Dilution Series

At first, the determination of the confocal volume by analyzing the fluorescence correlation of a sample with a known concentration will be discussed. For this purpose the number of particles in the confocal volume was analyzed via G0 for a Atto-655 dilution series covering six orders of magnitude, from 1 µM to 1 pM.

The preparation of this dilution series is described in section 3.1, where also a description of the experimental setup can be found. The acquisition times for the different samples were 5 to 10 minutes each, depending on the sample concentration (shorter acquisition times for higher concentrations). The cross-correlation was calculated according to section 2.5.3 using the SymphoTime Software.

3.2. Measuring the Confocal Volume with FCS 49

χ²

χ2

Fig. 3.3: Dilution series of Atto-655 in H2O: Top: apparent number of particles (black squares) and background corrected number of particles (red squares). Bottom: backround correction factorχ².

Figure 3.3 shows the particle numbers extracted from the correlation amplitudes for the different sample concentrations measured. Note that both axis have logarithmic scales to cover the large concentration range measured. The black squares are the apparent numbers of particles calculated ashN_appi= 1/G₀, while the green squares are the numbers of particles calculated considering the influence of uncorrelated background signal.

A linear dependence between the average number of particles and the concentration is expected with the slope giving the effective volume. While hN_appi (black squares) first de-creases with decreasing sample concentration this trend is inverted for low concentrations.

The increase at low concentrations is caused by the increasing contribution of the uncorre-lated background signal. As uncorreuncorre-lated background signal becomes more prominent at low sample concentration, damping of the correlation amplitude occurs (see section 1.3.3 or

refer-50 3. FCS, Confocal Volume, Concentration, Molecular Brightness and Artifacts

ence [56]). This reduction of the correlation amplitude apparently leads to a higher particle concentration. The damping of the correlation amplitude has to be taken into account if the signal to background ratio is low, which is the case for the samples with a concentration below 1 nM. The influence of the uncorrelated background on the correlation amplitude can be considered through a correction factor χ² as described in section 1.3.3:

1

χ² = 1

(1 +hbi/hfi)². (3.6)

hbiis the average background count rate measured on a sample containing blank solvent, and hfiis the count rate of the actual sample, reduced by the background count rate (hfi=hFi−

hbi). As can be seen in figure 3.3, χ² increases with decreasing concentration. Considering the influence of this uncorrelated background, the number of particles present on average in the effective volume can be calculated according to the following equation (see sec. 1.3.3):

hNi= 1

χ²G₀ . (3.7)

The background corrected particle numbers hNi are shown as green squares in figure 3.3.

A more or less linear dependence on the sample concentration down to a concentration of 50 pM is obtained.

It is worth noting thathNican be determined with high accuracy as shown in figure 3.4.

For sample concentrations between 50 pM and 100 nM the uncertainties are below 1%.

The accuracy of the concentration determination however is limited by the accuracy of the measurement of the effective volume.

To get a measure of the linearity of the dilution series the logarithm ofhNiwas calculated and plotted versus the logarithm of the pipetted sample concentration. The slope of a linear fit yields the exponent of the dependence, which for a linear function is expected to be 1.

The exponent found for the dilution series is 0.97±0.01, indicating almost linear behavior.

Unfortunately for the two highest concentrations, the excitation power had to be reduced to prevent detector saturation. Since the excitation power influences the size of the effective volume (see section 3.5.1), only concentrations smaller than 100 nM were fitted and are shown in figure 3.5. In this concentration region a logarithmically weighted fit yields an

3.2. Measuring the Confocal Volume with FCS 51

Fig. 3.4: Dilution series of Atto-655 in H₂O: Relative uncertainties of the background cor-rected numbers of particles,hNi, for the dilution series shown in figure 3.3.

effective volume of (0.98±0.03) f land an offset of (3.00±0.03)×10⁻³. The weighting was applied because, due to the logarithmically varied concentrations, ordinary fitting tends to overweight higher concentrations. The offset can be explained as originating from impurities in the solvent, most probably stemming from Tween 20. If we speculate, that the offset is due to impurities with the same molecular brightness as Atto-655, it would correspond to a concentration of 6.3×10⁻¹³ M.

To get an idea of the errors that might be caused by potential sample loss, experimental data were fitted additionally in two different concentration regions. For concentrations above 1 nM (5 nM ≤ c ≤ 50 nM) an unweighed linear fit yields an effective volume of (0.88± 0.01) f l while for concentrations below 100 pM an effective volume of (1.06±0.03) f l is found. The effective volume seems larger for smaller concentrations. This can be explained by sample loss due to adsorption on pipette tips and container walls. The uncertainties of the mentioned effective volumes do not include the uncertainties caused by the sample preparation. For the smallest sample concentration the uncertainties can reach 15%. For the higher concentrations these uncertainties are lower, therefore the extracted effective volume in the high concentration region is considered to be most trustworthy.

The effective volume determined from the complete dilution series (omitting the two highest concentrations) is (0.98±0.03) fl. The uncertainty, however, needs to be raised due

52 3. FCS, Confocal Volume, Concentration, Molecular Brightness and Artifacts

Fig. 3.5: Dilution series of Atto 655 in H₂O: Different linear fits and their relative deviations from the measured particle numbers (top).

to the uncertainties of the sample pipetting and potential sample loss due to adsorption.

Therefore the effective volume resulting from the dilution series is (1.0±0.1) fl

For comparison the effective volume has also been measured by imaging fluorescent mi-crospheres immediately before the FCS measurements (see also section 2.6). The resulting effective volume was (1.0±0.1)f l.