Quantitative PCR which meets mathematical ideals

William Alexander ALEXANDERW at cber.cber.fda.gov
Wed Sep 20 10:26:37 EST 1995

In Article <43p2jo$eqh at miasun.med.miami.edu>, tmiller at newssun.med.miami.edu
(Todd Miller - Pharmacology) wrote:
>In Article: 32130 of bionet.molbio.methds-reagnts
>Peter Doris <cbbpad at wpoffice.net.ttuhsc.edu>
>Subject: Quantitative PCR which meets mathematical ideals
>Message-ID: <42nsqd$h8g at hydra.acs.ttu.edu>
>Peter Doris said:
>I regret that I have missed some of the early discussion on quantitative 
>RT-PCR which seems to have generated much interest.
>Raeymaekers has done much to generate realistic mathematical models of 
>these reactions. Readers should also note his recent paper in Genome 
>Research 5:91-94, 1995.
>The real problem is that there has been no description of this method 
>which has been extensively validated and shown to meet not only the 
>theoretical requirements, but also demonstrated to accurately and 
>absolutely quantify RNA and DNA inputs. Raeymaekers' work has been 
>thorough and helpful on theoretical grounds and he has done much to 
>point up the considerations which must be met, though it has remained 
>unclear whether and how such considerations can be met.
>I hope this is not to say that Raeymaeker's theoretical description
>does not *need* to be met.  It does for the fundamental assumptions
>of equal amplification efficiency to be validated.  Unfortunately,
>many who use this technique have either never read Raeymaekers or
>just choose to ignore his work (I suspect the former predominates).

Do you also ignore the work of those who do follow Raeymaekers work?

>Then Peter Doris wrote: 
>This situation will change with a forthcoming publication which is 
>principally the work of Amanda Hayward-Lester (BioTechniques, in press). 
>This work has used novel HPLC column technology developed by Dr. Peter 
>Oefner (BioTechniques 16:898-908, 1994) to rapidly separate and 
>quantitate products of competitive RT-PCR reactions. The principal 
>findings are that titrations with slopes and R^2's close to unity are 
>routinely achievable using this system. HPLC provides some important 
>advantages which play a role in permitting quantitative accuracy. First, 
>there is no need to label reaction products, they can be detected and 
>quantified by UV absorbance as they elute from the column. Second, there 
>is no need for post-reaction sample processing prior to HPLC analysis - 
>reaction products can be directly injected into HPLC. Third, this 
>technology reveals aspects of competitive reaction kinetics which cannot 
>be seen when the same reaction products are analyzed on either agarose 
>or polyacrylamide gels. This new information is important to provide 
>accurate titrations. What is made clear by rversed phase ion-pair HPLC 
>is that these competition reactions readily generate heteroduplex 
>products, even when the native and competitor sequences share less than 
>65% homology.
>Well, Biotechniques isn't exactly my favorite journal for serious
>analyses of methods in molecular biology, but I will check it out.
>But about these heteroduplices.  I presume they must arise from some
>sort of "jumping" PCR, and that they make up a fairly significant
>proportion of the products.  I'm assuming you looked at the effect
>of homology strictly to examine this, because I don't think one would
>choose a competitor molecule with only 65% homology to the target in
>most instances.  The fact that you get a substantial amount of this
>raises even more questions about this technique--surely those who
>developed this didn't count on having these sorts of products?

Could you please read some more about PCR before you go on about problem
after problem.  Just because YOU haven't heard about this before does not
mean that no one else has.  Yes heteroduplexes can be a complication in
quantitation.  The heteroduplexes can and do form even when the same exact
primers are used in the amplification.  You "presume" that they "must" arise
from some sort of "jumping" PCR.  
An older paper explaining this "new" problem was published in 1989:  
Becker-Andre, M. and K. Hahlbrock.  "Absolute mRNA quantification using the
polymerase chain reaction (PCR). A novel approach by a PCR aided transcript
titration assay (PATTY)." (1989) Nucleic Acids Research. Vol. 17, No. 22,
pp. 9437-9446.   

The formation of heteroduplexes is explained in this paper and methods to
overcome this complication are also given.  Think about what is happening in
the tube during the PCR process.  If you use a competitor which has even
only one base difference from the target you will form some heteroduplexes. 
As the cycle number increases, the amount of primers will decrease and some
of each template will rehybridize to the other template when the reaction
cools.  If the base change is detected by a restriction endonuclease, then
these heteroduplexes will not be digested and might be presumed to contain
two strands of the original template even though they are heteroduplexes.  

This is explained in Fig. 4:
"Effects of heterodimeric DNA formation on the analysis of PCR products. 
Two DNA species with a single base difference (creating a restriction site)
are mixed in a 1:1 ratio and completely denatured.  After reannealing, an
apparent ratio of 3:1 is observed, because 50% of the DNA strands form
heterodimeric double-stranded DNA which is insensitive to digestion."

It doesn't take a lot of homology to cause hybridization between two single
stranded DNAs.  You also do remember how introns and exons were discovered,
don't you?

>Then Doris says:
> On non-denaturing gels we have not been able to visualize 
>these heteroduplicies as separate products (on denaturing gels, they 
>become irrelevant to the computation). This appears to be due to the 
>peculaiar migration of heteroduplexes which effectively contain both 
>double and single stranded DNA. Since the quantitation system depends on 
>the ratio of products and the presence of heteroduplices affects this 
>ratio, it is vital not only to detect them, but also to quantitate them 
>so as to calculate an accurate ratio.
>Exactly how do the amounts of these heteroduplex products figure in
>to the calculations?  How do you know whether to add them or subtract
>them, and from the target product or the competitor product?  Can
>these unexpected products be fit into Raeymaeker's equations?

These "unexpected" products can be accounted for mathematically.  They are
not really a problem in Raeymaeker's equations since he assumes in his
earlier paper that the PCR reactions are done using two sets of primers.
>Thanks for an interesting post.  It is nice to see that someone is
>seriously looking into this technique, which has been uncritically
>accepted by many scientists.  Maybe we need to get some PCR police
>to monitor all these spin-off PCR techniques...
>Todd Miller, PhD
>tmiller at newssun.med.miami.edu
I think what is needed is more reading.  If you have not grasped the great
power of PCR then as a scientist you should rethink your conclusions.  Yes
PCR quantitation can be done poorly, but that does not mean that it should
be ignored.  Because of its great power, PCR quantitation will be improved
again and again and you should consider keeping up with the advances.  Who
would have predicted the widespread use of lambda phage as a cloning vector
when it was first described?  Many steps were necessary to overcome such
problems as restriction sites, packaging, selection against phage without
inserts, etc. etc.  Keeping up can be the real problem, as it is for me :-(,
since so many people are publishing using this technique and it is necessary
to read all of the details (as you know). 

Bill Alexander
alexanderw at cber.cber.fda.gov

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