Hello all,
I'm looking to calculate the probability to have viral plaques appear in lower dilutions but not in the previous dilution.
We perform serial 10 fold dilutions (0.2 ml into 1.8ml media) in triplicate wells of a 6-well plate. The sample has an unknown amount virus and the following data was observed:
10^-3 - Too numerous to count; 10^-4 - 11, 12, 26; 10^-5 - 0 x 3; 10^-6 - 0, 1, 0
Can we assume this plaque in 10^-6 is statistically probable, or is it likely due to technical error?
A probability of having plaques at 10^-6 after having nothing in previous dilution and just 13 average in 10^-4 is low and most likely due to the tech error
It may not be due to tech error has I have seen this result many times over the years. I was often dealing with very low PFU/ml concentrations so these types of effects crop up even more. If the 10^-4 dilution has ca. 10 PFU then the next dilution would expect that there would be only ca. 1 PFU so the effects of the low concentration and the randomness of sampling can produce those effects.
There is a discreet probability associated with sampling from liquids containing very low numbers of viral particles and whether the sample that is taken will actually contain infectious particles. That probability is calculated by P=[(V-v)/V]^n, where V is the total volume, v is the sample volume, and n is the number of virus particles distributed through V. So, if you have 2 ml of a dilution that contains 13 PFU total and sample out 0.2 ml, that 0.2 ml has a 25% chance of containing 0 PFU. We don't know what volume of each dilution was added to the monolayer, but that would represent an additional sampling probability factor. So, it's statistically possible to happen and I do suspect that it happens in some virus samples more than others, perhaps due to stickiness issues with the pipette or pipette tips used. If it is seen routinely between assays then there might be other technical or virological factors at play.
Practically speaking, I would try to re-focus the dilution series on dilutions that give plaque numbers from wells that are not too crowded (and PFU are underestimated), and not too low, say between 1 and 5 plaques, where sampling probabilities really affect your final PFU/ml calculation (such as having 1 plaque or 3 plaques means a final calculation of 1 x 10^6 or 3 x 10^6 PFU/ml--a 3-fold range). If 4- or 5-fold dilutions are worked in, then it is possible to have a nicer series of plaque #'s that give a stronger sense of the actual starting concentration. It might mean 2 or 3 more dilutions per sample, but then the effects of sampling probability are much reduced and a single assay will more probably yield accurate measurements of all of the samples.
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