Poisson versus PCR distributions:
In our paper (Firth & Patrick, 2005), we assumed a Poisson
distribution to determine the fraction of sequences in an epPCR
library that contain exactly 0, 1, 2, 3, ... mutations, given the mean
number of mutations, m, per sequence.
Since publication of Firth & Patrick (2005), however, Drummond et
al. (2005) have revisited the pioneering work of Sun (1995) and
provided experimental evidence in support of his more accurate
equation describing the distribution of m. This 'PCR
distribution' takes into account the number of PCR thermal cycles
ncycles and the PCR efficiency eff (i.e. the probability
that any particular sequence is duplicated in a given PCR cycle). We
have therefore now included the PCR distribution as an optional
alternative to the Poisson distribution in PEDEL.
For large m, small ncycles, or low eff, the PCR
distribution is broader than the Poisson distribution. For low
m, large ncycles and large eff, the PCR
distribution approximates the Poisson distribution.
In a 'typical' epPCR (e.g. ncycles = 30, eff = 0.6,
m = 4), the estimated total number of distinct sequences in a
library typically agrees to within 5% for the two distributions, though
the sub-library statistics can show more variation.
If you know ncycles and eff, then we recommend that you
use the PCR distribution instead of the Poisson distribution.
Drummond et al. (2005) use the formula d =
ncycles × eff, where d is the number of
doublings. For example, if you start with 10^9 identical parent
sequences and amplify them in an epPCR to 10^15 sequences, then you
have had about d = 20 doublings (10^9 × 2^20 ~= 10^15),
and you can calculate eff = d ÷ ncycles.
Actually the d = ncycles × eff formula is
wrong. The correct formula is 2^d = (1+eff)^ncycles, so that the
efficiency is given by eff = 2^(d/ncycles) -
1 (PCR efficiency calculator).
Drummond D.A., Iverson B.L., Georgiou G., Arnold F.H. (2005). Why
high-error-rate random mutagenesis libraries are enriched in
functional and improved proteins, J. Mol. Biol.,
Firth A.E., Patrick W.M., (2005). Statistics of protein library
construction, Bioinformatics, 21, 3314-3315.
Sun F. (1995). The polymerase chain reaction and branching
processes, J. Comput. Biol., 2, 63-86.
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