Calibration

Since any scattering medium or any medium having a refractive index different from water changes the focal volume with respect to the standard volume in water, calibra- tion is one of the major challenges when it comes to performing FCS measurements in soft matter [22, 23]. To overcome this issue, other groups have developed new FCS techniques where an additional length scale introduces a robust intrinsic calibration, as already shortly mentioned in chapter 4.3. Dual focus FCS [56], for instance, uses the distance of the two foci for calibration, while scanning FCS [57–59] is calibrated via the scanning velocity. Another option used with increasing frequency, especially for measurements in cells, is two-photon FCS, where scattering is strongly reduced due to the long excitation wavelengths [60]. The experiments described above show that even without these techniques, reliable results can be achieved by considering the fact that the distortion of the focal volume due to scattering is independent of the tracer molecule and can thus be determined separately in an appropriate calibration measurement. This allows for the introduction of reliable calibration in scattering media.

6.4 Consequences for applications

6.4.2 Binding experiments

A particular interest within the context of this thesis are binding experiments in complex media. The performance of FCS binding experiments in such media was tested with the specific binding of annexin V to PS-vesicles in a solution of 25% vol PEGylated vesicles. As discussed in chapters 7 and 8, annexin V binds specifically to PS-lipids in a calcium-dependent manner, but does not show any specific binding to POPC-vesicles. The challenge is to separate the FCS signal changes due to scattering and crowding from changes resulting from binding events. FCS experiments were performed as a function of increasing concentrations of PS vesicles in solutions with fixed amounts of Alexa-labeled annexin in both, pure citrate buffer as well as a crowded PEG-liposome solution, each with calcium added in a concentration of 50 mM. The fractions of free proteins, ff ree,

and proteins bound to PS vesicles, fbound, were determined according to equation 4.9,

making use of the fact that the diffusion constant of free and vesicle-bound annexin differs by about a factor of 10.

Data evaluation was done for all data sets as follows: to achieve reliable fitting results for the fraction bound in a two-component analysis, the diffusion time of free protein and the structure parameter were fixed. As described above, it is important to consider the fact that the diffusion times, as well as the structure parameter vary with the volume fraction of the vesicle medium. The corrections for the scattering effect and slowdown due to crowding could be taken directly from Fig. 6.3(a) and (b) as determined from the GFP test experiments. The structure parameter at a certain vesicle concentration can then be calculated using equation 4.6 and the value of the particle number at that vesicle concentration taken from Fig. 6.3(a). The diffusion time at a certain vesicle concentration can be determined using equation 4.5 and the corresponding diffusion constant shown in Fig. 6.3(b). However, this way of making the corrections is based on the assumptions that the change of the focal volume in x- direction due to scattering is negligible and that the investigated molecule is as inert as GFP in the crowded medium. The later is not the case for annexin V, for instance, which shows weak unspecific bind- ing to PEGylated vesicles as described in chapter 8. Alternatively, the diffusion time and structure parameter for Alexa-labeled annexin in PEGylated vesicles can be directly measured in the crowded medium. Here, this was done by measuring annexin diffusion in a PS-free PEGylated vesicle solution. The structure parameter and diffusion time were determined from this measurement using equation 4.4 and then kept fixed for the succeeding analysis of experiments with increasing fraction of charged vesicles. Using equation 4.9, the fraction of free and bound annexin was determined. A typical two- component curve of annexin binding to PS-vesicles in highly concentrated PEGylated vesicle solution is shown in Fig. 6.4(a), and the resulting binding curve is shown in Fig. 6.4(b). Following the FCS experiment of annexin binding in highly concentrated vesicle solutions with increasing amount of PS-vesicles measurements were carried out in buffer. The binding curve determined in buffer and in concentrated PEGylated vesi- cle suspension match well. The use of corrected diffusion constants for FCS data in

6 Diffusion measurements in crowded, scattering media

(a) (b)

Figure 6.4: (a) Measured autocorrelation curve of annexin binding to PS-vesicles

in highly concentrated PEGylated vesicle solution (◦) and the corresponding fit curve. Residuals are shown below. (b) Fraction of annexin bound to PS-vesicles as a func- tion of the PS-vesicle concentration measured in buffer solution () and in highly- concentrated PEGylated vesicle solutions (◦). Uncorrected data in highly-concentrated PEGylated vesicle solutions (4) lead to an overestimation of binding.

crowded medium for both the free and bound annexin is critical as shown by the dashed line which indicates the outcome of the analysis without correction. Hence, binding mea- surements in highly concentrated vesicle solutions can be carried out if the optical, as well as hydrodynamic influences of the crowded medium, are taken into account. These findings allow for FCS measurements of dynamics and molecular interaction in turbid and crowded media. Thus, these results provide a basis for measuring and analyzing colloidal solutions used for pharmaceutical and cosmetic applications as well as in food industry.