# 923978-27-2 br Preparation of D collagen

Preparation of 3D collagen hydrogels

To prepare 1.2 mg/mL collagen type I hydrogel, we mix 1.2 mL of rat tail collagen (collagen R, 2 mg/mL; Matrix Bioscience, Mo¨rlenbach, Ger-many), 1.2 mL bovine skin collagen (collagen G, 4 mg/mL; Matrix Biosci-ence), 270 mL NaHCO3 (23 mg/mL), 270 mL 10 DMEM (Biochrom), and 43 mL NaOH (1 M) to adjust the pH to 10. The solution is then diluted with 3 mL of a mixture of one volume part NaHCO3 (23 mg/mL), one part 10 DMEM, and eight parts distilled H2O. All ingredients are kept on ice during the preparation process. 2 mL of the final collagen solution is pipetted in a 35-mm petri dish and polymerized in a tissue culture incubator at 37 C, 95% relative humidity, and 5% CO2 for 1 h. After polymerization, 2 mL of complete cell culture medium is added to prevent dehydration of collagen gels (17).

Collagen gel mechanical properties

To quantify the traction-force-induced deformations of the biopolymer network during cell migration, we implement the finite element approach described in (14). Finite elements are randomly filled with one-dimensional collagen fibers that buckle under compressive strains according to a buck-ling strain scale d0 and display a constant stiffness K0 during extension up to a linear strain range LS, beyond which the stiffness increases exponentially with a strain scale dS. For a 1.2 mg/mL collagen gel, these four material pa-rameters are K0 ¼ 1645 Pa, d0 ¼ 0.00032, LS ¼ 0.0075, and dS ¼ 0.033, as estimated from the stress versus strain relationship measured with a cone-plate rheometer and from the vertical gel contraction under uniaxial stretch (14) (Fig. S9).

3-D cell migration assays

To study the invasiveness of individual 923978-27-2 in 3-D collagen gels, 30,000 cells are mixed with 2.5 mL 1.2 mg/mL collagen solution and incubated for 4 h to ensure that cells have attained their typical elongated shape within the collagen gel. Subsequently, we image z-stacks with a z-distance of 10 mm, using a 10 objective with numerical aperture 0.30, a time interval of Dt ¼ 5 min between subsequent stacks, and a total duration of 24 h. We automatically track the x/y-position of all cells in the image series based on their characteristic intensity profile in the minimal and maximal intensity projections of the z-stacks using a custom Python script. All three cell conditions (MDA-control, MDA-lamA, and MDA-beads) are imaged in parallel.

For the analysis of the resulting trajectories, we only consider cells that have been tracked for at least 4 h. A cell is classified as motile if it moves away from its initial position by at least 20 mm during the 24-h observation period. For statistical testing of the motile fraction, we use a c-square test of independence of variables in a contingency table.

Cell speed s of a trajectory is computed as the mean absolute difference between two subsequent cell positions~rðtÞ recorded at a time interval Dt of
5 min:
s~v t t

t

To quantify the directional persistence of migrating cells, we compute the mean cosine of the turning angles between two subsequent 30-min trajec-tory segments:

q ¼ hcosðft Þit

Here, atan2 denotes the multivalued inverse tangent function. A value of q ¼ 0 indicates diffusive (Brownian) motion, a positive value indicates

persistent movement, and a negative value indicates antipersistent movement.

Finally, we determine the invasion distance of individual cells by the mean distance that each motile cell migrates within 1 h.

3-D force microscopy assay

15,000 cells are mixed with 1 mL unpolymerized collagen solution and incubated for 12 h before experiments. To compute the force-induced de-formations of the biopolymer network, the collagen fibers are imaged with confocal reflection microscopy using a 20 dip-in water-immersion objec-tive with numerical aperture 1.0. One image stack is recorded before cell forces are relaxed with 2 mM cytochalasin-D, and a second image stack is recorded 30 min after cytochalasin-D addition (Fig. 2, A–D). The first im-age stack represents the deformed state of the matrix, whereas the second image stack represents the undeformed force-free configuration of the matrix.

To compute cell forces, we follow the approach described in (14). First, the displacement field of the collagen network between the deformed and the undeformed image stack is measured using a particle image velocimetry algorithm. Second, an unconstrained force reconstruc-tion algorithm is used to calculate the cell forces. To this end, the matrix volume is tessellated and subdivided into a mesh of small (7.5 mm) finite elements of tetrahedral shape. For each tetrahedron, the constitutive equations that describe the relationship between the forces at the four no-des of the tetrahedron and the stresses and deformations are computed numerically. An iterative method is then used to modify the nodal forces of all finite elements until the measured and calculated matrix displace-ments match.