Pitching Single-Focus Confocal Data Analysis One Photon at a Time with Bayesian Nonparametrics

Abstract

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.

Direct Photon-by-photon Analysis of Time-Resolved Pulsed Excitation Data using Bayesian Nonparametrics

“…As follows from Bayesian logic, the sharper the posterior, the more conclusive (and certain) the estimate. 69,76,79 We first validate our approach on synthetic data where the ground truth is available. We then test our method on experimental data.…”

“…Across all spectroscopic and imaging applications, the photon is the basic unit of information. 69,86 Decoding information directly from single photon arrivals, with as few photons as possible without binning or correlating or other pre-processing of the data, is the main focus of our data-centric analysis strategy. Yet decoding information directly from single photon arrivals presents fundamental model selection problems.…”

“…We have previously exploited the Bayesian nonparametric (BNP) paradigm [65][66][67][68] to analyze single photon arrival traces in order to learn diffusion coefficients from minimal photon numbers drawn from single spot confocal experiments. 10,69 Traditionally, such photon arrivals were analyzed using tools from fluorescence correlation spectroscopy where very long traces were collected and auto-correlated in time. Just as with this the problem at hand, the direct photon-by-photon analysis demanded a different approach as the stochastic number of molecules contributing photons was unknown and an estimate of that number deeply impacted our diffusion coefficient estimate.…”

“…For example, in the case of FCS, if we are to learn diffusion coefficients directly from limited photon arrivals, we must know how to write down a likelihood or, put differently, we must know the number of molecules contributing photons that, in turn, dictate the form for the likelihood 69. As we do not know how many molecules we have, and what the appropriate likelihood should be, we have a model selection problem.…”

Extraction of rapid kinetics from smFRET measurements using integrative detectors

“… 1 – 6 Existing approaches for analyzing smFRET data include FRET efficiency histogram-based methods, although such methods discard the important temporal information encoded in donor and acceptor photon arrival sequences. 4 – 6 , 8 – 10 , 12 , 13 , 16 What is more, FRET efficiency histogram analysis is difficult to generalize beyond two conformational states. 17 In addition, because arbitrary binning is required to construct histograms, such methods often lead to inconclusive or erroneous estimates.…”