## 3 Results and Discussion
### Viscoelastic Properties
#### 3.2.1 Particle Tracking Microrheology
The increase is more distinct for the slope of G'' than G'' which leads to the crossover of the moduli. Group b mucus samples revealed lower rigidity as group a due to lower absolute G' and G''. For the mean frequency range, solid-like behavior can be found for most of the samples, which is typical for gels and in accordance to group a mucus samples. Neverthless, at higher frequencies, a convergence and finally crossover of G' and G'', a transition from a solid-like character to a liquid-like, viscous-dominant character (G'' > G''), happened. We assume that this may be linked to the mucin network. The rheological properties determined by PTM are based on the microspheres thermal diffusion and are directly affected by the microstructure of the sample. High frequencies are related to the short lag-times over which the microspheres movement was evaluated. Thus, short  
Figure 3: Mean of the MSDs and viscoelastic properties with slopes of the three groups. blue: group a; red: group b; yellow: group c. (**a**) Averaged MSDs; (**b**) Averaged viscoelastic properties. A crossover can be seen within groups b and c, occurring at a lower frequency for group c. The values given near the evaluation limits for each curve reveal the mean slope over the four measurement points near the evaluation limits. lag-times are connected to the local diffusion of the microspheres. The liquid-like character at high frequencies, is an indication for a less hindered diffusion of the microspheres over short times, compared to frequencies at which the elastic component (G') dominates. We assume that the crossover happens due to a looser mucin network and differences in the composition of the mucus samples of group b in comparison to group a. Several factors as pH, surfactant-concentration or salt concentration were reported to affect the gel building properties of mucins [21]. Moreover, the mucin content itself is the main component that affects the viscoelasticity of mucus [18; 20]. In the context of the mucus ingredients, the hydration level of mucus can be responsible for diluted or concentrated mucus. We assume that this is the reason for the observed differences. Group c mucus samples revealed the highest MSDs and lowest viscoelastic moduli compared to the other two groups, see Figures 2 and 3. A crossover of the moduli could be observed at frequencies \(\omega<\) 10 s\({}^{-1}\), frequencies lower than for group b mucus samples. As for group b, this leads to a change of tan\(\delta\), see Table 2. The highest diffusive exponents, at both evaluation limits, were found for group c. The absolute moduli of the samples within the group did not vary much, which is represented by the small standard deviation. A range of G' from 0.037 Pa to 0.40 Pa and G\" from 0.02 Pa to 0.03 Pa at the lower evaluation limit (\(\omega=\) 0.6 s\({}^{-1}\)) and G' from 0.40 Pa to 0.62 Pa and G\" from 0.87 Pa to 1.56 Pa at the higher evaluation limit (\(\omega=\) 194 s\({}^{-1}\)) were found, see Appendix A, Table A1. The crossover frequency was the lowest for mucus sample c4 and the highest for mucus sample c2. The slopes of the mean curves of G' and G\" increase with frequency, see Figure 3. The mean storage and loss modulus at the lower evaluation limit were smaller than for groups a and b. Group c mucus samples revealed the lowest absolute G' and G\" compared to group a, and group b. The liquid-like character dominates. However, at low frequencies, solid-like character was found. The crossover of G' and G\" happened at lower frequencies than for group b. This may be due to an even looser mucin network, compared to group b mucus samples. A statistical analysis, based on characteristic parameters at the limits of evaluation (Table 2), was performed to check on the independence of the proposed groups. The results are given in Table 3. All mean parameters, except the diffusive exponent \(\alpha\) at the higher evaluation limit (\(\tau=\) 1662 ms) and tan\(\delta\) at the lower evaluation limit (\(\omega=\) 0.6 s\({}^{-1}\)), showed differences among the groups (bold).