Nucleic Acids Research

RNA preparation

Competitive RT-PCR reactions were performed by preparation of total RNA from rat microdissected nephron tissue using RNAzol B (Tel-Test, Friendswood, TX). Male Sprague-Dawley rats were deeply anesthetized with pentobarbital (i.p., 40 mg/kg) and the abdominal cavity was opened. The renal artery was cannulated and the kidney perfused with saline solution, followed by a solution of collagenase (400 U/ml; Sigma, St Louis, MO). The kidney was then removed and cut along the cortico-medullary axis. The cut segments were placed into dissecting medium which was continuously oxygenated by bubbling compressed air through the medium. The medium contained an RNase inhibitor, 10 mM vanadyl ribonucleoside complex (New England Biolabs, Beverly, MA). Nephron segments were dissected free, identified on the basis of their renal origin and morphology, measured with a calibrated ocular micrometer, rinsed and added to RNAzol B (Tel-Test, Houston, TX) for extraction of RNA. Linear acrylamide (20 µg/ml) and yeast tRNA co-precipitants (Ambion, Austin, TX) were added to maximize yield. Recovered RNA was dissolved in a solution of yeast tRNA (100 ng/µl) and stored at -80°C. Integrity of RNA was validated by extraction of RNA from segments of kidney after completion of dissection. This provided sufficient RNA to be visualized by gel electrophoresis. Intact 18S and 28S bands were observed.

Competitor cDNAs were generated from native cDNAs contained in pGem4Z vectors by the creation of small insertion or deletion mutations in the native cDNA insert. When suitable restriction sites were present, deletions were produced by digestion out of a small contiguous segment of the cDNA followed by religation (T4 DNA ligase). When no suitable restriction and deletion strategy could be devised, insertion mutations were made by restriction digestion at a single site in the cDNA sequence contained in the plasmid vector and blunt-ended ligation (preceded by polishing of overhanging ends when necessary) of either heterologous cDNA sequence or of a synthetic, double-stranded oligonucleotide. RNA was synthesized in vitro from cDNA constructs by run-off transcription using a commercial kit (Novagen T7 transcription kit; Novagen, Madison, WI) from plasmid constructs containing RNA polymerase T7 promoter sequence upstream of the mutated target cDNA.

We employed competitors which differ from corresponding native sequences by between 14 and 145 bases. These bases were contiguous and were located between and at some distance from PCR primer binding sites. Purity of the synthetic competitor RNA is critical to accurate calibration of this competitor standard by UV absorbance spectroscopy. The transcript was precipitated in 0.3 M sodium acetate and isopropanol and the pellet was washed several times with 70% ethanol. Transcript size and purity were routinely verified by RNA gel electrophoresis. Yeast RNA (transfer or total) was added after UV calibration. All RNA preparations were stored at -70 to -86°C.

In addition to the mutant RNA, native RNA sequences were also transcribed in vitro and used to provide a calibrated source of native RNA which could be added to competitive RT-PCR reactions in known quantities. Yeast RNA was added to the in vitro transcribed native RNA after UV calibration. Using in vitro transcribed native RNA we were able to assess accuracy of the competitive RT-PCR system by simple comparison of the estimated native RNA input with the amount of native RNA actually added to the reaction.

General RT-PCR conditions

The following general reaction conditions were employed, except where variations are noted in Results. Each RNA mixture was reverse transcribed at 42°C for 25 min in a Peltier effect thermal cycler (MJ Research, Watertown, MA). Reaction volumes (10 µl) comprised PE Applied Biosystems (Foster City, CA) reagents including MMLV reverse transcriptase (2.5 U/µl) and random hexameric primers (2.5 µM). After heating the reactions to 99°C and cooling to 5°C, 40 µl PCR reaction mastermix containing AmpliTaq (NKA) or AmpliTaq Gold (CAN and CYP) DNA polymerase (1.25 U/40 µl) and 0.3 µM each primer was added to each tube. Standard cycling parameters were as follows: 2 min at 95°C, followed by 35-45 cycles comprising 50 s at 94°C, 60 s at 56°C and 70 s at 72°C, with a final extension for 5 min at 72°C.

PCR primers and products

For rat NKA the forward primer was an 18mer with sequence 5[prime]-CCCTAGTTCCCGCCTCTC (nt 124-141 in the cDNA sequence), the reverse primer was a 21mer, 5[prime]-TGGTCGTCCATAGACACTTCC (nt 349-369). PCR reaction product sizes were 245 bp for the native and 390 and 231 bp for the insertion and deletion mutant amplicons respectively.

For CAN the forward primer was a 23mer with sequence 5[prime]-GACTATGTTGACAGAGGGTACTT (nt 559-582 of the published sequence; 8) and the reverse primer was an 18mer, 5[prime]-GTGTACACACAGGAATTG (nt 788-806). PCR reaction product sizes were 218 bp for the mutant amplicon and 246 bp for the native form.

For rat CYP two forward primers were tested. Both were 20mers with the sequences 5[prime]-CAAGACCTCCTGGCTAGACG (nt 447-466 in the cDNA sequence; 7) and 5[prime]-TGGTACGGAAGGTGGAGAAC (nt 509-528). A single reverse primer was used. This was a 20mer with the sequence 5[prime]-TTGTGACTGGCTGCTTTCAC (nt 693-712). Depending on the primer combination employed (see below) the primers pairs generated 266 and 204 bp native amplicons respectively. Insertion mutant (competitor) amplicons were 290 and 228 bp respectively.

Gel electrophoresis and HPLC analysis of products

Authenticity of RT-PCR reaction products amplified from total RNA was verified by restriction fragment analysis. Reaction products were subject to digestion with restriction enzymes which cut at a single site within each amplicon. In all cases, fragments of the expected size were released by digestion with the appropriate enzyme.

RT-PCR reaction products were analyzed on agarose gels (NuSeive and Metaphor; FMC, Rockland, ME) under non-denaturing conditions. Ethidium bromide stained gels were examined under UV illumination to demonstrate visible reaction products. HPLC analysis of PCR reaction products was performed using a column (4.6 × 50 mm) packed with a novel polystyrene-divinylbenzene C18-bonded phase (DNASep[trade]; Transgenomic Inc., San Jose, CA). Reaction products were analyzed by direct injection of 5-10 µl reaction mixture into the HPLC system. The solvent system was a gradient of acetonitrile in 0.1 M triethylammonium acetate. Gradients were modified by adjusting the concentration of acetonitrile across the range 10-25% to optimize elution of products of different sizes and to maximize separation of similarly sized product peaks. The column temperature was maintained at 50°C by a heating oven. On-line UV detection (254 nm) coupled with a Hewlett-Packard calculating integrator was used to quantitate reaction products. Elution gradients were developed over 5-6 min. The general application of this technique to analysis of DNA has been reported elsewhere (9-11).

Computer modeling of competitive PCR

A computer model of competitive PCR has been developed using Microsoft Excel and was used to model the effects of changing amplification efficiency and initial target copy number on estimation errors in competitive PCR. This model (compcr) is available for downloading (http://www.grad.ttuhsc.edu/archive/index.html).

Accuracy of quantitation by competitive RT-PCR

Competitive RT-PCR reactions were performed in which both the native and the competitor RNA templates were added to reactions in known amounts and were transcribed in vitro. This allows the competitive reaction to be used to estimate the amount of native template present and this amount can then be compared with the known input. Such reactions were always performed against a background of yeast RNA. Table 1a below shows the relationship between the known input RNA amount and the estimated amount in a competitive system for NKA. In this system, the competitor differed from the native form by the presence of a 145 bp insert of contiguous, non-homologous sequence. The estimates obtained are inaccurate and reveal a 3.79-fold over-estimation.

We investigated whether this inaccuracy was attributable to RT or PCR efficiency by repeating this experiment using known starting quantities of DNA in place of RNA. Native and competitor plasmid cDNAs were used and the comparison was limited to the PCR reaction. The results are summarized in Table 1b and indicate that no significant estimation discrepancy results when known quantities of DNA inputs are employed. This test has been repeated for the other templates examined and the absence of estimation error in reactions starting with known DNA inputs has been a consistent finding. We conclude from these experiments that RT efficiency differences can occur in RNA templates which are >60% homologous. Such differences, however, are remarkably consistent for a given combination of native and competitor inputs. This allows a correction factor to be determined so that accurate quantification can still be achieved.

We examined the effect of increasing homology between the native and competitor RNA templates on relative RT efficiency. A new NKA competitor was synthesized which contained a 14 bp deletion compared with the native sequence and we repeated the estimation of known RNA inputs (Table 1c). In this case, the estimation discrepancy was removed and the system generated accurate estimates of starting copy quantity.

The versatility of competitive RT-PCR allows similar quantitative approaches to be devised for any target sequence. This flexibility has allowed us to generate gene quantitation systems for numerous genes of interest to our work. We have applied the same analysis to several of those genes. For example, a system for quantitating expression of rat CYP (7) employed a competitor constructed by ligating a 24 bp oligonucleotide into the native cDNA. The resulting RNA showed identical RT-PCR efficiency compared with the native. Another system was constructed for quantitating rat CAN subunit expression. This system employed a 28 bp deletion mutation to construct a competitor. This system revealed a 0.45 ± 0.031-fold (n = 5) under-estimation of actual copy number present in the sample, which was due to RT efficiency differences between the templates. The RT efficiency difference is once again highly consistent.

Additional experiments were performed in the rat CAN system to modify RT reaction conditions in order to determine whether RT efficiency differences between homologous templates could be reduced or eliminated. Broad ranging modifications were made in magnesium, dNTP and random hexamer concentrations, use of specific primers versus random priming, RNA pre-heating, RT reaction temperature and RT enzyme used (MMLV RTase, AMV RTase and rTTh polymerase). In some cases, small, significant improvements were achieved, however, the persistent RT efficiency differences were never eliminated (Table 2). Combination of each of the optimized conditions did not show any additive benefit on final reaction product ratio.

Table 1a. Relationship between actual known input RNA amount and amount estimated by competitive RT-PCR for Na,K-ATPase (n = 18)

	Mean	SEM
Estimation discrepancy	0.945	0.064
Slope	0.978	0.032
R2	0.989	0.005

Table 1b. Estimation error when known DNA inputs are used instead of known RNA inputs (n = 7)

	Mean	SEM
Estimation discrepancy	1.07	0.064
Slope	1.02	0.023
R2	0.99	0.026

Table 1c. RT-PCR quantification of known inputs of RNA using a highly homologous competitor RNA (14 base deletion, n = 12)

	Mean	SEM
Estimation discrepancy	0.945	0.064
Slope	0.978	0.032
R2	0.989	0.005

Estimation discrepancy is the fold difference between input amount and estimated amount. Slope and R² refer to the titrations (log competitor amount versus log ratio of native and competitor reaction product amounts) used to estimate the unknown. According to Raeymaekers' model (6), amplification of native and competitor templates which have identical amplification efficiencies throughout PCR should result in straight line titrations with a slope of one. SEM, standard error of the mean.

Table 2. Effect of varying several reverse transcription reaction components on relative RT efficiency difference observed between calcineurin A and its 28 bp deletion competitor template

Reaction component	Modification tested	RT efficiency ratio
Reverse transcriptase
Standard conditions	MMLV	0.33 ± 0.01
Test conditions	rTth AMV	0.44 ± 0.03, P < 0.01 0.31 ± 0.05, NS
RNA pre-heating
Standard conditions	No RNA pre-heating	0.38 ± 0.004
Test conditions	95°C pre-heat	95°C = 0.21 ± 0.02, P < 0.001
RNA pre-heating + DMSO (90%)
Standard conditions	No pre-heating, no DMSO	0.39 ± 0.005
Test conditions	50°C pre-heat + DMSO	0.21 ± 0.03, P < 0.001
Reverse transcription reaction temperature
Standard conditions (MMLV RTase)	42°C
Test conditions using MMLV RTase	37-77°C	Positive linear relationship between RT temperature and product ratio, R2 0.46, P < 0.05, range of ratios 0.31-0.49
Test conditions using AMV RTase	37-77°C	Positive linear relationship between RT temperature and product ratio, R2 0.33, P < 0.05, range of ratios 0.29-0.56
[MgCl2]
Standard conditions	5 mM	0.38
Test conditions	1-7.5 mM	No consistent effect observed
[dNTPs]
Standard conditions	1 mM
Test conditions	0.25-10 mM	Inverse linear relationship between [dNTP] at constant [Mg2+] (5 mM), R2 0.76, P < 0.01, range of ratios 0.17-0.53
[Random hexamers]
Standard conditions	2.5 µM
Test conditions	1.25-5 µM	Inverse linear relationship between hexamer concentration and product ratio,
		R2 0.9, P = 0.004, at 1.25 µM ratio = 0.62
RT priming
Standard conditions	Random hexamers	0.331 ± 0.019
Test conditions	18 bp CAN-specific primer	0.459 ± 0.016

The columns indicate the individual reaction component or procedure which was varied, the range of conditions or type of modification tested and the effect on the RT efficiency difference indicated as the ratio of reaction products. The goal was to identify reaction conditions which eliminate the difference in RT efficiency between the two templates, resulting in a ratio of 1.

HPLC analysis of competitive RT-PCR and theoretical models of competitive PCR reactions

The exponential nature of the PCR amplification reaction imposes two primary constraints which must be met in order for competitive PCR measurements to be accurate. First, the initial PCR amplification efficiency of native and competitor inputs during the first extension cycle must be identical. Second, the decline in amplification efficiency which occurs during subsequent extension cycles as reactions proceed towards a plateau must affect both native and competitor inputs identically. In calculating competitive RT-PCR reactions to obtain the unknown amount of a gene (U₀) present in a sample, a titration plot is made which relates log(U_n/C_n) to logC₀, the known amount of starting competitor RNA. Equation 1 below describes the relationship between these variables which allows logU₀ to be calculated (see Appendix for its derivation).

log(Un/Cn) = logU0 - logC0

1

Equation 1 indicates that such a plot will form a straight line having a slope of -1 [or of 1 if log(C_n/U_n) is plotted]. We have examined whether competitive RT-PCR meet these theoretical requirements. We examined whether competitions between constant amounts of native target and varying amounts of competitor resulted in titration lines which were linear and had a slope of unity. In each of our systems, these criteria are routinely achieved. For example, we obtained values of mean slope and R² for these reactions of 1.01 ± 0.01 and 0.99 ± 0.01 respectively (mean ± SEM, n = 18) for the rat NKA (14 bp mutation) system.

The quantification of reaction products by HPLC was essential to achieve these slope and linearity properties. As noted above, the titration line is a plot of the ratio of the native and competitor reaction product ratios against the initial input of competitor. If competitive reactions proceed to plateau, they may generate heteroduplex products which are not reliably resolved by gel electrophoresis. It is essential that reaction products are analyzed by a method which separates and accurately quantifies heteroduplex products (Fig. 1). By assessing the amount of heteroduplex product formed, it is possible to apportion the native and competitor strands present in the heteroduplexes to the actual product (native or competitor) which they represent, thereby providing a true reflection of final product ratios (9).

Figure 1. (Upper) HPLC analysis of products 1-4 indicates that heteroduplexes can be readily resolved. The elution sequence (from left to right of each chromatogram) is heteroduplex, 218 bp competitor product, 246 bp native product. (Middle) RT-PCR reaction products 1-4 were separated on a 4% high resolution agarose (Metaphor; FMC, Rockland, ME) gel. Heteroduplexes were unresolved. The right-most lane is a pUC18/HaeIII ladder; the loading wells were towards the top of the image. The native product is 246 bp and the competitor product is 218 bp. (Lower) Analysis of the same reaction products on a 4% NuSieve gel reveals much better separation of heteroduplexes. The slowest migrating band (for example, in lane B) is the heteroduplex. The middle band when three products are discernible is the native product and the lowest band is the competitor product.

In order to understand further potential sources of error in competitive PCR and to assess their magnitude we have extended our theoretical analysis to isolate the effects of changing amplification efficiency during the progress of PCR. This analysis requires that for the native and the competitor templates both initial amplification efficiency and the rate of decline of amplification efficiency are taken into account.

For example the equation

Euk = Eui - x × (Uk + Ck)/Pmax

2

is an equation in which the PCR amplification efficiency of the unknown template at the kth reaction cycle (E_uk) is related to the amplification efficiency in the first cycle (E_ui). The efficiencies are related by subtraction of the unknown and competitor products (U_k + C_k) accumulated at the beginning of the kth cycle, divided by the maximum amount of both products which can be produced by this reaction (P_max, i.e. the plateau amount), multiplied by a constant, x, which has a positive value equal to E_ui, which reflects the effect of increasing amplification cycle number to reduce the efficiency of amplification of U to a value <E_ui. This relationship was initially proposed by Raeymaekers (6), but has been modified here to constrain the value of x so that it is identical to E_ui; such a constraint is required or the products generated by the reaction will not cease increasing. To illustrate equation 2, if k is the second cycle, the value of U_k + C_k will be small compared with P_max, so even if increasing cycle number rapidly reduces amplification efficiency of U (i.e. even if x is a large value closer to 1 than 0), E_uk will still be very close to E_ui in the second cycle. However, as U_k + C_k becomes close to P_max, the importance of x in determining how much new reaction product is made in each cycle increases.

A similar equation can be constructed to describe changes in amplification efficiency of the competitor during the reaction:

Eck = Eci - y × (Uk + Ck)/Pmax

3

It can be seen from these two equations (2 and 3) that a critical question is does y = x for any particular combination of native and competitor amplicons?

We developed a computer model of competitive PCR to make predictions about the performance of these reactions when individual variables are altered singly or in combination. This model computes the number of reaction products accumulated at the end of each of 30 PCR cycles from the relationship Uk + 1 = U_k (1 + E_uk) (as in equations 2a and 3a in Appendix). The efficiency of amplification in each cycle is calculated from equations 2 and 3 above. We have used the model with parameters set at values indicated in Table 3 to estimate cycle-by-cycle product accumulation. As seen in Table 3, when initial amplification efficiencies and rates of decline of amplification efficiency are identical for both templates, unknown native template is accurately estimated by the model.

An important negative result indicated by the model is that the property of linearity is not one which reliably reflects whether templates are demonstrating ideal behavior in competitive PCR. Across the range of parameter values tested, in no instance was an R² value of less than 0.99 obtained. Another important negative result is that titration slope is only slightly better able to reflect whether reaction components are diverging from ideal behavior. Our modeling also indicates that deviation from ideal behavior can have large effects on accuracy, depending on the initial copy number. While these modeling observations are simulations which cannot be tested experimentally (since it is impossible to control amplification efficiency experimentally) they are instructive in cautioning against placing an excessive reliance during evaluation of assay performance on conformation with theoretical ideals of linearity and slope of titrations. They also indicate that entry into plateau in no way prevents accuracy of estimation, so long as initial amplification efficiency and rate of decay of amplification efficiency are identical for both templates.

An original purpose in validating competitive RT-PCR was to provide quantitative information which may reflect altered function in very small tissue samples (for example, microdissected nephron segments containing ~100 cells). Therefore, a reasonable sensitivity limit of the method would be the ability to quantify expressed genes, in replicate, from a single sample with sufficient resolution to detect differences of 40% between two populations using 6-10 representative individuals/population. The precision and sensitivity of this technique has allowed us to achieve this goal, as illustrated in measurements of expression of NKA in cortical collecting duct segments from 16-week-old spontaneously hypertensive rats and matched Wistar-Kyoto rats (mean ± SEM 3891 ± 211 versus 6948 ± 730 respectively, n = 5 per group, P = 0.004). Expression is reported as number of molecules of specific mRNA detected per 0.125 mm nephron.

Table 3. Computer modeling of the effects of template amplification efficiency on linearity, slope and estimation accuracy of competitive PCR titrations

Eu1	Ec1	x	y	R2	Slope	Actual starting copies	Estimated starting copies
1	1	1	1	1	1	10	10
1	1	1	1	1	1	100	100
1	1	1	1	1	1	1 000	1 000
1	1	1	1	1	1	10 000	10 000
1	0.8	1	0.8	1	1.001	10	207.6
1	0.8	1	0.8	1	1.001	100	1 838.4
1	0.8	1	0.8	1	1	1 000	13 255
1	0.8	1	0.8	1	1	10 000	93 343
0.9	0.5	0.9	0.5	1	1	10	9 397
0.9	0.5	0.9	0.5	1	1	100	86 533
0.9	0.5	0.9	0.5	1	1	1 000	511 716
0.9	0.5	0.9	0.5	1	1	10 000	2 200 235

E_u1 and E_c1 are the initial amplification efficiencies of the unknown and competitor templates respectively, x and y are the related constants which determine the rate of decline in their amplification efficiency through the course of the reaction. The correlation coefficient and slope of the titration lines generated in simple linear regression have been shown (R² and slope). Actual starting copies is the number of units of native template entered into the model at the `beginning' of the reaction. Estimated starting copies is calculated from the equation of the titration line which is generated from the model by setting the value of the log product ratio to 0 (i.e. log 1/1 = 0, the point where competitor and native are estimated to be present in identical quantities). Each simulation was for 30 cycles and the maximum total product accumulation in each reaction (P_max) was set at 2 × 10¹⁰ copies for all simulations. Titration regression lines are generated from five simulated reactions which usually include individual reactions which reach P_max and others which do not. The plateau of any particular reaction is strongly influenced by template initial amplification efficiency rates, rates of decline of amplification efficiency and starting copy number of both templates.

In order to probe further the sensitivity and precision in the lower range of competitive RT-PCR we have performed stepwise dilutions of similar RNA preparations to reduce the initial target copy number. We found that sensitivity was limited by the primers employed. It has not been possible to completely resolve whether this limit was a sequence-dependent phenomenon or due to quality of DNA synthesis. Resynthesis of primers improved performance. However, redesign of one of the primers for the rat CYP assay substantially improved sensitivity (12) and we observed that as few as 100 copies (Fig. 2) could be quantified. When inputs were further diluted 5- or 10-fold, reactions generally failed to make detectable products or made non-specific products. Therefore, after primer optimization, a general sensitivity limit of competitive RT-PCR appears to be >20 and <100 copies. It is uncertain to what extent RT and PCR contribute to limit sensitivity after optimization of PCR primers. Some templates may have greater RT efficiency and yield higher initial inputs to PCR reactions, thereby providing greater sensitivity.

Figure 2. The regression line shows the results of quantification by competitive RT-PCR of rat CYP gene expression in samples of serial dilutions of starting RNA equivalent to decreasing length of nephron tissue (three replicates per dilution level with results from each individual replicate plotted on the figure). Dilution of RNA resulted in progressive reduction in the amount of gene expression estimated. The regression which resulted from this dilution indicates that the expected reduction in abundance due to dilution was obtained (R² = 1.00, slope = 1.02). Accuracy was very well preserved even with initial copy numbers estimated to be as low as 100 per sample.

DISCUSSION

The present studies demonstrate that accurate quantitation of gene expression can be accomplished using RNA from small tissue samples by competitive RT-PCR coupled with dHPLC. The system is precise, even when RNA from samples as small as renal nephron fragments provide the starting templates. It is also highly sensitive. Furthermore, using a validated system in which known native inputs are used to test the estimation accuracy we have shown that accurate quantitation is unaffected by entry of reactions into a plateau phase. This characteristic eliminates the need for cycle-by-cycle sampling of reaction products to determine whether the reactions are in the exponential or the plateau phase. Analysis of reaction products by dHPLC permits rapid separation and accurate detection and quantification of heteroduplexes. Another property of the technique is its unlimited capacity for adaptation to new target genes.

The application of mathematical approaches to unraveling the complex nature of competitive, cyclical amplification has yielded some insights into the requirements for assay system validation. It should be noted that a thorough experimental validation of this model is not possible in the absence of means to control amplification efficiencies of native and competitor templates. The principal utility of the model is to clarify how erroneous estimates might occur, how large they may easily become and the validation necessary to avoid them. The model predicts that analysis of slope and linearity properties of titrations alone is an inadequate validation of the accuracy of the system. The most useful insight that this model yields is the requirement to validate that an assay system is producing accurate estimates by testing the estimation accuracy of the system against a range of known starting amounts of native template.

We employed this approach to determine whether the inaccurate estimations observed in some of our assay systems were due to RT or PCR amplification. In every case tested in which inaccuracy was present, it was always due to relative RT efficiency differences between the templates and never due to PCR. It was also a highly consistent inaccuracy, the magnitude of which could be determined. It could also, in some cases, be removed by redesign of the competitor template. These observations indicate that simply reducing the size of the internal mutation (for example, from 145 to 14-28 bp) will not always eliminate the RT efficiency difference. Others have reported that the presence of stem-loop structures predicted by RNA folding programs correlates with reduced reverse transcription (13). We analyzed whether any pattern of secondary structure formation determined by RNA secondary structure modeling (14) was correlated with the RT efficiency differences we observed. The resulting models reveal no simple relationship between overall secondary structural or relative stability differences between native and competitor templates and RT efficiency. However, the folding models suggest that the creation or loss of stem-loop structures at the location of the mutation may underlie the RT efficiency difference. Mutations to create a competitor which removed a predicted stem-loop structure correlated with increased reverse transcription efficiency relative to the corresponding native template. Conversely, creation of new stem-loop structure by the mutation correlated with reduced RT efficiency. These observations may prove to be reasonable explanations, however, the design of mutations intended to manifest predicted secondary structure differences from the native template for which they control and verification of the expected effect on RT efficiency is a necessary step in order to confirm these interesting, preliminary observations. Furthermore, intermolecular RNA interactions occurring between the heterogeneous RNAs expressed by differentiated cells might have an additional effect on relative RT efficiency. Our efforts to modify RT reaction conditions to remove the source of the RT efficiency difference were never fully successful.

Several advantages necessary for accurate analysis of competitive PCR reactions are provided by dHPLC. First, the eluting DNA can be detected and quantified by on-line UV absorbance. The separation is rapid, usually 5 min/sample, easily automated and reaction products can be analyzed without further treatment. Separation of DNA differing by only 5% in size is readily accomplished (10,15), allowing competitors to be constructed which are 95% similar in shared base sequence to the native amplicon. Separation is easily optimized to accommodate additional assay systems in which PCR products of various lengths are generated. The range of product sizes resolved is ~100-800 bp. Stability and performance of the non-porous polystyrene-divinylbenzene-based column matrix are excellent. We have run thousands of reactions over a single column without noticeable reduction in separation efficiency or increase in back pressure.

The ability to quantify at lower levels of abundance with accuracy and precision is influenced by a number of factors. Stochastic events in the various reactions which take place during RT and the early cycles of PCR have an influence on lower limits of sensitivity (16). Peccoud and Jacob have modeled these phenomena in the context of competitive PCR sensitivity using a computer simulation which incorporates the random nature of chemical reactions involving very low abundance reagents (17). Predictions from this model indicate that the critical threshold at which uncertainty in quantitation begins to rise rapidly is between 20 and 40 copies, depending on the amplification efficiency incorporated into the model. This modeling was limited to the PCR reaction and the additional step of RT adds further opportunity to reduce sensitivity, because RT efficiency also places a limit on the number of initial template molecules available for the competitive PCR reaction. The data we have generated on this subject provides an initial framework of reference in considering whether experimental goals requiring quantification of very low copy numbers are likely to be achieved with sufficient precision to make useful comparisons.

The completion of these studies demonstrates that, when adequately designed, applied and validated, competitive RT-PCR is a versatile tool for quantitative measurements of gene expression. All of the components necessary to establish new systems are readily available and can be applied to any gene sequence which is sufficiently well described. Our investigations of accuracy, sensitivity and precision indicate that accurate and precise measurements can be obtained, even in RNA extracted from microscopic tissue samples.

ACKNOWLEDGEMENTS

This publication is number 132-IMM from the Institute of Molecular Medicine for the Prevention of Human Diseases, University of Texas-Houston Health Science Center. This work was supported by grants from NIH DDK RO1 45538 (P.A.D.), T32 DDK07556-20 (A.H.L.), RO1-DK36199-10 (S.S.) and PO1-HG00205 (P.J.O.). C.A.H. was the recipient of an HHMI Fellowship. We are grateful to Betty Lonis for assistance in obtaining nephron specimens.

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APPENDIX

Equation 1a describes the accumulation of reaction products in PCR. It predicts that small variations in efficiency (E) can lead to dramatic variations in product yield.

U = U0(1 + E)n

1a

Where U is the final amount of reaction product, U₀ is the initial amount of DNA in the reaction, n is the number of cycles and E is the efficiency of the reaction.

The use of competitor template as a reference standard is a significant step in permitting quantitative accuracy in determining gene expression levels, but poses some interesting theoretical problems. The most obvious of these is that the processivity rate of Taq polymerase (~50 bases/s) may be sufficiently low that during the elongation step in the PCR reaction, shorter DNAs might be amplified with greater efficiency than longer ones. To understand the potential impact of a difference in amplification efficiency on validity of a standard requires a mathematical approach to PCR amplification and the effects of variations in efficiency on accumulation of amplified products. Raeymaekers has devised a model to predict the effect of variations in amplification efficiency on accuracy of competitive PCR (6). This model is described briefly below.

If the initial unknown amount of a gene U in a competitive RT-PCR reaction is U₀ and that of its specific (mutant) competitor RNA is C₀ and these templates are subjected to n reaction cycles in which the efficiency of amplification is E_u and E_c (positive values between 0 and 1) for the unknown and competitor respectively, then from equation 1a the amount of reaction products at the end of n cycles can be described by

Un = U0 · (1 + Eu)n	2a
Cn = C0 · (1 + Ec)n	3a

If the assumption that E_u and E_c are initially equal and remain equal (though not necessarily constant) throughout each cycle of the competitive RT-PCR reaction, then E_uk = E_ck for k cycles and for any cycle, U_k/C_k = U₀/C₀. Therefore, taking the logarithm

log(Uk/Ck) = logU0 - logC0

4a

This equation indicates that the log of reaction product ratios has a simple linear relationship to initial copy number of native and competitor templates which takes the form of y = ax - b, the equation for a straight line where the value of the slope of the line = 1.

AUTHOR'S NOTE

A computer program which runs in Excel on both Macintosh and Windows computers (Q-RT-PCR.xla) has been developed and released into the public domain to assist in the analysis of competitive RT-PCR reactions. It is available for downloading at http://www.grad.ttuhsc.edu/archive/index.html. The program cal-culates reaction product ratios from the UV absorbance value of the product peak areas. It corrects for size differences between products, re-allocates heteroduplex strands to the appropriate reaction product to which their components belong, performs regression analysis of titrations, provides statistical analysis (titration linearity, slope and P value of the regression) and estimates unknowns. Eventually we hope to interface this data analysis software directly with chromatography software so as to further minimize the post-PCR processing required to estimate unknowns.

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*To whom correspondence should be addressed. Tel: +1 713 500 2414; Fax: +1 713 500 2424; Email: pdoris@imm2.imm.uth.tmc.edu

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