The Optical Stretcher: A Novel Laser Tool to Micromanipulate Cells
Jochen Guck,* Revathi Ananthakrishnan,* Hamid Mahmood,* Tess J. Moon,†¶C. Casey Cunningham,‡
and Josef Ka ¨s*§¶?
*Center for Nonlinear Dynamics, Department of Physics, University of Texas at Austin, Texas 78712,†Department of Mechanical
Engineering, University of Texas at Austin, Texas 78712,‡Baylor University Medical Center, Dallas, Texas 75246,§Institute for Molecular
and Cellular Biology, University of Texas at Austin, Texas 78712,¶Texas Materials Institute, University of Texas at Austin, Texas 78712,
?Center for Nano- and Molecular Science and Technology, University of Texas, Austin, Texas 78712 USA
object is zero but the surface forces are additive, thus leading to a stretching of the object along the axis of the beams. Using
this principle, we have constructed a device, called an optical stretcher, that can be used to measure the viscoelastic
properties of dielectric materials, including biologic materials such as cells, with the sensitivity necessary to distinguish even
between different individual cytoskeletal phenotypes. We have successfully used the optical stretcher to deform human
erythrocytes and mouse fibroblasts. In the optical stretcher, no focusing is required, thus radiation damage is minimized and
the surface forces are not limited by the light power. The magnitude of the deforming forces in the optical stretcher thus
bridges the gap between optical tweezers and atomic force microscopy for the study of biologic materials.
When a dielectric object is placed between two opposed, nonfocused laser beams, the total force acting on the
For almost three decades, laser traps have been used to
manipulate objects ranging in size from atoms to cells
(Ashkin, 1970; Chu, 1991; Svoboda and Block, 1994). The
basic principle of laser traps is that momentum is transferred
from the light to the object, which in turn, by Newton’s
second law, exerts a force on the object. Thus far, these
optical forces have solely been used to trap an object. The
most common laser trap is a one-beam gradient trap, called
optical tweezers (Ashkin et al., 1986). Optical tweezers
have been an invaluable tool in cell biological research: for
trapping cells (Ashkin et al., 1987; Ashkin and Dziedzic,
1987), measuring forces exerted by molecular motors such
as myosin or kinesin (Block et al., 1990; Shepherd et al.,
1990; Kuo and Sheetz, 1993; Simmons et al., 1993; Svo-
boda et al., 1993), or the swimming forces of sperm (Tadir
et al., 1990; Colon et al., 1992), and for studying the
polymeric properties of single DNA strands (Chu, 1991).
In contrast, the optical stretcher is based on a double-
beam trap (Ashkin, 1970; Constable et al., 1993) in which
two opposed, slightly divergent, and identical laser beams
with Gaussian intensity profile trap an object in the middle.
This trapping is stable if the total force on the object is zero
and restoring. This condition is fulfilled if the refractive
index of the object is larger than the refractive index of the
surrounding medium and if the beam sizes are larger than
the size of the trapped object. In extended objects such as
cells, the momentum transfer primarily occurs at the sur-
face. The total force acting on the center of gravity is zero
because the two-beam trap geometry is symmetric and all
the resulting surface forces cancel. Nevertheless, if the
object is sufficiently elastic, the surface forces stretch the
object along the beam axis (see Fig. 1) (Guck et al., 2000).
At first, this optical stretching may seem counterintuitive,
but it can be explained in a simple way. It is well known that
light carries momentum. Whenever a ray of light is reflected
or refracted at an interface between media with different
refractive indices, changing direction or velocity, its mo-
mentum changes. Because momentum is conserved, some
momentum is transferred from the light to the interface and,
by Newton’s second law, a force is exerted on the interface.
To illustrate, let us consider a ray of light passing through
a cube of optically denser material (see Fig. 2). As it enters
the dielectric object, the light gains momentum so that the
surface gains momentum in the opposite (backward) direc-
tion. Similarly, the light loses momentum upon leaving the
dielectric object so that the opposite surface gains momen-
tum in the direction of the light propagation. The reflection
of light on either surface also leads to momentum transfer
on both surfaces in the direction of light propagation. This
contribution to the surface forces is smaller than the contri-
bution that stems from the increase of the light’s momentum
inside the cube. The two resulting surface forces on front
and backside are opposite and tend to stretch the object
(Guck et al., 2000). However, the asymmetry between the
surface forces leads to a total force that acts on the center of
the cube. If there is a second, identical ray of light that
passes through the cube from the opposite side, there is no
total force on the cube, but the forces on the surface gen-
erated by the two rays are additive. In contrast to asymmet-
ric trapping geometries, where the total force is the trapping
force used in optical traps, the optical stretcher exploits
surface forces to stretch objects. Light powers as high as
800 mW in each beam can be used, which lead to surface
forces up to hundreds of pico-Newton. There is no problem
with radiation damage to the cells examined, which is not
surprising because the laser beams in the optical stretcher
Received for publication 15 August 2000 and in final form 6 May 2001.
Address reprint requests to Jochen Guck, University of Texas at Austin,
Center for Nonlinear Dyanmics, RLM14.206, 26th and Speedway, Austin,
TX 78712. Tel.: 512-475-7647; Fax: 512-471-1558: E-mail: jguck@
© 2001 by the Biophysical Society
767 Biophysical JournalVolume 81August 2001 767–784
are not focused, minimizing the light flux through the cells
in comparison to other optical traps (see Viability of
Stretched Cells). To demonstrate this concept of optical
deformability, we stretched osmotically swollen erythro-
cytes and BALB 3T3 fibroblasts.
Human erythrocytes, i.e., red blood cells (RBCs), were
used as initial test objects. Red blood cells offer several
advantages as a model system for this type of experiment in
that they lack any internal organelles, are homogeneously
filled with hemoglobin, and can be osmotically swollen to a
spherical shape. They are thus close to the model of an
isotropic, soft, dielectric sphere without internal structure
that we used for the calculation of the stress profiles (see
below). Furthermore, they are very soft cells and deforma-
tions are easily observed. As an additional advantage, RBCs
have been studied extensively and their elastic properties
are well known (Bennett, 1985, 1990; Mohandas and Evans,
1994). The only elastic component of RBCs is a thin mem-
brane composed of a phospholipid bilayer sandwiched be-
tween a triagonal network of spectrin filaments on the inside
and glycocalix brushes on the outside (Mohandas and
Evans, 1994). The ratio between cell radius ? and mem-
brane thickness h, ?/h ? 100. This means that the bending
energy is negligibly small compared to the stretching energy
(see Deformation of Thin Shells). Thus, linear membrane
theory can be used to predict the deformations of RBCs
subjected to the surface stresses in the optical stretcher. By
comparing the deformations observed in the optical
stretcher with the deformations expected, we quantitatively
verified the forces predicted from our calculations.
The BALB 3T3 fibroblasts under investigation are an
example of typical eukaryotic cells that, in contrast to
RBCs, have an extensive three-dimensional (3D) network
of protein filaments throughout the cytoplasm as the main
elastic component (Lodish et al., 1995). In this network,
called the cytoskeleton, semiflexible actin filaments, rod-
like microtubules, and flexible intermediate filaments are
arranged into an extensive, 3D compound material with the
help of accessory proteins (Adelman et al., 1968; Pollard,
1984; Elson, 1988; Janmey, 1991). Classical concepts in
polymer physics fail to explain how these filaments provide
mechanical stability to cells (MacKintosh et al., 1995), but,
in most cells, cytoskeletal actin is certainly a main deter-
minant of mechanical strength and stability (Stossel, 1984,
Janmey et al., 1986; Sato et al., 1987; Elson, 1988).
The actin cortex is a thick (?/h ? 10) homogeneous layer
just beneath the plasma membrane. In cells adhered to the
substrate, additional bundles of individual actin filaments,
called stress fibers, insert into focal adhesion plaques and
span the entire cell interior. Dynamic remodeling of this
network of F-actin facilitates such important cell functions
as motility and the cytoplasmic cleavage as the last step of
mitosis (Pollard, 1986; Carlier, 1998; Stossel et al., 1999).
Cells are drastically softened by actin-disrupting cytochala-
sins (Petersen et al., 1982; Pasternak and Elson, 1985) and
stretcher. The cell is stably trapped in the middle by the optical forces from
the two laser beams. Depending on the elastic strength of the cell, at a
certain light power the cell is stretched out along the laser beam axis. The
drawing is not to scale; the diameter of the optical fibers is 125 ? 5 ?m.
Schematic of the stretching of a cell trapped in the optical
due to one laser beam incident from the left. (A) A small portion of the
incident light is reflected at the front surface. The rest enters the box and
gains momentum due to the higher refractive index inside. On the back, the
same fraction is reflected and the exiting light loses momentum. The lower
arrows indicate the momentum transferred to the surface. (B) The resulting
forces for a light power of 800 mW at the front and the back are Ffront?
105–306 pN and Fback? 108–333 pN, respectively, depending on the
refractive index of the material. Note that the force on the back is larger
than the force on the front. (C) Due to the difference between forces on
front and back, there is a total force, Ftotal? Fback? Ffront? 3 ? 27 pN,
acting on the center of gravity of the box. This total force pushes the box
away from the light source. An elastic material will be deformed by the
forces acting on the surface, which are an order of magnitude larger than
the total force.
Momentum transfer and resulting forces on a dielectric box
768 Guck et al
Biophysical Journal 81(2) 767–784
gelsolin (Cooper et al., 1987), indicating the importance of
actin. More recently, frequency-dependent atomic force mi-
croscopy (AFM)-based microrheology showed that fibro-
blasts exhibit the same viscoelastic signature as homoge-
neous actin networks in vitro (Mahaffy et al., 2000).
Another experiment (Heidemann et al., 1999) investigated
the response of rat embryo fibroblasts to mechanical defor-
mation by glass needles. Actin and microtubules were
tagged with green fluorescent protein and the role of these
two cytoskeletal components in determining cell shape dur-
ing deformation was directly visualized. Again, actin was
found to be almost exclusively responsible for the cell’s
elastic response, whereas microtubules clearly showed flu-
In nonmitotic cells, microtubules radiate outward from
the microtubule-organizing center just outside the cell nu-
cleus (Lodish et al., 1995). They serve as tracks for the
motor proteins dynein and kinesin to transport vesicles
through the cell. Microtubules are also required for the
separation of chromosomes during mitosis (Mitchison et al.,
1986; Mitchison, 1992). Intermediate filaments are unique
to multicellular organisms and comprise an entire class of
flexible polymers that are specific to certain differentiated
cell types (Herrmann and Aebi, 1998; Janmey et al., 1998).
For example, vimentin is expressed in mesenchymal cells
(e.g., fibroblasts). Vimentin fibers terminate at the nuclear
membrane and at desmosomes, or adhesion plaques, on the
plasma membrane. Another type of intermediate filament is
lamin, which makes up the nuclear lamina, a polymer cortex
underlying the nuclear membrane (Aebi et al., 1986). Inter-
mediate filaments are often colocalized with microtubules,
suggesting a close association between the two filament
networks. Both microtubules and intermediate filaments are
thought to be less important for the elastic strength and
structural response of cells subjected to external stress (Pe-
tersen et al., 1982; Pasternak and Elson, 1985; Heidemann
et al., 1999; Rotsch and Radmacher, 2000). However, in-
termediate filaments become more important at large defor-
mations that cannot be achieved with deforming stresses of
several Pascal. Intermediate filaments are also more impor-
tant to elasticity in adhered cells as opposed to suspended
cells, where the initially fully extended filaments become
slack (Janmey et al., 1991; Wang and Stamenovic, 2000).
Despite these experiments, a quantitative description of the
cytoskeletal contribution to a cell’s viscoelasticity is still
missing. The optical stretcher can be used to measure the
viscoelastic properties of the entire cytoskeleton and to shed
new light on the problem of cellular elasticity.
The ability to withstand deforming stresses is crucial for
cells and has motivated the development of several tech-
niques to investigate cell elasticity. Atomic force micros-
copy (Radmacher et al., 1996), manipulation with micro-
needles (Felder and Elson, 1990), microplate manipulation
(Thoumine and Ott, 1997), and cell poking (Dailey et al.,
1984) are not able to detect small variations in cell elasticity
because these detection devices have a very high spring
constant compared to the elastic modulus of the material
probed. The AFM technique has recently been improved for
cell elasticity measurements by attaching micron-sized
beads to the scanning tip to reduce the pressure applied to
the cell (Mahaffy et al., 2000). Micropipette aspiration of
cell segments (Discher et al., 1994) and displacement of
surface-attached microspheres (Wang et al., 1993) can pro-
vide inaccurate measurements if the plasma membrane be-
comes detached from the cytoskeleton during deformation.
In addition, all of these techniques are very tedious and only
probe the elasticity over a relatively small area of a cell’s
surface. Whole-cell elasticity can be indirectly determined
by measurements of the compression and shear moduli of
densely packed cell pellets (Elson, 1988; Eichinger et al.,
1996), or by using microarray assays (Carlson et al., 1997).
However, these measurements only represent an average
value rather than a true single-cell measurement, and de-
pend on noncytoskeletal forces such as cell–cell and cell–
substrate adhesion. The optical stretcher is a new tool that
not only circumvents most of these problems, but also
permits the handling of large numbers of individual cells by
incorporation of an automated flow chamber, fabricated
with modern soft lithography techniques, that guides cells
through the detector.
MATERIALS AND METHODS
The buffer for the RBCs was derived from Zeman (1989) and Strey et al.
(1995) and consisted of 100 mM NaCl, 20 mM Hepes buffer (pH 7.4), 25
mM glucose, 5 mM KCl, 3 mM CaCl2, 2 mM MgCl2, 0.1 mM adenine, 0.1
mM inosine, 1% (volume) antibiotic-antimycotic solution, 0.25–1.5% al-
bumin, and 5 units/ml heparin. All reagents were purchased from Sigma
(St. Louis, MO) unless stated otherwise. Red blood cells were obtained by
drawing ?10 ?l of blood from the earlobe or fingertip. The blood was
diluted with 4 ml of the buffer. Because the buffer has a physiological
osmolarity (?270 mOsm), the RBCs initially have a flat, biconcave,
disc-like shape. However, the buffer was then diluted to lower the osmo-
larity to 130 mOsm, at which point the RBCs swell to assume a spherical
shape. The average radius of the swollen RBCs was measured to be ? ?
3.13 ? 0.15 ?m using phase contrast microscopy. The error given is the
standard deviation (SD) of 55 cells measured. The refractive index of
spherical RBCs, n ? 1.378 ? 0.005 (Evans and Fung, 1972), the refractive
index of the final buffer was measured to be n ? 1.334 ? 0.001, both of
which were used for the calculations in the RBC stretching experiments.
Eukaryotic cell preparation
As prototypical eukaryotic cells, BALB 3T3 fibroblasts (CCL-163) were
obtained from American Type Culture Collection (Manassas, VA) and
maintained in Dulbecco’s Modified Eagle’s Medium with 10% nonfetal
calf serum and 10 mM Hepes at pH 7.4. For cells to be trapped and
stretched in the optical stretcher, they must be in suspension. Because these
are normally adherent cells, single-cell suspensions for each experiment
were obtained by incubating the cells with 0.25% trypsin-EDTA solution
at 37°C for 4 min. After detaching, the activity of trypsin-EDTA was
inhibited by adding fresh culture medium. This treatment causes the cells
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Biophysical Journal 81(2) 767–784
to stay suspended as isolated cells for 2–4 h. Once in suspension, the cells
assumed a spherical shape. Their average radius was ? ? 9.2 ? 2.8 ?m
(SD of 20 cells measured), and their average refractive index, n ? 1.370 ?
0.005, was measured using index matching in phase contrast microscopy
(see Fig. 3) (Barer and Joseph, 1954, 1955a,b). The refractive index of the
cell medium, which was used for the calculations of the fibroblast shooting
and stretching experiments, was measured to be n ? 1.335 ? 0.002.
For the fluorescence studies of the actin cytoskeleton of BALB 3T3
cells in suspension, we used TRITC-phalloidin (Molecular Probes, Inc.,
Eugene, OR), a phallotoxin that binds selectively to filamentous actin
(F-actin), increasing the fluorescence quantum yield of the fluorophore
rhodamine several-fold over the unbound state (Allen and Janmey, 1994).
This assures that predominantly actin filaments are detected rather than
actin monomers. Before staining, the cells were spun down and gently
resuspended in a 4% formaldehyde solution for 10 min to fix the actin
cytoskeleton. They were then washed three times with PBS, permeabilized
with a 0.1% Triton-X 100 solution for 2 min, and washed three more times.
Then the cells were stained with a 1-?g/ml TRITC-phalloidin solution for
10 min, followed by a final washing step (3? with PBS). Fluorescence
images were acquired with an inverted microscope (Axiovert TV100, Carl
Zeiss, Inc., Thornwood, NY) and deconvolved using a Jansson–van Cittert
algorithm with 100 iterations (Zeiss KS400 software).
Silica and polystyrene beads
The silica and polystyrene beads used for the calibration of the image
analysis algorithm and for the shooting experiments were purchased from
Bangs Laboratories, Inc. (Fishers, IN). Their radii were ? ? 2.50 ? 0.04
?m (SD) and ? ? 2.55 ? 0.04 ?m (SD), respectively, as given in the
specifications provided by the manufacturer. Using index matching, their
indices of refraction were measured to be n ? 1.430 ? 0.003 for silica
beads using mixtures of water and glycerol, and n ? 1.610 ? 0.005 for
polystyrene beads using mixtures of diethyleneglycolbutylether and
?-chloronaphthalene. The index of refraction of water, used for the calcu-
lation of the forces on the silica and polystyrene beads in the shooting
experiments, was measured to be n ? 1.333 ? 0.001.
The setup of the experiment (see Fig. 4) is essentially a two-beam fiber
min solution with refractive index n ? 1.370 ? 0.005. At the matching
point, the contrast between cell and surrounding is minimal. The lighter
parts of the cytoplasm have a slightly lower refractive index, whereas the
darker parts have a slightly higher refractive index than the bulk of the cell.
The cell’s radius is ? ? 8.4 ?m.
Phase contrast image of a BALB 3T3 fibroblast in an albu-
splitter (BS), and coupled into optical fibers (OF) with two fiber couplers (FC). The inset shows the flow chamber used to align the fiber tips and to stream
a cell suspension through the trapping area. Digital images of the trapping and optical stretching were recorded by a Macintosh computer using a CCD
Setup of the optical stretcher. The intensity of the laser beam is controlled by the acousto-optic modulator (AOM), split in two by a beam
770 Guck et al
Biophysical Journal 81(2) 767–784
trap (Constable et al., 1993). A tunable, cw Ti-Sapphire laser (3900S,
Spectra Physics Lasers, Inc., Mountain View, CA) with up to 7W of
light power served as light source at a wavelength of ? ? 785 nm (30
GHz bandwidth). An acousto-optic modulator (AOM-802N, IntraAc-
tion Corp., Bellwood, IL) was used to control the beam intensity, i.e.,
the surface forces. This can be done with frequencies between 10?2and
103Hz, thus allowing for time-dependent rheological measurements in
the frequency range most relevant for biological samples. The beam
was split in two by a nonpolarizing beam-splitting cube (Newport
Corp., Irvine, CA) and then coupled into single-mode optical fibers
(mode field diameter ? 5.4 ? 0.2 ?m, NA 0.11). The fiber couplers
were purchased from Oz Optics, Ltd. (Carp, ON, Canada) and the
single-mode optical fibers from Newport. The optical fibers not only
simplify the setup of the experiment, they also serve as additional
spatial filters and guarantee a good spatial mode quality (TEM00). The
maximum light powers achieved in this setup were 800 mW in each
beam at the object trapped. The power exiting the fiber was measured
before and after each experimental run to verify the stability of the
coupling over the 1–2-h period. All power values given are measured
with a relative error of ?1% (SD).
For trapping and stretching cells in the optical stretcher, the fibers’
alignment is crucial. For the RBCs, a solution similar to the one
described in Constable et al. (1993) was used: a glass capillary with a
diameter between 250 and 400 ?m was glued onto a microscope slide,
and the fibers were pressed alongside so that they were colinear and
facing each other (not shown in Fig. 4). Red blood cells were so light
that they sunk very slowly and could be trapped out of a cell suspension
placed on top of the fiber ends. For the BALB 3T3 fibroblasts, we used
a flow chamber geometry (see inset of Fig. 4) that allowed us to stream
a suspension of cells directly through the gap between the optical fibers.
After successfully trapping one cell, the flow was stopped and the cell’s
elasticity was measured. Then the cell was released and the flow was
started again until the next cell was trapped. The microscope slide, or
the flow chamber, was mounted on an inverted microscope equipped for
phase contrast and fluorescence microscopy. Phase contrast images of
the trapping and stretching were obtained with a CCD camera
(CCD72S, MTI-Dage, Michigan City, IN). The pixel size for all mag-
nifications used was calibrated with a 100 lines/mm grating, which
allowed for absolute distance measurements. The side length of the
square image pixels was 118 ? 2 nm for the 40? objective with
additional 2.5? magnification lens, used for the cell-size measure-
ments. To measure larger distances, such as the distance between the
fiber tip and the trapped object, we used a 20? objective, which
resulted in an image pixel size of 611 ? 5 nm/pixel. All stretching
experiments were done at room temperature.
After completing the experiments, image data were analyzed on a Macin-
tosh computer to quantify the deformation of a cell in the optical stretcher.
The algorithm was developed in the scientific programming environment
MATLAB (MathWorks, Inc., Natick, MA), which treats bitmap images as
matrices. Figure 5 A shows a typical phase contrast image of an RBC
stretched at moderate light powers (P ? 100 mW). The boundary of the
cell in the image is the border between the dark cell and the bright halo.
The goal was to extract the shape of the cell from this image to use the
quantitative information for further evaluation.
image of a stretched spherical RBC. The diameter of the cell is about 6 ?m. (B) The original image mapped onto a rectangle. The inside of the cell
is the lower part of the picture. (C) Line scan across the cell boundary from top to bottom after squaring the grayscale values. (D) Line scan after
thresholding and division by the first spatial derivative. (E) The zigzag line is the boundary of the cell as extracted from the binary image. The smooth
line is the inverse Fourier transform of the three dominant frequencies in the original data. (F) The white line shows the image of this smooth line
representing the boundary of the cell as detected by the algorithm converted back into the cell image. The line matches the cell’s boundary to a high
Illustration of the algorithm used for the image analysis of the cell deformation in the optical stretcher. (A) Original phase contrast
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Biophysical Journal 81(2) 767–784
The algorithm consists of the following steps. First, the geometrical
center of the cell is found and used as the origin of a polar coordinate
system. The grayscale values along the radii outward from the center
are reassigned to Cartesian coordinates (see Fig. 5 B). Essentially, the
image is cut along one radius and mapped onto a rectangle. The bottom
of Fig. 5 B is the interior of the cell and the top is the outside. The cell
boundary is along the wavy line between the black and the white bands.
Next, the image is squared to enhance the contrast between cell and
background. The effect of this filter can be seen in Fig. 5 C, which
shows a line scan across the cell boundary. If we assume that the
boundary between inside and outside coincides with the first peak,
when moving from the outside to the inside of the cell, where the slope
of the line scan is zero, we can drastically enhance the signal-to-noise
ratio by dividing the data by their first spatial derivative. Because this
would also enhance peaks in the background noise, we first threshold
the image at a low value to set the background to zero. The combined
effect of this mathematical filter can be seen in Fig. 5 D. The first peak,
taken as the cell boundary, is then easy to detect (zigzag line in Fig.
5 E). The resolution up to this point is identical to the pixel resolution
of the microscope/CCD system, i.e., 118 ? 2 nm/pixel. To further
improve this resolution, we use the physical constraint that the cell
boundary has to be smooth on this length scale. This is implemented by
Fourier-decomposing the boundary data and by filtering out the high
spatial frequency noise, which increases the resolution to an estimated
?50 nm. The smooth line in Fig. 5 E is the inverse Fourier transform of
the remaining frequencies. The information about the deformation of
cells is then extracted from the resulting function. Figure 5 F shows the
original cell with the boundary as detected with this algorithm.
In general, this sort of image analysis can yield resolutions down to ?11
nm (see, for example, Ka ¨s et al., 1996), which is well below the optical
resolution of the microscope and also below the pixel resolution. The
reason, in short, is that we do not want to resolve two close-by objects,
which is limited to a distance of about half the wavelength. Instead, the
goal is to detect how much an edge, characterized by a large change in
intensity, is moving.
The absolute size determination of an object using this algorithm
depends somewhat on the exact definition of the boundary between object
and surrounding medium in the phase-contrast image. Our choice, as
described above, was driven by the investigation of images of silica beads
with known size. The estimated resolution of ?50 nm is in agreement with
measurements of these beads, which have a radius of ? ? 2.50 ? 0.04 ?m
(SD). This resolution is certainly sufficient to discriminate between
stretched and unstretched cells as reported further below. The advantages
of this algorithm are its speed, precision, and its ability to detect the shape
of any cell.
While the radii of the cells were measured with the algorithm, the
distances between the fiber tip and the cell, d, were measured in a simpler
way by counting pixels in images. For the 20? objective, this can be done
with a pixel resolution of ?0.6 ?m.
for different ratios between the beam radius w and the object’s radius ?. The radii of the polystyrene bead and the fibroblast used for this calculation were
? ? 2.55 ?m and ? ? 7.70 ?m and the refractive indices were n2? 1.610 and n2? 1.370, respectively. The total light power P ? 100 mW for all profiles.
The concentric rings indicate the stress in Nm?2(note the different scales). The resulting total force after integration over the surface acting on the center
of gravity of the object is noted in each case.
Surface stress profiles for one laser beam incident from the left on a polystyrene bead (top row) and a BALB 3T3 fibroblast (bottom row)
772Guck et al
Biophysical Journal 81(2) 767–784
RESULTS AND DISCUSSION
Total force for one beam
The simplest way to describe the interaction of light with
cells is by ray optics (RO). This approach is valid when the
size of the object is much larger than the wavelength of the
light. The diameter of cells, 2?, is on the order of tens of
microns. Cell biological experiments, such as the optical
stretching of cells, are performed in aqueous solution, and
water is sufficiently transparent only for electromagnetic
radiation in the near infrared (the laser used was operated at
a wavelength of ? ? 785 nm). Thus, the criterion for ray
optics, 2??/? ? 25–130 ? ? 1, is fulfilled (van de Hulst,
The idea is to decompose an incident laser beam into
individual rays with appropriate intensity, momentum, and
direction. These rays propagate in a straight line in uniform,
nondispersive media and can be described by geometrical
optics. Each ray carries a certain amount of momentum p
proportional to its energy E and to the refractive index n of
the medium it travels in, p ? nE/c, where c is the speed of
light in vacuum (Ashkin and Dziedzic, 1973; Brevik, 1979).
When a ray hits the interface between two dielectric media
with refractive indices n1and n2, some of the ray’s energy
is reflected. Let us assume that n2? n1and n2/n1? 1,
which is the case for biological objects in aqueous media,
and that the incidence is normal to the surface. The fraction
of the energy reflected is given by the Fresnel formulas
(Jackson, 1975), R ? 10?3. The momentum of the reflected
ray, pr? n1RE/c, and the momentum of the transmitted ray,
pt? n2(1 ? R)E/c (Ashkin and Dziedzic, 1973; Brevik,
1979). The incident momentum, pi? n1E/c, has to be
conserved at the interface. The difference in momentum
between the incident ray and the reflected and transmitted
rays, ?p ? pi? pr? pt, is picked up by the surface, which
experiences a force F according to Newton’s second law,
where P is the incident light power and Q is a factor that
describes the amount of momentum transferred (Q ? 2 for
reflection, Q ? 1 for absorption). For partial transmission of
one laser beam hitting a flat interface at normal incidence as
described above, Qfront? 1? R ? n(1 ? R) ? ?0.086 (n1
? 1.33, n2? 1.43, n ? n2/n1). This force acts in the
backward direction, away from the denser medium (see also
Fig. 2). The transmitted ray eventually hits the backside of
the object and again exerts a force on the interface. Here,
Qback? [n ? Rn ? (1 ? R)](1 ? R) ? 0.094, and the force
acts in the forward direction, again away from the denser
medium. For the total force acting on the object’s center of
gravity, Qtotal? Qfront? Qback? 0.008. The total force is
obviously an order of magnitude smaller than either one of
the surface forces.
If the ray hits the interface under an angle ? ? 0, it
changes direction according to Snell’s law, n1sin ? ?
n2sin ?, where ? is the angle of the transmitted ray. In
this case, the vector nature of momentum has to be taken
into account and R becomes a function of the incident
angle ?. R is taken to be the average of the coefficients
for perpendicular and parallel polarization relative to the
plane of incidence. This is a negligible deviation from the
true situation (the error in the stress introduced by this
simplification is smaller than 2% for n2? 1.45, and
smaller than 0.5% for n2? 1.38), but it simplifies the
calculation and preserves symmetry of the problem with
respect to the laser axis. The components of the force in
terms of Q on the front side, parallel and perpendicular to
the beam axis, are
parallel??? ? cos(0) ? R cos?? ? 2??
? n?1 ? R?cos?2? ? ? ? ??
? 1 ? R???cos?2??
? n?1 ? R????cos?? ? ??
? Qfront???cos ?,
perpendicular??? ? sin?0? ? R sin?? ? 2??
? n?1 ? R?sin?2? ? ? ? ??
? n?1 ? R????sin?? ? ??
? Qfront???sin ?,
where ? is the angle between the beam axis and the direc-
tion of the momentum transferred. Similarly, on the back
the components of the surface force are
parallel??? ? ?1 ? R?????n cos?? ? ??
? nR???cos?3? ? ??
? ?1 ? R????cos?2? ? 2???
? Qback???cos ?,
perpendicular??? ? ?1 ? R????? ? n sin?? ? ??
? nR???sin?3? ? ??
? ?1 ? R????sin?2? ? 2???
? Qback???sin ?.
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Biophysical Journal 81(2) 767–784
Subsequent reflected and refracted rays can be neglected
because R ? 0.005 for all incident angles. The magnitude of
the force in terms of Q on either the front or the backside is
Qfront/back??? ? ??Qfront/back
which is a function of the incident angle ?, and the direction
of the force is
?front/back??? ? arctan?
The forces on front and back are always normal to the
surface for all incident angles. Thus, the stress ?, i.e., the
force per unit area, along the surface where the ray enters
and leaves the cell is
where I(?) is the intensity of the light. Figure 6 shows stress
profiles calculated for spherical objects with the refractive
index of polystyrene beads, and with the average refractive
index of RBCs hit by one laser beam with Gaussian inten-
sity distribution. The profiles are rotationally symmetric
with respect to the beam axis. The sphere acts as a lens and
focuses the rays on the back toward the beam axis, which
results in a narrower stress profile. Integrating this asym-
metrical stress over the whole surface yields the total force
on the object’s center of mass, which pushes the object in
the direction of the beam propagation. At the same time, the
applied stress stretches the object in both directions along
the beam axis. Due to the cylindrical symmetry, the total
force has only a component in the direction of the light
propagation, which is generally called scattering force. If
the object is displaced from the beam axis, this symmetry is
broken. It experiences a force, called gradient force, per-
pendicular to the axis, which pulls the object toward the
highest laser intensity at the center of the beam if the
refractive index of the object is greater than that of the
surrounding medium. Because the gradient force is restor-
ing, after the object reaches the axis, it will stay there as
long as no other external forces are present and the gradient
force is zero.
The stress profile and the total force depend on the ratio
between beam radius w and sphere radius ?, and on the
relative index of refraction, n ? n2/n1. If there is only one
beam shining on the object, the total force will accelerate it.
Because the beam is slightly divergent (the beam radius
doubles from w ? 2.7 ?m at the fiber tip to w ? 5.4 ?m
over a distance of 70 ?m), the beam radius w, and therefore
the stress profiles and the total force, are functions of the
distance d from the fiber end (see Fig. 8). Smaller beam size
with respect to the object results in higher light intensity and
thus greater stress on the surface (w/? ? ? 1). As the beam
radius w increases with increasing distance d and w/? ap-
proaches one, the light intensity and the magnitude of the
surface stress decrease. However, the total force increases
because the asymmetry between the front and back becomes
more pronounced. As the beam size becomes much larger
than the object (w/? ? ? 1), the surface stresses and the total
force vanish, because less light is actually hitting the object.
The highest total forces (w/? ? 1) calculated for polystyrene
beads in water and RBCs in their final buffer for a light
power of P ? 100 mW are Ftotal? 28.6 ? 0.9 pN and Ftotal
? 1.82 ? 0.06 pN, respectively. The relative error in the
force calculations, due to uncertainties in the measurement
of the relevant quantities (indices of refraction, light power,
radius, distance between fiber and object) as given earlier,
is 3.2%. In general, the magnitude of the surface stress
and the total force increase with higher relative indices of
The change in total force as the object is pushed away
from the light source can be measured by setting the accel-
erating total force Ftotalequal to the Stokes drag force acting
on the spherical object,
Ftotal? 6???v, (7)
where ? is the viscosity of the surrounding medium and v is
the velocity of the object. The viscous drag on a spherical
object can depend strongly on the proximity of boundaries.
A correction factor a can be found in terms of the ratio
between the radius of the sphere ? and the distance to the
closest boundary b (Svoboda and Block, 1994),
? · · ·
The Reynolds number is on the order of 10?4, so inertia can
be neglected. The measurement of the total force on differ-
ent objects was used to investigate to what extent cells can
be approximated as objects with a homogeneous index of
refraction (see Shooting Experiments).
Stress profiles for two beams
A configuration with two opposing, identical laser beams
functions as a stable optical trap where the dielectric object
is held between the two beams. When the object is trapped,
the surface stresses caused by the two incident beams are
additive. Fig. 7 shows the resulting stress profiles for RBCs,
which are rotationally symmetric with respect to the beam
axis. If the object is centered, the surface stresses cancel
upon integration, and the total force is zero. Otherwise,
restoring gradient and scattering forces will pull the object
back into the center of the trap. The trapping force is the
minimal force required to pull the object completely out of
774 Guck et al
Biophysical Journal 81(2) 767–784
the trap, which is equal to the greatest gradient force en-
countered as the object is displaced.
Again, the shape of the profile changes depending on n
and the ratio w/?. The smaller the beam size with respect
to the object, the greater the stress in the vicinity of the
axis. However, the trap is not stable if the beams are
smaller than the object. This has been discussed and
experimentally shown by Roosen (1977). For w/? ? ? 1,
the surface stresses become very small. The ideal trap-
ping situation is when the beams are only slightly larger
than the object (w/? ? 1). For example, for w/? ? 1.1, the
peak stresses ?0along the beam axis for RBCs trapped
with two 100-mW beams, ?0? 1.38 ? 0.05 Nm?2. The
relative error in the stress calculations, due to uncertain-
ties in the measurement of the relevant quantities as
given earlier, is 3.0%. In this case, the stress profile can
be well approximated by ?r(? ) ? ?0cos2(?) (see Fig. 7
for w/? ? 1.1). This functional form of the stress profile
makes an analytical solution of the deformation of certain
elastic objects tangible.
Deformation of thin shells
Erythrocytes were used initially because they are soft, easy
to handle and to obtain, and their deformations are easily
observed. They are also much more accessible to theoretical
modeling than eukaryotic cells with their highly complex
and dynamic internal structures. Thus, RBCs can be con-
sidered well-defined elastic objects that can be used to
verify the calculated stress profiles. The only elastic com-
ponent of RBCs is a thin composite shell made of the
plasma membrane, the two-dimensional cytoskeleton, and
the glycocalix. The ratio between shell radius ? and shell
thickness h, ?/h ? 100. In this case, membrane theory can
be used to describe deformations due to surface stresses
(Mazurkiewicz and Nagorski, 1991; Ugural, 1999).
Membrane theory is the simplification of a more general
theory of the deformation of spherical shells in which the
bending energy Ubof the shell is neglected and only the
membrane (or stretching) energy Umis considered. It can be
shown that the ratio of those two energies for the case of
axisymmetric stress, as applied with the optical stretcher, is
Ub/Um? 4h2/3?2? 10?4for RBCs. The stress ?rapplied
to a spherical object in the optical stretcher has the form, ?r
? ?0cos2(?), as shown above. Spherical coordinates are an
obvious choice, where the radial direction is denoted by r,
the polar angle by ?, and the azimuthal angle is ?. The
coordinate system is oriented such that the incident angle of
the rays, ?, in the previous section is identical to the polar
angle ? (the laser beams are traveling along the z-axis). The
total energy U of a thin shell consists of the membrane
energy and the work done by the stress applied and is given
U ? 2??2??
2?1 ? v2????
? ?rur? sin??? d?,
where ??and ??are the strains in the polar and meridional
direction, respectively, uris the radial deformation of the
membrane, E is the Young’s modulus, and ? is the Poisson
ratio. The connections between the strains and the deforma-
in each beam was P ? 100 mW for all profiles. The radius of the RBC used for this calculation was ? ? 3.30 ?m, and the refractive index was n2? 1.378. The
concentric rings indicate the stress in Nm?2. The peak stresses ?0along the beam axis (0° and 180° direction) are given below each profile. The trapping of the
cell for w/? ? 1 is unstable (see text). The dashed line for w/? ? 1.1 shows the ?r(?) ? ?0cos2(?) approximation of the true stress profile.
Surface stress profiles on an RBC trapped in the optical stretcher for different ratios between the beam radius w and the cell radius ?. The total power
The Optical Stretcher 775
Biophysical Journal 81(2) 767–784
??u?cot??? ? ur?, (10b)
where u?is the deformation in meridional direction. The
radial and meridional displacements, which describe the
experimentally observed deformation of the dielectric ob-
ject in the optical stretcher, can be found by using Euler’s
du?? 0 (11a)
where F is the integrand of the energy functional,
Using Eqs. 10, 11, and 12 and the explicit form of ?r(?), we
find the following expressions for the radial and the merid-
ional deformations of the membrane,
4Eh??5 ? v?cos2??? ? 1 ? v?
u???? ??2?0?1 ? v?
As expected from the symmetry of the problem, the defor-
mations urand u?are independent of the azimuthal angle ?,
and there is also no displacement u?in this direction. Figure
11 shows the shapes of thin shells calculated with Eq. 13a
for ? ? 0.5, which is normal for biological membranes, and
Eh ? (3.9 ? 1.4) ? 10?5Nm?1, which was found to be the
average for RBCs from the experiments (see below) for
increasing stresses ?0. Because these equations are linear,
they only hold for small strains (?10%). In the microscope
images, which are cross-sections of the objects because the
focal depth of the objective is much smaller than the diam-
eter of the RBCs, only the radial deformations can be
observed. The direct comparison between the theoretically
expected deformations ur(?) and the experimentally ob-
served radial deformations help to establish the RO model
as valid explanation for the optical stretching of soft dielec-
To test the assumptions underlying the RO calculations as
described above, we measured the total force acting on
different objects. It was not clear if it was permissible to
model living cells with their organelles and other small-
scale structures as homogeneous spheres with an isotropic
index of refraction. Although this assumption is obvious for
RBCs homogeneously filled with hemoglobin, it might be
questionable in the case of eukaryotic cells containing or-
ganelles and other internal structures (see Fig. 3). In this
series of experiments, individual silica beads, polystyrene
beads, or fibroblasts were trapped in the optical stretcher.
The setup was identical to the one used for the trapping and
stretching of RBCs (see Experimental Setup and Fig. 4).
After stably trapping the objects, we blocked one of the
laser beams. The total force from the other beam accelerated
the object away from the light source.
The total force was determined using Eqs. 7 and 8 and the
velocities, radii, and distances measured during the experi-
ment. In our setup, the distance b between the moving
objects and the coverslip as closest boundary was b ?
62.5 ? 2.5 ?m (half the diameter of the optical fiber). In the
case of the silica and polystyrene beads, this distance is
about 25 times the radius of the beads and the correction
factor a ? 1.023. For the cells, the distance is ?7–9 times
the radius and a ? 1.072–1.090. The viscosity ? used in the
calculation was that for water at 25°C, ? ? 0.001 Pa s.
Figure 8 shows the total force measured as a function of the
distance d between the fiber tip and the object, as well as the
total force as expected from our RO calculations. The error
bars shown are statistical errors in the experimental data.
The relative errors introduced by the uncertainties in the
measurements of radii, velocities, and distances are negli-
gibly small (1.1–3.1%). It is not surprising that the experi-
mental data points for silica beads and polystyrene beads
match the theory because these are truly spherical and have
an isotropic index of refraction. The fact that, also, the
experimental results for the cells matched the theory was
proof that even eukaryotic cells can be treated using this
simple RO model. The magnitude and the dependence of the
total force on the distance d are in good agreement with the
results by (Roosen, 1977).
Stretching of erythrocytes
Single, osmotically swollen RBCs were trapped in the op-
tical stretcher at low light powers (P ? 5–10 mW). The light
power was then increased to a higher value between P ? 10
and P ? 800 mW for approximately 5 s, an image of the
stretched cell was recorded, and the light power was de-
creased again to the original value. During the short time
intervals when stress was applied, we did not observe any
creep, i.e., any increase in deformation during the duration
776 Guck et al
Biophysical Journal 81(2) 767–784
of the stretching. Also, the cells did not show any hysteresis
or any kind of plastic deformation up to P ? 500 mW.
Figure 9 shows a sequence of RBC images recorded at
increasing light powers. It is obvious that the deformation
increased with the light power used. The radius along the
beam axis increased from 3.13 ? 0.05 ?m in the first image
to 3.57 ? 0.05 ?m in the last image, a relative increase of
14.1 ? 0.3%, whereas the radius in the perpendicular di-
rection decreased from 3.13 ? 0.05 ?m to 2.77 ? 0.05 ?m
(relative change ?11.5 ? 0.2%).
From the radius of the cell, the distance between cell and
fiber tips, the refractive indices of cell and medium, and the
power measured, we calculated the stress profiles for each
cell using the RO model. As mentioned earlier, the relative
error in the stress calculation is 3.0%. The peak stress in the
last image of Fig. 9 was calculated as ?0? 1.47 ? 0.03
Nm?2. Figure 10 shows the relative increase in radius along
the beam axis (? ? 0) and the relative decrease perpendic-
ular (? ? ?/2) versus the peak stress ?0for 55 RBCs. The
error bars shown are statistical errors. The relative errors in
the calculation of the relative changes and the peak stresses
due to uncertainties in the relevant quantities measured are
comparatively small. The solid line in Fig. 10 shows a fit of
ur(0)/? (see Eq. 13a) to the experimental data. For the fit, the
errors in the peak stresses were neglected and a singular
value decomposition algorithm was used. The data points
were weighed with the inverse of the standard deviations.
The resulting slope was 0.080 ? 0.011 m2N?1, which
yielded Eh ? (3.9 ? 1.4) ? 10?5Nm?1. The intercept was
zero. The correlation coefficient for the fit was, r ? 0.92,
excluding the last data point. This shows that up to ?0? 2
Nm?2(P ? 350 mW) and relative deformations of about
10%, the response of the RBCs was linear. In this regime,
linear membrane theory can be used to describe the defor-
mation of RBCs.
In the literature, usually the cortical shear modulus Gh is
given, rather than the Young’s modulus Eh. The quantities
are related by Gh ? Eh/2(1 ? ?) ? Eh/3. In our case, the
shear modulus, Gh ? (1.3 ? 0.5) ? 10?5Nm?1. This value
is in good agreement with values reported previously from
micropipette aspiration measurements, which yielded shear
moduli in the range 6–9 ? 10?6Nm?1(Hochmuth, 1993).
Micropipette aspiration is the most established technique for
measuring cellular elasticities, and the value for the shear
the fiber tip and the object. The data points are from measuring the total force on the objects in the optical stretcher after obstructing one of the laser beams.
The solid lines represent the total forces calculated using ray optics. The radii of the silica beads, the polystyrene beads, and the fibroblasts were ? ? 2.50 ?
0.04 ?m, ? ? 2.55 ? 0.04 ?m, and ? ? 7.70 ? 0.05 ?m, and the refractive indices were n2? 1.430 ? 0.003, n2? 1.610 ? 0.005, and n2? 1.370 ?
0.005, respectively. The total light power P is indicated in each case. The error bars represent standard deviations; the error in the distance measurement
was ?0.6 ?m.
The total forces from one laser beam on silica beads, polystyrene beads, and BALB 3T3 fibroblasts as functions of the distance d between
The Optical Stretcher777
Biophysical Journal 81(2) 767–784
modulus of the RBC membrane has been confirmed many
times and is well accepted.
More recently, optical tweezers were used to measure the
shear modulus with very differing results. In these experi-
ments, beads were attached to the membrane on opposite
sides of the RBC, trapped with optical tweezers, and then
displaced. The values found ranged from (2.5 ? 0.4) ?10?6
Nm?1(He ´non et al., 1999) to 2 ? 10?4Nm?1(Sleep et al.,
mW in each beam. The power was then increased to the higher power given below, which lead to the stretching shown underneath, and then reduced again
to 5 mW. The stretching clearly increases with increasing light power. The radius of the unstretched cell was ? ? 3.13 ? 0.05 ?m, and the distance between
the cell and either fiber tip was d ? 60 ?m. The images were obtained with phase contrast microscopy. Any laser light was blocked by an appropriate filter.
Typical sequence of the stretching of one osmotically swollen RBC for increasing light powers. The top row shows the RBC trapped at 5
a function of the peak stress ?0. The error bars for the relative deformations and the peak stresses are standard deviations. The solid line shows a fit of Eq.
13a as derived from membrane theory to the data points using a singular value decomposition algorithm. The linear correlation coefficient for this fit, r ?
0.92, (excluding the last data point) indicates a linear response of the RBCs to the applied stress. Beyond a peak stress ?0? 2 Nm?2the deformation starts
deviating from linear behavior.
Relative deformation ur/? of RBCs along (positive values) and perpendicular (negative values) to the laser axis in the optical stretcher as
778Guck et al
Biophysical Journal 81(2) 767–784
1999). Because this technique applies point forces to the
membrane, the stress is highly localized and leads to non-
linear deformations. The discrepancy between these values
and the established values for the shear modulus can prob-
ably be attributed to this different load condition.
Furthermore, the theoretically expected and the observed
shapes of RBCs in the optical stretcher coincide well (see
Fig. 11). The white lines are the shapes of thin shells with
RBC material properties as predicted by linear membrane
theory subjected to the surface profile calculated by the RO
model. These lines were overlaid on the images of the
stretched RBCs in Fig. 9. The excellent agreement between
the predicted and the observed shaped shows that using RO
theory is sufficient to calculate the surface stress on cells in
the optical stretcher. An ab inito treatment of the interaction
of a spherical dielectric object in an inhomogeneous elec-
tromagnetic wave using Maxwell’s equations and surface
stress tensor would be much more difficult and is also not
necessary in this case. The RO model is powerful enough to
accurately predict the qualitative and the quantitative aspect
of the stretching. Ray optics has the additional benefit of
being much more accessible.
Beyond ?0? 2 Nm?2, the response of the RBCs
became nonlinear and the shapes observed began to di-
verge from the ones expected from the linear membrane
theory. Figure 12 shows the response of such a cell. At a
peak stress of ?0? 2.55 ? 0.10 Nm?2, the cell was
stretched from a radius along the beam axis of 3.36 ?
0.05 ?m to 6.13 ? 0.05 ?m (relative change 82 ? 3%),
whereas the perpendicular radius decreased from 3.38 ?
0.05 ?m to 2.23 ? 0.05 ?m (relative change ?34 ? 2%).
For the same cell, this transition from linear to nonlinear
response was repeatable several times. Due to the vari-
ance in age, size, and elasticity between individual cells,
the point of transition differed between different cells. If
stretched even further (beyond ?0? 3 Nm?2), the cells
would rupture, as proven by the visually detectable re-
lease of hemoglobin from the cells.
Stretching of eukaryotic cells
Similar to most eukaryotic cells, BALB 3T3 fibroblasts are
heavily invested by an extensive 3D cytoskeletal network of
polymeric filaments, mainly actin filaments, which is
largely preserved even in the suspended state (see below).
Because these cells resemble solid spheres made of a non-
(white lines). The peak stresses ?0calculated using ray optics, which are shown with each image, were used for the membrane theory calculations. The
resulting theoretical shapes, calculated with Eq. 13a, were overlaid on the original images from Fig. 9 to show the excellent agreement between the two
for all peak stresses.
Comparison between the deformations of RBCs observed in the optical stretcher and the deformations expected from membrane theory
The top part shows the undeformed cell trapped at 5 mW with a radius ?
? 3.36 ? 0.05 ?m. In the lower part, the cell is stretched with a peak stress
?0? 2.55 ? 0.10 Nm?2to ? ? 6.13 ? 0.05 ?m along the beam axis, an
increase of 82 ? 3%. After reducing the power, the cell returned to its
An example of an RBC stretched beyond the linear regime.
The Optical Stretcher 779
Biophysical Journal 81(2) 767–784
uniform, complex compound material, we expected that
they would not be stretched as significantly as RBCs, which
are essentially thin shells. Figure 13 shows a fibroblast (A)
trapped at P ? 20 mW light power and (B) stretched with
P ? 600 mW. The peak stress in this case was, ?0? 5.3 ?
0.2 Nm?2, and the relative deformation along the beam axis
was 5.43 ? 0.04%, and ?2.25 ? 0.01% in the perpendic-
ular direction. The small degree of deformation of this
fibroblast is only possible to detect by using the algorithm
for the extraction of the cell boundary (C). Any eukaryotic
cell can be stretched this way. Although the applied stress
can be calculated and the resulting deformation of cells can
be measured, it would be incorrect to calculate a Young’s
modulus assuming a homogeneous elastic sphere. It would
require complex modeling and probably time dependent
measurements to extract elastic properties of the different
Viability of stretched cells
The viability of the cells under investigation was an impor-
tant issue because dead cells do not maintain a representa-
tive cytoskeleton. Even though care had been taken to avoid
radiation damage to cells in the optical stretcher by selecting
a wavelength (785 nm) with low absorption, their viability
was checked on a case-by-case basis. Our approach to this
was twofold. The appearance of BALB 3T3 cells is signif-
icantly different when they are not alive. Living cells in
phase contrast microscopy show a characteristic bright rim
around their edge. Dead cells usually have no sharp contour
and appear diffuse. After a cell had been trapped and
stretched for several minutes, it was compared with other
cells that had not been irradiated. In all cases, the cells
looked alike and normal. A second, more careful approach
was the use of the vital stain Trypan Blue. As long as a cell
is alive, it is able to prevent the dye from entering the
cytoplasm. When the cell is dead or does not maintain its
normal function, the dye will penetrate the cell membrane
and the whole cell appears blue. After adding 5% (volume)
Trypan Blue to the cell suspension, no staining was ob-
served. These tests show that the cells survived the condi-
tions in an optical stretcher without any detectable damage.
It is not obvious that it is possible to use two 800-mW
laser beams for the deformation of such delicate objects as
cells without causing radiation damage. An important con-
sideration is the careful choice of the least damaging wave-
length. For the trapping of inanimate matter, such as glass or
silica beads, the choice of wavelength is not critical. Using
a short wavelength might be desirable for optical tweezers
because it results in higher gradients and better trapping
efficiencies because the spot size of a focused beam is about
half the wavelength of the light used. However, short wave-
lengths are not appropriate to preserve biological objects
such as cells because the absorption by chromophores in
cells is low in the infrared and increases with decreasing
wavelength (Svoboda and Block, 1994). The absorption
peaks of proteins, for example, are found in the ultraviolet
region of the electromagnetic spectrum. Therefore, re-
searchers resorted to the 1064 nm of an Nd-YAG laser and
achieved better results (Ashkin et al., 1987). At first sight,
this choice seems also less than optimal because 70% of a
cell’s weight is water (Alberts et al., 1994), which absorbs
more strongly with increasing wavelength. Most cells
trapped with optical tweezers do not survive light powers
greater than 20–250 mW, depending on the specific cell
type and the wavelength used (Ashkin et al., 1987; Ashkin
and Dziedzic, 1987; Kuo and Sheetz, 1992). However,
recent work on optical tweezers shows that local heating of
water can be ruled out as limiting factor in optical trapping
experiments in the near infrared region. Theoretical calcu-
lations predict a temperature increase of less than 3 K/100
mW in the wavelength range 650-1050 nm for durations of
is less obvious than for the RBCs. Still, the radius increased from (A) ? ? 11.23 ? 0.05 ?m for the cell trapped at 20 mW to (B) ? ? 11.84 ? 0.05 ?m
along the beam axis at 600 mW, and decreased from 11.53 ? 0.05 ?m to 11.27 ? 0.05 ?m in the perpendicular direction. This is a relative deformation
of 5.43 ? 0.04% and ?2.25 ? 0.01%, respectively, for a peak stress ?0? 5.3 ? 0.2 Nm?2. The deformation can be seen much easier in (C) where the
outlines of the stretched and unstretched cell, found with the image analysis algorithm, are overlaid.
The stretching of a BALB 3T3 fibroblast in the optical stretcher. Due to the more extensive cytoskeleton of eukaryotic cells, the deformation
780Guck et al
Biophysical Journal 81(2) 767–784
up to 10 s (Scho ¨nle and Hell, 1998). This is in agreement
with earlier experimental work, where an average temper-
ature increase of ?1.00 ? 0.30°C/100 mW at powers up to
400 mW was observed in Chinese hamster ovary cells
(CHO cells) trapped in optical tweezers at a wavelength of
1064 nm (Liu et al., 1996).
Even though heating due to water absorption seems to be
unimportant in trapping experiments, the cells could still be
damaged by radiation in other ways. Studies directly mon-
itoring metabolic change and cellular viability of biological
samples trapped in optical tweezers addressed this concern.
Microfluorometric measurements on CHO cells (Liu et al.,
1996) show that up to 400 mW of 1064-nm cw laser light
does not change the DNA structure or cellular pH. Still, the
right choice of wavelength is important, because rotating E.
coli assays reveal that there is photodamage with maxima at
870 and 930 nm and minima at 830 and 970 nm (Neuman
et al., 1999). There seems to be evidence that the presence
of oxygen is involved in the damage pathway but the direct
origin of the damage remains unclear. According to this
study, damage at 785 nm, the wavelength we used, is at least
as small as at 1064 nm, the most commonly used wave-
length for biological trapping experiments. Also, the sensi-
tivity to light was found to be linearly related to the inten-
sity, which rules out multi-photon processes.
In the light of these findings, it is not surprising that we
did not observe any damage to the cells trapped and
stretched in the optical stretcher. This becomes even more
plausible if one considers that the beams are not focused and
the power densities are lower than in optical tweezers by
about two orders of magnitude for the same light power
(?105rather than 107W/cm2). Thus, much higher light
powers, i.e., higher forces, can obviously be used without
the danger of “opticution”.
Cytoskeleton of cells in suspension
Finally, because there was some concern that eukaryotic
cells, apart from leukocytes, might dissolve their actin cy-
toskeleton when they are in suspension, we examined the
actin cytoskeleton of BALB 3T3 fibroblasts in suspension
using TRITC-phalloidin labeling and fluorescence micros-
copy. Figure 14 clearly shows that suspended cells do have
an extensive actin network throughout the whole cell. In
particular, the peripheral actin cortex can be seen at the
plasma membrane. The only features of the cytoskeleton not
present in suspension are stress fibers, which is consistent
with the absence of focal adhesion plaques in suspended
cells. Even without stress fibers, the BALB 3T3 displayed a
large resistance to deformation in the optical stretcher.
Stress fibers are predominantly seen in cells adhered to a
substrate and are less pronounced in cells embedded in a
tissue matrix. Thus, the situation with many stress fibers is
probably as unphysiologic as the lack thereof in suspended
Our finding is in agreement with other studies that report
the disappearance of stress fibers and a redistribution of
actin. Furthermore, these studies show that the influence of
the cytoskeleton on the deformability of normally adherent
cells such as bovine aortic endothelial cells (Sato et al.,
1987), chick embryo fibroblasts (Thoumine and Ott, 1997),
and rat embryo fibroblasts (Heidemann et al., 1999) can be
investigated when the cells are in suspension.
This view is supported by recent frequency-dependent
AFM microrheology experiments, comparing in vitro actin
gels and NIH3T3 fibroblasts (Mahaffy et al., 2000). These
experiments showed that the viscoelastic signature of the
cells resembled that of homogeneous actin gels, so that the
elastic strength of cells can be almost entirely attributed to
the actin cortex, which is still present in suspended cells.
There is actually an advantage to investigating cells in
suspension, because most polymer theories are for in vitro,
isotropic actin networks. It might be especially interesting
to be able to compare these theories with data from living
cells in which only the actin cortex is present and anisotro-
pic structures such as stress fibers are absent.
CONCLUSION AND OUTLOOK
Although the possibility of optically trapping biological
matter with lasers is well known and commonly used, the
optical deformability of dielectric matter had been ignored.
The optical stretcher proves to be a nondestructive optical
tool for the quantitative deformation of cells. The forces
exerted by light due to the momentum transferred are suf-
ficient not only to hold and move objects, but also to
directly deform them. The important point is that the mo-
mentum is predominantly transferred to the surface of the
object. The total force, i.e., gradient and scattering force,
which traps the object, arises from the asymmetry of the
resulting surface stresses when the object is displaced from
its equilibrium position and acts on the center of gravity of
sion. The cell had been fixed and the actin cytoskeleton labeled with
TRITC-phalloidin. The left panel shows the original image and the right
panel shows the same cross-section through the cell after deconvolution.
Clearly, the cell maintains a filamentous actin cytoskeleton even in
Fluorescence image of a BALB 3T3 fibroblast in suspen-
The Optical Stretcher781
Biophysical Journal 81(2) 767–784
the object. These trapping forces are significantly smaller
than the forces on the surface because the surface forces
almost completely cancel upon integration. This is most
obvious in a two-beam trap as used for the optical stretcher.
When the dielectric object is in the center of the optical trap,
the total force is zero, whereas the forces on the surface can
be as high as several hundred pico-Newton. In synopsis, the
forces applicable for cell elasticity measurements with the
optical stretcher range from those possible with conven-
tional optical tweezers to those achieved with atomic force
Somewhat surprising was the finding that the surface
forces pull on the surface rather than compressing it. The
RO approach readily explains this behavior by the increase
of the light’s momentum as it enters the denser medium and
the resulting stresses on the surface. An equivalent approach
would be to think in terms of minimization of energy. It is
energetically favorable for a dielectric object to have as
much of its volume located in the area with the highest
intensity along the laser beam axis. The result is that the cell
is pulled toward the axis. Even though this is conceptionally
correct, it would be much harder to calculate.
The optical deformability of cells can be used to distin-
guish between different cells by detecting phenomenologi-
cal differences in their elastic response as demonstrated for
RBCs and BALB 3T3 fibroblasts. At the same time, trapped
cells did not show any sign of radiation damage, even when
stretched with up to 800 mW of light in each beam, and
maintained a representative cytoskeleton in suspension. In
the same way, the optical stretcher can be used for quanti-
tative research on the cytoskeleton. For example, it is com-
monly believed that the actin part of the cytoskeleton, and
especially the actin cortex, is most important for the elas-
ticity of the cell. This hypothesis can be easily tested using
the optical stretcher to measure the elasticity after geneti-
cally altering the relative amount of the three different main
cytoskeletal components and their accessory proteins.
There might also be a biomedical application of the
optical stretcher. Due to its simple setup and the incorpo-
ration of an automated flow chamber, the optical stretcher
has the potential to measure the elasticity of large numbers
of cells in a short amount of time. We expect to be able to
measure one cell per second, which is a large number of
cells compared to existing methods for measuring cell elas-
ticity. Given the limited lifespan of a living cell sample in
vitro, the measurement frequency is crucial to ensure good
statistics. This naturally suggests the optical stretcher for
applications in the research and diagnosis of diseases that
result in abnormalities of the cytoskeleton. Better knowl-
edge of the basic cell biology of the cytoskeleton contrib-
utes to the understanding of these disorders and can affect
diagnosis and therapy of these diseases. Cytoskeletal
changes are significant in, and are even used to diagnose,
certain diseases such as cancer. Existing methods of cancer
detection rely on markers and optical inspection (Sidransky,
1996). Using measurements of cytoskeletal elasticity as an
indicator for malignancy could be a novel approach in
oncology. For example, effects of malignancy on the cy-
toskeleton that have been reported include increasing dis-
order of the actin cytoskeleton (Koffer et al., 1985; Taka-
hashi et al., 1986), changes in the absolute amount of total
actin and the relative ratio of the various actin isoforms
(Wang and Goldberg, 1976; Goldstein et al., 1985; Leavitt
et al., 1986; Takahashi et al., 1986; Taniguchi et al., 1986),
an overexpression of gelsolin in breast cancer cells
(Chaponnier and Gabbiani, 1989), and the lack of filamin in
human malignant melanoma cells (Cunningham et al.,
1992). All of these changes will likely result in an altered
viscoelastic response of these cells that can be detected with
the optical stretcher. In fact, models of actin networks
(MacKintosh et al., 1995) show that the shear modulus
scales with actin concentration raised to 2.2. Even a slight
decrease in actin concentration should result in a detectable
decrease of the cell’s elasticity. In this way, the optical
stretcher could advance to a diagnostic tool in clinical
laboratories. This novel technique would require minimal
tissue samples, which could be obtained using cytobrushes
on the surfaces of the lung, esophagus, stomach, or cervix,
or by fine-needle aspiration using stereotactic, ultrasono-
graphic, or MRI guidance (Dunphy and Ramos, 1997; Fa-
jardo and DeAngelis, 1997).
The authors would like to thank Alan Chiang, Benton Pahlka, Christian
Walker, and Robert Martinez for their help with the experiments. We are
grateful to Rebecca Richards-Kortum, John Wright (National Science
Foundation Integrative Graduate Education and Research Training pro-
gram user facility), Carole Moncman, Eric Okerberg, and Kung-Bin Sung
for their invaluable suggestions and assistance with the fluorescence mi-
croscopy, and to David Humphrey, Martin Forstner, and Douglas Martin
for many supporting discussions.
The work was supported by the Whitaker Foundation grant #26-7504-94,
and by the National Institutes of Health grant 26-1601-1683.
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