Separating Structural Heterogeneities from Stochastic Variations in Fluorescence Resonance Energy Transfer Distributions via Photon Distribution Analysis

Abstract

We establish a probability distribution analysis (PDA) method for the analysis of fluorescence resonance energy transfer (FRET) signals to determine with high precision the originating value of a shot-noise-limited signal distribution. PDA theoretical distributions are calculated explicitly including crosstalk, stochastic variations, and background and represent the minimum width that a FRET distribution must have. In this way an unambiguous distinction is made between shot-noise distributions and distributions broadened by heterogeneities. This method simultaneously and effectively extracts highly resolved information from FRET distributions. The theoretical histograms match the exact profile of histograms generated from constant transfer efficiency experimental data with a chi2 near unity. The chi2 surface suggests an ultimate level of precision with FRET of < 1% of the Förster radius. Distributions of FRET signals in donor-acceptor-labeled DNA were unambiguously identified as being broader than shot-noise variations could explain. A model describing a Gaussian distribution of distances was tested with the PDA method and demonstrated 5 A inhomogeneities due to dye motions. The capability of this method to recover quantitative information from FRET distributions has potential applications for studying molecular conformations and dynamics. Potential sources for artifacts such as acceptor photobleaching, spectrally different observation volumes, and fluctuations of the Förster radius are ruled out.

Shot-Noise Limited Single-Molecule FRET Histograms: Comparison between Theory and Experiments

“…Although rational numbers are dense in the interval [0, 1], the distribution of numbers obtained as a ratio of two integer numbers is not uniform in this interval, as illustrated by the comb distribution of Citing ref 32, "the discrete nature of the distribution leads to features that introduce binning artifacts in the generation of histograms: probability 'spikes' at certain values and probability 'voids' around the spikes". Although histograms were generated in logarithmic scale in ref 32, the same question of how to determine the optimal bin size to generate histograms (in our case, PRH's) occurs in these two approaches.…”

“…Namely, the probability of this to occur is given by the binomial law, with the replacement of E in eq 9 by an unknown parameter ε (10) The value of the parameter ε will be used as an adjustable parameter in the following, but could in principle be calculated from the knowledge of all relevant experimental parameters (leakage, direct excitation, γ factor) as discussed by Antonik et al 32 and in Appendix C.…”

“…47 Antonik et al have investigated the amount of distance fluctuation needed to explain the discrepancy between their smFRET measurements and the shot-noise-only theoretical prediction. 32 Note that this will affect the measured FRET efficiencies (and thus the PRH) only if these different configurations have lifetimes comparable to or longer than the diffusion time (quasi-static distribution of distances). Fluctuations on significantly shorter time scales (<50 μs) would indeed result in complete averaging of the measured FRET efficiency within the diffusion time.…”

“…I D is the donor excitation intensity, is the absorption cross section of the acceptor at the donor excitation wavelength. We can rewrite (32) Finally, following ref 14 (33) where is the absorption cross section of the donor at the donor excitation wavelength.…”

“…First, to avoid having to deal with bursts having different durations, they slice the detected bursts into pieces of equal duration (1 ms) and consider each slice as a new effective burst. The main issue with this treatment is that it reduces the burst size (total number of counts in a burst), therefore increasing the effect of shot noise on the calculated histogram (be it the ratio of donor to acceptor count histogram as in ref 32 or the PRH in this work). Also, as burst durations might not be commensurate to the chosen constant slice duration, a lot of photons will be discarded because they correspond to slices of duration less than 1 ms. A more efficient way would be to look at the burst distribution as a bidimensional one, BSD(S, τ): each burst is characterized not only by its total number of photons S (discrete, integer variable) but also by its duration τ (continuous, real variable).…”