separation of the heteroduplex fraction from both homoduplices by temperature gradient gel electrophoresis (7), for example, provides easy identification of the equivalence point, since the relative maximum of heteroduplex formation within a given titration experiment indicates a 1:1 ratio of competitor and target sequences, independent of the absolute degree of heteroduplex formation (6).
Nevertheless, the application of competitive PCR is still time-consuming, especially for large sample numbers, due to the need of multiple measurements for the identification of the different equivalence points. In the present study, we describe the theoretical development and experimental evaluation of a method which allows the calculation of target sequence copy number from a single-tube competitive PCR using a homologous competitor sequence. As shown for the detection of Human Papilloma Virus 16 (HPV16)-DNA, the method allows quantitation of the target sequence even for copy numbers deviating from the equivalence point. Moreover, single-tube quantitation is independent of the degree of heteroduplex formation in the double cut mode. We demonstrate that single-tube measurements as predicted by the theory allow linear quantitation within at least two orders of magnitude with good precision, using simple standard gel electrophoresis and video densitometry for signal detection. Additionally, it is shown that the single cut mode of competitive PCR can be used for single-tube quantitations, provided that complete heteroduplex formation has taken place.
MATERIALS AND METHODS
Construction of the internal competitor sequence
For generation of the homologous competitor sequence the plasmid pU16Pl.8 (pUC19xHPV16, ORF E6, E7) containing the E6 and E7 open reading frames of HPV16 was subjected to site-directed PCR mutagenesis (8). The single wild-type RsaI restriction site (GTACTGCAAGC) was mutated to a new single NheI cleavage site (GA*ACTGCT*AGC, the asterisks indicate the mutated positions). As a result, the competitor sequence differs in two out of the 124 bp sized final PCR product. Following ligation of the mutated PCR fragment into pUC19 and transformation into Escherichia coli, the new restriction site was verified by direct PCR-sequencing. Standardized reference plasmid solutions were prepared by plasmid-midipreparation using caesium chloride gradient ultracentrifugation followed by spectrophotometric quantitation of the DNA. Since the distance between the former RsaI site and the new NheI site is 5 bp, both sequences may be identified either by single cleavage individually (single cut mode) or by double cleavage with RsaI and NheI simultaneously (double cut mode). Hence, this competitor could be used for experimental evaluation of the double cut mode as well as the single cut mode of single point competitive PCR.
PCR amplification
The competitive PCR was carried out as a one-step procedure as well as nested PCR using a Landgraf-Thermocycler (Langenhagen, Germany). A maximum of 20 µl of DNA solution, containing the indicated amounts of target and competitor DNA (see below), 40 µM of each dNTP, 20 pmol of the outer and inner 5[prime]- and 3[prime]-primers, respectively, 1 U Taq DNA polymerase (Amersham/USB) and 5 µl of amplification buffer (Amersham/USB) were put together in a final volume of 50 µl, topped with 50 µl of mineral oil and subjected to thermal cycling.
For nested PCR, two amplifications, each with 30 cycles, were carried out as follows: 120 s denaturation at 93°C, 90 s annealing at 49°C (first PCR) or 56°C (second PCR), respectively, 60 s primer extension at 72°C or 120 s at 72°C for the last cycle. Single-step PCR was done for amplification of high copy number templates (>105 copies per reaction) using only the inner primer pair at 56°C annealing temperature. For generation of the first PCR product (size 307 bp) the outer primer pair reported previously (9) was used: upper primer 5[prime]-ACC GAA AAC GGT TGA ACC GAA AAC GGT-3[prime], lower primer 5[prime]- AAT AAT GTC TAT ATT CAC TAA TT-3[prime]. The second inner PCR product (size 124 bp) was generated using the primer pair reported (10): upper primer 5[prime]- ATG TTT CAG GAC CCA CAG GA-3[prime] and lower primer 5[prime]- CCT CAC GTC GCA GTA ACT GT-3[prime].
Analysis of competitive PCR experiments
Analysis of the double cut as well as single cut experiments were carried out using PAGE (T = 11%, C = 5.1%, height 80 mm, width 100 mm, ethidium bromide staining) resolving a 5 bp length difference. As a result, the double cut competitive PCR experiment shows the maximum number of three bands: the restriction resistant heteroduplex fraction (124 bp), the larger fragment of the homoduplex competitor sequence following cleavage by NheI (98 bp) and the larger fragment of the homoduplex target sequence following cleavage by RsaI (93 bp). In contrast, the single cut experiment shows two bands, one of which represents the combined fractions of heteroduplices together with the homoduplex target sequence (124 bp) while the other comprises the NheI cleaved competitor homoduplex sequence.
The volume of each band was measured using video densitometry (E.A.S.Y., Herolab, Germany), corrected for molecular weight of the fragments and normalized. The detection of ethidium bromide stained DNA fragments in our experimental set-up was determined to be linear within a concentration range of one order of magnitude (Fig.
Figure 1. Dose-response curve of video densitometric signal detection. The indicated amounts of the uncut inner PCR product (124 bp) were subjected to gel electrophoresis and analysed by video densitometry. The linear fit is indicated by the solid line (y = 0.99x + 2.49, coefficient of correlation = 0.99).
Calculation of the unknown target sequence copy number from single point measurements
The calculation of copy numbers of the target sequence from single point measurements was carried out for the double cut strategy using equations 9-11 and for the single cut strategy using equation 15, respectively.
RESULTS
Description of a model for variable formation of heteroduplices
A direct calculation of the target copy number on the basis of the measured signal ratio is only feasible if either no formation of heteroduplices has occurred or the equivalence point has been found exactly. It has been described (6) that the proportion of the combined heteroduplices fraction comes to a relative maximum if the ratio of target and competitor sequence becomes 1 (equivalence point). The theoretical basis for this finding is the assumption that all the single strands of competitor and target sequence will rehybridize according to their concentration-dependent probability of collision. Extending these basic ideas, we describe in the following the development of a more generalized model which reveals that copy numbers of the target sequence deviating from the equivalence point can also be determined even in the presence of partial heteroduplex formation.
Figure 2. Theoretical relative signals of homoduplex and the combined heteroduplex fractions as function of the ratio of target to competitor sequence copy number according to equations 6-8. The probability of rehybridization of the target homoduplex (AA), the competitor homoduplex (BB) and both heteroduplices (AB1, AB2) can be calculated following complete denaturation:
p(AA) = fa+a-; p(BB) = fb+b-; p(AB)1 = fa+b-; p(AB)2 = fa-b+
1
with a+ and a- as the pre-denaturation concentrations of both single strands of the target sequence, b+ and b- for the pre-denaturation concentrations of both single strands of the competitor sequence and f for a factor of proportion. Moreover, identical amplification of all single strands during PCR is assumed.
Figure 3. Strategies for signal evaluation of single-tube quantitation experiments using a homologous mutated competitor. (A) Simultaneous and specific cleavage of both competitor and target sequences and analysis by a single gel electrophoretic run (double cut experiment). (B) Separate specific cleavage of target and competitor amplicons followed by individual gel electrophoretic separations (double cut experiment). Note that an additional calculation of the heteroduplex signal is necessary. (C) Specific cleavage of the competitor sequence alone and single gel electrophoretic run (single cut experiment). Note that complete denaturation and rehybridization has to be ensured before signal evaluation; HD, heteroduplex; CS, competitor sequence; TS, target sequence; for details according to equations 9-11 and 15 see text. On condition that (i) the pre-denaturation concentrations of the homohybrid of the target sequence (a) equals a+ and a- and the competitor sequence (b) equals b+ and b- (no preferential amplification of distinct single strands during PCR); (ii) p(AB)1 equals p(AB)2 (no preferential formation of an individual type of heteroduplex); and (iii) the sum of all rehybridization probabilities equals 1 (complete rehybridization) the equation: leads to: The relative proportions of all homoduplex sequences can now be calculated using the probabilities for rehybridization as described by equation 1. The relative fractions of the target sequence FTS, the competitor sequence FCS and the combined heteroduplex fraction FHD are given by equation 2: It should be noticed that equation 2 is valid only when complete denaturation and rehybridization according to the probabilities of collision have taken place. Figure Considering equations 2 and 4 we concluded that it should be possible to describe all transitional states between complete rehybridization and the absence of any rehybridization event. Combining 2 and 4 and introducing the rehybridization parameter DRH equation 5 is obtained: DRH by definition varies between 0 and 1 and represents the relative degree of rehybridization. A purely competitive reaction is therefore described by DRH = 0 whereas complete rehybridization is defined by DRH = 1. For a given degree of heteroduplex formation, equation 5 assumes that a single partial denaturation and rehybridization process and the accumulation of multiple smaller ones, for example occurring in the course of each PCR cycle, can be described mathematically in the same way. Equation 5 gives the basis for the determination of the target sequence copy number for single tube quantitations using the double cut as well as the single cut mode of signal evaluation.
2
3
4
5
Determination of target sequence copy number in the double cut mode
Figure
 |
6 |
 |
7 |
 |
8 |
The unknown number of target sequences (and DRH) can now be calculated from each combination of two equations out of the three given equations 6-8.
 |
9 |
 |
10 |
 |
11 |
As a consequence, the unknown target sequence copy number (a) can be determined if the number or the concentration of competitor sequences is known and at least two relative signals have been determined. Moreover, the results are independent of the degree of heteroduplex formation. Furthermore, it should be noticed that identical results from equations 9-11 are inevitably obtained, since the sum of equations 6-8 equals one, resulting in a linear relationship between the equations. Therefore, one out of the three equations is sufficient for determination of the target sequence copy number.
Determination of the target copy number using the single cut mode
The gel electrophoretic analysis of competitive PCR experiments following a single restriction digest of PCR products results in the generation of two signals, one of which represents the sum of both heteroduplex fractions together with the uncut homoduplex (Fig.
 |
12 |
 |
13 |
Since the sum of both relative signals equals 1, there is only one independent equation which offers a solution to either the target sequence copy number (a) or the degree of heteroduplex formation (DRH). It follows that the value calculated for the target sequence copy number in a single cut experiment is dependent upon the degree of heteroduplex formation:
 |
14 |
In general, however, the degree of rehybridization (or heteroduplex formation) is not known. Therefore, calculation of target sequence copy number using a single cut experiment is feasible only if either rehybridization is complete (DRH = 1) or heteroduplex formation can be excluded (DRH = 0):
 |
15 |
 |
16 |
Equation 15 serves as a tool for determination of unknown target sequence copy numbers in the single cut mode of competitive PCR provided that the number of competitor sequences is known and the reaction mixture has undergone complete denaturation and rehybridization before measurement.
Evaluation of the effect of heteroduplex formation on single-tube quantitation using the double cut mode of analysis
As theoretically outlined above, target copy numbers can be determined independently from heteroduplex formation using one of the equations 9-11 and two relative signals. In order to obtain experimental proof of this crucial issue we performed `pseudo'-quantitation experiments varying the degree of heteroduplex formation (DRH) between 0 and 1 and, in addition, the ratio of target and competitor sequence number. In order to ensure defined values for the degree of heteroduplex formation, the experiments were performed not using competitive PCR, in which the degree of rehybridization is hard to predict, but were carried out by complete denaturating and rehybridizing of one aliquot of a defined mixture of target and competitor sequences, which were purified and quantitated beforehand. In the next step defined mixtures using the completely rehybridized aliquot, which is characterized by the maximal formation of heteroduplices (DRH = 1), and the untreated aliquot (DRH = 0) were prepared. Following double cleavage, the mixtures were separated by PAGE, analysed by video densitometry and evaluated using one of the equations 9-11. As can be clearly seen there is a strong variation in the relative proportion of the heteroduplex bands for both ratios of competitor to target sequence (Fig.
A
 B  |
Figure 4. (A) Rehybridization experiments using the double cut analysis: purified competitor and target sequence DNA were premixed at ratios of 1:2 and 1:1. Defined mixtures, representing various relative degrees of heteroduplex formation as indicated above each lane, were prepared of an untreated (DRH = 0) and completely denaturated and rehybridized aliquot (DRH = 1) and subjected to the double cut analysis; HD, heteroduplex (125 bp); CS, competitor sequence (98 bp); TS, target sequence (93 bp); inverse illustration of ethidium bromide fluorescence). (B) Effect of heteroduplex formation on the evaluation of relative copy numbers using the double cut experiment shown in (A). The relative copy numbers were calculated with equations 9-11 and plotted against the degree of heteroduplex formation for the indicated ratios of competitor and target sequence. It was pointed out that with DRH = 1 (maximal relative formation of heteroduplices) and DRH = 0 (no heteroduplex formation), simplified forms of equation 14 can be applied for single-tube quantitation experiments. In contrast, calculations using the equations 15 and 16 should cause significant deviations in the case of transitional heteroduplex formation. Rehybridization experiments with single cut analysis (Fig. Figure 5. Effect of heteroduplex formation on relative copy number evaluation in single cut experiments. These were carried out analogous to the double cut experiments shown in Figure 4A. As indicated in the graphs, equations 15 and 16 were used for data evaluation (for details see text).
Experimental evaluation of the effect of heteroduplex formation on single-tube quantitations using the single cut mode of analysis
Evaluation of the linear range of single-tube competitive PCR quantitation using double cut analysis
To examine the practicability of single-tube competitive quantitations we investigated whether this method is capable of the correct determination of target copy numbers, even with increasing distance from the equivalence point. In addition, the linear range of single tube competitive PCR using a single competitor concentration was to be determined. For this purpose, a constant amount of competitor sequence (2 × 108 copies) was mixed with varying copy numbers of target sequence (2.6 × 106 up to 5.8 × 109 copies; see Table 1 for the numerical data) covering a range of more than 3 orders of magnitude (Fig.
Linear range of the single-tube competitive PCR using the single cut analysis
The receiver/operator characteristic was also investigated for the single cut mode of the single-tube competitive PCR. Aliquots of the same competitive PCRs as used before for double cut analysis, were subjected to the single cut analysis and were evaluated according to Figure
Table 1.
| Lane (Fig. 6A) |
Input copy number | Output copy numbera (double cut mode) |
Output copy number (single cut mode) |
| 1 | 2.60 × 106 | 9.20 × 106 | -b |
| 2 | 3.90 × 106 | 7.69 × 106 | - |
| 3 | 5.85 × 106 | 1.28 × 107 | - |
| 4 | 8.78 × 106 | 1.70 × 107 | - |
| 5 | 1.32 × 107 | 2.09 × 107 | 1.43 × 107 |
| 6 | 1.98 × 107 | 2.41 × 107 | 1.72 × 107 |
| 7 | 2.96 × 107 | 3.23 × 107 | 2.42 × 107 |
| 8 | 6.67 × 107 | 7.51 × 107 | 3.83 × 107 |
| 9 | 1.00 × 108 | 1.00 × 108 | 5.11 × 107 |
| 10 | 2.25 × 108 | 1.67 × 108 | 1.10 × 108 |
| 11 | 3.38 × 108 | 5.14 × 108 | 1.12 × 108 |
| 12 | 5.06 × 108 | 3.92 × 108 | 1.11 × 108 |
| 13 | 7.59 × 108 | 6.73 × 108 | 1.10 × 108 |
| 14 | 1.14 × 109 | 1.33 × 108 | 1.47 × 108 |
| 15 | 1.71 × 109 | 1.90 × 109 | - |
| 16 | 2.56 × 109 | 3.38 × 109 | - |
| 17 | 3.84 × 109 | 1.35 × 1010 | - |
| 18 | 5.77 × 109 | 4.06 × 109 | - |
Intraassay precision of the single-tube competitive PCR
To determine the precision of the single-tube method, eight measurements of each different defined target competitor mixture varying the absolute copy numbers between 2×102 (7 aM) and 6 × 105 (20 fM) were performed, using the nested competitive PCR assay. All measurements within one order of magnitude were carried out using a single competitor concentration. The data obtained from the repeated experiments are shown in Figure
A
 B  |
Figure 6. (A) Single-tube quantitations (double cut mode) using a constant amount of competitor sequences of 2 × 108 and varying copy numbers of target sequences (2.6 × 106 to 5.8 × 109 copies; see Table 1 for the exact data) for measurement of the input/output characteristic of the method; HD, heteroduplex (125 bp); CS, competitor sequence (98 bp); TS, target sequence (93 bp); inverse illustration of two ethidium bromide stained gels. (B) Input/output characteristic of the single-tube quantitation using the double cut analysis. The figure shows the log of output copy number as evaluated from the double cut experiment shown in (A) according to equations 9-11 plotted against the log of input copy number of target sequences. The solid line represents the linear fit of the data (coefficient of correlation = 0.98); see Table 1 for the numerical data.
Figure 7. Input/output characterisitics of the single-tube quantitation using the single cut mode of analysis. The log of the output target copy number was calculated by equation 15 and plotted against the corresponding log of input copy number of target sequences. The solid line represents the linear fit of the data indicated by open circles (coefficient of correlation = 0.99); see Table 1 for the numerical data.
Figure 8. Precision of single-tube quantitation experiments. (A) Repeated single-tube experiments of constant amounts of target and competitor sequences within different ranges of concentrations either by nested competitive PCR (open symbols) or single step PCR (closed symbols); each experimental series is connected by a dotted line. (B) Percentage standard deviation of the precision measurements shown in (A) plotted against the mean copy number.
A
B
DISCUSSION
Accurate quantitation of DNA and RNA by competitive PCR presupposes the availability of a suitable competitor sequence. According to principal theoretical considerations the competitor and target sequence should be amplified with identical efficiencies. Otherwise, even small differences in amplification efficiency might cause significant quantitation errors due to the exponential growth of these deviations in the course of PCR (11). The application of homologous mutated competitors has been hampered so far by complications as a result of heteroduplex formation. A direct copy number calculation from the signals of target and competitor sequence is feasible exclusively if their copy numbers are identical. Therefore multiple PCRs with varying competitor sequence numbers are required to determine this equivalence point, provided a uniform heteroduplex formation in different samples has been ensured.
As an extension and generalization of considerations reported previously (2,4,6), the mathematical approach described in the present study allows direct copy number calculations from single-tube competitive PCRs, independent of the degree of heteroduplex formation. This could be demonstrated by the rehybridization experiments in which identical copy numbers were obtained by double cut analysis using equations 9-11 although the portion of heteroduplices was systematically varied (Fig.
The other important prediction from the theoretical model is that the copy number can be determined at any given ratio of competitor to target sequence, which is the prerequisite for single-tube competitive PCR quantitations. For the experimental verification of this prediction defined mixtures of different numbers of target sequences with a constant number of competitor sequences were prepared and measured using the single-tube competitive PCR. The reactions were analyzed by the double cut (Fig.
The precision of the single-tube quantitation represents another important aspect with relevance for potential applications of the method. Repeated intraassay measurements of target sequence copy numbers resulted in standard deviations of ~5% regardless of whether single-step PCR (copy numbers >105) or nested PCR (copy numbers <105) was used (Fig.
In conclusion, we have clearly shown that the theoretical predictions, derived from our model of variable denaturation and rehybridization of competitive PCR products, can be verified experimentally and, moreover, can be used for the highly efficient and reliable single-tube quantitation of target sequences within a linear range of at least one order of magnitude (single cut mode) or more than two orders of magnitude (double cut mode). By this method, a wide range of target concentrations as well as multiple samples with similar target concentrations can be detected quantitatively carrying out a far lower number of competitive PCRs than would have been necessary to identify multiple points of equivalence. Moreover, this can be achieved using standard techniques such as PAGE and video densitometry. In addition, the analysis of single-tube competitive PCR can be carried out using any other technique which is capable of separation and/or detection of at least two PCR products, one of which has to be a pure homoduplex. For example, combination of single-tube competitive PCR with an ELISA technique (12), separation of DNA fragments using high resolution HPLC (13) or capillary electrophoresis (14) as well as radioimaging of gel electrophoretically separated fragments might provide further improvement of efficiency and dynamic range of the method.
ACKNOWLEDGEMENTS
We are grateful to Ute Paeslack for excellent technical assistance, Jean Zeyßig for helping us with our English and Dr J. Lüscher-Firzlaff for providing the plasmid pU16Pl.8. This work was funded in part by Deutsche Krebshilfe/Dr Mildred Scheel foundation W105/94/Se1.
REFERENCES
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