Dynamic Ranges of Detection and Real Time PCR Quantification

Calculation

First of all, let’s assume that a target gene concentration has been estimated together with its relative uncertainty, by applying the Poisson law as explained in the item [Poisson Law application].

Relative Uncertainty

Depending on the target concentration value in the well, the Relative Uncertainty forms a U-Curve which is made of 2 asymptotic curves:

• The sampling error curve, occurring at low target concentrations (on the left side in the [Figure A] below);
• The quantification error curve, occurring at high target concentrations (on the right side in the [Figure A] below).

Sampling Error

The sampling error can be approximated as follows:

CU_sampling∼((z_c)/sqrt(C₀V))

      where V is the total partition volume, C₀ is the well concentration, and z_c = 1.96 for a confidence level of 95%.

• Note that, whatever the total number of partitions N and the confidence level z_c the relative uncertainty is always minimized at p/N∼79.7, which corresponds to the white point lying on the U-Curve in the [Figure 1] above.

Minimal & Maximal Limits of Detection

The Minimal & Maximal Limits of Detection are represented by 2 vertical lines framing the U-Curve:

• The Minimal Limit of Detection LODminLODmin at 95% (left vertical dotted line in the [Figure 1] above) is the smallest target concentration in the well for which probability of having at least 1 positive partition is more than 95%. If the Limit of Blank is zero, we have:

LOD_min = 3/V

• The Maximal Limit of Detection LOD_max at 95% (right vertical dotted line in the [Figure A] above) is the highest target concentration in the well for which probability of having at least 1 negative partition is more than 95%) for N ranging from 10,000 to 1,000,000:

LOD_max∼10 N/V

• The Dynamic range of Detection DrD at 95% is the number of decades from LOD_min to LOD_max at 95%. If the Limit of Blank is zero, we have:

DrD∼log10(N)+0.5

• The Minimal & Maximal Limits of Quantification are defined with respect to a maximal relative uncertainty U_max which is considered as acceptable for the current digital PCR experiment:
  • The Minimal Limit of Quantification \(LOQ_{min}\) at 95% is the smallest target concentration in the well for which the relative uncertainty at 95% is smaller than U_max .Its value is given by the first intersection point of the 95% U-Curve and the horizontal line y = U_max (which corresponds to the blue point lying on the U-Curve in the [Figure 1] above).
  • The Maximal Limit of Quantification LOQ_max at 95% is the highest target concentration in the well for which the relative uncertainty at 95% is larger than U_max Its value is given by the second intersection point of the 95% U-Curve and the horizontal line y = U_max (see the [Figure 1] above).

Dynamic Range of Quantification

Finally, the Dynamic range of Quantification DrQ associated with an acceptable uncertainty value U_max is given by this formula:

DrQ(U_max) = LOQ_max(U_max) − LOQ_min(U_max)

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