Analysis and uncertainty quantification of DNA fluorescence melt data: Applications of affine transformations

Fluorescence-based measurements are a standard tool for characterizing the thermodynamic properties of DNA systems. Nonetheless, experimental melt data obtained from polymerase chain-reaction (PCR) machines (for example) often leads to signals that vary significantly between datasets. In many cases, this lack of reproducibility has led to difficulties in analyzing results and computing reasonable uncertainty estimates. To address this problem, we propose a data analysis procedure based on constrained, convex optimization of affine transformations, which can determine when and how melt curves collapse onto one another. A key aspect of this approach is its ability to provide a reproducible and more objective measure of whether a collection of datasets yields a consistent "universal" signal according to an appropriate model of the raw signals. Importantly, integrating this validation step into the analysis hardens the measurement protocol by allowing one to identify experimental conditions and/or modeling assumptions that may corrupt a measurement. Moreover, this robustness facilitates extraction of thermodynamic information at no additional cost in experimental time. We illustrate and test our approach on experiments of Förster resonance energy transfer (FRET) pairs used study the thermodynamics of DNA loops.