User manual

Droplet Digital
™
PCR Applications Guide | 95
Appendix B: Technical Error Bars in Droplet Digital
™
PCR
Fig. 1. Subsampling error due to analyzing part of a larger whole.
Count molecules in a subsample
(1/12
th
shown here).
60 molecules in sample.
Subsample 1/12
(5 molecules expected).
Most of the 25 subsamples contain 4, 5, or 6
molecules — this uncertainty is what we mean
by subsampling error.
The error due to subsampling is given as:
Standard deviation = √M
Coefficient of variation =
where M = expected number of target molecules in the ddPCR reaction.
√M
M
Whenever you subsample from a larger volume with the intent to measure properties of
the whole volume, random effects will lead to slightly different measurements from the
subsampled volume. Subsampling error is most significant at low concentrations.
While some quantification systems do not directly report the subsampling error, the
standard error of the mean (the typical error reported for replicates) implicitly combines all
the different sources of error, including the subsampling error.
Subsampling example: Suppose a person has a total of 100,000 copies of a particular
target in his or her blood (5 L total volume) and you take 5 ml of plasma. On average,
this 5 ml will contain 100 copies of target. But if you take 100 x 5 ml samples, about 16%
of them will contain less than 90 copies and about 16% of them will contain more than
110 copies of target. This type of variability is inherent in any type of subsampling.
Figure 1 illustrates subsampling error that arises because a small volume was taken from a
large amount of starting material. If the 12 µl of sample has 5 target molecules/µl and you
take 1 µl of the sample (1/12th of the whole) and count the number of molecules in that
subsample, you may expect to see 5 molecules. However, it is unlikely that you’ll see
exactly 5. Instead, you might see 3, 4, 6, 7, or 8 molecules. This uncertainty is what we
mean by the subsampling error.
Subsampling statistics provide a lower limit on the measurement error, completely
independent of the instrument used for measurement. Any additional error introduced by
instrumentation would be added on top of this error. In ddPCR in the low concentration
regime, this unavoidable subsampling error is the most significant source of measurement
error. More droplets will not change this error: 200 targets in 20,000 droplets and 200
targets in 100,000 droplets (five wells) will lead to the same subsampling error.