ABSTRACT
The rate of amplification of abundant PCR products generally declines faster
than that of less abundant products in the same tube in the later cycles of
PCR. As a consequence, differences in product abundance diminish as the number
of PCR cycles increases. Rehybridization of PCR products which may interfere
with primer binding or extension can explain this significant feature in late
cycles. Rehybridization occurs with a half-time dependent on the reciprocal of the DNA concentration. Thus, if
multiple PCR products are amplified in the same tube, reannealing occurs faster
for the more abundant PCR products. In RT-PCR using an internal control, this results in a systematic bias against
the more abundant of the two PCR products. In RNA fingerprinting by arbitrarily
primed PCR (or differentially display of cDNAs), very large or absolute
differences in the expression of a transcript between samples are preserved but
smaller real differences may be gradually erased as the PCR reaction proceeds. Thus, this `C
o
t effect' may systematically cause an underestimate of the true difference in starting template concentrations. However, differences in starting template concentrations will be better preserved in the less abundant PCR products. Furthermore, the slow down in
amplification of abundant products will allow these rarer products to become
more visible in the fingerprint which may, in turn, allow rarer cDNAs to be
sampled more efficiently. In some applications, where the object is to
stochiometrically amplify a mixture of nucleic acids, the bias against abundant
PCR products can be partly overcome by limiting the number of PCR cycles and,
thus, the concentration of the products. In other cases, abundance
normalization at later cycles may be useful, such as in the production of
normalized libraries.
The efficiency of each cycle of PCR amplification is a function of the
efficiency of primer binding and the proportion of molecules that extend to
completion. These factors are controlled by many parameters, such as buffer
type, polymerase type and concentration, primer concentration and the extent
and stability of the primer match with the template. In practice, these
variables are generally subsumed into a single adjustment in the base `x' of
the equation for amplification, x
n
, where n is the number of PCR cycles. The value of the base, x, would ideally
be 2, but even in the best reactions the base generally does not exceed 1.9.
For earlier cycles of PCR the base hardly changes and this constancy is the
foundation of many methods for calculating the relative or absolute amounts of
nucleic acids (e.g.,
1
-
4
). At later cycles, the efficiency of PCR eventually declines. This decline can
occur for a number of reasons, including a decline in primer and dNTP
concentration as they are incorporated into PCR products and the accumulation of inhibitors, such as pyrophosphate, and competitors, such as primer dimer. These factors, and progression from polymerase excess to
template excess, compounded by the gradual decline in functional enzyme,
eventually result in a declining rate of amplification. These factors, however,
do not sufficiently explain the non-exponential or `plateau' effect.
During the late cycles of PCR a phenomenon occurs that has been largely
neglected and which cannot be explained by the effects mentioned above. As the
reaction proceeds, the PCR product strands become sufficiently concentrated
that they reanneal to some extent during the time spent below the DNA melting
temperature at each cycle, which is often a few minutes. Reannealing may interfere with primer binding. The phenomenon that we refer to as the `C
o
t effect' was first suggested by Innis and Gelfand (
1
). Our data and that of Suzuki and Giovanonni (
5
) demonstrate this effect. This `C
o
t effect' may be of particular importance when more than one PCR product is
being amplified as, for example, in arbitrarily primed PCR fingerprinting of
DNA (
6
,
7
) and RNA (
8
,
9
), where many products are being compared, side-by-side, between PCR reactions. These applications of PCR rely on the
detection of differences of PCR product abundance between samples well beyond
the exponential phase of the reaction. As a consequence, if reannealing takes
place to a significant extent during late cycles, the more abundant products in
the fingerprint systematically amplify less efficiently and a large difference
in the abundances of template samples is reduced in the final fingerprint.
However, differences between starting templates in the same sample are also
diminished in the final product, allowing other products that are rarer to catch up. This may be advantageous, as will be explained.
Total RNA was prepared from different stages of the life cycle of
Trypanosoma brucei brucei
GUTat3.1. The procyclic stage (Pc), was cultured
in vitro
, while the slender (Sl) and stumpy (St) bloodstream forms were grown in mice.
Cultures and recovery of parasite pellets were performed under standard
conditions (
10
,
11
), and RNA was purified using the guanidinium thiocyanate-cesium chloride method (
12
). RNA arbitrarily primed PCR fingerprints were obtained as previously described
(
9
,
13
), using either two different 10mer oligonucleotide primers of arbitrary
sequences, or a combination of a 10mer arbitrary primer and a 11mer derived
from the 5' mini-exon sequence of the trypanosomes mRNA (
14
,
15
). Differentially amplified RAP-PCR products were isolated using single-stranded conformation polymorphism (SSCP) gels and sequenced as
previously described (
16
).
Reverse transcription was performed on RNA at three concentrations per sample (500, 250 and 125 ng per reaction), using a mixture of three
different anchored-dT primers [(T)
12
-G,A or C]. RNA (5 [mu]l) was mixed with the same volume of RT mixture for a 10 [mu]l final reaction containing 50 mM Tris pH 8.3, 50 mM KCl, 4 mM
MgCl
2,
10 mM DTT, 0.2 mM of each dNTP, 2 [mu]M of primer and 13 U of MuLV-reverse transcriptase. Reverse transcription was performed at 37oC for 1 h (after a 5 min ramp from 25 to 37oC), the enzyme was inactivated by heating the samples at 94oC for 2 min, and the mixture containing newly
synthesized cDNA obtained was diluted 4-fold in water. PCR was performed using two primers (19 or 20mers) chosen
from the sequence characterized previously 5'-AATGAAAGTTACGATAGCGG and 5'-AAAGACAACGGAGATGGCA for the ESAG transcript (GenBank
accession no. U53929), and 5'-TGAAGCAGAAGACAATCAGG and 5'-AAAAATGCCAGTAGCAGGAC for the other transcript, called `BET-2' (GenBank accession no. U49238). Diluted cDNA
(5 [mu]l) was mixed with 5 [mu]l PCR mixture for a 10 [mu]l final reaction containing 10 mM Tris pH 8.3, 10 mM KCl, 4 mM MgCl
2
, 0.2 mM of each dNTP, 1.5 [mu]M of each primer, 0.5 [mu]Ci [[alpha]-
32
P]dCTP and 2 U of Ampli
Taq
polymerase Stoffel fragment (Perkin-Elmer-Cetus, Norwalk, CT). Thermocycling was performed with a GeneAmp PCR
System 9600 thermocycler (Perkin-Elmer-Cetus), using a low stringency thermal profile. The same results
were obtained using either of the two following cycling conditions: varying
number of cycles of 94oC for 30 s, 35oC for 30 s and 72oC for 50 s or five cycles of 94oC for 30 s, 40oC for 30 s and 72oC for 50 s, followed by various numbers of cycles
of 94oC for 30 s, 60oC for 30 s and 72oC for 50 s, as described in the figure legends. Amplification
products (5 [mu]l) were mixed with 15 [mu]l formamide dye solution, denatured at 68oC for 15 min, and 2.2 [mu]l was loaded onto a 6% acrylamide-43% urea gel, prepared in 1* TBE buffer. Electrophoresis was performed using
a sequencing apparatus at 50 W for ~3 h. The gel was dried under vacuum and placed on Kodak BioMax X-Ray film for <= 5 days.
Autoradiograms were scanned and peaks displayed using the software NIH Image
v1.57. Peak heights were determined and the background from the negative
control RNA lanes was subtracted. The peaks were measured for the lowest of the three RNA concentrations used at each data point. Deviations from a non-linear response in the autoradiogram were controlled for by using a low
film exposure and a standard consisting of a serially diluted radioactive
marker. Observed densities were adjusted using this calibration curve. Graphs
of the data were plotted in Microsoft Excel 5.0 on a Power Mac 7100. The
proportion of the RNA sample that generated the PCR product of interest was
plotted on the X-axis. The Y axis plotted the observed to expected ratio of DNA synthesis.
In Figure
3
, the observed synthesis at each ratio was normalized against the synthesis seen
in the slender RNA sample for cycle number. This normalized number (between 0
and 1) was then divided by the fractional ratio of the RNA sample that
generated the PCR product of interest (i.e., 0, 0.11, 0.17, 0.33, 0.50, 0.67,
0.83 or 1) to obtain the deviation from expected.
PCR products were cut from the acrylamide gel and disintegrations of
32
P were counted in EcoScint scintillation fluid for 5 min in a Packard
Scintillation counter. The molarity of the product was then determined
directly, based on the radioactivity, the number of cytosines in the product,
and the specific activity of the dCTP in the reaction.
These experiments were initially prompted by a desire to develop a simpler
method to determine the relative abundance of specific RNA transcripts between
samples. Methods for determining the relative abundance of RNAs between samples
include Northern blots, S1 protection, primer extension and RT-PCR using internal controls and/or sampling a PCR reaction in the
exponential phase. These methods are very effective but quite labor intensive.
We speculated that if specific primers for RT-PCR were used for PCR at low stringency, in addition to the desired
product many reliable arbitrary products would be generated, as occurs in
arbitrarily primed PCR of DNA (
6
,
7
) and of RNA (
8
,
9
). These extra products might lead to stochiometric sampling of the specific product in
the context of largely invariant PCR products derived from transcripts that are
not differentially regulated. Unlike a typical PCR reaction in which there is
only one desired product, any individual product in a fingerprint contributes
only a small fraction to the total mass. Thus, as the reaction becomes
saturated for the limiting component (usually the enzyme), all the products
should be affected to the same degree so that the reaction slows down for all
the products equally. This would, in principle, preserve the differences for
any individual product between samples.
There was considerable precedent for this possibility. In the case of DNA
fingerprints, differences in the abundance of PCR products between samples
correlate with differences in the amount of the template DNA, as evidenced by
the lower intensity of polymorphic bands in the DNA fingerprints of F1 mice
versus two different inbred parentals (
17
). This observation has been extended to detect chromosomal amplifications and deletions in cancers (
18
,
19
). Similarly, RNA fingerprinting using arbitrarily primed PCR and differential
display on an acrylamide gel has been used extensively to detect differentially expressed RNAs. It has generally been
assumed that differences in the intensity of a cDNA product between two RNA
fingerprints from an isogenic source is due to corresponding differences in the
sampled RNA, even beyond the exponential phase of the PCR reaction. These
observations were consistent with the generally held opinion that all PCR
products are similarly affected by the limitation of reagents as PCR exits from
the exponential phase, while preserving any intrinsic sequence-dependent differences in amplification efficiency and the bias against longer PCR products (e.g.
20
,
21
).
There were few plausible explanations for the lack of stochiometric
amplification of the titrated ESAG product. Despite a lack of claims to have
demonstrated this effect in the literature perhaps, the amount of PCR product
was sufficient to allow it to reanneal, thus inhibiting amplification and
allowing products of lower concentration to catch up. At lower DNA
concentrations in earlier cycles the difference between samples would still be
present and would gradually disappear as the reaction progressed (Fig.
2
). This phenomenon was also seen using different specific primers directed
against ESAG, and specific primers directed against another novel differentially expressed gene, Bloodstream expressed transcript-2 (BET-2) (Fig.
4
).
We set out to develop a PCR strategy for determining the relative abundance of
specific transcripts among RNA samples using specific primers at low
stringency. In addition to a product from the transcript of interest, at low
stringency a series of other PCR products representing many other transcripts
are generated, mostly from RNAs that do not differ between the samples. These
other products represent internal controls. At a lower number of cycles or when
the product of interest represents a small fraction of the total amount of DNA
in the fingerprint, the estimates of relative abundance are more reliable. The
low stringency PCR strategy with specific primers is much simpler than other
methods for measuring relative levels of transcripts, as long as the number of
cycles is limited. However, we also showed that when approaching saturating levels of amplification there is a normalization phenomenon that affects relative abundance.
Rehybridization appears to be responsible for the bias against PCR of abundant
products in the late cycles of PCR. There seem to be few other plausible
alternatives but even if rehybridization is not the cause, the phenomenon has some interesting consequences that are worthy of discussion. This phenomenon complicates use of PCR
fingerprints to look for differences in DNA content, such as has been done for
cancer, because the sensitivity of detecting subtle differences in ploidy would
be diminished. Nevertheless, differences are actually seen (e.g.,
18
,
19
). If enough fingerprints are generated then there is a good chance that even a
small change in the copy number of a chromosome or subchromosomal region will
be represented in a relatively rare PCR product. Because rarer products are at
lower concentration the normalization process would take place less
efficiently. Thus, real differences in abundance of sequences between samples
may remain reflected in these less prominent products.
In the case of RNA arbitrarily primed PCR fingerprinting and differential
display the situation is more complex. For the more prominent PCR products in
the fingerprint, modest differences in the abundance of the source transcript
between RNA samples are reduced as the reaction progresses. It therefore
appears that, for prominent cDNA products, the differences between RNA samples must be large to be
observed.
We have previously argued that if two different RNA sequences in the same tube
prime and amplify with equal efficiency but have a 100-fold difference in abundance this would result in PCR products that
preserved the starting ratio of 100:1 (
9
,
20
). This would result in a very severe bias against sampling rarer transcripts in
the fingerprint. The data presented here indicates that the slowing of
amplification of the more abundant PCR products would allow the rarer PCR
products in the same tube an opportunity to amplify. Thus, the ratio might be
somewhat normalized, which works in favor of sampling rare RNAs because rare
cDNA PCR products have a chance to `catch up', but places retrictions on
quantitative interpretation. The extent of the remaining bias against rare
transcripts is unknown.
Overall, we would predict that in both DNA fingerprinting and RNA fingerprinting
the trend would be for differences in the fingerprints to
underestimate the difference in the original templates. This underestimate would
be most severe for the more prominent products in the gel.
It would be helpful to be able to model the effect of rehybridization. However,
rehybridization generally becomes important at the same stage in the PCR
amplification as many other factors that cause the reaction to become non-exponential. This phase of the reaction is difficult to model. The
coincidence of non-exponential amplification and rehybridization at late stages of PCR is
probably the reason why rehybridization has been largely ignored as a factor in
the plateau of PCR amplification: there were already plenty of explanations for
the decline in PCR at this stage in the process. Only the differential effect
on products of different molarities in the same tube distinguishes
rehybridization from these other factors that cause non-exponential amplification in late cycles.
If the observations we have made are generally true then presumably they would
be seen in the data of others, particularly in the data from PCR-based quantitation methods that involve an internal control. For example,
in a recent study by Borrielo
et al
. (
4
), exogenous globin mRNA was titrated against endogenous TNF-[alpha] RNA and the product ratios were shown to be generally linear at
the 24th, 26th and 28th cycle. A starting ratio of 2:1 resulted in a product
ratio that increased from 0.2 to 0.25 to 0.3 as the cycles increased from 24 to
26 to 28 (fig. 2 in that reference). This would be predicted by the
rehybridization hypothesis; the ratios would deviate towards 1.0 as the number
of cycles increase.
In the study by Gilliland
et al
. (
2
), GM-CSF RNA was titrated versus increasing amounts of a plasmid carrying the
GM-CSF gene. After 40 cycles (near enzyme and substrate saturation) the ratio
of plasmid DNA product to cDNA product was not linear and deviated in the
direction we would predict; with increasing amounts of plasmid DNA the ratio
does not increase as fast as otherwise expected (fig. 4 in that reference).
Similarly, in the paper by Bouaboula
et al.
(
3
), where they meticulously validate a multispecific internal control for RT-PCR, the ratio of the starting template and standard are linearly
reflected in their product ratios except, as we would predict, when they differ
markedly in starting ratios. In their data the deviation occurs at both ends of
the titration; the ratio systematically favors the less abundant products, the
template at one end of the curve and the standard at the other. Their data also
show that at large ratios of template and standard the differences in products
are diminished between the 25th and 30th cycles, also as we would predict (fig. 5 in that reference).
In all the cases discussed, and in many others, the authors were aware that
their quantitation was best in a certain range around a product ratio of 1:1.
Thus their conclusions are not compromised by the phenomenon we observe in
their data. Indeed, observation of the phenomenon in their data is confirmation
of the quality of their experiments. However, experiments that involve more
than one PCR product in a reaction and proceed into the non-exponential phase need not always display the rehybridization effect. This
C
o
t effect should be reduced if the number of cycles is limited or if the amount
of primer or some other component has been limited so that the final product
does not accumulate to a concentration above ~0.01 [mu]M where rehybridization becomes a factor. Indeed, limiting the total
molarity of PCR products is wise in quantitation experiments where product
ratios are expected to be large and where PCR extends into the non-exponential phase.
Suzuki and Giovanonni (
5
) have independently demonstrated a particularly dramatic example of this
phenomenon, which they observed when amplifying a mixture of two rRNA gene templates. They showed that
the results fit a kinetic model in which the reannealing of genes progressively
inhibits the formation of template-primer hybrids.
The normalization phenomenon is certainly a disadvantage when one wants to
preserve the stochiometry among initial template products, such as when
surveying nucleic acids from mixtures of organisms. One way to minimize alterations in stochiometry would be to ensure
that the products remain as dilute as is practical. However, in a case where
one actually wants to normalize a sample, such as when the extent of diversity
in a sample is the question of interest, the rehybridization phenomenon can be exploited and even enhanced. For example, the reaction could be held at
each cycle at above the
T
m
of the primers but below the melting point of the PCR products. This would
allow reannealing to proceed for a chosen time, only limited by the half life
of the enzyme and other components which could be replenished if necessary.
Such limits will put a practical cap on the complexity of the DNA that can be
reannealed. Nevertheless, assuming crossover PCR does not garble the results,
it is possible that hundreds or perhaps thousands of separate PCR products
could be partly normalized in a single tube in a few hours or days.
Applications to normalized libraries from DNA and RNA fingerprints and from
complex nucleic acid samples can be envisioned.
In summary, PCR seems to involve a rehybridization or `C
o
t effect' at high DNA concentrations that has implications for the design and
interpretation of PCR amplification experiments that contain multiple PCR
products and proceed to high product concentrations.
We thank Dr Charles Davis and Karen Arnold (Division of Infectious Diseases,
U.C.S.D. Medical Center, CA) for providing the
T.brucei
stock, and growing the bloodstream forms of the parasite. This work was
supported in part by the UNDP/World Bank/WHO Special Programme for Research and
Training in Tropical Diseases (no. 910020), and the US National Institutes of
Health grants CA 68822, NS33377, AI32644 and AI34829. F.M-D. was supported in part by a Lavoisier Fellowship (Ministère Français des Affaires Etrangères) and Galderma Inc., La Jolla, CA.
REFERENCES
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