General methods for quantitative interpretation of results of digital variable-volume assays

In digital assays, devices are typically considered to require precisely controlled volumes since variation in compartment volumes causes biases in concentration estimates. To enable more possibilities in device design, we derived two methods to accurately calculate target concentrations from raw results when the compartment volume may vary and may not follow known parametrically described distributions. The Digital Variable Volume (dvv) method uses volumes of ON compartments (those with positive signals) and the total sample volume, while the Digital Variable Volume Approximation (dvva) method uses the number of ON compartments, the total number of compartments, and a set of separately measured volumes. We verified the trueness of the dvv and dvva methods using simulated assays where volumes followed an empirical distribution (based on measured droplet volumes) and well known distributions with a wide range of standard deviations. We applied both methods to digital PCR experiments with polydisperse volumes, and also derived equations to estimate standard errors and limits of detection. The dvv method allows the compartment volume to follow any distribution in each assay run, the dvva method allows for quantification without in-assay volume measurements, and both methods potentially enable new designs of digital assays.