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Fluorescence correlation spectroscopy
Fluorescence correlation spectroscopy (FCS) is frequently used in physical chemistry to gain thermodynamic and kinetic information but also in biochemical, biological and physical research. The underlying reason is that with FCS very fast reactions, e.g. chemical reactions in the time region of a few micro seconds, as well as slow processes, e. g. the diffusion of proteins in living cells, which occur on the milliseconds to seconds time scale, can be monitored simultaneously.
An advantage of FCS compared with other spectroscopic methods is that only a very small amount of fluorescent molecules in a very small detection volume is needed, because with this method small deviations from a pure random (Poisson-) distribution are detected. For the measurement of FCS in living cells this means e. g. that the expression level of the fluorescently labeled protein has to be very low and thus, FCS measurement can be conducted under nearly physiological conditions which increases the significance of this data a lot.
In fluorescence correlation spectroscopy one analyzes the fluorescence fluctuations around a mean value within a characteristic time span to determine kinetic parameters on a molecular level. To this end very low concentrations (nM) and very small measurement volumes (fl) are needed because otherwise either the signals of many particles will be superimposed or the fluorescence light is covered by the background signal, both effectively reducing the fluctuations. Thus, FCS is often measured in a confocal microscope setup. The time domain of the fluctuations (kinetics) to be analyzed can cover several orders of magnitude (picoseconds up to seconds).
The necessary prerequisite for observing processes with FCS is the fact that these events have to influence the fluorescence intensity as seen by the detector in a systematic manner, e. g. induce bright and dark states of the molecule. These processes might be translational diffusion (diffusion of the molecule in and out of the detection volume), photophysical (fluorescence and triplet characteristics), photochemical (photo destruction, quenching) and chemical processes (equilibrium reactions). During the dwell time of the fluorescent molecules to be examined in the detection volume these are excited permanently so that a burst of photons is emitted (figure 2). The diffusion of a molecule through the detection volume can thus be observed by the detection of the hereby generated photons. The experimental data bases are time traces of the fluorescence intensity (detection signals as function of time).
Instruments with FCS capability are either equipped with dedicated hardware correlators or record continuously the photon stream registered by the detectors. In the first case, the experimental setup directly provides a correlation curve that can be analyzed in ChiSurf. Nowadays, both, counting electronics that continuously registers the photon stream as well as hardware correlators with nano-second time-resolution can be programmed to inexpensive FPGAs allowing for inexpensive counting electronics (see: FPGA-correlator and FPGA time to digital converter).
When a photon stream is recorded, this photon stream needs to be correlated to be analyzed by FCS. Raw photon streams can be correlated either by ChiSurf, tttrlib, Kristine, PAM, or other software correlators. Using software correlators as opposed hardware correlators is advantageous, as the photon stream can be filtered before correlation, e.g., to reduce the contribution of aggregates to the correlation curve (see: example).
FCS curves that have either been recorded with hardware correlators, or that have been computed with software correlators can be analyzed in ChiSurf. Like, fluorescence decay curves, FCS curves can be grouped in sets of similar model functions and globally analyzed. Like in TCSPC analyis the posterior distribution of the model parameters can be sampled to provide accurate error estimates.
Critical for accurate error-estimates, is the use of correct weights to calculate noise weighted sum of squared deviations. ChiSurf can either process FCS curves with error estimates for every correlation channel or calculate weights based on the average mean count rate in the detectors and the correlation channel. When using ChiSurf to correlate photon traces, the photon traces are sub-sampled to estimate the uncertainties of the correlation channels as weights.
In the absence of uncertainty estimates, ChiSurf uses the count rates in the two detection channel to estimate the weights for the calculation of a reduced chi2 (sum of uncertainty weighted squared deviations). The FCS curves contain the count rates a third column.
| time | correlation amplitude | Count rates |
|---|---|---|
| x | x | Count rate channel 1 |
| x | x | Count rate channel 2 |
Example:
0.000013596 4.215956672 58.66342588
0.000027192 3.877174447 18.26390096
0.000040788 3.670140866 0
0.000054384 1.622390478 0
0.00006798 3.647555398 0
0.000081576 3.918581193 0
0.000095172 4.016451624 0
If an uncertainty estimate was determined during the correlation, the estimate can be provided in a fourth column. If ChiSurf detects a fourth column, by default the error estimates in the fourth column are used.
| time | correlation amplitude | Count rates | Uncertainty estimates |
|---|---|---|---|
| x | x | Count rate channel 1 | x |
| x | x | Count rate channel 2 | x |
| x | x | x |
Example
0.0000135960 4.2159566719 58.6634258798 0.1173561188
0.0000271920 3.8771744466 18.2639009558 0.1369719319
0.0000407880 3.6701408664 0.0000000000 0.1328885542
0.0000543840 1.6223904783 0.0000000000 0.0939976902
0.0000679800 3.6475553977 0.0000000000 0.0925570969
0.0000815760 3.9185811930 0.0000000000 0.1180750814
0.0000951720 4.0164516241 0.0000000000 0.0998301511
0.0001087680 3.9562236783 0.0000000000 0.1109485817