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«Der Naturwissenschaftlichen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr. rer. nat. vorgelegt ...»

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developed a PDMS device, which we called “O-ring” (Fig 2.8). The O-ring can be washed and autoclaved for future use.

Figure 2.8: The amnion in cell culture II.

(A) Example of an extracted and cut amnion placed in a 10 cm culture dish. (B) To prevent the building of ruffles in 35 mm dishes we developed the O-ring. The cast was milled from hard plastic (right side). The ring itself (left side) was made of PDMS which is filled into the cast as a liquid. Subsequently the cast with the liquid PDMS was baked over night at 64°C.



3.1 Effects of matrix stiffness and steric hindrance on cell migration in 3D 3.1.1. Morphological properties of biopolymer networks Beyond the blind spot The mesh size of the extracellular matrix (ECM) is an important parameter that governs its mechanical properties and influences the ability of cells to colonize and migrate through the ECM[14, 20, 21]. It can be defined as the 3D spacing between the fibers and the interstitial fluid.

However, in biopolymer networks, widely used as an ECM mimicking material, the low solid (protein) fraction of typically 0.05% to 0.5% (w/v) makes it difficult to apply traditional measures of porosity. Measures like the void ratio are not sensitive enough to be useful. In a similar way, hydrodynamic permeability can only serve as an indirect measure of pore size and critically depends on the validity of hydrodynamic models.

Evaluating the pore size of these networks is considerably more accurate when microscopic images of the network structure are used.

A widely used imaging modality is confocal reflectance microscopy (CRM) [22, 23, 44]. This methodology offers a fundamental advantage over confocal fluorescence microscopy (CFM) because the network does not have to be labeled with fluorophores, which is both time consuming and expensive. Moreover, less laser power is required to obtain the image stack with CRM, making it possible to avoid cell damage during live cell imaging [14, 44, 47]. These advantages make CRM a preferred method for observing cell migration simultaneously with the network structure.

However, also CRM has one major disadvantage. Because CRM only detects light that is reflected back into the microscope lens, it preferentially visualizes horizontal fibers. Thus, CRM suffers from a blind spot in that it misses fibers with an angle steeper than a certain cut-off angle [48]. Therefore, networks imaged with CRM appear anisotropic, and fewer fibers are visible, resulting in a substantial overestimation of the pore size of the network. In the following, we describe a method to evaluate the unbiased pore size from CRM images of biopolymer networks by evaluating the cut off angle in different setups.


To illustrate the blind spot effect, we simultaneously imaged collagen gels in CRM and confocal fluorescence microscopy (CFM). The data obtained with CFM show an isotropic distribution of fibers, whereas the data obtained with CRM preferentially show fibers aligned horizontally with the imaging plane (Fig 3.1.1).

Figure 3.1.

1: The blind spot in confocal reflection microscopy. (A-B) Maximum intensity projection of 3 x-y slices (total thickness 1.0 µm) of a 0.3 mg/ml collagen gel simultaneously imaged with CFM (A) and CRM (B). (C-D) Projected view of 15 x-z slices (total thickness 4.75 µm) of the same sample imaged with CFM (C) and CRM (D). Compared to CFM, CRM does not detect vertical fibers. The scale bar of 20 µm applies to all panels. Stacks were imaged with 512×512 pixels with a size of 317×317×335 nm.

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Figure 3.1.

2: 3D reconstruction of a 0.3 mg/ml collagen gel. (A-B) Reconstruction of a 50 µm image stack (512x512 pixel with pixel size 317x317x335nm). Image stacks were obtained simultaneously in CFM (A) and CRM (B). (C) The CRM signal is subtracted from the CFM signal and the difference is plotted in green. Co-plotted in orange is the CRM signal. Clearly, vertical fibers that are visible in CFM are invisible in CRM. Scale bar represents 10 µm.

To verify that the effect is independent of the protein concentration of a network, we imaged several networks of different concentrations with CRM and CFM and found similar results (Fig 3.1.3). The blind spot effect could be observed in all networks.


Figure 3.1.

3: Different concentrations of collagen monomers influences pore size. x-y projections of CFM (A-C) and CRM (D-F) images (3 slices, total thickness 1 µm) from collagen gels polymerized at different monomer concentrations of 0.6 mg/ml (A,D), 1.2 mg/ml (B,E) and

2.4 mg/ml (C,F). With increasing concentrations, the pore sizes become smaller and the network denser. The scale bar of 20 µm applies to all panels. Stacks were imaged with 512 x 512 pixels with a size of 317 nm x 317 nm x 335 nm. Fluorescence mode images appear denser compared to reflection mode images because of the blind spot effect.

To test whether the blind spot effect in CRM also occurs in other biopolymer systems, we repeated the same measurements on fibrin gels, another widely used ECM mimicking material. X-z slices of the reconstituted fibrin gels obtained with CRM clearly demonstrate that also vertical fibrin fibers are missing (Fig. 3.1.4 and SI Movie_1).


Figure 3.1.

4: The blind spot effect in fibrin networks. (A) Maximum intensity projection of 3 x-y slices (total thickness 1.0 µm) of a 1.0 mg/ml fibrin gel imaged with CRM. (B) Maximum intensity projection of 15x-z slices (total thickness 4.75µm) of the same sample as in (A).

Similar to the collagen gels shown in Fig. 3.1.1, vertical fibers in fibrin gels are missing.

To evaluate the pore sizes of biopolymer networks from such directionally biased data, the missing vertical fibers have to be taken into account. The brightness of fiber segments imaged with CRM depends on their polar angle θ [48]. As mentioned above, only fibers with angles larger than θcut relative to the optical axis can be observed (Fig.

3.1.4 A). This cut-off angle depends predominantly on the numerical aperture of the imaging system. To determine the value of θcut in our microscopy system equipped with a 1.0 NA objective, we quantified the probability density distribution of collagen fiber angles in the CRM data (Fig. 3.1.4 B). To verify that it does not matter which biopolymer is used, we repeated the measurement with a fibrin network (Fig 3.1.6 A).


Figure 3.1.

5: Distribution of fiber orientation. (A) In CRM, the brightness of fiber segments depends on their polar angle θ, as illustrated by different shades of red (more saturated color indicates brighter CRM signal). Only fibers with angles larger than θcut, relative to the optical axis, can be observed. This cut-off angle depends on the numerical aperture of the objective lens. (B) Distribution of polar angles of a collagen network measured with CRM (blue line, 20x objective, 1.0 NA) compared to the distribution of polar angles for a collagen network measured with CFM (black solid line). The polar angle distribution of the fluorescent data set follows the expected sin(θ) distribution of an ideal, isotropic network (black dotted line). The fraction of fiber segments that are visible in CRM is given by the ratio of the integrals of both frequency distributions. The cut-off angle θ cut is chosen so that the grey area equals the integral of the polar angle distribution for the CRM data.

The density distribution of polar angles for both biopolymers are identical (Fig. 3.1.6 A), indicating that the angular characteristics of light reflection of collagen and fibrin fibers are similar. For comparison, we also measured the probability density distribution of collagen and fibrin fiber polar angles in the CFM data (Fig 3.1.5 B and 3.1.6 A, black lines). Both probability density distributions closely follow the sinθ dependency expected for an isotropic random line network, which demonstrates that our collagen and fibrin networks are indeed isotropic.

Next, we define the cut-off angle θcut such that the integral over the isotropic angle distribution in the interval (θcut, 90°) (Fig. 3.1.5 B and Fig. 3.1.6 A, gray areas) equals the total integral over the fiber angle distribution from the CRM data. The cut-off angle, θcut,, is 51° in our standard system with an NA=1.0 objective for both, fibrin and collagen data.


Figure 3.1.

6: Distribution of fiber orientation for different biopolymers and objectives. (A) Distribution of polar angles of a fibrin (grey line) and a collagen (blue line) network measured with a 20x NA=1.0 water immersion objective with CRM, and in a collagen network measured with CFM (black solid line) that follows the expected sin(θ) distribution of an isotropic network (black dotted line). When measured with the same objective, there is no difference in the cut off angle, regardless of which biopolymer is imaged. The cut off angle is again chosen so that the grey area equals the integral of the polar angle distribution for the CRM data. (B) Distribution of polar angles of a fibrin network measured with CRM and 3 different water immersion objectives (20x, 0.7 NA (red line), 20x, 1.0 NA (grey line) and 63x, 1.2 NA (green line)) compared to the distribution of polar angles for a fibrin network measured with CFM (black solid line). The polar angle distribution of the fluorescent data set follows the expected sin(θ) distribution of an ideal, isotropic network (black dotted line). As expected, a higher numerical aperture increases the fraction of visible fibers.

To measure how the cut-off angle depends on the numerical aperture of the objective in use, we measured the polar angle distribution for fibrin gels imaged with CRM using either a water immersion 63x objective with NA=1.2 or a water immersion 20x objective with NA=0.7. As previously suggested [69], the cut-off angle increases with lower numerical aperture (Fig. 3.1.5 B); for a 63x NA=1.2 objective, we found that θcut = 46°, and for a 20x NA=0.7 objective, θcut = 62° (Tab 3.1.1).


Cut off angle θcut Magnification Numerical aperture 20x water immersion 20x water immersion 63x water immersion 40x water immersion (SHG) Table 3.1.1: The cut off angle depends on the numerical aperture. CRM stacks from the same collagen networks were obtained with water immersion objectives with different numerical apertures. As expected the cut off decreases with increasing numerical aperture, indicating that more fibers are visible with higher NA. Note that the SHG measurements were performed on a collagen gel.

Second harmonic generation imaging (SHG) also suffers from a blind spot effect

Second harmonic generation imaging is another popular mode to image collagen networks. In SHG, contrast is obtained because molecules which are not symmetric cause anisotropy of the exciting laser light. In the created oscillating field, the light, called the second harmonic, has twice the frequency and half the wavelength of the incident light [70, 71]. Similar to CRM, SHG also exhibits an emission probability that depends on the orientation of the excited fibers [30, 41]. To test if this leads to a blind spot, we acquired 3D data stacks of collagen gels with SHG in backscatter mode. Once again, vertical fibers cannot be detected by this imaging modality (Fig. 3.1.7 A).


Figure 3.1.

7: The blind spot in collagen gels imaged with second harmonic generation (SHG). (A, B) SHG images of a 0.3 mg/ml collagen gel. (A) Maximum intensity projection of 3 x-y slices (total thickness 0.93 µm). (B) Maximum intensity projection of 15x-z slices (total thickness 4.65 µm) of the same sample as in (A). Similar to CRM (Fig. 3.1.1 and 3.1.4), SHG images preferentially show horizontal fibers.(C) Distribution of the polar angles of the SHG signal from a 0.3 mg/ml collagen network shows systematic deviations from the sin dependency expected for an isotropic network. The polar angle distribution is similar to data obtained with CRM. The cut-off angle under SHG for a 40x NA=1.1 objective is 48°.

Note that the generation of second harmonics can only be caused by molecules without a symmetric center, for example collagen or at interfaces with a high difference in refractive index [71-74]. As fibrin is a symmetric molecule, it cannot be imaged with SHG.

To verify that the presented method to evaluate the pore size from directionally biased data is also valid for SHG data, we repeated the evaluation of the cut off angle for SHG measurements with collagen (Fig. 3.1.7 B).

We observed similar cut-off angles in second harmonic generation images of collagen networks in backscatter mode, where we find a cut off angle of θcut SHG = 48° for a 40x NA=1.1 water immersion objective (Tab. 3.1.).

Rayleigh distribution of nearest obstacle distances (NOD) as a measure of pore size distribution

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For a simulated random line network with a line thickness of one voxel, the distribution of nearest obstacle distances calculated for randomly chosen points of the fluid phase follows a Rayleigh distribution (the complete theoretical approach is provided in the supplementary information) ( ) ( ( )) (1) √ Networks with a high density have narrow distributions with a prominent peak. For networks with lower densities, the peak shifts to the right and the distribution broadens (Fig. 3.1.8 A). Conveniently, the Rayleigh distribution relates the peak and the width of the distribution curve with only one free parameter – the average distance rmean.

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