Don't Be Fooled by Randomness: Valid p-Values for Single Molecule Microscopy

The human mind shows extraordinary capability at recognizing patterns, while at the same time tending to underestimate the natural scope of random processes. Taken together, this easily misleads researchers in judging whether the observed characteristics of their data are of significance or just the outcome of random effects. One of the best tools to assess whether observed features fall into the scope of pure randomness is statistical significance testing, which quantifies the probability to falsely reject a chosen null hypothesis. The central parameter in this context is the p-value, which can be calculated from the recorded data sets. In case of p-values smaller than the level of significance, the null hypothesis is rejected, otherwise not. While significance testing has found widespread application in many sciences including the life sciences, it is hardly used in (bio-)physics. We propose here that significance testing provides an important and valid addendum to the toolbox of quantitative (single molecule) biology. It allows to support a quantitative judgement (the hypothesis) about the data set with a probabilistic assessment. In this manuscript we describe ways for obtaining valid p-values in two selected applications of single molecule microscopy: (i) Nanoclustering in single molecule localization microscopy. Previously, we developed a method termed 2-CLASTA, which allows to calculate a valid p-value for the null hypothesis of an underlying random distribution of molecules of interest while circumventing overcounting issues. Here, we present an extension to this approach, yielding a single overall p-value for data pooled from multiple cells or experiments. (ii) Single molecule trajectories. Data from a single molecule trajectory are inherently correlated, thus prohibiting a direct analysis via conventional statistical tools. Here, we introduce a block permutation test, which yields a valid p-value for the analysis and comparison of single molecule trajectory data. We exemplify the approach based on FRET trajectories.