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AFM stiffness nanotomography of normal, metaplastic and dysplastic human esophageal cells
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2011 Phys. Biol. 8 015007
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IOP PUBLISHING PHYSICAL BIOLOGY
Phys. Biol. 8(2011) 015007 (10pp) doi:10.1088/1478-3975/8/1/015007
AFM stiffness nanotomography of
normal, metaplastic and dysplastic
human esophageal cells
A Fuhrmann1,4,JRStaunton
1,4, V Nandakumar2, N Banyai1,
PCWDavies
1,3 and R Ros1,5
1Department of Physics, Arizona State University, Tempe, AZ 85287, USA
2Center for Biosignatures Discovery Automation, Biodesign Institute, Arizona State University, Tempe,
AZ 85287, USA
3Beyond Center, Arizona State University, Tempe, AZ 85287, USA
E-mail: robert.ros@asu.edu
Received 31 July 2010
Accepted for publication 21 October 2010
Published 7 February 2011
Online at stacks.iop.org/PhysBio/8/015007
Abstract
The mechanical stiffness of individual cells is important in tissue homeostasis, cell growth,
division and motility, and the epithelial–mesenchymal transition in the initiation of cancer. In
this work, a normal squamous cell line (EPC2) and metaplastic (CP-A) as well as dysplastic
(CP-D) Barrett’s Esophagus columnar cell lines are studied as a model of pre-neoplastic
progression in the human esophagus. We used the combination of an atomic force microscope
(AFM) with a scanning confocal fluorescence lifetime imaging microscope to study the
mechanical properties of single adherent cells. Sixty four force indentation curves were taken
over the nucleus of each cell in an 8 ×8 grid pattern. Analyzing the force indentation curves,
indentation depth-dependent Young’s moduli were found for all cell lines. Stiffness
tomograms demonstrate distinct differences between the mechanical properties of the studied
cell lines. Comparing the stiffness for indentation forces of 1 nN, most probable Young’s
moduli were calculated to 4.7 kPa for EPC2 (n=18 cells), 3.1 kPa for CP-A (n=10) and
2.6 kPa for CP-D (n=19). We also tested the influence of nuclei and nucleoli staining organic
dyes on the mechanical properties of the cells. For stained EPC2 cells (n=5), significant
stiffening was found (9.9 kPa), while CP-A cells (n=5) showed no clear trend (2.9 kPa) and a
slight softening was observed (2.1 kPa) in the case of CP-D cells (n=16). Some
force–indentation curves show non-monotonic discontinuities with segments of negative slope,
resembling a sawtooth pattern. We found the incidence of these ‘breakthrough events’ to be
highest in the dysplastic CP-D cells, intermediate in the metaplastic CP-A cells and lowest in
the normal EPC2 cells. This observation suggests that the microscopic explanation for the
increased compliance of cancerous and pre-cancerous cells may lie in their susceptibility to
‘crumble and yield’ rather than their ability to ‘bend and flex’.
SOnline supplementary data available from stacks.iop.org/PhysBio/8/015007/mmedia
4A Fuhrmann and J R Staunton contributed equally to this work.
5Author to whom any correspondence should be addressed.
1. Introduction
The mechanical stiffness of individual cells is important in
tissue homeostasis [1], cell growth, division and motility
[2,3], and the epithelial–mesenchymal transition in the
1478-3975/11/015007+10$33.00 1© 2011 IOP Publishing Ltd Printed in the UK
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(b)(a)
(c)
Figure 1. Schematic of cell indentation with combined AFM–CLSM setup and force–indentation curves. (a) A sample scanning AFM with
piconewton force resolution and nanometer spatial resolution is mounted on a dual color confocal fluorescence microscope with the
capability to measure fluorescence lifetimes of the fluorophores (fluorescence lifetime imaging microscopy, FLIM). The AFM tip is aligned
with the confocal volume, enabling simultaneous optical and force measurement in a single scan. Each indentation generates a
force–indentation (F–δ) curve, four of which are plotted in (b). According to the Hertz model, the Young’s modulus Eis directly
proportional to the force Fand inversely proportional to the 3/2 power of the deformation δ. Consequently, in (c) we plot F2/3against δand
implement a piecewise linear fitting algorithm on the F2/3–δcurves. Hertzian behavior corresponds to a single straight line, such as in the
EPC2 curve. Changes in slope, such as in the CP-A and CP-D stained curves, reflect changes in E(δ)with increasing indentation depth,
corresponding to non-Hertzian behavior. Negative slopes, such as in the CP-D unstained curve, reflect cytoskeletal instabilities (see figure 6).
initiation of cancer [4]. Various techniques have been applied
to study the mechanical properties of cancer cells (for a
comprehensive review, see [5]). Guck et al developed a
special optical tweezer system called the optical stretcher
[6]. The combination of the stretcher with microfluidic
networks allowed for the elastic screening of cells. Using
the optical stretcher, it was determined that cancer cells
are generally softer than normal cells. Recently, the
group of Guck applied this method to the diagnosis of
oral cancer [7]. The micropipette aspiration technique was
used by Ward et al to show that cells transformed with
Ras-T24 oncogene exhibiting increased tumorigenicity also
had increased deformability [8]. Another very promising
technique to measure the mechanical properties of cells
is particle-tracking microrheology, introduced by the Wirtz
group [9] (for an extensive recent review, see [10]). With
this method, also called nanorheology, the local viscoelastic
properties of a living cell can be probed by the analysis of the
movement of sub-micrometer fluorescent beads injected into
the cell. This technique allows simultaneous measurement
of local mechanical properties with high spatial resolution at
different places inside the cell.
Another approach, which allows measurement of local
as well as cell-wide mechanical properties, is atomic force
microscopy (AFM) [11]. The stiffness of cells can be
determined with high lateral resolution by using a sharp AFM
tip as a probe. For these experiments, cells are adhered to a
surface and a sharp AFM tip is pushed into the cell surface,
while the indentation depth and probe deflection are recorded.
AFM was used to map the stiffness (Young’s modulus) of
a cell during proliferation [12]. This method has also been
applied to different cancer cells, and in agreement with the
optical stretcher data, cancer cells were found to be a factor
2–10 softer than benign cells [13–15]. For benign (MCF-10A)
and cancerous (MCF-7) breast cell lines, it was reported that
the Young’s moduli depend on the loading rate (i.e. the rate
at which force is applied) [16]. Alternatively, a micrometer-
sized sphere on the AFM cantilever can be used to measure the
global mechanical properties of the cell [17,18]. The Hertz
model [19], describing the simple case of the deformation
of two perfectly homogeneous smooth bodies touching under
load, is most commonly used for the analysis of AFM-based
cell mechanical experiments [20]. For thin samples such as
areas in the lamellipodia, Mahaffey et al used the Chen and
Tu extensions of the Hertz model to get the storage and loss
moduli of adhered and non-adhered regions, respectively [17].
In this paper, we present findings from our study of
the local mechanical properties of the nuclear regions of
esophageal cell lines in different phases of premalignancy.
We compared cells from a normal squamous cell line (EPC2)
[21] and two Barrett’s Esophagus columnar cell lines (CP-
A and CP-D) and also studied the influence of organic dyes
on their mechanical properties. CP-A was derived from
biopsies taken from a region of non-dysplastic metaplasia
and CP-D was derived from biopsies taken from regions of
high-grade dysplasia [22]. Previous cytogenetic studies have
revealed p16 deletion and wild-type p53 in CP-A, and both
p16 and p53 deletion in CP-D. The cell lines were shown to
be karyotypically similar to in vivo counterparts [22,23]. To
the best of the authors’ knowledge, this is the first comparative
elasticity study of premalignant cells.
For our experiments, we used a combination of an AFM
with a confocal laser scanning microscope (CLSM) capable of
measuring the fluorescence lifetimes of the dyes (fluorescence
lifetime imaging microscopy, FLIM) (figure 1(a)). The ability
to move the sample and objective independently allows for
precise alignment of the AFM probe and laser focus with
an accuracy down to a few nanometers [24]. This enables
2
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
direct correlation of the point of indentation and the sub-
cellular structures in the FLIM image. To apply the Hertz
model to heterogeneous materials like cells, we developed
algorithms for the segmental analysis of force–indentation
curves. This enables the quantification of stiffness as it varies
with indentation depth (figures 1(b) and (c)).
2. Materials and methods
2.1. Cell culture
Immortalized Barrett’s Esophagus (BE) cells derived from
non-dysplastic metaplasia (CP-A cells) and high-grade
dysplasia (CP-D cells) [22,23] and normal esophageal cells
(EPC2 cells) were used for the experiments. Cells from
all studied cell lines were cultured in Keratinocyte-serum-
free medium 1 ×(Invitrogen, Carlsbad, CA). The medium
contained L-glutamine and calcium chloride. Additional
supplements added to the medium prior to use were bovine
pituitary extract (1 ×25 mg, Invitrogen) and epidermal growth
factor—human recombinant (1 ×2.5 μg, Invitrogen).
2.2. Sample preparation
The cultured cells were then seeded at ∼30% confluence into
50 mm glass bottom petri dishes (Fluorodish, World Precision
Instruments) and incubated with growth medium at 37 ◦C and
5% CO2for a period of 72 h. The medium was exchanged with
1 ml imaging assay buffer (Enzo Life Sciences) prior to AFM
measurements to provide an optically clear medium optimized
for fluorescence imaging. The solution was also buffered for
CO2and pH 7.5 by adding 25 mM HEPES. For experiments on
stained cells, 5 μl of 1:5 diluted stock solution of Nuclear ID
Red (Enzo Life Sciences) and 5 μl of 1:5 diluted stock solution
of Nucleolar ID Green (Enzo Life Sciences) were added to the
medium 30 min prior to AFM measurements and allowed to
diffuse with gentle swirling.
2.3. Combined AFM–CLSM setup
The combined AFM–CLSM setup we used consists of a
sample scanning AFM (MFP-3D Bio, Asylum Research,
CA) and a single molecule sensitive confocal fluorescence
microscope (Microtime 200, PicoQuant, Germany), equipped
with 470 nm and 640 nm lasers for excitation, a high-
end 100 ×1.45 NA oil immersion objective (Olympus,
San Diego, CA) and two single-photon counting modules
for detection [24]. The mechanical link between the two
systems is the AFM sample stage, which is mounted onto
an Olympus IX-71 inverted microscope. With this setup,
the fluorescence dynamics can be followed on time scales
from sub-nanoseconds to seconds. This setup is ideal for
FLIM. The underlying technique (time-tagged time-resolved
single photon recording) allows us to simultaneously record
timing and fluorescence intensity information, both spectrally
and spatially resolved, on a single photon basis. While
the sample scanning AFM acts as master, the parallel time-
correlated single-photon counting (TCSPC) data acquisition
serves as a slave: start and stop scan line information from
the AFM are transferred to the TCSPC electronics, enabling
us to achieve online synchronized and matched AFM and
fluorescence images with direct access to ns time-resolved
single-photon data.
2.4. AFM nanoindentation
Soft silicon AFM probes with nominal spring constants k≈
10 pN nm−1(MSNL, Veeco Instruments, Santa Barbara, CA)
were used for the indentation experiments. The spring constant
of each cantilever was determined from the thermal noise
spectrum [25,26]. The AFM tip and the confocal volume
were aligned using the pattern of back-scattered light [24].
After the alignment, the AFM tip is fully retracted and the
sample stage is moved until a cell of interest is under the tip.
A FLIM image of the cell in two frequency bands (green and
deep red) is acquired while the tip is still retracted. In the FLIM
image, the cell nucleus is identified and precisely located. The
nucleus is brought directly under the AFM tip. In a (∼5μm)2
region, an 8 ×8 grid of indentations is acquired with
2μms
−1approach and retract speeds in force volume mode
with a trigger force of 1 nN. After indentation, a subsequent
FLIM image is taken of the cell with exactly the same settings
as the preliminary image. The two images are superposed
in software (ImageJ [27]) to determine the extent to which
the cell moved during the measurements. If the cell moved
more than ∼1μm, then the data are discarded and are not
further analyzed. The alignment of the tip is then verified
as above and another cell can be located and measured.
After measurements, the probes were imaged with a scanning
electron microscope and the tip radii were determined to be in
the range of 50 nm.
2.5. Data analysis
Each indentation generates a force–indentation (F–δ) curve
to be saved and analyzed with custom written software (Igor
Pro, Wavemetrics, Portland, OR). The curves are corrected for
cantilever bending. All force data points are incremented by a
constant so that they are all positive, subsequently raised to the
2/3 power and then plotted in a F2/3–δcurve. According to the
Hertz model [19] of a sphere indenting an elastic half-space,
the Young’s modulus Eis directly proportional to the force F
and inversely proportional to the 3/2 power of the deformation
δ:
F=4
3
E
(1−ν2)
√δ3R,
where Fis the load distributed over the contact area, Ris the
radius of the sphere, νis the Poisson ratio of the surface, δis
the deformation of the sample and Eis the Young’s modulus
of the sample. Here, the AFM tip is approximated as a sphere
of radius Ron a cantilever deflected by a force F. The cell is
approximated as a flat, isotropic material with a Poisson ratio
of 0.4 that is elastically deformed by the AFM tip in the limit
of small strains [28]. Accordingly, the F2/3–δcurve should be
linear [29], with a slope directly proportional to E2/3:
F 2/3
δ =4
3
E
(1−ν2)√R2/3
.
3
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
In practice, however, the F2/3–δcurves generated by AFM-
based nanoindentation are not simply linear. Rather, linear
segments corresponding to layers with different stiffness can
be seen at different depths. We therefore invoke a robust
piecewise linear fitting algorithm to reconstruct the curves
into segments of constant Young’s modulus E(δ) at different
depths. The algorithm works by first fitting a line in a small
region of the curve and then iteratively extrapolating it until
a parameter-sensitive deviation threshold is exceeded. Then
another small line is fitted in the adjacent region and the process
repeats until the whole curve is fitted. The algorithm first fits
the baseline and determines the contact point in this manner,
and then fits the indentation region. It is worth noting that
determination of the contact point is critical in AFM force–
indentation analyses, but our scheme is less sensitive to errors
in contact point determination than those that fit power curves
from the contact point through the entire indentation.
To characterize statistical distributions, we used a kernel
smoothing density estimate function (‘ksdensity.m’, Matlab,
Mathworks, Natick, MA).
3. Results and discussion
3.1. Combined AFM-nanoindentation and CLSM
For the nanoindentation experiments, we used a combined
AFM–CLSM setup, which allows the alignment of the AFM
tip with the confocal volume, resulting in a precise correlation
of the fluorescence images and the point of indentation. AFM
tips with tip radii of ∼50 nm were used in order to get
precise alignment and to probe the mechanical responses at
the nanoscale. Figure 1(a) shows a schematic of AFM–
CLSM cell indentation. The AFM tip is cycled up and down
while the force acting on the tip is recorded. Figure 1(b)
shows representative force–indentation curves (F–δcurves).
To fit the Hertz model, data points are plotted in the F2/3–δ
curves (figure 1(c)), whose slopes are proportional to E2/3.
The curves show different slopes, requiring the calculation
of depth-dependent Young’s moduli. In figure 1(c), the blue
curve from a normal squamous EPC2 cell shows a steep incline
after the tip hits the cell surface, representing stiff behavior at
this point. In contrast, compliant behavior is exemplified by
the orange curve from a dysplastic CP-D cell stained with
organic dyes. We also observed curves whose slopes increase
non-monotonically (green, CP-A unstained) and saw-tooth
patterns (red, CP-D unstained).
In order to precisely localize the cell nuclei and nucleoli,
we chose to employ FLIM rather than regular fluorescence
because of its higher contrast. The lifetimes of the
fluorophores’ excited states depend on the decay pathways
available, which are sensitive to any number of highly
localized environmental conditions that might influence the
cell’s mechanical properties [30]. Figure 2shows fluorescence
lifetime images of a single CP-D cell stained with nuclear and
nucleolar dyes, in its entirety (figure 2(a)) and in a close-
up of the nucleus (figure 2(b)). The images integrate data
from the emission spectra of both dyes. The intensity of
photons in each pixel is represented by the brightness of
Table 1. Kernel smoothing density estimates of modal Young’s
moduli and distribution full widths at half maxima (FWHM) from
figure 3.
Number Total number Modal Young’s FWHM
Cell type of cells of indentations modulus (kPa) (kPa)
EPC2
unstained
18 1152 4.72 7.17
CP-A
unstained
10 640 3.08 5.64
CP-D
unstained
19 1216 2.64 5.49
EPC2
stained
5 320 9.89 17.96
CP-A
stained
5 320 2.98 7.04
CP-D
stained
16 1024 2.12 5.65
the pixel, and the average lifetime of photons detected in
each pixel is represented by the color. Different fluorescence
lifetimes of the two dyes allow the superposition of the two
image channels. In figure 2(a), distinct chromatin fibers
in the nucleus are light blue-green in color. Small blue
ellipses in the cytoplasm indicate mitochondrial DNA. The
shorter lifetime of mtDNA may be due to lower pH in the
mitochondrial matrices. In figure 2(b) the nucleoli are yellow-
red. A topography map of the same field of view is shown in
figure 2(c). The cell is indented 64 times in an 8 ×8grid. In
each indentation, the AFM probe presses into the cell until 1 nN
of force is applied, whereupon the tip is retracted. The vertical
position of the AFM cantilever at maximum indentation is
plotted to visualize a stiffness-dependent measure of its height.
The Young’s modulus of the final fit line in the F2/3–δcurve
from each indentation in 2(b) is plotted in figure 2(d). The
stiffness of the cell is clearly heterogeneous on length scales
of ∼1μm. No obvious correlation can be seen between the
fluorescence image and the AFM data, perhaps because the
nuclear membrane redistributes the load applied by the tip.
The central nuclear region exhibits soft spots, while the nuclear
membrane in the bottom corners appear stiffer.
3.2. Mechanical properties for deep indentations
To investigate and compare the elasticities of the nuclei
of EPC2, CP-A and CP-D cells, nuclei from several cells
were indented 64 times each in 8 ×8gridsin(∼5μm)2
areas. The Young’s moduli of the final fit lines were
calculated. The six distributions of moduli from the three
different cell lines, both unstained (figure 3(a)) and stained
(figure 3(b)), were assessed with a kernel smoothing density
(KSD) algorithm. Supplementary figure 1available from
stacks.iop.org/PhysBio/8/015007/mmedia demonstrates that
the KSD characterizes the distributions very well. Because
there is yet no specific model for the distribution of
Young’s moduli at the spatial resolution of AFM-based
nanoindentation, we use the KSD as a model-independent
statistical estimate of the modal Young’s modulus and
4
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(a)
(b)
(c)
(d)
Figure 2. Adherent dysplastic CP-D esophageal cell analyzed with combined fluorescence lifetime imaging and AFM-based
nanoindentation. Confocal fluorescence lifetime images of the cell labeled with nuclear dye emitting in red and nucleolar dye emitting in
green (a) in its entirety and (b) in a close-up of the nucleus. Pixels are color mapped to average fluorescence lifetime and intensity mapped
to photon count. The AFM tip is aligned with the confocal volume before scanning. Topography (c) and elasticity (d) from 8 ×8AFM
force map of the same area as (b) with a trigger force of 1 nN. Height is calculated from the AFM cantilever’s vertical position at maximal
indentation. Young’s moduli are calculated with the Hertz model from the final region of each force–indentation curve.
distribution width (see table 1). The modal Young’s modulus
of unstained EPC2 was 4.7 kPa, and those of unstained
CP-A and CP-D were 3.1 kPa and 2.6 kPa, respectively.
The non-dysplastic CP-A cells in this study are thus softer
than the normal EPC2 cells by a factor of ∼1.5, while
the dysplastic CP-D cells are softer by a factor of ∼1.8.
These noteworthy premalignant variations in stiffness suggest
that mechanical compliance increases gradually along with
the morphological changes marking the progression from
metaplasia to neoplasia. The changes in compliance we
found complement previous reports that malignant cells are
softer than their normal counterparts by factors ranging from 2
to4[13,14,16].
We also tested the influence of nuclear and nucleolar dyes
on the mechanical properties of the cells (figure 3(b)). For
EPC2 cells stained with Nuclear ID Red and Nucleolar ID
Green, significant stiffening was found (9.9 kPa). This is in
accordance with single cell compression experiments on cells
stained with various cell tracing dyes [31]. In contrast, the
stained CP-A showed no clear trend (2.9 kPa) and a slight
softening was observed (2.1 kPa) in the case of stained CP-D.
We speculate that this surprising effect reflects systemic
differences in the metabolic and regulatory processes that
govern cytoskeletal stability in the abnormal cell lines.
3.3. Segmental analysis of force–indentation curves
To better understand the nature of the mechanical
differences between these cells, we analyzed the force–
indentation curves to get the Young’s modulus as a
function of the indentation depth. In contrast to
curve fitting approaches [32,33], our algorithm detects
Hertzian-like segments and analyzes the Young’s modulus,
depth and length of these segments. Figures 4(a)
and (b) depict 3D elasticity maps of CP-A and CP-D cells,
respectively. The surface heights and Young’s moduli are
calculated from force maps as in figure 2. The surface is
color mapped to the Young’s modulus. Additionally, three
horizontal black lines are projected on the surface of each cell.
These lines correspond spatially to the elasticity tomograms in
figures 4(c) and (d). Each tomogram consists of 32 vertical
stacks. Each stack contains information about a single
indentation. The top of each stack corresponds to the height at
which the AFM tip first contacts the cell, as estimated by
the linear piecewise fitting algorithm. Each colored band
corresponds to the Young’s modulus from a single linear
segment fitting a region of the F2/3–δcurve. The bottom of
the stack corresponds to the depth at which the trigger force is
reached, and is therefore the same color as the corresponding
position of the surface in figures 4(a)or(b). The greater
5
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(a)
(b)
Figure 3. Distributions of Young’s moduli of EPC2, CP-A and
CP-D esophageal cell nuclei. Kernel smoothing density estimates of
Young’s moduli calculated from the final region of each (of n)
force–indentation curves collected from 8 ×8 force maps of cell
nuclei. FLIM images are taken (before) to identify nuclei and
determine scanning region (∼5μm)2of the force maps and (after)
to verify that cell has not moved appreciably (1μm) during
measurement. Data from (a) unstained EPC2 (n=1152), CP-A
(n=640) and CP-D (n=1216) cell nucleus indentations. The
modal Young’s modulus is highest for EPC2, intermediate for CP-A
and lowest for CP-D (see table 1). Data from (b)EPC2(n=320),
CP-A (n=320) and CP-D (n=1024) cells labeled with both
nuclear and nucleolar dyes indicate that with these dyes, the modal
Young’s modulus of EPC2 increases by a factor of 2, that of CP-A is
unchanged and that of CP-D decreases slightly (see table 1).
heights of the CP-D vertical stacks indicate that the CP-D
cell is more deformable than the CP-A cell. The CP-D cell
appears to be more laterally mechanically homogeneous than
the CP-A cell, as indicated by the nearly uniform distribution of
yellow bands beginning at about 80% of the total indentation
depth. Neither cell is mechanically homogeneous radially,
especially as evidenced by the multitude of extremely narrow
white bands, representing negative slopes on the F2/3–δcurve
(breakthrough events, see below).
Because the F2/3–δcurves of living cells are so frequently
not simply linear, but rather piecewise linear, a single cited
value for the Young’s modulus of a cell cannot accurately
express the cell’s elasticity. We therefore plot Young’s moduli
as a function of indentation depth in the form of 2D histograms
in figure 5. These histograms quantify the depth dependence
of cell stiffness and illustrate important differences between
these cell lines that cannot be distinguished by nominal depth-
independent values of Young’s moduli. The starting depth,
stopping depth and slope of each linear segment from each
F2/3–δcurve are used to bin the segments horizontally by
indentation depth into 25 nm bins and vertically by the Young’s
modulus calculated from their slopes into 50 bins spaced
logarithmically over five decades, up to 100 kPa. Each
segment exceeding 25 nm indentation spans multiple bins.
The histograms are color mapped by counts per bin. Segments
with negative slopes are excluded.
On each histogram, we have superposed a black curve
plotting the (E,δ) coordinate solutions of the Hertz equation
for F=1 nN. Because our measurements are performed with a
fixed trigger force, an ideal Hertzian cell with constant Young’s
modulus (as in figure 1(c), blue F2/3–δcurve) would occupy
a horizontal band of bins spanning from the vertical axis to
the Hertz curve. A cell of lower (higher) Young’s modulus
will be indented more (less). The curve thus provides a point
of comparison for the way each cell line differs from an ideal
Hertzian cell. A stress hardening cell with monotonically
increasing Young’s modulus (as in figure 1(c), orange F2/3–
δcurve) should occupy bins forming a convex curve on the
histogram, contributing to the portion of the distribution near
the origin. A cell with non-monotonic changes in Young’s
moduli (as in figure 1(c), green and red F2/3–δcurves) occupies
bins in a more complicated pattern, contributing to the portion
of the distribution to the right of the Hertz curve.
The degree to which the Young’s modulus varies with
indentation depth differs significantly among the cell lines
and with the addition of fluorescent dyes. Data from (n)
indentations on (m) cells are shown: unstained (a) EPC2
(n=1152, m=18), (b) CP-A (n=640, m=10), (c) CP-
D(n=1216, m=19); and stained (d) EPC2 (n=320,
m=5), (e) CP-A (n=320, m=5) and (f) CP-D (n=1024,
m=16). In the case of (a) unstained EPC2, the red
horizontal band of peaks at ∼5 kPa is somewhat Hertzian.
However, many EPC2 F2/3–δcurves show hardening with
depth. Unstained CP-D (c) exhibits an isolated cluster (in
contrast to a horizontal band) of peaks from ∼1to2kPa.
The characteristic total indentation depths can be estimated
by looking at how far to the right each distribution spreads.
The bright blue region of the CP-D distribution is very broad
and extends considerably past the Hertz curve to ∼1500 nm.
The bright blue region of the EPC2 distribution extends only
to ∼800 nm. The CP-D cells are evidently much more
deformable than the EPC2 cells, irrespective of the calculated
Young’s moduli. Typical cell heights ranged from 7 to
13 μm, depending on size and shape, corresponding to strains
∼10%. Interestingly, the dyes had adverse effects on the
different cell lines. The dye apparently caused a decrease
in deformability and increase in stiffness of EPC2, opposite
effects on CP-D, and an increase in deformability but no
change in stiffness in the case of CP-A.
The strain borne by a cell during indentation is clearly
not a simply linear function of the stress. Moreover,
6
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(a)(b)
(c)(d)
Figure 4. 3D elasticity maps and corresponding elastic tomograms of CP-A and CP-D cells. 3D elasticity maps of typical (a)CP-Aand
(b) CP-D cells. Height and Young’s moduli are calculated as in figure 2. The black lines on surfaces correspond to the elasticity tomograms
shownin(c)and(d). Surfaces and tomograms are color mapped to Young’s modulus. In a tomogram, each vertical rectangular stack depicts
a single indentation. The AFM tip contacts the cell at the top and retracts at the bottom of each stack. Tall (short) stacks occur at points
where the cell is more (less) deformable. The white bands in the stack indicate breakthrough events (see figure 6). The CP-D cell not only
has a lower Young’s modulus toward the end of the indentation, but it is also more homogeneous and more deformable than the CP-A cell.
the distributions exhibit neither simple strain hardening nor
softening, but rather a mixture of the two. These changes
in stiffness could possibly reflect either active rearrangement
in which stretch-induced membrane stress activates Rho
signalling [34], or passive rearrangement in which the
applied load causes geometrical changes such as buckling
[31]. The nanoscale details of the cytoskeleton’s response
to nanoindentation remain unknown, but further development
of combined fluorescence techniques may shed light on the
processes involved.
3.4. Discontinuities in the force–indentation curves
In order to further investigate this nonlinearity we focused
on segments of the F2/3–δcurves that exhibit negative
slopes. Linear segments of F2/3–δcurves with negative
slope occur when the resistance levied by the cell against
the AFM tip is suddenly relieved, allowing it to descend
further into the cell with less applied force. An example of
this is shown in figure 6(a). In most cases, the segments
of negative slope reflect large changes in applied force
over very small distances. We propose that these changes
correspond to events in which stresses induced by the AFM
tip on cortical structures are transferred by intermediate
filaments to stress fibers deeper in the cytoskeleton that
break, ultimately allowing superficial material to displace
or slip past the disrupted filamentous matrix. We therefore
denote such occurrences ‘breakthrough events’. The number
of breakthrough events can thus be seen as a measure of
structural integrity. We expect that breakthrough events
should be most frequent in cells with cytoskeletons weakened,
for example, by underexpression of actin-binding proteins
(ABPs) such as filamin A, downregulation of which is
known to occur following the differentiation of neuronal
cells [35], and may likewise occur following metaplastic
transformation. Apart from its structural role as an actin
crosslinker, filamin has been shown to modulate epidermal
growth factor receptors (EGFR) [36], which are known
to be deregulated in squamous malignancies [21]. We
found that the frequency of incidence of breakthrough
events differs significantly between the normal EPC2,
metaplastic CP-A and dysplastic CP-D cells. Figure 6(b)
shows the percentages of total indentations exhibiting 1, 2,
3 and 4 or more breakthroughs for stained and unstained
cells of each cell type. The probability of observing
breakthrough events increases considerably from EPC2 to
CP-A to CP-D. The probability of multiple breakthroughs
follows the same pattern of increase. This observation
7
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(a)(d)
(b)(e)
(c)(f)
Figure 5. 2D elasticity histograms of Young’s modulus versus indentation depth. The F2/3–δcurves are reconstructed piecewise with linear
segments. The starting depth, stopping depth and slope of the linear segments are then used to construct a 2D histogram of Young’s modulus
versus indentation depth. Each segment is binned horizontally by indentation depth into 25 nm bins and vertically by the Young’s modulus
calculated from its slope into 50 bins spaced logarithmically over five decades, up to 100 kPa. The histograms are color mapped by counts
per bin. Unstained (a)EPC2(n=1152), (b)CP-A(n=640), (c)CP-D(n=1216) cells and stained (d)EPC2(n=320), (e)CP-A(n=
320) and (f)CP-D(n=1024) cells are shown. The black curve plotting the (E,δ) coordinate solutions of the Hertz equation for F=1nN
applied force. Hertzian behavior (i.e. depth-independent moduli) is characterized by horizontal bands of uniformly occupied bins, such as
the red peak in (a) at 5 kPa from 0 to 400 nm. The degree to which the Young’s modulus varies with indentation depth differs significantly
among the cell lines and with the addition of fluorescent dyes.
suggests that the microscopic explanation for the increased
compliance of cancerous and pre-cancerous cells may lie in
their susceptibility to ‘crumble and yield’ rather than their
ability to ‘bend and flex’.
We also expected that cells with greater structural integrity
should require a greater applied force in order for the AFM
tip to elicit a breakthrough. When we summed the changes in
force Ffrom each breakthrough to get the total breakthrough
force from a single indentation, and compared Fof those
curves exhibiting at least one breakthrough, we found no
clear difference between the cell lines (supplementary figure 2
available from stacks.iop.org/PhysBio/8/015007/mmedia).
8
Phys. Biol. 8(2011) 015007 A Fuhrmann et al
(a)(b)
Figure 6. Nanoscale cytoskeletal instability quantified by the
frequency of incidence of breakthrough events. Linear segments of
F2/3–δcurves with negative slope occur when the resistance levied
by the cell against the AFM tip is suddenly relieved, allowing it to
descend further into the cell with less applied force. We propose
that these ‘breakthrough events’ correspond to disruptions of
pre-stressed tensile structures in the cytoskeletal mesh due to
transverse compression by the AFM tip. The percentages of
indentations with (exactly) 1, 2, 3 and 4 or more breakthrough
events are plotted. Breakthrough events are most frequent in the
CP-D cells, as corroborated by the multitude of narrow white bands
in the elasticity tomograms in figure 4(d). Interestingly, CP-D
exhibited more and EPC2 exhibited less breakthroughs with the use
of the nuclear and nucleolar dyes.
Since only a modest percentage of the measured curves
exhibited breakthroughs, larger sample sizes may be necessary
to see a trend in these data.
4. Conclusion and outlook
Metaplastic CP-A and dysplastic CP-D precancerous
esophageal cells were found to be significantly softer than
normal EPC2 cells. Additionally, staining the nuclei and
the nucleoli with organic dyes was found to produce adverse
effects on the mechanical properties of the different cell
lines: EPC2 showed significant stiffening, while CP-A
showed greater deformability and CP-D showed softening.
Correlations between stiffness and the spatial arrangement of
chromatin fibers or nucleoli in the nucleus were not evident;
however, labeling other subcellular structures might reveal
correlations in future work.
We also developed a robust piecewise linear fitting
algorithm to determine indentation depth-dependent Young’s
moduli. Our segmental analysis of force–indentation curves
was used to clarify distinctions between stiffness and
deformability in cells with nonlinear strain-hardening. In
stiffness tomograms and 2D histograms, we identified subtle
differences in the distributions of the mechanical properties
of the cell lines. Divergence from Hertzian behavior was
assessed in terms of F2/3–δcurves whose slopes increase
non-monotonically. The frequency of segments with negative
slope (‘breakthroughs’) in AFM force–indentation curves may
also prove to be a useful parameter in the characterization of
cytoskeletal stability.
Even in the earliest stages of cancer development, the
mechanical properties of the cell are altered. This study,
conducted on a cell line model of pre-neoplastic progression
in the human esophagus, suggests that the correlation between
increased elasticity and malignancy holds even in the early
stages of metaplastic transformation. While measurements
on explanted cells would strengthen the case, our results are
consistent with the growing body of evidence from a variety
of different experimental techniques and cell types that cells
in later stages of many cancers are abnormally soft.
To gain deeper cytomechanical insight, more
sophisticated models must face the structural and
morphological heterogeneity of the cell head on. Possible
approaches are finite element methods [37,38] or subcellular
element models [39]. With the development of appropriate
analytical techniques, the AFM shows promise in its ability
to probe the elasticity of cells even deep within the
cytoskeleton. Future developments of quantitative mechanical
nanotomography methods will not only facilitate better
understanding of mechanical properties deep within the cell,
it will also illuminate the authentic mechanics of cells in more
physiological conditions by rendering possible the elastic
analysis of cells embedded in ECM-like matrices.
Acknowledgments
The authors acknowledge support from NIH (U54 CA143682)
and Arizona State University. JRS was supported by GAANN
(P200A090123). The esophageal epithelial cell lines were
kindly provided by Dr Carlo Maley. We thank Patti Senechal-
Willis and Courtney Hemphill for their assistance with cell
culture and sample preparation. We gratefully acknowledge
the use of the SEM facilities within the Center for Solid
State Science at Arizona State University. We thank Olaf
Schulz for help with the combined AFM/CLSM setup and
determination of the AFM tip radii with SEM. The help of
Dr Felix Koberling, Dr Marcelle Koenig, (PicoQuant GmbH)
and Dr Deron Walters, Jacob Viani (Asylum Research) in the
synchronization of the AFM with the FLIM setup is gratefully
acknowledged.
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