## Introduction

FCS is often used to study dynamic processes of molecules in solution. However, experimental factors can seriously influence the analysis of such FCS data records. Typical factors include artifacts of the measuring system, stray light, triplet states of the fluorophore, impurities or the background of the sample. As these factors are not constant, but vary greatly from sample to sample, the analysis of an FCS experiment can often be problematic and prone to errors. It is therefore desirable to clean the data records according to physical laws before performing a specific data analysis.

One physical value that follows a clear mathematical distribution probability is the fluorescence decay. The method of Fluorescence Lifetime Correlation Spectroscopy (FLCS) described here uses the fluorescence decay behavior to clean the FCS datasets. FLCS can be used, for instance, to eliminate artifacts of the measuring system or separate data records from a mixture of several fluorophores, which can then each be analyzed individually. This type of evaluation yields clear and reproducible results, even for the smallest fluorophore concentrations.

## Single molecule spectroscopy

Introduced in the seventies, the principle of Fluorescence Correlation Spectroscopy [1–3] describes the study of fluorescing single molecules in solution in an ellipsoidal volume. Combined with confocal microscopy [4], FCS has become an important measuring method for the study of molecular dynamics and concentrations.

In an FCS experiment, the typically continuous excitation light is focused onto a point in the tissue or solution. By using a confocal set-up, molecules within a volume of approximately 0.3 femtoliters can then be observed (Figure 1A). This volume is determined by the excitation and emission wavelength, the objective and the size of the confocal pinhole.

The experiment is essentially based on Brownian motion: Molecules diffuse through the detection volume, are excited and emit light. The subject of measurement is the thereby generated temporal change in fluorescence intensity (Figure 1B), which may, however, be influenced by other photophysical processes as well.

The first step in analyzing FCS data is to calculate an autocorrelation from the measured fluorescence intensities. Then, a suitable model function with variable parameters is fitted to the obtained autocorrelation function (ACF), from which, for example, the fluorophore concentration or the diffusion constant can be derived. The challenge when analyzing the ACF is finding a suitable model function with variable parameters that describes not only the actual properties of the fluorophores, but also the influencing experimental factors. As each additional influence requires at least one additional parameter, the complexity and therefore the tendency of the analysis to contain errors is increased. If a sample also has more than one fluorophore, the diffusion behavior of each fluorophore influences the resulting ACF, which is not a case of a simple linear combination, but a complex superposition of the individual signals.

## Different methods

Over the years, various versions of FCS have been established to deal with the problems associated with ACF analysis. All these methods have the aim of cleaning the data of background artifacts and allowing the simultaneous study of several fluorescing molecules.

The most commonly used method is fluorescence cross-correlation spectroscopy (FCCS), in which the fluorescence is simultaneously recorded with two detectors [11]. Detector afterpulsing, one of the most common experimental artifacts, for example, can be eliminated with FCCS. This is a phantom pulse occurring during the measurement caused by feedback in the detector. The interference signal is removed by distributing the emitted photons in equal parts onto two detectors and then calculating a cross correlation from the two data records.

FCCS also allows the separation of fluorophores with different spectral emission wavelengths, thereby enabling separate data analysis for determining diffusion constants and concentration. Besides this, cross correlation of the two signals provides information on a potential interaction of the molecules under investigation. However, the complexity of the experimental setup should not be underestimated. The detection volume of the separately detected fluorophores has to overlap 100 %, which is no trivial matter due to the dependence of the detection volume sizes on the excitation and emission wavelength. Also, absolute spectral separation of the fluorescence can frequently not be achieved, which in turn makes data record analysis more difficult.

Other approaches separate the data mathematically, for instance on the basis of a difference in the diffusion constant. However, the diffusion constant of the molecules must differ by at least a factor of 1.6 [5] to obtain useful results. Therefore, this measuring method does not allow simple reading of the molecule concentration or diffusion constant, but is based on highly complex mathematical fitting of the ACF, including assumptions that are generally impossible to prove by experiment and therefore extremely error-prone.

## Improvements through time-correlated single photon measurement

The above problems can be circumvented with the method of Fluorescence Lifetime Correlation Spectroscopy. In an FLCS experiment, not only the time change of the fluorescence intensity, but also the specific fluorescence decay behavior of the fluorophores after a pulsed excitation is measured and then used for cleaning the FCS data records. Instead of making assumptions for the analysis of the measurement data, FLCS is based on a purely mathematical evaluation method.

Basically, FLCS is a combination of FCS and Time-Correlated Single Photon Counting (TCSPC), which is the most suitable method for measuring the fluorescence decay behavior of single molecules. TCSPC requires a pulsed excitation laser and single photon-sensitive detectors.

## Experimental principles

For FLCS experiments, the TCSPC measurement is performed in a special "time-tagged time-resolved" (TTTR) measurement mode. Here, two mutually independent times are measured for each detected photon: firstly, the time between the onset of the excitation pulse and the arrival of the detector signal (microscopic arrival time) with picosecond resolution, and secondly the time from the beginning of the experiment to the registration of the particular photon (macroscopic arrival time).

The microscopic arrival time is used to produce a TCSPC histogram that describes the particular fluorescence decay behavior. The macroscopic arrival time can be used just like in any classic FCS experiment to calculate the change in the fluorescence intensity over time and determine the diffusion constant and concentration through the calculation of an ACF.

For an FCS experiment in which a fluorophore mixture is subject to continuous excitation, there is a certain probability for each single photon detected that it was emitted by Fluorophore A or Fluorophore B. This probability is constant in time, because there is no defined moment of excitation. FLCS is based on the simple fact that pulsed excitation creates a specific excitation time, meaning that the detection probability of a photon emitted by Fluorophore A or Fluorophore B changes in time (Figure 2A). Photons detected shortly after excitation are more probably emitted by the faster decaying fluorophore (shorter lifetime), whereas late photons are more likely to be emitted by the slower decaying fluorophore (longer lifetime). On the basis of the time-dependent detection probability, a mathematical method can be applied to set up statistical probability filters that assign a probability of origin to each photon arrival time [10] (Figure 2B).

To set up a suitable distribution filter, corresponding histograms of the constituent components are required besides the TCSPC histogram of the measurement itself. If, for example, one wants to separate fluorophores, TCSPC histograms of the pure fluorophores are needed. To remove the stray light component from the measurement, an additional measurement without the fluorophores is necessary. The distribution filter then assigns to each photon arrival time the probability with which the photon originates from the particular component. This data separation therefore takes place at single-photon level. The separated data records can then be analyzed independently of each other by calculating an ACF.

This type of statistical analysis is not only applicable to the emissions of the examined fluorophores, but is equally suitable for describing artifacts of the measuring system, such as dark count rate and afterpulsing of the detectors (Figure 3A). Literature on the subject already contains examples of the successful splitting of a measurement data record into as many as 4 sub-components [7].

In general, it is important to note that FLCS uses the entire fluorescence decay behavior for separation and not the average fluorescence lifetime that can be determined from it. Fluorophores or components can be mathematically separated from each other if they show a different profile in the TCSPC histogram.

## Sample applications

The functionality, effectiveness and stability of the FLCS method has been proved in an extremely wide range of applications, not only *in vitro* but also *in vivo*. Even in simple FCS experiments analyzing only extremely small concentrations of a fluorescent dye, the use of FLCS leads to greater precision and reproducibility in the measurement of molecule concentration and diffusion speed. Figure 3 shows an FLCS measurement of the dye Atto655, dissolved in ethylene glycol. Because of the large stray light component in low-molar solutions, only about 60 % of the detected photons originate from the dye, which has a negative effect on the determined fluorophore concentration. In the comparison of the autocorrelation curves with and without lifetime-filtered data analysis (Figure 3C) it can be seen that by eliminating the measurement background, which contains stray light and system artifacts (Figures 3Aand 3B**,** red line), a far smaller number of molecules is detected, which constitutes a good approximation of the set molecule concentration (10 pM) of the solution. The method has also been applied with great success for *in vivo *cell measurements, in which FLCS was used to remove flavinoids and NADH molecules present in the cell from the data record [8].

The laboratory of Maïté Coppey-Moisan at the University of Paris Diderot in France was recently able to demonstrate that it is also possible to remove spectral crosstalk of the GFP in the mCherry detection channel with the fluorescent proteins GFP and mCherry in an *in vivo* FCCS experiment [9]. Here, the GFP was excited with a pulsed laser and the mCherry with a continuous wave laser. This enabled a protein interaction study without mathematical fitting of the ACF.

## Summary

FLCS is a sophisticated method for determining molecular concentrations and dynamics. Due to its physical law, the fluorescence decay behavior can be described with a statistic distribution probability, which is useful for separating the measurement data and cleaning the FCS data records of artifacts. FLCS thus enables more precise and reproducible determination of molecular concentration and diffusion times. This in turn leads to a comparability of the generated data between different measurement systems that was not possible before now.

## References

- Magde D, Elson E, Webb W: Thermodynamic Fluctuations in a Reacting System – Measurement by Fluorescence Correlation Spectroscopy. Physical Review Letters 29:11 (1972) 705–708, American Physical Society; DOI: 10.1103/PhysRevLett.29.705
- Elson EL, Magde D: Fluorescence correlation spectroscopy. I. Conceptual basis and theory. Biopolymers 13:1 (1974) 1–27; DOI: 10.1002/bip.1974.360130102
- Magde D, Elson EL, Webb WW: Fluorescence correlation spectroscopy. II. An experimental realization. Biopolymers 13:1 (1974) 29–61; DOI: 10.1002/bip.1974.360130103
- Rigler R, Widengren J: Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy. Bioscience 3 (1990) 180–183.
- Meseth U, Wohland T, Rigler R, Vogel H: Resolution of fluorescence correlation measurements. Biophysical Journal 76:3 (1999) 1619–31; DOI: 10.1016/S0006-3495(99)77321-2
- Kapusta P, Wahl M, Benda A, Hof M, Enderlein J: Fluorescence lifetime correlation spectroscopy. Journal of Fluorescence 17:1 (2007) 43–8; DOI: 10.1007/s10895-006-0145-1
- Rüttinger S, Kapusta P, Patting M, Wahl M, Macdonald R: On the resolution capabilities and limits of fluorescence lifetime correlation spectroscopy (FLCS) measurements. Journal of Fluorescence 20:1 (2010) 105–14, DOI: 10.1007/s10895-009-0528-1
- Gärtner M, Mütze J, Ohrt T, Schwille P: Fluorescence lifetime correlation spectroscopy for precise concentration detection in vivo by background subtraction. Proceedings of SPIE 7368 (2009) 73681V–73681V-7; DOI: 10.1117/12.831572
- Padilla-Parra S, Audugé N, Coppey-Moisan M, Tramier M: Dual-color fluorescence lifetime correlation spectroscopy to quantify protein-protein interactions in live cell. Microscopy Research and Technique 74 (2011) 788–793; DOI: 10.1002/jemt.21015
- Böhmer M, Wahl M, Rahn H-J, Erdmann R, Enderlein J: Time-resolved fluorescence correlation spectroscopy. Chemical Physics Letters 353:5–6 (2002) 439–445; DOI: 10.1016/S0009-2614(02)00044-1.
- Kohl T, Heinze KG, Kuhlemann R, Koltermann A and Schwille P: A protease assay for two-photon crosscorrelation and FRET analysis based solely on fluorescent proteins. Proc Natl Acad Sci USA 99 (2002) 12161–12166.

**This article has originally been published in German in: BioPhotonik 2 (2011) 42–45.English reprint with kind permission from AT-Fachverlag GmbH**