Polarizing cytoskeletal tension to induce leader
cell formation during collective cell migration –
Supporting Information
S. Rausch1,2, T. Das1,2, J.R.D. Soiné4,5, T.W. Hofmann1,2, C.H.J. Boehm1,2, U.S.
Schwarz4,5, H. Boehm1,2,3*, and J.P. Spatz1,2
1
Department of New Materials and Biosystems, Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569
Stuttgart, Germany
2
Department of Biophysical Chemistry, University of Heidelberg, Im Neuenheimer Feld 253, 69120 Heidelberg, Germany
3
CSF Biomaterials and Cellular Biophysics, Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart,
Germany
4
University of Heidelberg, Bioquant, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany
5 Institute
for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany
* corresponding author: Heike Boehm, heike.boehm@is.mpg.de,
Additional Materials and Methods
Unless otherwise stated, all chemicals were purchased from Sigma Aldrich, Germany.
In order to obtain geometrically well defined cell collectives we employed microstencil masks made of poly-dimethylsiloxane (PDMS). Circular features of 350 µm
diameter were created as openings in a thin membrane of about 60 µm height. In
addition to perfectly circular structures we also designed circular structures with four
additional protrusions evenly distributed on the circles perimeter. These protrusions
are either small hemispheres or small triangles (see Fig.1 in main manuscript). The
hemispheres and triangles encompass each an area of about 2000 µm 2 and an
angular sector of 23° and 20° respectively.
Cell culture and cell seeding.
About 1x106 MDCKII (Health Protection Agency, Porton Down, UK) cells were evenly
distributed into each microstencil and allowed to adhere for 90 min before the
medium containing all non adhered cells was removed. Micro-stencils were then
incubated under cell culture conditions for additional 16 hours to obtain confluent cell
layers with proper cell-cell contacts.
Inhibition experiments.
Inhibition experiments were conducted in OptiMEM to reduce interference by serum
proteins. For control experiments cell collectives were incubated for one hour in OptiMEM containing DMSO (1µL per mL of medium) before the stencil mask was
removed. The experiment was then conducted in standard cell culture medium.
Traction force microscopy.
To ensure cell attachement PAA was functionalized with fibronectin from bovine
plasma with the coupling agent sulphosuccinimidyl-6-(4-azido-2-nitrophenylamino)
hexanoate (Sulfo-SANPAH). Cells were seeded on the substrate with micro-stencils
in the procedure described above. Images of the bead displacement were acquired
on an inverted Observer fluorescence microscope (Zeiss, Germany) equipped with a
40x objective. An additional reference image of the bead positions in the relaxed gel
was taken after cells had been removed by incubation in trypsin for 1hour.
Evaluation of actin belt.
Cell collectives with highly curved protrusions were prepared as described above.
Cells were fixed before removal of the stencil mask and stained with TRITC-labeled
phalloidin. Images of stained cell collectives (40x objective) were recorded and
stitched, showing cell collectives as a whole.
Image analysis was fully automated using self-written MATLAB routines. First, the
orientation of the collectives of a sample, i.e. the rotation angle α with respect to the
horizontal (Additional File 8, Fig S8B) as well as the center of each collective
(Additional File 8, Fig S8A), was computed by means of fitting algorithms.
Subsequently, all points within an approximately 4 µm wide region along the
boundary of a collective were transformed into polar coordinates, which were used to
segment the boundary region into four quadrants. Then the angle coordinate of the
points was adapted to lie in a region between 0° and 90° (Additional File 8, Fig S8A
and Fig S8B) such that in an ideal collective the tips of the highly curved protrusions
in each quadrant are placed at 45° (Additional File 8, Fig S8B). Intensities were
normalized by the mean intensity of the selected boundary regions of the respective
cell collective. Mean values and standard error of the mean were calculated and
significance was determined using the Mann-Whitney-Wilcoxon test.
Model Description.
As previously described by Edwards and Schwarz [1]. The thickness of the colony
monolayer ( h » 1mm ) is two orders of magnitude smaller than the lateral extension.
Therefore a two-dimensional plane stress approximation is appropriate. The colony
Cauchy stress σ is written as the sum of the internal elastic stress and a constant
isotropic pressure term s condij where s con < 0 is a scalar constant that represents the
active and isotropic contractility of the layer:
s ij =
ö
Eh æ
n
ekkdij ÷ + s condij
çeij +
ø
(1+ n ) è
1- n
(1)
Here E is the Young's modulus, n the Poisson's ratio, and h the height of the colony.
The strain tensor e is a measure for deformation and is related to the local colony
displacement u via the nonlinear relation
1 æ ¶u ¶u ¶u ¶u ö
eij = çç i + j + k k ÷÷
2 è ¶x j ¶xi ¶x j¶x j ø
(2)
This treatment is analogous to the problem of thermal expansion/contraction of a
material that is associated with an effective temperature difference DTeff with
s con µ DTeff (linear thermoelasticity). Since the colony is able to transmit traction stress
to the elastic substrate underneath, an effective linear elastic coupling is introduced
with coupling constant k . This describes the elastic response of the substrate
material in first order. By considering static equilibrium the system state is
determined by the steady version of Cauchy`s momentum equation whereas the
elastic coupling appears as harmonic body force:
Ñs - k u = 0
(3)
We solved eq. (3) numerically with respect to the displacement field u for given
colony geometry. For this we used the commercial finite element method (FEM)
software COMSOL 4.2. For the mechanics of the colony monolayer we assume a
Young's modulus of E = 400Pa and a Poisson ratio of u » 0.5 in agreement with AFM
indentation measurements on single MDCK cells [2]. For comparison of measured
and modeled traction fields, the contractility s con and the elastic coupling constant k
were used as fit parameters adjusted according to the maximal values of measured
displacement and traction stress. Here, model traction was calculated from the force
balance T = k u where u is the numerical solution of the simulated displacement field.
1.
Edwards CM, Schwarz US. Force localization in contracting cell layers. Phys.
Rev. Lett. 2011 Sep 16;107(12):128101.
2.
Harris AR, Charras GT. Experimental validation of atomic force microscopybased cell elasticity measurements. Nanotechnology. 2011 Jul
28;22(34):345102.