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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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To verify that the treatment with glutaraldehyde does not change the pore size regardless of the collagen concentration, we repeated the pore size measurement with treated and untreated collagen gels of different concentrations. Again, we could confirm that the treatment with the cross-linker glutaraldehyde did not result in a difference in pore sizes, no matter which concentration was used (Fig. 3.1.12, B).

personal communication, data provided in bachelor thesis of Janina Lange, ‚Bestimmung der

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Figure 3.1.

12: Cross-linking does not change the pore size of collagen networks. (A) Characteristic pore size of a 1.2 mg/ml collagen gel (mean ± sd from 5 fields of view of 4 gels for each condition). Glutaraldehyde treatment did not change the pore size of the gels. (B) Pore sizes versus collagen concentration (mean ± sd, from 5 fields of view of at least 3 gels for each condition).


3.1.2. Mechanical properties of biopolymer networks

Besides the morphological properties of the ECM, mechanical properties are also known to influence cell migration. On flat 2D surfaces, for example studies showed that cell migration is faster on soft substrates, while it is more directed on stiffer ones [8-11].

At the same time the spreading area of the cells and the number of focal adhesions was increased, when the cells migrated on stiffer substrates [11].

The influence of mechanical properties of the ECM on 3 dimensional cell migration is more difficult to evaluate. The stiffness of biopolymer networks is supposed to increase when the protein monomer concentration is increased. However an increase in protein concentration also leads to a decrease in pore size (Fig. 3.1.10). Although several studies tried to derive the influence of matrix stiffness on cell migration in 3D by varying the protein concentration of the biopolymer networks in use, it has to be pointed out that a change in concentration inevitably leads to a change in stiffness and pore size.

Therefore, the influence of matrix stiffness cannot be defined precisely, if only the concentration of the protein is changed.

Here we present a method of how the mechanical properties of a collagen network can be adjusted, without altering the pore size of the network and how the influence of matrix stiffness on 3D migration can be evaluated. As shown before, the chemical cross-linker glutaraldehyde did not change the pore size of a collagen network (Fig.

3.1.12). However, the highly reactive aldehyde groups of glutaraldehyde bind covalently to the N- and C-terminal ends of a collagen fibril [55-57]. Due to the fact that collagen fibers are assembled of collagen fibrils, the cross-linking between the fibrils lead to a stiffer fiber, without affecting the resulting network structure, and therefore the pore size. The disadvantage of glutaraldehyde cross-linking, however, was the requirement to remove toxic unbound aldehyde groups from the gels by thorough washing with TRIS-buffer over a time course of at least 24h before we were able to perform cell experiments with these gels. Different cross-linking methods like nonencymatic glycation would not be cell toxic, but would also not have the advantage of not changing the pore size [62].

To evaluate the stiffness of biopolymer networks measurements with a conventional shear rheometer have been performed [80]. The resulting stress strain relationship showed the answer of a non-linear material (Fig 3.1.13).


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Strain (%) Figure 3.1.

13: Illustration of a stress-strain curve of collagen. In a shear rheometer the bulk rheology of a collagen network can be monitored over a large scale. However, the shear rheometer does not provide sufficient resolution in the range of interest for cellular forces in the linear and exponential range (red circle) of low strain (figure provided from Stefan Münster, Lehrstuhl für physikalisch-medizinische Technik).

Although, the shear rheometer can resolve a broad spectrum of applied strain it is not sensitive enough to resolve the range of small strain in detail. Especially this range would be interesting in combination with cell migration experiments because it is within the force spectrum a cell can exhibit during migration through a network [82].

Therefore we applied also microrheologic methods to evaluate the mechanical properties of our collagen gels.

To measure the bulk stiffness (Young‟s modulus) of our collagen, we applied a uniaxial strain and measured the resulting force with an extensional rheometer (Fig 3.1.14, A). The gel stiffness increased approximately linearly with increasing collagen concentrations from 45 Pa at the lowest concentration to 550 Pa at the highest concentration (Fig 3.1.14, B, black bars).


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To estimate the micromechanical properties of collagen at a force and deformation scale e applied relevant for cells, we used a magnetic tweezer setup (Fig 3.1.15, A, inset).

forces between 1 nN and 10 nN to 5 µm diameter beads bound to the collagen gel surface, and measured the resulting bead displacements. Bead displacements were on the order of several micrometers except for 0.3 mg/ml collagen gels, where displacements exceeded 10 µm at the highest force (Fig 3.1.15, A, black lines). The recorded bead displacements for all gels increased with time according to a weak power-law, with an exponent around 0.12 for control gels, suggesting a predominantly elastic behavior (Fig. 3.1.16, A). All gels stiffened with increasing forces, with more pronounced stiffening for higher concentrated gels (Fig 3.1.15, B, black lines).

Micromechanical stiffness scaled approximately linearly with collagen concentration similar to the bulk stiffness data.


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As expected, collagen stiffness increased with increasing collagen concentration, in line with previous studies [15, 83, 84].

To increase the stiffness of the collagen gels, we treated the gels with glutaraldehyde after polymerization and repeated the stiffness measurements with the extensional rheometer and the magnetic tweezer. Results showed that after glutaraldehyde treatment, gel stiffness increased by 4-6 fold in extensional rheometer measurements (Fig 3.1.14, red bars). Microrheology measurements with a magnetic tweezer revealed more effects of glutaraldehyde. After glutaraldehyde treatment, the power-law exponent decreased to values below 0.05 (Fig 3.1.16, B), indicating that cross-linked gels were nearly perfectly elastic, in agreement with previous findings [80]. Micromechanical gel stiffness roughly scaled with the bulk stiffness for the different collagen concentrations, although the increase of the micro scale stiffness after glutaraldehyde treatment was somewhat less pronounced (2-4-fold) compared to the bulk stiffness. This can be explained by the higher mechanical stress levels in the magnetic tweezer experiments that lead to a gel stiffening and, as shown previously, to a collapse of the differential force-displacement responses for different gels [80].


Figure 3.1.

16: Power-law exponent from creep-experiments with magnetic tweezers. (A) During the application of force steps from 1 to 10 nN, the displacement of beads coupled to collagen fibers can be fitted with a power law [9, 65]. The power-law exponent β defines the dissipative properties of the material, where 0 corresponds to an elastic solid and 1 to a viscous fluid. Untreated collagen gels showed predominantly elastic behavior (β ~ 0.1). (B) Glutaraldehyde treatment further enhanced the elastic behavior of the collagen gels (β 0.05).


3.1.3 Influence of morphological and mechanical properties on cell migration Cell invasion depends on mechanical and morphological properties We next performed an invasion assay to evaluate the ability of tumor cells to migrate through gels with different stiffnesses and pore sizes. MDA-MB 231 breast carcinoma cells were seeded on top of the gels, and after three days of incubation, we determined the invasion profile as described in [85] and in the Materials and Methods section.

Cell invasiveness showed a pronounced biphasic response with collagen concentration:

Invasion was poor for diluted gels (0.3 ml/ml), reached a maximum at a collagen concentration of 1.2 mg/ml, and then decreased at higher collagen concentrations (Fig 3.1.17, A-D, black profiles and Fig. 3.1.18, A, black bars). When the collagen gels were stiffened with glutaraldehyde, a similar biphasic response was observed, but the

maximum invasiveness shifted to lower collagen concentrations and larger pore sizes:

Invasiveness greatly improved for the more diluted gels (0.3 and 0.6 mg/ml), started to decrease at intermediate concentrations (1.2 mg/ml) and stopped nearly completely at the highest gel density of 2.4 mg/ml (Fig 3.1.17, A-D, red profiles and Fig 3.1.18, A, red bars).


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Figure 3.1.

17: Cell invasion depends on matrix pore size and stiffness. (A-D) The invasion profile of MDA MB 231 cells is expressed as the probability to find a cell at or below a given invasion depth in control gels (black) and glutaraldehyde-treated gels (red). Shaded areas indicate ±1 SE around the mean from at least 90 fields of view measured on at least 3 different gels prepared on different days.

From the magnetic bead measurements where we apply forces between 1-10 nN, we estimate that the traction force of a single focal adhesion site, which has been evaluated to be around 5 nN/µm2 [82], cannot deform a dense collagen network by more than a few microns, and even less than 1 µm in the case of glutaraldehyde-treated gels. This is in agreement with previous results of a reduced translocation of fibers by cells seeded in dense collagen gels [86]. Given that dense gels of 2.4 mg/ml have a pore size below 3 µm, the decreased cell invasiveness at high collagen concentrations in particular after glutaraldehyde treatment can thus be explained by a strong steric hindrance of the collagen fiber network.

It is less clear, however, why cell invasiveness was also impaired in soft diluted gels with large pore sizes but was increased after glutaraldehyde treatment (Fig. 3.1.18, A).


Our data of reduced 3D migration in soft gels is in agreement with recent data showing that the migration speed of cells in compliant microfabricated channels decreased with decreasing matrix stiffness, mostly due to poor cell polarization [87]. The microfabricated channels with diameters between 10 - 40 µm, however, were as large or larger than the cell diameter, and thus steric hindrance did not play a role in that study.

In fact, according to another recent study where cells migrated through porous but stiff membranes of a Boyden chamber, steric hindrance effects emerge only for channel diameters below 5 µm, with some cell lines being able to migrate through pores with diameters below 1 µm [23].

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Figure 3.1.

18: Cell invasion depends on matrix pore size and stiffness. From the invasion profiles, a characteristic invasion depth was defined as the depth that 5% of the cells reached within 3 days of culture. As a guide to the eye, a log-normal curve was fitted to the results. (A) Cell invasion showed a biphasic dependence on collagen concentration, with a maximum around 1.2 mg/mg (black bars). This maximum was shifted towards smaller collagen concentrations around 0.6 mg/mg in glutaraldehyde-treated gels (red bars). (B) A similar biphasic response of cell invasiveness was observed after cell treatment with the MMP-inhibitor GM6001 (25 mM).

On the one hand, our observation of impaired 3D migration in soft gels is in contrast to reports that cells tend to migrate faster on soft planar 2D substrates [8, 10, 88]. On the other hand, our data is in line with more recent studies that showed a biphasic response of 2D cell migration speed to substrate stiffness; cells on soft substrates failed to polarize and therefore did no migrate persistently [87, 89]. However, although the invasion behavior of MDA-MB 231 cells responded strongly to changes in matrix stiffness and pore size, the cell shape did not change and remained highly elongated, with eccentricities close to unity for all conditions (Fig 3.1.19, A).


Even in untreated dilute gels with low stiffnesses in the range of 50 -100 Pa we see a high degree of cell elongation (Fig. 3.1.19). Therefore, the impaired migration in the softest gels was not attributable to impaired cell polarization but may be a sign of cellular mechanotransduction, although the molecular details are currently elusive.

Alternatively, cells in soft gels may be durotactically trapped in regions with a sufficiently high local stiffness.

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Figure 3.1.

19: Cell shape does not depend on matrix pore size and stiffness. (A) The eccentricity of invaded cells (mean ± SE of at least 20 cells) did not change with collagen concentration or glutaraldehyde treatment (red bars). (B) Bright-field images of invaded cells showed elongated shapes for all conditions. Scale bar represents 20 µm.


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