Some draft notes to support design and analysis for upcoming experiments.
We would like to use BCoV as a spike-in to measure the recovery efficiency during sample processing through NA extraction. We have a solution of BCoV for which we do not know the concentration (the spike-in stock solution). We can measure BCoV using qPCR. But we do not have a standard available (which would be required to estimate the absolute concentration of BCoV). Nevertheless, we can estimate recovery efficiency by estimating the concentration of BCoV in the extraction elutant relative to the concentration in the spike-in stock solution. I now spell this out in detail.
Let \(R\) be the recovery efficiency, which I define as the fraction of BCoV gene copies from the sample that are in the elutant, or \[\begin{align} R = \frac{\text{copies in elutant}}{\text{copies in sample}}. \end{align}\] Our goal is to experimentally estimate \(R\).
Let \(s\) be the concentration of BCoV target gene in the spike-in stock solution in gene copies per mL. Let \(v\) be the volume of spike-in solution added to the (raw) sample. Let \(V_0\) be the volume of the sample. A total of \(sv\) gene copies are added to sample, resulting in a concentration of the BCoV target gene in the spiked sample of \(sv/V_0\).
Let \(V_1\) be the volume of the extraction elutant. Let \(C_1\) be the absolute concentration of BCoV (in gene copies per mL) in the elutant and \(c_1\) be the concentration relative to \(s\), so that \(C_1 = c_1 s\). We use qPCR to measure the extraction elutant of the sample; let \(q\) be the resulting Cq value.
When performing our qPCR measurements of BCoV, include a triplicate serial dilution of the BCoV spike-in solution, which we will use to create a standard curve (SC) for BCoV that relates the Cq values of the dilution samples to the relative concentration (concentation relative to the concentration \(s\) of the undiluted sample). We will use the SC to convert the measured Cq values for our extractions to relative concentrations, giving an estimate of the relative concentration \(\hat c_1\).
The recovery efficiency equals the copy number in the elutant (\(c_1 s V_1\)) divided by what we spiked into the sample (\(s v\)),
\[\begin{align} R = \frac{c_1 s V_1}{s v} = \frac{c_1 V_1}{v}. \end{align}\]
Note that the unknown factor \(s\) cancels, allowing us to estimate recovery efficiency from known (estimated) quantities,
\[\begin{align} \hat R = \frac{\hat c_1 V_1}{v}. \end{align}\]