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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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(B) SEM image from a fibrin clot reveals the fibrillar structure of fibrin (image adapted from [37]).

4 I INTRODUCTION

Because of their low solid (protein) fraction of typically 0.05% to 0.5% (w/v), traditional measures of porosity are not sensitive enough for such networks to be useful.

Similarly, hydrodynamic permeability can only serve as an indirect measure of pore size and critically depends on the validity of hydrodynamic models. Rather, network morphology is best characterized by a mesh size, or pore size, given by the 3D spacing of the fibers within the interstitial fluid that can be directly obtained from microscopic images. Moreover, it is the pore size and inter-fiber cross-link distance that most critically sets the steric hindrance for the migrating cells and the networks mechanical properties [15, 18, 38-42].

There are several approaches for quantifying the network pore size from images of the network structure. Scanning electron microscopy (SEM) has excellent resolution [12, 37, 41, 43] but requires the samples to be dehydrated and, thus, can only visualize a potentially collapsed network structure. By contrast, light microscopy methods can be applied to a fully hydrated sample even when it is containing living cells. A widely used imaging modality is confocal reflectance microscopy (CRM) [22, 23, 44-46]. It offers a fundamental advantage over confocal fluorescence microscopy (CFM) in that the networks need not be labeled with fluorophores, which is both time consuming and expensive. Moreover, less laser power is required to obtain the image stack with CRM, which helps 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.

CRM has a major disadvantage, however. 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. Similarly, second harmonic generation microscopy (SHG), another popular imaging mode for collagen, also suffers from an anisotropic transfer function [30, 41, 49]. If, however, the cut-off angle for the missing fibers is known, it seems possible to correct for the blind spot effect. Such an approach would allow users to employ the convenient methods of CRM and SHG and still evaluate the pore size distribution of the network without bias.

This work introduces a method to determine the unbiased pore size of a biopolymer network even when it is imaged with CRM and SHG. As a mathematically well-defined

I INTRODUCTION 5

and robust measure for the network pore size, we introduce the nearest obstacle distance. In the case of random networks, regardless of isotropy or anisotropy, it can be shown that the distribution of nearest obstacle distances follows a Rayleigh distribution.

Furthermore, if fibers oriented above a cut-off angle are systematically removed from the network, the nearest obstacle distance still follows a Rayleigh distribution with a scaling parameter that is a monotonic function of the cut-off angle.

Therefore, we can fit a Rayleigh distribution to the distribution of the nearest obstacle distances obtained from confocal reflection images and second harmonic generation images, and then simply re-scale the distribution function by a correction factor to predict the unbiased pore size distribution of the full network. We verify the validity of our approach by comparing the pore size distribution predicted from confocal reflection data with the pore sizes directly measured with confocal fluorescence on the same collagen samples. Furthermore, we demonstrate how the nearest obstacle distance can be converted to a previously established pore size measure - the covering radius transform.

However, not only the morphological properties of a 3D ECM are opted to influence cell migration, also the mechanical properties of the surrounding network might dictate cellular migration behavior. For non-porous degradable PEG-based hydrogels, cell migration speed and migration persistence has been shown to decrease with increasing matrix stiffness [50].

3D cell migration studies where the matrix protein concentration and hence matrix stiffness was changed, however, have reported inconsistent data. Cell migration speed in a 3D porous collagen network was shown to decrease with increasing matrix protein concentration and hence higher stiffness [23]. By contrast, in a porous Matrigel network, cell migration speed was shown to exhibit a biphasic response, with a maximum speed at intermediate matrix protein concentrations [12]. These results are difficult to interpret, however, as matrix protein concentration not only determines the matrix stiffness but also pore size and adhesion ligand density [15, 16, 51], all of which can influence cell migration speed [12, 23, 52, 53].

In this work the stiffness of porous, fibrillar collagen gels was changed independently from pore sizes, using the chemical cross-linker glutaraldehyde [54, 55]. The highly reactive aldehyde groups of glutaraldehyde bind covalently to the N- and C-terminal ends of the collagen fibrils and increase matrix stiffness without changing the pore size [56, 57]. We show that glutaraldehyde treatment notably increases the stiffness of the

6 I INTRODUCTION





network by a factor of 4-6, which is an advantage over transglutaminase, which increase the stiffness only by a factor of 1.5 -2, or riboflavin [58-61]. In contrast to nonencymatic glycation, we will show that glutaraldehyde does not change the pore size of the network [62]. By using glutaraldehyde as a cross-linker, we can therefore separate the effects from matrix stiffness on cell migration from those of pore sizes.

With cell invasion experiments, we show that higher matrix stiffness promotes 3D cell migration in gels with large pores where steric effects are small. By contrast, in gels with small pore sizes, increasing matrix stiffness amplifies the steric hindrance of the matrix and therefore impairs cell migration.

II MATERIALS AND METHODS 7

II MATERIALS AND METHODS

2.1 Collagen gel preparation Collagen matrices were produced under sterile conditions and with all ingredients held on ice to avoid premature polymerization. In order to avoid bubbles, extra care was taken while mixing the ingredients.

For every experiment a stock solution was prepared and diluted with buffer solution (consisting of 8 ml H2O, 1 ml 10xDMEM and 1 ml NaHCO3, solution was adjusted to pH 10 with 1M NaOH) until the final concentration was reached.

A 2.4 mg/ml collagen stock solution was mixed out of 1.2 ml Collagen R (2 mg/ml rat collagen type I; Serva, Heidelberg, Germany) and 1.2 ml Collagen G (4 mg/ml bovine collagen type I; Biochrome). Moreover 270 µl of a 0.25 M NaHCO3 buffer solution and 270µl 10×DMEM (Biochrome) were added. To adjust the pH to 10, 43 µl of a 1M NaOH solution was added.

1.2 ml of the mixture was pipetted in 35 mm cell culture dishes and polymerized in a cell culture incubator at 95 % humidity, 5 % CO2 and 37° C. After 2 hours, 2 ml of 1xDMEM complete medium were added. To prevent polymerization at different temperatures, the dishes were not placed on top of each other.

2.2 Preparation of fluorescently labeled collagen gels

To obtain fluorescent images of collagen gels, a fraction of the Collagen G stock solution was labeled with 5- (and 6) carboxytetramethylrhodamine-succinimidyl-ester (TAMRA SE, Invitrogen, Carlsbad, CA, USA) at 4°C according to the manufacturer‟s protocol. To minimize possible alterations of the polymerized network due to the labeling process, the labeled Collagen G solution was mixed with unlabeled stock solution at a volume ratio of 1:6. The mixture of collagen solutions was used to prepare the gels as described above.

8 II MATERIALS AND METHODS

2.3 Preparation of unlabeled and labeled fibrin gels

Lyophilized, plasminogen-free human fibrinogen and a lyophilized human alphathrombin solution (both from Enzyme Research Laboratories, South Bend, IN) were rehydrated according to manufacturer instructions and immediately frozen in aliquots at

-80°C.

Prior to experiments, aliquots were thawed and thrombin was kept on ice, whereas fibrinogen was kept at room temperature. Both fibrinogen and thrombin were diluted with a buffer solution (0.15M NaCl/20mM HEPES at pH 7.4) to twice the final concentration each, and fibrin gels were polymerized by mixing these solutions 1:1 by volume. Polymerization was allowed for at least 30min at room temperature, after which 1ml of buffer was added to prevent evaporation.

For fluorescently labeled fibrin gels, the fibrinogen stock solution was labeled with

TAMRA-SE at room temperature following the same protocol as for collagen. A 1:6

vol/vol mixture of labeled and unlabeled fibrinogen monomer was used to synthesize the gels.

2.4 Confocal microscopy

The confocal microscope employed in all confocal measurements was an upright Leica SP5X (Fig. 2.1, A) equipped with an argon laser emitting wavelengths of 458 nm, 476 nm, 488 nm, 496 nm and 514 nm as well as two laser diodes, emitting 543 nm and 633 nm. All laser lines can be used in fluorescent or reflection mode. Fluorescent or reflectance signals are monitored with internal photomultipliers.

Scanning of the probes was mostly performed with a conventional scanner at a speed of 100 to 400 Hz and a line average of 3. In the case of long term experiments with living cells, an 8000 Hz fast scanner was employed. With a line average of 3, the scanner, in combination with a galvanic stage, can image a 50 µm stack with a step width of 350nm in ~ 30 seconds. Therefore, scans were taken fast enough in order to prevent cell damages caused by intensive laser light exposure.

To be able to monitor migrating cells over several hours, the microscope was equipped with an incubation chamber where temperature, humidity and CO2 flow could be controlled. To prevent samples from drying out, an additionally perfusion system

II MATERIALS AND METHODS 9

was build and installed, where purified, sterilized water was added into the chamber with a constant flow (Fig 2.1 B, C).

–  –  –

Figure 2.1: Confocal microscope with perfusion system.

(A) Leica SP5 X upright laser scanning microscope equipped with the 1.0 NA 20x water immersion objective. (B) Perfusion system for the objective with a needle system to pump water into the chamber. If the perfusion system is needed it can be attached to the objective via screw. (C) Perfusor to pump water into the chamber.

For pore size evaluation stacks of optical sections were acquired with a Leica 20x dip-in water-immersion objective (NA = 1.0). To measure the effect of numerical aperture on the cut-off angle, some of the images were also acquired with a Leica 20x waterimmersion objective (NA = 0.7) or a Leica 63x water-immersion objective (NA = 1.2), both corrected for imaging through a 170 µm glass coverslips. CRM stacks were recorded by collecting the reflected light of the 488 nm argon laser line in one channel;

CFM stacks were simultaneously acquired by collecting light between 571 nm and 772nm in a second channel while the sample was also illuminated with a 543 nm HeNe laser. All images were recorded at 512×512 pixels with a digital magnification of 4.55, resulting in a pixel size of 317×317 nm; a total of 597 z-slices with a spacing of 335 nm were collected for each stack. Every line was averaged 3 times during scanning.

10 II MATERIALS AND METHODS

2.5 Second harmonic generation imaging

Collagen hydrogels were excited with a femtosecond-pulsed Ti:Sa-Laser (Vision II, Coherent, Santa Clara, CA) set to 810 nm. SHG signals were collected at 405 nm using a multiphoton microscope (TriM-Scope II, LaVision Biotech, Bielefeld, Germany) with a Zeiss 40x NA=1.1 water immersion objective. Voxel size was 310×310×310 nm;

scanning speed was set to 1200 Hz with a 2x line average.

2.6 Binarization of image stacks

A binarized data set, with pixels values of 1 representing the solid phase (fiber), and values of 0 representing the fluid phase, was obtained using a template-matching algorithm that simultaneously performs a binarization and skeletonization of the image stack [63].

In the algorithm, small subsets of the image stack are compared to a template representing a diffraction-limited fiber cross section. Matching voxels are classified as fibers based on a mismatch threshold that is iteratively optimized for each image stack so that the final skeletonized network obeys a universal property of voxelized random line networks, namely, solid-phase voxels have most likely three solid-phase neighbors in a 3×3×3 pixel neighborhood. All isolated solid phase voxels are regarded as image noise and are removed. The method is self-adapting, largely insensitive to the signal and noise in the image, and free of user-selected parameters [63]. However, the pore size characterization and conversion presented in this work does not rely on a specific skeletonization and binarization method.

2.7 Pore size evaluation with covering radius transform

A second method to determine the pore size distribution of a binarized fiber network is the covering radius transform (CRT) [64]. For every voxel of the liquid phase, the Euclidean distance to the center of the next solid phase voxel is determined. This distance can be interpreted as the radius of a pure liquid-phase sphere around that voxel.

The CRT assigns every voxel of the fluid phase the value of the radius of the largest possible liquid-phase sphere, placed anywhere, that covers that pixel. This results in a

II MATERIALS AND METHODS 11

complete coverage of the fluid space by overlapping spheres with a distribution of radii.



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