Single-molecule localization microscopy has the ability to measure spatial proximity between individual molecules with tens of nanometers precision. Extracting meaningful biological results, however, requires fully characterizing the distribution of molecular behaviors, which in turn, necessitates analyzing large numbers of individual measurements. Making large numbers of replicate measurements in a single imaging session has been made possible in recent years by large area detectors that afford an ultrawide field-of-view as well as fast frame rates. A remaining barrier to ultrawide-field imaging is that optical aberrations become pronounced when imaging far away from the central optical axis, which can compromise the precision and accuracy of point-spreadfunction (PSF) fitting across the field-of-view. Here, we present a computational phase retrieval routine based on vectorial PSF models to account for the spatially-variant aberrations in two color channels of a 3D singlemolecule localization microscope. By computationally correcting the aberrations during data post-processing, we are able to localize emitters in an ultrawide filed-of-view with improved precision and accuracy compared to approaches based on analytical PSF models. The use of a spatially-variant PSF model enables accurate emitter localization in x, y and z over the entire field-of-view, so that the reconstructed super-resolution images and singlemolecule trajectories accurately reproduce the relative spatial arrangement among all localized emitters.

Fluorescence correlation spectroscopy (FCS), is a widely used tool routinely exploited for in vivo and in vitro applications. While FCS provides estimates of dynamical quantities, such as diffusion coefficients, it demands high signal to noise ratios and long time traces, typically in the minute range. In principle, the same information can be extracted from microseconds to seconds long time traces; however, an appropriate analysis method is missing. To overcome these limitations, we adapt novel tools inspired by Bayesian non-parametrics, which starts from the direct analysis of the observed photon counts. With this approach, we are able to analyze time traces, which are too short to be analyzed by existing methods, including FCS. Our new analysis extends the capability of single molecule fluorescence confocal microscopy approaches to probe processes several orders of magnitude faster and permits a reduction of photo-toxic effects on living samples induced by long periods of light exposure.

One way to achieve spatial resolution using fluorescence imaging—and track single molecules—is to use wide-field illumination and collect measurements over multiple sensors (camera pixels). Here we propose another way that uses confocal measurements and a single sensor. Traditionally, confocal microscopy has been used to achieve high temporal resolution at the expense of spatial resolution. This is because it utilizes very few, and commonly just one, sensors to collect data. Yet confocal data encode spatial information. Here we show that non-uniformities in the shape of the confocal excitation volume can be exploited to achieve spatial resolution. To achieve this, we formulate a specialized hidden Markov model and adapt a forward filtering-backward sampling Markov chain Monte Carlo scheme to efficiently handle molecular motion within a symmetric confocal volume characteristically used in fluorescence correlation spectroscopy. Our method can be used for single confocal volume applications or incorporated into larger computational schemes for specialized, multi-confocal volume, optical setups.

Fluorescence time traces are used to report on dynamical properties of molecules. The basic unit of information in these traces is the arrival time of individual photons, which carry instantaneous information from the molecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus, it is theoretically possible to monitor molecular dynamics at such timescales from traces containing only a sufficient number of photon arrivals. In practice, however, traces are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-they are collected and temporally autocorrelated over several minutes. So far, it has been impossible to analyze dynamical properties of molecules on timescales approaching data acquisition without collecting long traces under the strong assumption of stationarity of the process under observation or assumptions required for the analytic derivation of a correlation function. To avoid these assumptions, we would otherwise need to estimate the instantaneous number of molecules emitting photons and their positions within the confocal volume. As the number of molecules in a typical experiment is unknown, this problem demands that we abandon the conventional analysis paradigm. Here, we exploit Bayesian nonparametrics that allow us to obtain, in a principled fashion, estimates of the same quantities as FCS but from the direct analysis of traces of photon arrivals that are significantly smaller in size, or total duration, than those required by FCS.

Fluorescence time traces are used to report on dynamical properties of biomolecules. The basic unit of information drawn from these traces is the individual photon. Single photons carry instantaneous information from the biomolecule, from which they are emitted, to the detector on timescales as fast as microseconds. Thus from confocal microscope it is theoretically possible to monitor biomolecular dynamics at such timescales. In practice, however, signals are stochastic and in order to deduce dynamical information through traditional means-such as fluorescence correlation spectroscopy (FCS) and related techniques-fluorescence signals are collected and temporally auto-correlated over several minutes. So far, it has been impossible to analyze dynamical properties of biomolecules on timescales approaching data acquisition as this demands that we estimate the instantaneous number of biomolecules emitting photons and their positions within the confocal volume. The mathematical structure of this problem demands that we abandon the normal ("parametric") Bayesian paradigm. Here, we exploit novel mathematical tools, namely Bayesian nonparametrics, that allow us to deduce in a principled fashion the same information normally deduced from FCS but from the direct analysis of significantly smaller datasets starting from individual photon arrivals. We discuss the implications of this method in helping dramatically reduce phototoxic damage on the sample and the ability to monitor out-of-equilibrium processes.