Measurement of Cellular Contractile
Forces Using Patterned Elastomer
The adhesive interaction of cells with their neighbors
and with the extracellular matrix is a characteristic
feature of all metazoan organisms. Cell adhesion is
essential for cell migration, tissue assembly, and the
direct communication of cells with their immediate
environment. These interactions are mediated via specific
cell surface receptors that specifically interact with
the external surface, and link it, across the membrane,
with the actin cytoskeleton (Geiger et al.
, 2001). These
multimolecular complexes are subjected to constant
mechanical perturbation, generated either by the
cellular contractile system or by changes in the neighborhood
of the cell. To list just a few examples, in the
course of cell migration, focal adhesions (FA) are
formed, where contractile microfilament bundles,
consisting of actin and myosin, are anchored. Their
pulling on the substrate is involved in regulating the
adhesion itself, as well as in coordinating the persistent
forward movement of the cell. Mechanical perturbations
are generated by diverse external factors, such
as muscle contraction, blood flow, gravitational forces,
and acoustic waves. Both internal and external forces
apparently act at adhesion sites and modulate their
organization and signaling activity (Geiger and
Bershadsky, 2001; Riveline et al.
, 2001; Galbraith et al.
2002). In view of the major physiological significance
of these cellular forces, it appears important to develop
approaches for the accurate measurement of cellular
forces with an appropriate sensitivity and spatial resolution
(Beningo and Wang, 2002; Roy et al.
, 2002). This
article describes an approach for measuring such
forces using the patterned polydimethylsiloxane
(PDMS) elastomer as an adhesive substrate and cells
expressing fluorescent focal adhesion molecules
(Balaban et al.
, 2001). These experiments demonstrated
that cells maintain a constant stress at focal adhesion
sites, of the order of ~5nN
, and that changes in
cellular contractility lead rapidly to changes in FA
organization. This article describes the technique used
for the preparation of the patterned elastomeric substrate
and for measuring the cellular forces.
II. MATERIALS AND
Photoresist: Microposit S1805 (Shipley, Marlborough,
Developer: Microposit MF-319 (Shipley)
HMDS or tridecafluorooctyltrichlorosilane (UCT,
Spinner (Headway Research, Inc., Garland TX)
Mask aligner (Karl Suss, MJB3, Germany)
Chrome mask with desired pattern, or transparency
Digital hot plates
PDMS: Sylgard 184, Dow Corning
No. 1 glass coverslips (diameter 25 mm)
The DeltaVision microscopy system (Applied
Precision Inc., Issaquah, WA) is used in these experiments.
Similar microscopy systems could be used for
such purpose, provided that they are capable of accurately
acquiring high-resolution images (512 × 512
pixels or better) at a high sensitivity (allowing for lowdose
recording) and high dynamic range (12 bit or
Bulk calibration: weights, clamps
Calibrated micropipettes with elastic constants 10-
E. Image Analysis
Image analysis software: Priism (Applied Precision
Data analysis software: Matlab (The Mathworks,
Natick, MA) (This software can be purchase with
image analysis toolbox and used to perform the
image analysis as well)
F. Calculation of Forces
A detailed description of this calculation is provided
in a web site established by Dr. Ulrich Schwartz
This step provides molds consisting of a pattern
of photoresist on silicon wafer that will be used for the
patterning of elastomer substrates, a technique termed
"soft lithography" (Whitesides et al.
, 2001). It relies on
access to a clean room with basic optical lithography.
It also assumes the availability of the chrome mask
with the pattern of interest. For high-resolution patterns
(features below 1 µm), such masks are produced
by electron beam lithography (also available in many
clean room facilities). For low-resolution patterns
(5µm features and more), transparencies with appropriate
resolution (5080dpi) can be used.
B. Elastomer Substrates
- Clean silicon wafer in acetone and then immediately
wash with methanol and blow dry.
- (Optional) Bake for 20min in a 120°C oven.
- Dispense HMDS in the middle of the wafer until
full coverage and spin at 6000rpm for 1 min.
- Dispense S1805 photoresist in the middle of the
wafer covering approximately one-third of the
wafer and spin at 5000rpm for 30s.
- Soft bake on hot plate at 80°C for 5 min.
- Make sure the wafer and the mask are in contact
in the mask aligner.
- Expose for 10s. This number is only an estimate;
exposure and development times have to
be adjusted for the specific exposure system.
Typically an exposure of 100-140 mJ/cm2 is
- Develop for 10s (see aforementioned comment).
- Hard bake for 5 min in a 120°C oven.
- In order to prevent sticking between the mold
and the PDMS, an additional spin of HMDS can
be performed at this stage. Alternatively, overnight
exposure to vapors of tridecafluorooctyltrichlorosilane
can be done.
- Dice the wafer with a scriber in small pieces of
about 5 × 5 mm. Each of these pieces can be reused
as a mold many times for patterning of the PDMS
- Pour about 30 ml of part A of the Sylgard 184 kit.
Add 1 part of B (cross-linker) for 50 parts of A (in
weight): Mix thoroughly.
- Cover and let stand on bench until bubbles are
scarce (typically 30min).
- Coat glass coverslips with the PDMS mixture.
For large patterns that can be seen with low-resolution,
long working distance objectives, put a few drops of
the mixture in the middle of the coverslip on a flat
surface covered with aluminium foil and let flow
until the whole coverslip is covered. For short working
distance objectives, a thinner layer is needed.
This can be achieved by spinning No.1 coverslips at
1000rpm on a spinner equipped with a 0.05-in. rotating
head or "chuck." Alternatively, coverslips coated
with PDMS can be put vertically to allow the flow of
excess PDMS and attain a thinner thickness (typically
- Place the coated coverslips on aluminium foil
and bake in an oven at 65°C for 25 min until the top
layer of the PDMS has started to solidify.
- Place the rest of the PDMS mixture in the oven
for bulk calibration purposes (see Section III,D).
- Place a piece of the mold in the center of each
coverslip (the patterned side of the mold should be in
contact with the PDMS) and put back in oven
- Delicately separate the mold from the patterned
- Glue each patterned coverslip to the botton of a
35-mm tissue culture plate with a 15-mm hole. This
step can be done with melted paraffin.
- Wash the coverslip and dish extensively with
phosphate-buffered saline (PBS).
- Incubate at 4°C overnight with a solution of
10µg/ml of fibronectin in PBS.
- Before plating the cells, wash the fibronectin
solution with fresh plating medium twice and incubate
the substrates with medium at 37°C for 1h.
- Plate cells at appropriate dilution and incubate
immediately until observation.
Images are recorded, using phase-contrast or fluorescence
optical mode, with a DeltaVision system
digital microscopy system. This system is based on a
Zeiss inverted microscope equipped with filter sets for
multiple color microscopy and a high-resolution, scientific-
grade CCD camera. Images are acquired using
high numerical aperture oil objectives for the highresolution
pattern and focal adhesion detection (Fig.
3); long distance objectives are used for semiquantitative
estimates of force using large patterns (Fig. 2).
Image processing is conducted primarily using the
Prism software of the DeltaVision system.
D. Calibration of Elastic Properties of
The aim of this step is to determine whether the
cured PDMS is an elastomer and to obtain the two
parameters that characterize its elasticity, namely the
Young modulus (Y
) and the Poisson ratio (σ)
1. Bulk Calibration
|FIGURE 1 Bulk calibration of the elastomer.
A stripe of PDMS
prepared in parallel to
preparation of elastomer substrates is
its elastic properties. The procedure consists of
the stripe to increasing masses while
measuring the force-extension
Cut strips of cured elastomer (see Section III,B, step
5). Typically a strip of 100 × 30 × 5 mm can be used.
Hold each side with clamps wider than the strip. With
a marker, draw two lines on the elastomer, away from
the clips, separated by about 50mm. The distance
between the lines is marked as L in Fig. 1. Add increasing
, to the lower clamp and measure
the total increase in length, dL
, until dl > L
. Plot the
with m expressed in kilograms. Verify
that the relation is linear and extract the linear coefficient,
α. The Young modulus
(in Pa) is given by
with A = w*h
, the cross section of the strip (in m2
The strips should be stretched overnight to verify that
they relax to their original length, L
, once the weights
2. In Situ Calibration
In order to verify that the plating of cells does not
modify the elastic characteristics of the surface, in situ
calibration of the elasticity of the patterned substrate
is performed under a microscope.
Mount the calibrated micropipette on a micromanipulator.
Approach the surface slowly, keeping the
micropipette parallel to the patterned elastomer
surface. Once the tip of the micropipette is in contact
with the surface, acquire an image of the patterned
elastomer and of the tip of the pipette. Slowly move
the stage by 2-3 µm in order to create a stress between
the micropipette and the surface. Acquire a new image
of the deformed pattern and of the micropipette
bending. Usually, images at different magnifications
are necessary in order to visualize the distortions of the
pattern and of the micropipette. The force exerted by
the micropipette is measured directly by quantifying
the deflection of the pipette in the image. Verify that
the calculation of force using the bulk Young modulus
agrees with the known force exerted by the calibrated
|FIGURE 2 Rapid semiquantitative estimate of forces (Balaban et al., 2001). A large grid-patterned elastomer is used for the easy
visualization of distortions. (a) A rat cardiac fibroblast exerts forces
on the elastomer substrates, which result in deformations of the grid
(marked by arrows). (b) Once the forces are relaxed by adding an
inhibitor of contractility, the grid returns to its original regular
shape. Grid size: 30 µm.
E. Image Analysis
|FIGURE 3 From displacements to forces (Balaban et al., 2001).
(a) Phase-contrast image of a small part of a fibroblast on the highresolution
dot pattern. Arrows denote displacements of the center
of mass of the dots relative to the relaxed image. Pitch size: 2µm.
(b) Fluorescence image of the same field of view showing locations
of the focal adhesions. The length of the arrows here indicates the
forces at each focal adhesion,
calculated from displacement data.
Substrates with low resolution patterns such as the
30-µm grid shown in Fig. 2 can provide semiquantitative
estimates of the mechanical perturbation due to
cells and is useful for the rapid comparison between
different cell types or conditions. However, for the
quantitative measurement of the forces at single adhesion
sites, high-resolution patterns of dots (Fig. 3a), as
well as fluorescence tagging of adhesion sites, are
needed (Fig. 3b). In this section, it is assumed that the
following images are available for the same field of
Registration of Images
- Phase contrast of cells on a high-resolution
pattern of dots ("dot_force.tif").
- Phase contrast of the high-resolution pattern of
dots, after forces have been relaxed ("dot_relaxed.tif"),
namely after treatment with acto-myosin inhibitors or
trypsinization. Alternatively, locations of the dots in
the relaxed pattern can be generated directly as ("center_relaxed.dat") by assuming the regularity of
- Fluorescence image of adhesion sites
In order to correct for eventual shifts during image
acquisitions, all three images should be aligned using
fixed reference points. Typically, corrections of a few
pixels shift in x
might be needed; angular shift are
The step is performed using the registration option
of the image analysis software.
Detection of the Pattern
This step automatically detects the dots in the two
phase-contrast images and outputs their center-ofmass
coordinates to an ASCII file. It is important to use
the same parameters for both images.
3. Detection of Focal Adhesions
- Filter "dot force.tif " and dot relaxed.tif" with a
large kernel in order to correct for background
- Depending on the image quality, use a high pass
filter with a small kernel to enhance the dots contrast
on both images.
- Perform segmentation for the detection of the
dots. Verify that the segmentation detected the dots
properly. Correct manually for eventual defects.
- Save the center of mass coordinates of the dots
in each picture in two separate ASCII files
("center_relaxed.dat" and "center_force.dat").
- Using Matlab, load the two ASCII files and
arrange in pairs nearest neighbors according to their
center of mass coordinates to identify equivalent dots
between the two files. This will work for most of the
image where there are no displacements. In areas
where displacements are larger than the distance
between dots, manual corrections might be needed
(see Section III,F). Save data as an ASCII file
("lines.dat") whose first two columns are the x and y coordinates of the dots in "center relaxed.dat" and the D
last two columns are the x and y coordinates of the
equivalent dots from "center_force.dat".
- Visualization of the displacements: load
"lines.dat" using a procedure for drawing arrows in
the image analysis software (DrawArrows in Prism) on
top of the phase-contrast images. Correct for wrong or
missing arrows. Save corrections.
This step automatically detects focal adhesions in
the fluorescence image of cells with GFP-tagged focal
adhesion protein (Zamir et al.
, 1999). ("focals.tif") and outputs their center-of-mass coordinates to an ASCII
file ("focals.dat"). The segmentation procedure is analogous
to the detection of dots in the pattern.
F. Calculation of Forces
The main advantage of flat elastic substrates is that
they interfere little with cell adhesion as traditionally
studied on glass or plastic surfaces. In particular, by
using transparent elastomers such as PDMS, one can
use the normal setups for light microscopy. The main
disadvantage of flat elastic substrates is that a computational
technique has to be implemented to calculate
force from displacement. For the procedure described
here, a package with Matlab routines can be downloaded
people/schwarz/ElasticSubstrates/. For well-spread
cells, one can assume that forces are applied to the top
side of the elastic film mainly in a tangential fashion.
Because the PDMS film is much thicker than typical
displacements on its top side, one can moreover
assume that displacements follow from forces as in the
case of an elastic half-space. Because we focus on
forces from single focal adhesions, where force is localized
to a small region of space (namely the focal adhesion),
we finally assume that each focal adhesion
corresponds to one point force. Then displacement
follows from force as described by the well-known
Boussinesq solution for the Green function (Landau
and Lifshitz, 1970). Since we only consider the case of
small deformations (i.e., magnitude of strain tensor
| < 1), we deal with linear elasticity theory, and
deformations resulting from different force centers can
be simply added up to give overall deformation at a
given point. However, because the Green function of a
point force diverges for small distance r
, we first
use the Matlab program "data.m" to clear the file
"lines.dat" from all displacement data points, which
are closer to the positions of the focal adhesions in
"focals.dat" than a distance of the order of the size of
focal adhesions [this procedure can be justified with
the concept of a force multipolar expansion (Schwarz et al.
, 2002)]. This gives a new file "newlines.dat",
which together with "focals.dat" is used by our main
Matlab program, "inverse.m". Since we are interested
in force as a function of displacement, but the
Boussinesq solution from linear elasticity theory
describes deformation as a function of force, we now
have to solve an inverse problem. Because the elastic
kernel effectively acts as a smoothing operation that
removes high-frequency data, this inversion is ill
posed in presence of noise in displacement data: small
differences in displacement data can result in large differences
in the force pattern. Due to the noise problem, we only can estimate force through a χ2
Moreover, the target function has to be extended by a
so-called regularization term, which prevents the
program from reproducing every detail of displacement
data through a force estimate with unrealistically
large forces. Therefore, we add a quadratic term in
force to the target function, which guarantees that
forces do not become exceedingly large. The regularization
procedure introduces an additional variable,
the regularization parameter λ, whose value is fixed by
the program "inverse.m" with the help of the so-called
discrepancy principle, which states that the difference
between measured displacement and displacement
following from the force estimate should attain a
certain nonvanishing value. Because the target function
remains quadratic for the simple regularization
term used, it can be inverted easily by singular value
decomposition. For this purpose, the Matlab program
"inverse.m" uses the freely available package of
Matlab routines Regularization Tools
by P. C. Hansen.
Finally the force estimate is saved in a new ASCII file
"forces.dat", which for each entry in "focals.dat" gives
the corresponding force estimate. Force calibration
assumes the value σ = 0.5 for the Poisson ratio and
requires values for Young modulus Y
resolution. The resolution of this procedure depends
on the details of the force pattern under consideration,
but can be estimated by data simulation. Even under
the most favorable conditions, which can be achieved
experimentally in regard to quality of displacement
data, the original force cannot be reproduced completely
and regularization is required to arrive at a reasonable
estimate. Spatial and force resolutions have
been found to be better than 4µm and 4nN
Therefore the calculated point force should be
correlated with other properties of a focal adhesion
only when no other focal adhesions are closer than the
spatial resolution of our method.
- The mixing of the PDMS should be done in many
strokes (typically for a few minutes) and preferably in
plastic dishes with lids.
- Because of variations between batches, the 50:1
ratio of the Sylgard kit might need adjustment.
- The first bake of the PDMS layer should be fine
tuned: too much baking before putting the mold will
result in a poor pattern, whereas insufficient baking
will result in difficulties separating the mold from the
PDMS. Baking times can be reduced by increasing the
- Before dicing the patterned wafer, make sure the
scriber is good by practicing on a similar unpatterned
- The choice of the cells to use is important:
immortalized cell lines often exert forces that are
below the force resolution of this method.
- Focal adhesions formed on PDMS may differ, at
the molecular level, from those formed on other substrates
and their composition (e.g., type of integrin)
should be examined.
BG is the E. Neter Prof. for cell and tumor biology.
NQB is supported by the Bikura program of the
Israel Science foundation and is a fellow of the Center
for Complexity; The Horowitz Foundation.
Balaban, N. Q., Schwarz, U. S., et al.
(2001). Force and focal adhesion
assembly: A close relationship studied using elastic micropatterned
substrates. Nature Cell Biol
Beningo, K. A., and Wang, Y. L. (2002). Flexible substrata for the
detection of cellular traction forces. Trends Cell Biol
Feynman, R. P. (1964). The Feynman Lecture on Physics
. Addison &
Galbraith, C. G., Yamada, K. M., et al.
(2002). The relationship
between force and focal complex development. J. Cell Biol
Geiger, B., and Bershadsky, A. (2001). Assembly and mechanosensory
function of focal contacts. Curr. Opin. Cell Biol
Geiger, B., Bershadsky, A., et al.
(2001). Transmembrane crosstalk
between the extracellular matrix-cytoskeleton crosstalk. Nature
Rev. Mol. Cell Biol
Landau, L. D., and Lifshitz, E. M. (1970). "Theory of Elasticity."
Pergamon Press, Oxford.
Riveline, D., Zamir, E., et al.
(2001). Focal contacts as mechanosensors:
Externally applied local mechanical force induces growth
of focal contacts by an mDial-dependent and ROCK-independent
mechanism. J. Cell Biol
Roy, P., Rajfur, Z., et al.
(2002). Microscope-based techniques to study
cell adhesion and migration. Nature Cell Biol
Schwarz, U. S., Balaban, N. Q., et al.
(2002). Calculation of forces at
focal adhesions from elastic substrate data: The effect of localized
force and the need for regularization. Biophys. J
Whitesides, G. M., Ostuni, E., et al.
(2001). Soft lithography in biology
and biochemistry. Annu. Rev. Biomed. Eng
Zamir, E., Katz, B. Z., et al.
(1999). Molecular diversity of cell-matrix
adhesions. J. Cell Sci
(Pt. 11), 1655-1669.