Gys de Jongh wrote:
> Dr. Duncan Clark <Duncan at nospam.demon.co.uk> wrote in message
> news:DwEuJhAPdvg4EA7h at genesys.demon.co.uk...> >
> > OK so what we still need is a simple way to calculate errors and not in
> > the linear fashion that Stratagene erroneously published. I think that
> > many moons ago Boehringer published a table in one of their Biochemica's
> > (shortly after the launch of Expand) showing the percentage of products
> > with errors for Taq and Expand after 15, 20, 25 and 30 cycles and for
> > products from 100bp to over 1000bp.
> > There is also another Boehringer Biochemica (April 95, pp 34-35) that
> > calculates error rates in a lacI based system for various polymerases in
> > PCR. Basically they used a lacI containing pUC19 (white) and PCR'd the
> > whole plasmid. Any errors introduced in lacI that inactivate lacI will
> > give blue or pale blue colonies upon ligation and transformation of the
> > amplified plasmid into an appropriate host.
> > The error rate per bp was calculated with a re-arranged equation from
> > Keohavong and Thilly (PNAS 86, 9253).
> > f= -ln F / d x b bp
> > where F is the fraction of white colonies
> > d is the number of duplications
> > 2(superscript)d = output DNA/input DNA
> > b is the effective target size of the (1080bp) lacI gene i.e. 349 bp
> > There are 349 phenotypically identified single base substitutions
> > (nonsense and and mis-sense) at 179 codons (approx 50% of coding region)
> > within the lacI gene.
> > From this one can calculate the error rate which for Taq comes out at
> > around 2.6 x 10E-5 and for Pwo (Pfu) 3.2 x 10E-6
> > So what's the point. Presumably with more rearrangement, assuming 20
> > duplications, a 3kb target size and the above error rates one can
> > calculate the % fraction with errors. I'll leave someone else to do the
> > maths!
> thank you for the references ; I'll look them up. The points for me are that
> I would like to have , at least some idea , about the source and propagation
> of errors in a sequencing project. (Involving PCR and cycle sequencing
> steps). Second I'm just curious. Third math's is one of my hobby's. The
> total number of wrong copied bases in a long dna molecule can be regarded as
> "a number of events in a space or time dimension" . It is thus very probable
> that the errors are poisson distributed. For a poisson distribution :
> P(k)=exp (-n*p) * (n*p) ^ k / k! Where in our case P(k)=the chance for k
> errors in the whole molecule , n=number of bases , p=error rate per base ;
> your f. For k=0 this leads to : P(0)=exp (-number of base pairs * error rate
> per base pair) . As (n*p)^0=0 and 0!=0 . P(0) is the fraction of colonies ;
> your F. Taking the natural log , rearranging and dividing by by number of
> doublings leads to the formula you gave. In my posting of 12-jan I proposed
> to calculate the P(0) (your F) directly from chance theory with :
> (1-p_wrong)^number of base pairs . For a 3000bp target and an error rate of
> 2.6 x 10E-5
> exp(-2.6 x E-5 x 3000) = 0.924964 Poisson
> (1-2.6 x 10E-5)^3000=0.924963 Direct
>> This make me feel a bit less sliced.
> Which makes me happy
> Thanks again
I like your discussion with Duncan, but I have some questions. When you
calculate P(k) in the last post, you find that P(0)=0.92396. If I understand
that right, it means that there is roughly a 92% chance to get error-free
amplification, or, in other words, only 8% of all fragments will contain one
(or more) mistakes. Apart from a gut feeling that this percentage is way too
low, I don´t understand how your calculation via poisson distribution depends
on the number of cycles. It is clear that mistakes accumulate, so the
percentage of "wrong" fragments MUST depend on the cycle number.
Be it as it may, can anyone of you answer the following practical question?
If I have a 3000 bp fragment, how many doubling (cycles) may I perform to get
less than, say 5%, of error-containing fragments with Pfu or Taq. This would
allow us to think of a rule-of-thumb to estimate the amount of template to use,
and the number of cycles to perform.