Data registration and selective single-molecule analysis using multi-parameter fluorescence detection

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

“…23 In both algorithms, three parameters are needed to define a burst: the averaging time window, T, the minimum number of photons per window, M, and the minimum number of photons per burst, L.…”

“…These bursts of photons are naturally those we are interested in, and the question arises regarding how to define their beginning and end. Several algorithms have been proposed, based either on time-trace binning and thresholding 26 or interphoton time averaging and thresholding, 23 and, more recently, maximum likelihood statistical analysis. 34 Here, we propose a novel burst detection scheme taking advantage of ALEX, that allows us to separate donor-only and acceptor-only bursts from doubly labeled bursts, as well as to interrupt a burst when one of the dyes bleaches.…”

“…As we have seen, this assumption is incorrect, since the acceptor and donor counts are distributed according to the binomial law (eq 10). In some cases (ε ≪ 1), a binomial law of parameters (ε, N) is well-approximated by a Poisson law of identical mean εN, but in general, this is not the case, as can be seen from the different variances of the two distributions (20) where Π(n|μ) is the Poisson distribution of mean μ (21) If one ignores this limitation, it is possible to proceed formally and note that, for large enough mean values, a Poisson distribution is well-approximated by a γ distribution γ(ν, λ), which is in a sense its extension to noninteger values (22) Using a known property of independent γ distributions A and D of means a and d, the random variable r = A/A + D can be shown to be well-approximated by a β distribution (23) Using a = εS and d = (1 − ε)S and the properties of β distributions, we obtain that the random variable r has a mean and standard deviation approximately equal to (24) This latter value is the estimate of the upper bound to the PRH width proposed by Dahan The next step toward a better understanding of the contribution of shot noise to the PRH was made by Gopich and Szabo, who first presented a complete analysis of the theoretical shape of the PRH using a fixed time bin approach and simple models of excitation profiles. 29 In particular, they obtained theoretical expressions for the standard deviation of the PRH in diverse cases (including two-state model molecules).…”

“…34 Zhang and Yang have compared an approach based on information theory and a standard binning/thresholding method, showing that the two have comparable performance for shorter time bins (down to 100 μs). 34 Although they did not perform comparisons with the time lag based method originally introduced by the Seidel group, 23 it is expected that a similar result will hold in this case, as both rely on thresholding.…”

“…21 If pulsed-laser excitation is used rather than continuous-wave laser excitation, time-correlated single-photon counting (TCSPC) measurements can also provide lifetime information, which, in addition to helping identify the molecular species in a single burst, can also be used to measure FRET efficiency. 22,23 In general, however, the number of photons in a single burst is usually insufficient to perform any time-trace analysis, except in a few rare cases of long bursts. 24 Instead, in smFRET diffusion experiments, quantities are computed at the burst level using all photons in each burst and then histogrammed.…”