Data Analysis

34 2. Confocal Fluorescence Microscopy and Single Molecule Detection

0 0.1

-1 0

1 -1

0 1 z (µm) r (µm)

0.50 1

-1 0

1 -1

0 1 z (µm) r (µm)

0 0.1

-1 0

1 -1

0 1 z (µm) r (µm)

0 0.1

-1

1 -1

0 1 z (µm) r (µm)

EID

CEF

MDF

Gauss 3D

Fig. 2.3: Excitation Intensity Distribution (EID), Collection Efficiency Function (CEF), Molecule Detection Function (MDF) and its 3D Gaussian approximation. Note that ex-cept for the CEF, the z-axis has been cut at the 1/e² value of its respective maximum. The flat area therefore represents the 1/e² extension of the EID and the MDF respectively.

2.5. Data Analysis 35

For the experiments of chapter 3 a PicoHarp USB-connected TCSPC box (PicoQuant GmbH, Berlin) was used. The F¨orster Resonace Energy Transfer (FRET) experiments of chapter 4 acquisition were done using a TimeHarp (PicoQuant GmbH Berlin) TCSPC PCI-board. The time resolution of the PicoHarp is 16pswhile the TimeHarp has a time resolution of 40 ps. The data was stored in the proprietary (but documented) Time Tagged Time Resolved (t3r) file format.

The main advantage of recording data in the t3r mode is that the complete temporal and spatial information of all photons detected is stored and a variety of possible analysis strategies can be applied to the very same data set. Thet3rfiles are the basis for the different analyzing schemes briefly outlined in the following sections.

2.5.1 Image Analysis

The t3r file contains x, y and z coordinates of every detected photon, from which the ac-tual image can be reconstructed. This has been done with the PicoQuant software available together with the acquisition system (MicroTime 200 (TimeHarp) and SymphoTime (Pico-Harp) respectively). The images were then exported from the PicoQuant software in bmp format and loaded for further analysis into IgorPro (a scientific analysis program, similar to Origin from Wavemetrics, Portland USA). The 3D renderings of the confocal volume were done with MatLab (MathWorks, Massachusetts USA).

2.5.2 Instrument Response Function (IRF)

The lower limit of the time resolution for TCSPC measurements is ultimately given by the jitter of the TCSPC electronics. Practically the limits are however set by the jitter of the detector response and the excitation pulse duration. A measure of the time resolution of the measuring system is the Instrument Response Function (IRF). The IRF is measured as the response of the system to the excitation pulse. Figure 2.4 shows the IRF, recorded with a mirror placed on top of the microscope objective (instead of the sample). The reflected excitation light is attenuated by an OD3 neutral density filter whereas the bandpasses, used for fluorescence detection, are removed. The width of the IRF has been measured to be 0.54 ns (FWHM). The so-called diffusion tail (causing the asymmetry of the curve in fig-ure 2.4) is a featfig-ure of all single-photon APDs and is caused by carrier generation in the

36 2. Confocal Fluorescence Microscopy and Single Molecule Detection

FWHM 0.54 ns

Fig. 2.4: Measured Instrument Response Function (IRF) neutral layers below the avalanche region.

2.5.3 Fluorescence Correlation Spectroscopy

For Fluorescence Correlation Spectroscopy experiments fluorescence intensities were recorded over a time span of several minutes. Correlations were calculated using the PicoQuant soft-ware according to the algorithm published in [68]. Figure 2.5 shows a simplified scheme of the algorithm. The fluorescence intensity trace is obtained by binning the detected fluorescence photons and the correlation of the intensity trace is calculated as the product of the intensity trace at timet and the same intensity trace delayed by the lag timeτ. Since the correlation curve is calculated for lag times ranging from nanoseconds up to seconds, the bin width is increased logarithmically with the lag time. For simplicity, the changing bin size is not shown in figure 2.5.

The calculated FCS curves were exported to an ASCII file and further analysis and fit-ting e.g. with the autocorrelation function was done in IgorPro and Origin (OriginLab, Massachusetts USA).

2.5.4 Determination of the Fluorescence Lifetime

As already mentioned, thet3rdata files contain information about the time span between the exciting laser pulse and the detected photon (micro time). Fluorescence lifetime histograms are built up by histogramming the photon arrival times with respect to the excitation pulse.

Depending on the experiment, histograms can be obtained individually for the different

detec-2.5. Data Analysis 37

single photon detection binning

calculation of self-similarity for different lag times (τ)

0.001 0.01 0.1 1 10 100 lag time

correlation

1 2

3

1×1 1×2

1×3 τ1

τ2

F(t+τ1) F(t+τ2) F(t)

τ1

τ2

fluorescence intensity trace

Fig. 2.5: Calculation of the FCS (autocorrelation) curve: Fluorescence intensity traces are obtained by binning the detected photons. The correlation is calculated as the product of the fluorescence fluctuations at every time t and the corresponding fluctuations at lag time t+τ

tion channels (one lifetime histogram per detection channel). When using Pulsed Interleaved Excitation (PIE) as in chapter 4, additionally to the detection channels, different histograms are built up for the two excitation pulses used. The discrimination of fluorescence photons excited by the first or the latter pulse is done in the micro time range. If the fluorescence yield per burst exceeds some 100 photons, lifetime histograms of single bursts can be ana-lyzed. Practically such high count rates have not been achieved in the FRET experiments discussed in chapter 4 and the burst-wise fluorescence lifetime analysis therefore will not be discussed further. The fluorescence lifetime can be extracted from the lifetime histogram by fitting with an exponential decay function. The fluorescence lifetime histograms are not only formed by fluorescence photons but also by scattered light from the excitation laser pulse. To measure short times, the lifetime histogram therefore has to be deconvoluted with the IRF.

During the fit process, an exponential decay function is convoluted with the measured

38 2. Confocal Fluorescence Microscopy and Single Molecule Detection

Fig. 2.6: Screenshot of the lifetime fitting routine of the PicoQuant SymphoTime Software.

The top blue curve represents the fluorescence lifetime histogram, the red curve the IRF. The fit is shown in black and the residues are shown in blue at the bottom. The fitted parameters can be found on the right side.

IRF. The least square fit routine is then used to vary the parameters of the exponential decay function and finally yields the fluorescence lifetime(s) of the experimental curve. Besides the fluorescence lifetime, amplitude and background, another parameter is introduced, i.e. the shift between the IRF and the experimental lifetime histogram. Since measured in different experiments, IRF and fluorescence lifetime histograms may be shifted with respect to each other. This leads to uncertainties, since the relative temporal position of the IRF and the fluorescence signals are not known exactly. As a result, the uncertainty of the time zero is reflected in the determined fluorescence lifetime.

The fitting of the lifetime histograms was done with the SymphoTime Software, a screen-shot of the fitting process is shown in figure 2.6. The sample in this case was a 5 nM aqueous ATTO-655 solution. When considering the IRF, the lifetime histogram could be fitted with a monoexponential decay function yielding a fluorescence lifetime of 1.6 ns for this dye solution, which is in accordance with literature [69].