MOTIVATION: Many recent advancements in single-molecule localization microscopy exploit the stochastic photoswitching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging, preventing key insight into the cellular structures and processes under observation. RESULTS: Modelling the photoswitching behaviour of a fluorophore as an unobserved continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localizations from a single photoswitching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a direct stochastic optical reconstruction microscopy experiment involving an arbitrary number of molecules. We demonstrate that when training data are available to estimate photoswitching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localizations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein linker for activation of T cells on the cell surface of the T-cell immunological synapse. AVAILABILITY AND IMPLEMENTATION: Software and data available at https://github.com/lp1611/mol_count_dstorm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Coherence is a well established measure of linear dependency between a pair of stationary random processes in the frequency domain. Wavelet coherence measures the linear dependency between a pair of signals in time-scale space and is therefore more suitable for non-stationary processes. Until now it has only been considered in relation to regularly sampled ordinary time-series. Here, for the first time, it is applied to point processes on the real line. We consider smoothing the individual wavelet spectra by averaging over a set of orthogonal Morse wavelets and show that under the assumption of independent Poisson processes the Goodman distribution is appropriate.