Autocorrelation curve

Pigure 8.8a and b, respectively, show fluorescence autocorrelation curves of R6G in ethylene glycol and R123 in water at 294.4 K. The solid lines in these traces are curves analyzed by the nonlinear least square method with Eq. (8.1). Residuals plotted on top of the traces clearly indicate that the experimental results were well reproduced by the... 

Figure 8.8 Typical fluorescence autocorrelation curves of R6G in ethylene glycol (a) and R123 in water (b) without the NIR laser light with calculated curves (solid line) based on Eq. (8.1) and residuals. Fluorescence autocorrelation curves of R6G in ethylene glycol (c) and R123 in water (d) under irradiation of the NIR laser at several powers up to 240 mW. The inset of Figure 8.8d shows a magnified view of a partofthe figure enclosed by a rectangle.

Figure 8.12 Typical fluorescence autocorrelation curve (gray closed circles) of the CdTe quantum dots with 4.6 nm diameter in water with a calculated curve (solid line) based on Eq. (8.1) (a) and based on Eq. (8.3) (b). Residuals are also indicated at the top of each trace.

Figure 8.13 Autocorrelation curves for the CdTe quantum dots with diameter 4.9 nm at the excitation laser power from 10-200 XW (a). Comparison of the shapes of these autocorrelation curves by normalization (b).

Fig. Bll.2.1. Autocorrelation curves for Rhodamine 6G and various micelles loaded with ODBR (reproduced with permission from Hink and Visser3 ).

Figure 3. Autocorrelation curves (bold continuous lines) of the mean energy fluctuation of total and potential energy for mode m, and their corresponding exponential and damped oscillatory fits (thin dotted lines).

Setup and principle of FCS and FCCS have been reviewed extensively previously [12,13]. The technique is based on the statistical analysis of equilibrium fluorescence fluctuations induced by, e.g., the d3mamics of fluorescent molecules in a tiny observation volume. By correlating these fluctuations with itself at a later time r, an autocorrelation curve is obtained, which can be fitted to an appropriate model function to extract the characteristic time scales of the system. The two basic parameters of a FCS autocorrelation curve are the decay time, reflecting time scales of molecules dynamics, and the amplitude, indicating the average number of particles in the detection volume. 

Autocorrelation curves for GFP PAR-2 and NMY-2 GFP on the cortex are depicted in Fig. 7.3. The peaks in the autocorrelation curve correspond to the scan beam returning to the same measurement volume after T = l/300s and form the autocorrelation at the same location after each cycle. The diffusion behavior of GFP PAR-2 differs from that of NMY-2 GFP on the cortex. Free two-dimensional diffusion cannot describe the behavior of GFP PAR-2... 

Fig. 7.3. Autocorrelation curves from sFCS measurements of GFP PAR-2 (a) and NMY-2 GFP (b) on the cortex. Peak amplitudes are denoted by Mack dots...

Imaging of the labeled embryos displayed the known distribution of the polarity involved protein PAR-2 and the actomyosin cortex protein NMY-2 during different stages of development. FCS measurements in the cytoplasm yielded autocorrelation curves for GFP PAR-2 with a diffusive or subdiffu-sive behavior. The diffusion coefficient for NMY-2 GFP is smaller, indicating much slower diffusion. The autocorrelation functions of NMY-2 GFP exhibit a sharp decay of the autocorrelation function, suggesting contributions of directed flow. Comparison of the diffusion coefficient of PAR-2 and NMY-2 with a reference protein of similar size in the cytoplasm indicates that both proteins are part of a larger complex or multimerize (data not shown). 

These two extreme models cannot be distinguished from a poor autocorrelation curve with a logarithmic time scale. Conventional analyses for cases with anomalous diffusion use alternative types of equation with fractal consideration with an exponent on D or t as... 

Both equations are useful to obtain well-defined D values in each experiment based on a fitting method. Although we understand that the form in Eq. (33.9) is more general, the numerical data from FCS measurement is not sufficient to obtain the full lineshape of D(t) in Eq. (33.9). Seki et al. obtained an analytical solution of autocorrelation curves for D(L) in a step function [39]. They proved that the solution lineshape is different from that of normal diffusion with a non-linear least square algorithm if the deviation from Eq. (33.17) is too small. Even in this case of moderate anomalous diffusion, the observed value of D changes sensitively,depending on f or I. 

Autocorrelation curves of the afterpulsing are shown in Fig. 6.50. The afterpulsing is not very strong, but extends over a period of more than 10 ps. 

In the experiments described below, FCS measurements were performed for varying concentrations of ORB added to the studied solution of micelles. The obtained autocorrelation curves were fitted to the function, assuming the presence of two types of fluorescent particles (free probe and labeled micelles) characterized... 

Data analysis. In the analysis of the measured autocorrelation curve, an inverse Laplace transformation (ILT analysis) was performed employing the algorithm REPES [28] to obtain the distribution of relaxation times. This program is similar to... 

One of the predominant sources of fluctuations in addition to diffusion in PCS is from intersystem crossing to the lowest excited triplet state of the fluorophore [38]. Correlations due to triplet crossing tend to be dominant at very short lag times in comparison with the part of the autocorrelation curve dominated by diffusion (see figures 2.9 and 2.12). Numerous triplet state studies have been conducted principally using the organic dyes rhodamine 6G (R6G) and fluorescein [42,54]. A model for the autocorrelation function of a signal whose fluctuations derive from a combination of diffusion and triplet crossing has been developed [54],... 

Figure 2.14 Autocorrelation curves calculated for the fluorescent dye rhodamine 6G in water at different concentrations of potassium iodide. Reprinted from Widengren, etal., Fluorescence correlation spectroscopy of triplet states in solution—a theoretical and experimental stud /. Journal of Physical Chemistry99 (1995) 13368-13379 with permission from the American Chemical Society.)...

The second method to estimate the standard deviation of an autocorrelation curve is by analysis of a series of consecutively measured autocorrelation curves [37] and is given by. 

Figure 5.2 Example of the experimental procedure, (a) Autocorrelation curves for beacon (o) and control ( ) at r = 45°C, 0.2 M NaCl. Both beacon and control have loops of 21 Yresidues, (b) Ratio of the two curves...

Just as for any other fluorescence microscopy technique, the choice of the fluorescent probe is of significant importance for PCS. Drops in the autocorrelations curves can occur as a result of photophysical and photochemical processes. In particular, the contribution of saturation effects and triplet blinking has been investigated [97, 98] and the rates of intersystem crossing and triplet decay as well as the excitation cross section of fluorophores could be determined [12]. In addition, antibunching is determined by the photophysics of the fluorophore. Therefore, the choice of appropriate dyes is essential to obtain meaningful results. Apart from that, the fluorescent probe should also serve as a selective label to... 

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