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Optics Letters

A fast, flexible algorithm for calculating correlations in Fluorescence Correlation Spectroscopy

Ted A. Laurence, Samantha Fore, Thomas R. Huser

Published Oct 13, 2005• 1 citation
OpenAlex

Abstract

A new algorithm is introduced for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The correlation is first rewritten as a counting operation on photon pairs. For each photon, the contribution to the correlation function for each subsequent photon is calculated for arbitrary bin spacings of the correlation time lag. By retaining the bin positions in the photon sequence after each photon, the correlation can be performed efficiently. Example correlations for simulations of FCS experiments are shown, with comparable execution speed to the commonly used multiple-tau correlation technique. Also, wide bin spacings are possible that allow for real-time software calculation of correlations even for high count rates ({approx}350 kHz). The flexibility and broad applicability of the algorithm is demonstrated using results from single molecule photon antibunching experiments.

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Fast, flexible algorithm for calculating photon correlations

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We introduce a new algorithm for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The algorithm is based on rewriting the correlation as a counting operation on photon pairs and can be used with arbitrary bin widths and spacing. The flexibility of the algorithm is demonstrated by use of FCS simulations and single-molecule photon antibunching experiments. Execution speed is comparable to the commonly used multiple-tau correlation technique. Wide bin spacings are possible that allow for real-time software calculation of correlations, even for high count rates.

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Laser Physics•Jul 29, 2009•25 citations
A new algorithm is introduced for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The correlation is first rewritten as a counting operation on photon pairs. For each photon, the contribution to the correlation function for each subsequent photon is calculated for arbitrary bin spacings of the correlation time lag. By retaining the bin positions in the photon sequence after each photon, the correlation can be performed efficiently. Example correlations for simulations of FCS experiments are shown, with comparable execution speed to the commonly used multiple-tau correlation technique. Also, wide bin spacings are possible that allow for real-time software calculation of correlations even for high count rates ({approx}350 kHz). The flexibility and broad applicability of the algorithm is demonstrated using results from single molecule photon antibunching experiments.
We introduce a new algorithm for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The algorithm is based on rewriting the correlation as a counting operation on photon pairs and can be used with arbitrary bin widths and spacing. The flexibility of the algorithm is demonstrated by use of FCS simulations and single-molecule photon antibunching experiments. Execution speed is comparable to the commonly used multiple-tau correlation technique. Wide bin spacings are possible that allow for real-time software calculation of correlations, even for high count rates.
The formation of protein complexes with other proteins and nucleic acids is critical to biological function. Although it is relatively easy to identify the components present in these complexes, it is often difficult to determine their exact stoichiometry and obtain information about the homogeneity of the sample from bulk measurements. We demonstrate the use of single molecule photon-pair correlation spectroscopy to distinguish between discrete numbers of molecules in biological complexes. Fluorescence photon antibunching is observed from a single molecule by employing time-correlated single photon counting in combination with a Hanbury-Brown and Twiss coincidence setup. In addition, pulsed laser excitation and time-tagged time-resolved data collection allow for the measurement of photon arrival times with nanosecond time resolution. The interphoton time distribution between consecutively arriving photons can be calculated and provides a measure of the second-order temporal correlation function. Analysis of this function yields an absolute measure of the number of molecules, N, present in a given complex. It is this ability to measure N that renders this technique powerful for determining stoichiometries in complex biological systems at the single molecule level. We investigate the counting efficiency and statistics of photon antibunching of specifically designed biological samples labeled with multiple copies of the same fluorescent dye and derive conclusions about its use in the analytical evaluation of complex biological samples.
We present an optical technique, called AB/FCS-fingerprinting, capable of characterizing fluorophore independence in aqueous solution using two-photon excitation microscopy and time-correlated single photon counting. Fluorescence correlation spectroscopy (FCS) is used to monitor fluctuations in the intensity of emissions. Auto- or cross-correlation analysis of these fluctuations can measure the average number of fluorescent molecules in an aqueous sample. Photon antibunching (AB) is observed from single quantum entities, which can emit only one photon at a time. By recording the number of coincident photons detected as a function of time between photon detections, AB analysis is used to determine the number of independent emitters in a sample. In AB/FCS-fingerprinting, the number of independent emitters in a sample is compared with the average number of fluorescent molecules in the same sample using a microscope that can be rapidly reconfigured to measure either AB or FCS from serial dilutions of a florescent sample. Since the number of fluorescent molecules is not necessarily equal to the number of independent emitters, a comparison of these values can provide insight into the independence of fluorophores in molecular assemblies. We validated this technique by measuring AB/FCS-fingerprinting of serial dilutions of mVenus, mNeonGreen, and an organic fluorophore, Alexa-Fluor-488. Experimental results were in good agreement with Monte-Carlo antibunching simulations for a single quantum emitter and with the predictions of a zero-truncated Poisson distribution model for photon antibunching from monomeric fluorophores in solution.
Correlation functions are nowadays routinely computed using time-tagged photon information instead of a hardware autocorrelator. The algorithm developed by Laurence et al. [ Opt. Lett. 31 , 829 ( 2006 ) 10.1364/OL.31.000829 ] is a powerful example. Despite its ease of implementation and fast computation process, it presents a prevalent noisy feature at the short time-lag range when computed on commonly used logarithmically spaced bins. We identified that arbitral logarithmic spacing produces the mismatch between the edges of generated bins and acquisition frequency, resulting in an aliasing artifact at the short time-lag range of the correlation function. We introduce a binning method that considers the acquisition frequency during the bin generation. It effectively eliminates the artifact and improves the accuracy of the autocorrelation. Applying the binning method herein can be particularly crucial when one extracts photophysical processes from fluorescence correlation spectroscopy or the diffusion coefficient of nanoparticles from dynamic light scattering at the time range below 10 −5 s lag time.
We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state lifetime, even in the limit of very low photocounting rates. The method derives from a simple relation between the fluorescence spectral dynamics of a single radi-ating dipole and its fluorescence intensity correlations at the outputs of a continuously scanning Michelson interferometer. These findings define an approach to investigate the fast fluorescence spectral dynamics of single molecules and other faint light sources beyond the time-resolution capabilities of standard spectroscopy experiments.
Acquisition of quantitative information from microscopic biological samples is highly desirable in the context of the emerging field of systems biology. We derive a statistical approach to estimate the number of fluorescent molecules in the observation volume based on a confocal microscope for single-molecule detection. The method employs ps-pulsed laser sources for excitation and time-correlated single-photon counting with 4 avalanche photon diodes (APDs) for detection of individual photons. The feasibility for estimating the number of molecules is shown based on simultaneous emission and detection of multiple photons (photon-antibunching) under realistic experimental conditions. In theory, it should be possible to estimate the number of molecules with errors of less than 1% by using novel photo-stabilizing agents. The proposed method puts into perspective its application for high-resolution microscopy without the need for photo-switching or photo-activation of fluorescence dyes.