Intracellular elasticity and viscosity in the body,
leading, and trailing regions of locomoting neutrophils
MASARU YANAI,1 JAMES P. BUTLER,1,2 TOMOKO SUZUKI,1,3 AKIO KANDA,1
MASASHI KURACHI,3 HIDEO TASHIRO,3 AND HIDETADA SASAKI1
1Department of Geriatric and Respiratory Medicine, Tohoku University School of Medicine,
Sendai 980-8574; 3Laboratory for Photo-biology, Photodynamics Research Center,
Institute of Physical and Chemical Research (RIKEN), Sendai 980-0868, Japan;
and 2Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02115
cytoskeleton; biomechanics; pseudopodia
NEUTROPHILS ARE AN important cell type in the inflammatory response and in host defense mechanisms. Their
chemotactic response is characterized by locomotion
through the formation of pseudopods. Such pseudopods
are easily visualized, but the mechanical processes by
which they form, protrude, and subsequently translate
the main body of the cell are still unknown. Because the
processes of transendothelial migration, locomotion in
stroma, and transepithelial migration require significant deformation of neutrophils, the neutrophil cytoskeleton must be correspondingly remodeled through the
processes of polymerization and depolymerization. This
response is presumably inhomogeneously distributed
between at least the locomotory pseudopod and the
main body of the cell.
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C432
There are two distinct classes of ideas about the
evolving structure of the pseudopod. One (5, 6, 12) is
that the pseudopod is formed by compression, through
polymerization of cytoskeletal filaments, especially actin, which then allows the pseudopod to ‘‘grow’’ at its
tip. The other (10, 19, 25) is that the pseudopod core is
essentially a passive fluid, which streams into the
pseudopod as a result of intracellular pressure; the
pseudopod cortex polymerizes in an annular fashion,
but the core remains in an essentially sol or fluid state.
These two mechanisms can be distinguished in the
living cell if regional measurements of the elastic modulus, or stiffness, and viscosity of the intracellular milieu could be made. In the pseudopodial compression
model, the stiffness of the leading region would be at
least as great as that in the body or trailing region; in
the pseudopodial fluid core model, the viscosity and
especially the stiffness of the leading region would be
much less than those in either the body or trailing region. (Note that throughout this paper, we use the phrase
‘‘leading region’’ to denote the protruding pseudopod as
a whole and not the subcortical region immediately
proximate to the pseudopodial membrane. See DISCUSSION for the potential importance of this distinction.)
Utilizing the recently developed laser optical trap, or
‘‘optical tweezers,’’ we measured both the dynamic
forces on, and the displacements of, individual intracellular granules in living neutrophils, selected from each
of the three regions. From these data, we estimated the
elastic modulus and viscosity in the leading region, the
body, and trailing region and assessed the regional
differences in these rheological properties.
MATERIALS AND METHODS
Reagents. Krebs-Ringer phosphate with dextrose (KRPD)
was constituted by (in mM) 115 NaCl, 14 dextrose, 6 KCl, 4.6
MgSO4 · 7H2O, 3.5 NaH2PO4 · 2H2O, and 16 Na2HPO4 in water. Normosmotic RPMI 1640 medium with L-glutamine was
purchased from GIBCO-BRL. Mono-Poly Resolving Medium,
a separation medium of blood cells into mononuclear and
polymorphonuclear (PMN) leukocytes, was purchased from
Dainippon Pharmaceutical. FBS was obtained from Cansera
International. Cytochalasin D and nocodazole were purchased from Sigma Chemical.
Preparation of cells. Human neutrophils were isolated from
whole blood by a density gradient technique using Mono-Poly
Resolving Medium according to the manufacturer’s directions. Briefly, 24 ml of peripheral blood were drawn from
normal subjects with a heparinized syringe. The sample was
put in a 50-ml sterile polypropylene tube and centrifuged at
175 g for 20 min at room temperature. The upper platelet-rich
0363-6143/99 $5.00 Copyright r 1999 the American Physiological Society
Downloaded from http://ajpcell.physiology.org/ by 10.220.33.2 on June 17, 2017
Yanai, Masaru, James P. Butler, Tomoko Suzuki, Akio
Kanda, Masashi Kurachi, Hideo Tashiro, and Hidetada
Sasaki. Intracellular elasticity and viscosity in the body,
leading, and trailing regions of locomoting neutrophils. Am.
J. Physiol. 277 (Cell Physiol. 46): C432–C440, 1999.—To
investigate the mechanisms underlying pseudopod protrusion in locomoting neutrophils, we measured the intracellular
stiffness and viscosity in the leading region, main body, and
trailing region from displacements of oscillating intracellular
granules driven with an optical trap. Experiments were done
in control conditions and after treatment with cytochalasin D
or nocodazole. We found 1) in the body and trailing region, the
granules divided into a ‘‘fixed’’ population (too stiff to measure) and a ‘‘free’’ population (easily oscillated; fixed fraction
65%, free fraction 35%). By contrast, the fixed fraction in the
leading region was ⬍5%. 2) In the body and trailing region,
there was no difference in stiffness or viscosity, but both were
sharply lower in the leading region (respectively, 20-fold and
5-fold). 3) Neither cytochalasin D nor nocodazole caused a
decrease in stiffness, but both treatments markedly reduced
the fixed fraction in the body and trailing region to ⬍20% and
⬍40%, respectively. These observations suggest a discrete
lattice structure in the body and trailing region and suggest
that the developing pseudopod has a core that is more
fluidlike, in the sense of a much lower viscosity and an almost
total loss of stiffness. This is consistent with the contraction/
solation hypothesis of pseudopodial formation.
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RHEOLOGY OF LOCOMOTING NEUTROPHILS
on each image, so that the position of the center of the trap
was recorded on each image. There was approximately one
frame delay in writing the image; this time delay of 30 ms was
subtracted from all clock times. The amplitude and phase of
the oscillating granule were determined by locating the
granule centroid at its positive and negative extremes and
at the time of the zero crossing of the trap. This was
performed on a Macintosh computer using the public domain
National Institutes of Health (NIH) Image program (developed at the United States NIH and available on the Internet
at http://rsb.info.nih.gov/nih-image/). A grid with 10-µm
squares was used for calibration, and one pixel on the image
was determined to be equal to 50 nm.
Oscillation protocol. For each series of experiments, we
measured the trap amplitude, the granule amplitude, and the
phase of the oscillating granule relative to the trap. The trap
amplitude, a0, was measured by trapping an extracellular
granule or plastic bead and oscillating it at full laser power in
the medium to ensure that the displacement of the granule
faithfully represented the displacement of the center of the
trap. The a0 was taken as half the peak-to-peak displacement.
This calibration of a0 was done before every sequence of
intracellular granule measurement.
The intracellular granule amplitude x0 was estimated, as
above, by half the peak-to-peak displacement. To determine
the phase ␾ of the granular motion relative to the trap, we
note that the displacement of a granule when the trap crosses
zero, denoted xz, is given by xz ⫽ x0 sin␾ (note that for the
granule lagging behind the trap motion, ␾ ⬍ 0). The xz was
estimated as one-half the difference of the displacement of the
granule at the two zero crossings of the trap per cycle. The
phase was then taken to be
␾ ⫽ sin⫺1(xz /x0)
(1)
We selected intracellular granules (or occasional aggregates) whose diameters were ⬃0.6 µm (range 0.5–0.7 µm) for
the study. These granules were trapped and oscillated by the
optical tweezers with an amplitude a0 of 0.5 µm and at
frequencies of 0.3, 1, and 3 Hz. The experimental runs were
performed at the leading region where granules flowed in, the
main body not proximate to the nucleus, or the trailing
region.
Estimating the elastic modulus G and viscosity ␩. The
primary data, together with the force/length characteristics
of the optical trap described below, were then used to compute
the elastic modulus (or stiffness) G and the viscosity ␩ of the
cytoplasmic milieu, characterized as a simple viscoelastic
material, with parallel stiffness and viscous elements. The
displacement of the granule lags behind the trap displacement, and therefore the computation of the corresponding
force is indirect, through the combined granule plus trap
system.
To this end, we first derive the equation of motion for the
driven granule. Let x and a be, respectively, the timedependent displacement of the granule and the trap center,
both with respect to a stationary laboratory coordinate system, the zeros of both being chosen as the point about which
the oscillations take place. The displacement of the trap
relative to the granule is thus (a ⫺ x); let the spring constant
of the trap (i.e., the force per unit length of displacement of
granule relative to the trap center, determined by calibration
runs described below) be denoted k. Let G1 and ␩1 be,
respectively, the uniaxial stiffness (force per unit length of
granule displacement) and damping (force per unit granule
velocity) of the cytoplasmic medium. There is a simple
relationship between G1 and ␩1 and the desired material
descriptors G and ␩ described below. Because the granule and
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plasma layer was carefully removed using a Pasteur pipette
and was replaced by the same amount of KRPD. After being
mixed gently, it was equally divided into four sterile polypropylene tubes. Mono-Poly Resolving Medium (4 ml) was gently
added so as to underlay the blood without significant mixing
in each tube. The samples were then centrifuged at 330 g for
25 min at room temperature. This procedure resulted in the
following four layers, in order from the top: KRPD solution,
monocyte/lymphocyte layer, PMN cell layer, and red blood cell
layer. The PMN cell layer was collected and rinsed with
KRPD solution. It was then centrifuged at 250 g for 10 min.
KRPD was removed, and the PMN cells were resuspended
with 10 ml of medium (RPMI Medium 1640 ⫹ 5% FBS).
Chamber preparation. A chamber was prepared with two
clean uncoated coverslips as the top and the bottom surfaces,
separated by ⬃600 µm using sheet paraffin wax spacers.
Edges of the coverslips were sealed with valap (beeswaxlanolin-petrolatum, 1:1:1 by wt). Two 23-gauge needles had
been introduced into the space before sealing to be used as
entrance and exit ports. Gentle suction on the exit needle or
gravity drainage was used for filling. The sample was placed
on a heated microscope stage maintained at 37°C. Many of
the cells remained floating or adhered to the glass surface
only loosely, appearing round and inactivated. A modest
fraction adhered to the glass strongly and began to spread
and locomote. The chamber was then rinsed with 2 ml of
medium to remove floating or loosely adherent cells. The
remaining neutrophils, in the process of lamellipodial protrusion and locomotion, were used for this study.
Inhibition of F-actin formation and microtubule assembly.
To disrupt F-actin or microtubules, we introduced cytochalasin D or nocodazole into the chamber, diluted, respectively, to
2 and 10 µM in medium containing 0.1% DMSO. The sample
was then incubated at 37°C for 5 or 10 min, respectively.
Video-enhanced differential interference contrast microscopy with optical tweezers. Samples were observed under a
differential interference contrast microscope (Diaphot
TMD300; Nikon) equipped with a Plan Apochromat ⫻100
oil-immersion objective lens (numerical aperture 1.4), an
oil-immersion condenser lens for high-magnification objectives (numerical aperture 1.4), and a 100-W halogen lamp.
Images were detected with a Newvicon tube video camera
(C2400–07; Hamamatsu), enhanced with an image processor
(DVS-3000; Hamamatsu), and recorded at 30 frames/s with a
super-VHS videocassette recorder (SVO-9650; Sony). A video
printer (UP-860; Sony) was used for video prints of taped
images. A linearly polarized laser beam from a Nd:YAG laser
(SL902T; Spectron Laser Systems) emitting at 1,064 nm was
introduced into the epifluorescence port of the microscope
with the aid of galvano mirrors and collimating lenses. The
laser beam was manipulated in two dimensions over the field
of camera view using the galvano scanner controller (CX-660;
General Scanning), which was operated by an external voltage signal from a function generator (Iwatsu). The position of
the trap center was monitored on the video image by a
superposed digital recording of the voltage level. Rotation of a
Glan-laser polarizer or half-wave plate inserted between the
laser and galvano scanner allowed attenuation of the laser
beam and hence different trap forces in different experiments.
The laser power was monitored by a thermal detector (model
835; Newport). The force/displacement characteristics of the
trap were determined by oscillating isolated granules in
medium, as described below.
Displacement data collection. Each frame to be analyzed
on the videotape was captured by a frame grabber card
(CinemaGear; Interware, Tokyo, Japan). Clock time, laser
power, and the relative displacement of the trap were printed
C434
RHEOLOGY OF LOCOMOTING NEUTROPHILS
the trap are mechanically in series, the force (F) applied to the
granule, given by the sum of the elastic and viscous forces, is
equal to the force applied by the trap
F ⫽ G1 x ⫹ ␩1 ẋ ⫽ k (a ⫺ x )
(2)
where the overdot denotes differentiation with respect to
time.
In the complex Fourier domain, the trap and granule
displacements can be written as
a ⫽ a0 cos (␻t ) ⫽ Re (a0 ei␻t )
x ⫽ Re (x̃ei␻t )
(3)
where ␻ is the angular frequency, i ⫽ 冑⫺1, x̃ is the complex
displacement, and t is time. The equation of motion then
simplifies to the algebraic expression
(4)
Our measurements of the amplitude ratio and phase of the
oscillating granule are then equivalent to the determination
of the complex transfer function T
T⫽
x̃
a0
⫽
k
k ⫹ G1 ⫹ i␻␩1
⫽ 0 T 0 ei␾
(5)
where
0 T 0 ⫽ x0 /a0
␾ ⫽ arg T ⫽ sin⫺1 (xz /x0)
(6)
The spring constant of the trap, k, is proportional to the laser
power P; thus
k/k90 ⫽ P/P90
(7)
where k90 is the spring constant of the trap at full laser power,
P90, which in our case is 90 mW. The presence of the variable k
in Eq. 5 implies that our measurements of the transfer
function T are functions of two variables, k and ␻, and
therefore a simple Bode plot representation of the data is not
possible. By contrast, the inverse transfer function (T⫺1;
easily computed from the inverse amplitude ratio and negative phase) is given by
T ⫺1 ⫺ 1 ⫽ G1/k ⫹ i␩1␻/k
(8)
Having made measurements at various frequencies ␻ and at
various laser powers (and hence various values of k), we
finally estimate G1 and ␩1 from this expression as follows.
With T⫺1 ⫺ 1 taken to be the dependent variable and 1/k and
␻/k independent variables, G1 and ␩1 are estimated, together
with their SEs, by constrained linear regression [0 intercept
for the real part (Re) when 1/k ⫽ 0 and for the imaginary (Im)
part when ␻/k ⫽ 0].
To translate these uniaxial moduli into the more conventional material moduli, where the elastic moduli and viscosity
have units of force / area and force ⫻ time / area, respectively,
we first note the simple relationship between force and
velocity in Stokes flow of a sphere of radius r moving with
velocity u in a medium of viscosity ␩: F ⫽ 6␲␩ru. This is the
same as writing the damping force as F ⫽ ␩1ẋ, from which we
make the immediate identifications
␩ ⫽ ␩1/6␲r
G ⫽ G1/6␲r
(9)
RESULTS
In all, successful measurements were made on ⬎1,000
granules in ⬎200 cells. The distribution of these measurements over the three cellular regions (body, leading
region, and trailing region) and the three treatment
groups (control, cytochalasin D, and nocodazole) is
displayed in matrix form in Table 1.
Three frames from the video taken during the oscillation of a typical granule are shown in Fig. 1. They show
the granule at its maximum positive displacement from
the origin, x0, its displacement when the trap center
crosses zero, xz, and its maximum negative displacement from the origin, ⫺x0. Figure 1, top, shows the
sinusoidally varying trap displacement, the granule
displacement, and the times at which the images were
taken. The granule amplitude is systematically less
than the trap amplitude, and the granular motion lags
behind the trap.
Table 1. Regional and treatment distribution
of measured granules
Cell Region
Treatment
Body
Normal
128/26
Cytochalasin D 97/18
Nocodazole
122/21
Totals
347/65
Leading Region
Trailing Region
Totals
201/36
92/15
88/21
381/72
183/33
116/22
82/19
381/74
512/95
305/55
292/61
1,109/211
Distribution of the number of oscillating granules measured and
the number of individual cells studied as a function of cellular region
studied and treatment group. Number of granules (N ) and the
number of cells (M ) are shown as N /M.
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(G1 ⫹ k ⫹ i␻␩1)x̃ ⫽ ka0
for the viscosity and, by analogy, the stiffness modulus. The
SEs for these parameters also scale like 1/6␲r and are the
values used to compute statistical significance of potential
regional or treatment differences in rheological characteristics.
Calibrating the stiffness of the trap (i.e., the value of k90 )
can be easily accomplished using the same methodology as
described above. This is important, since the stiffness of the
trap depends on the optical properties of the trapped object,
especially its index of refraction. This is not known for
intracellular granules, but the force / length characteristic of
the trap for granules actually used in the experiments can be
measured directly. The calibration procedure is as follows and
is similar to the method of Simmons et al. (15). If an
extracellular granule (obtained from spontaneously lysed cell
debris) is oscillated in RPMI 1640 medium, the same governing equations as above still apply. However, in this case, it is
known a priori that the stiffness of the medium is zero and
that the viscosity is essentially that of water, here taken to be
0.01 poise. Thirty-one measurements of amplitude decrement
and phase delay were performed, with laser power ranging
from 0.4 to 1.3 mW and frequencies from 0.1 to 1.5 Hz.
Equations 7 and 8 can then be solved for the trap stiffness k90.
The result of these measurements showed that, for 0.3-µm
radius granules, k90 was given by 0.030 pN/nm.
Statistical analysis. Regional differences (body, leading
region, and trailing region) and treatment differences (normal, cytochalasin D, and nocodazole) were assessed by twoway ANOVA. Statistical significance was assessed a priori at
P ⬍ 0.05, but posterior significances were found to be much
stronger.
RHEOLOGY OF LOCOMOTING NEUTROPHILS
C435
In the body and trailing regions of the control group
of cells, many granules were so rigid that no observable
oscillation took place; searching was required to find
granules that could be oscillated. Granules whose
amplitudes were so low that they could not be reliably
measured (x0 /a0 ⬍ 0.4 at maximum laser power) or
were being dragged by intracellular motions beyond
the trap’s strength were not included in the data
analysis (and are not part of the counts displayed in
Table 1). Inspection of the data revealed that very few
granules had relative displacements in the range of
0.4–0.6; they were either much too stiff to be measured
(the ‘‘fixed’’ population) or had displacements typically
in the range 0.6 ⬍ x0 /a0 ⬍ 1.0 (the ‘‘free’’ population).
The distribution of the percentage of free granules over
the three cellular regions and over the three treatment
groups is shown in Fig. 2. In the main body or trailing
region of control neutrophils, the fractions of granules
displaying fixed behavior and free behavior were ⬃65
and 35% respectively. By contrast, the fixed fraction in
the leading region regardless of treatment was ⬍5%,
implying an apparent absence of the fixed population in
this region. Both cytochalasin D and nocodazole induced a reversal in the free and fixed populations; the
fixed fraction in the body and trailing region of cells
treated with cytochalasin D fell to ⬍20% and with
nocodazole fell to ⬍40%. By contrast to control conditions, in both treatment cases the population of fixed
granules was outweighed by the population of free
granules.
As described in MATERIALS AND METHODS, the transfer
function can be used to estimate the uniaxial elastic
modulus G1 and viscosity ␩1. In Fig. 3A, we show
Re(T⫺1 ⫺ 1) versus 1/k for all measurements (means ⫾
SE) on free granules in the separate regions of the cell
under control conditions. The constant of proportional-
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Fig. 1. Three images of a neutrophil spanning one-half cycle of the oscillation of a granule. This granule is in the
developing pseudopod, leading region of the cell. The laser power was 24 mW, and the frequency was 1 Hz. Top
shows the sinusoidal displacement of the center of the optical trap, with amplitude a0, and the sinusoidal
displacement of the granule, with amplitude x0. The phase of the granular motion relative to the trap is denoted ␾.
Note that ␾ ⬍ 0 represents the granule lagging behind the trap. The times at which each image was taken are
labeled A, B, and C at top. Trap amplitude a0 was 0.55 µm, and the ⫾a0 and zero displacements are shown below the
granule in A-C. In this run, the granule amplitude x0 was 0.48 µm, and the ⫾x0 displacements are shown above the
granule in A-C. Bar corresponds to 1.0 µm. A: image at maximum negative displacement of the granule, ⫺x0. Ratio
of x0 to the maximum trap displacement is used in the calculation of the transfer function magnitude (Eq. 6).
B: image when trap displacement is 0. Granule displacement at this time equals xz and is used in the calculation of
the phase lag (Eq. 1). C: image at maximum positive displacement of the granule x0.
C436
RHEOLOGY OF LOCOMOTING NEUTROPHILS
Fig. 2. Fractions of granules found in the free (open bars) and fixed
(filled bars) populations, sorted by region (body, leading region, and
trailing region) and by cell condition [normal (N) and treatment with
either cytochalasin D (cyto-D) or nocodazole (Noco)].
ity between Re(T⫺1 ⫺ 1) and 1/k, or slope of this graph,
is an estimate of the uniaxial elastic modulus G1 (this
comes from the real part of Eq. 8). In Fig. 3B, we show
the corresponding data for ImT⫺1 versus ␻/k, where the
slope is an estimate of the uniaxial viscosity ␩1 (from
the imaginary part of Eq. 8).
Figure 4 shows a bar graph representation (means ⫾
SE) of the values of the material properties G (Fig. 4A)
and ␩ (Fig. 4B) for the three regions of the cell and for
the three conditions of control, treatment with cytochalasin D, and treatment with nocodazole. These values
were obtained from the corresponding uniaxial values
of Eq. 9. For both G and ␩, there was no significant
difference between the body and trailing regions. Surprisingly, neither cytochalasin D nor nocodazole had
any effect on either G or ␩ in these regions. By contrast,
both G and ␩ are significantly lower in the leading
region under all conditions when compared with either
the body or trailing region. Interestingly, G and ␩ in the
leading region were not significantly different between
control and nocodazole treatment conditions, whereas
both G and ␩ in the cytochalasin D group (while less
than the corresponding values in the body or trailing
region) were significantly higher than G and ␩ in the
normal and nocodazole groups. Morphologically, the
neutrophils treated with cytochalasin D also showed a
marked drop in the speed of pseudopodial protrusion,
including occasional stoppages.
DISCUSSION
There are three main issues addressed by these
experiments on locomoting neutrophils: 1) the presence
of fixed and free populations of granules; 2) regional
differences (body, leading region, and trailing region) in
intracellular stiffness and viscosity; and 3) differences
in these rheological properties when the neutrophils
Fig. 3. Summary of all data (means ⫾ SE) on free granules collected
in the leading region, body, and trailing region of neutrophils in
control conditions. Data are expressed in the form suggested by Eq. 8,
where the slopes of the relationship between the real (Re) and
imaginary (Im) parts of T⫺1 ⫺ 1 (where T is the measured transfer
function) and the independent variables 1/k and ␻/k are, respectively,
estimates of the uniaxial stiffness and viscosity. A: plot of Re(T⫺1 ⫺ 1)
vs. 1/k for the three neutrophil regions in normal conditions. Slopes
are estimates of the different uniaxial stiffnesses in these regions. B:
similar to A, a plot of ImT⫺1 vs. ␻/k. Slopes are estimates of the
different uniaxial viscosities in these regions.
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are treated with either of the cytoskeletal disrupters
cytochalasin D or nocodazole.
Fixed and free granules. In the body and trailing
region of normal cells, there appeared to be a discontinuous distribution of granule properties; the granules
behaved in effect as if there were two distinct populations. In the fixed granule population, trapped granules
exhibited little if any oscillatory displacement, even at
maximum laser power. In the free granule population,
trapped granules could easily be oscillated. These
observations are consistent with a discrete lattice structure to the cytoskeleton, at least in the body and
trailing regions, with fixed granules mechanically or
chemically bound to it and with free granules in the
lattice interstices sampling the cytosolic component of
the intracellular milieu. Our data suggest that the
lattice spacing, or size of such granular ‘‘cages,’’ would
be at least about the magnitude of our oscillation
amplitudes (1 µm peak to peak), since a smaller size
would have prevented virtually any successful observa-
RHEOLOGY OF LOCOMOTING NEUTROPHILS
tions of oscillatory displacements. We cannot speculate
on an upper bound for the cage size, since the population of fixed to free granules could be determined by
biochemical factors independent of mechanical constraints. On the other hand, a cursory inspection of the
Brownian motion of the granules (magnitude and mix-
ing) suggests that the cages are probably not much
larger than the above estimate. Future studies with
variable oscillation amplitudes may shed light on this
question.
The fraction of granules in the fixed population fell to
essentially zero in the leading region. This is consistent
with the idea that there is a marked depolymerization
of the cytoskeletal structure at the site of and during
the course of pseudopod protrusion.
It is known that there are at least four different types
of granules in neutrophils (1) that in turn can be
classified by whether they remain within the cell,
performing intracellular lysosomal functions, or
whether they are exocytotic or secretory. This observation invites two competing hypotheses. First, the fixed
granule population may consist of the nonsecretory
type, whereas the free granule population is of the
secretory type. In this case, we speculate that the
transport of the free secretory granules may be effected
by directed Brownian motion while the nonsecretory
granules remain fixed. This notion of directed Brownian transport would be a consequence of directed
cytoskeletal remodeling that allows for granular transport without an active transport mechanism. By contrast, the converse hypothesis may be true, wherein the
fixed granules are secretory in nature and are transported by molecular motors, and the nonsecretory
granules remain free but caged.
Regional differences. First, we note that, in all experiments, neither the stiffness nor the viscosity was
significantly different between the main body and the
trailing region of the cell. This is perhaps not surprising, to the extent that the evolving dynamic activity is
preferentially restricted to the region near the protruding pseudopod. On the other hand, our observations of
significantly lower viscosity, and especially stiffness, in
the leading region have direct implications to the
rheological nature of the protruding pseudopod during
locomotion. The fact that both G and ␩ are lower in the
leading region implies that the pseudopodial core is
more fluidlike. This is inconsistent with the hypothesis
that the core is a continually growing body of polymerizing actin in compression, which would lead to a relatively larger stiffness compared with the cell body.
Rather, it is more suggestive of simple fluid flow of the
sol state of the cytoplasm, driven presumably by intracellular pressure secondary to cortical contraction. (See
below for remarks on the rheological properties of the
core versus the pseudopodial tip.)
This interpretation is further strengthened by inspection of the relaxation time constants. For the simple
parallel viscoelastic description used in this work, the
time constant ␶, defined by ␶ ⫽ ␩/G, is a convenient
parameter that describes the extent to which fluidlike
behavior can be quantified. Thus a purely elastic
medium is characterized by ␶ ⫽ 0, whereas a purely
fluid medium is characterized by ␶ ⫽ ⬁. We find, for the
body, trailing region, and the leading region, that
␶(body) ⫽ 0.34 s, ␶(trailing region) ⫽ 0.48 s, and
␶(leading region) ⫽ 1.71 s. The observation that the
rheological time constant is longer in the leading region
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Fig. 4. Bar graph showing the material stiffness G and viscosity ␩ in
the body, leading region, and trailing region of the neutrophil in
normal conditions (open bars), after treatment with cytochalasin D
(filled bars), or after treatment with nocodazole (hatched bars). Data
are presented as means ⫾ SE. A: regional and treatment differences
in stiffness G. There is no significant difference between body and
trailing regions or between body and trailing regions across treatment groups. Both body and trailing regions are significantly different from the leading region in each group (** P ⬍ 0.0001). Stiffness in
normal and nocodazole groups was not different in the leading region;
both are different from the cyto-D group in the leading region (P ⬍
0.0001). NS, not significant. B: regional and treatment differences in
viscosity ␩. Comparisons that showed significance here are the same
as in A.
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RHEOLOGY OF LOCOMOTING NEUTROPHILS
Finally, there are a number of other experimental
techniques by which to assess rheological properties of
cells. We cannot make any direct comparisons at this
time, however, because, unlike previous methods, the
work reported here estimates intracellular stiffness
and viscosity in different regions within individual
living and locomoting cells. By contrast, rheological
measurements made with cell aspiration into a micropipette (8) involve large-scale distortions of the entire cell
and do not distinguish among different cell regions.
Estimates of stiffness (21, 22) by magnetic twisting
cytometry are restricted to large populations of cells
and represent a weighted average of any regional
differences in how ligand-coated beads bind to the cell
membrane. Cell poking experiments are done on single
cells (7, 24), but the separate assessment of stiffness
and viscosity between the body or trailing region on the
one hand, and the leading region on the other, appears
to be technically difficult.
Differences in rheological properties with cytochalasin D or nocodazole treatment. Cytochalasin D and
nocodazole are known to disrupt the cytoskeleton
through inhibition of polymerization of the filamentous
actin and microtubules, respectively. These compounds
have been used extensively in investigations of the role
played by the cytoskeleton in cell mechanics (3, 24) and
in the identification of receptor binding to the cytoskeleton (21, 22). In all such experiments, the cell stiffness
decreases with treatment with either drug. In sharp
contrast to these observations, we found no differences
in either stiffness or viscosity in the body or trailing
regions of neutrophils with or without treatment with
either cytochalasin D or nocodazole.
How might these apparently contradictory observations be reconciled? Recall that, in the body and trailing
region of control cells, there appeared to be in effect two
distinct populations of granules, one fixed and the other
free. Despite the lack of difference seen between the
rheological properties shown by free granules in the
control and in the cytochalasin D or nocodazole treatment group, one striking difference did emerge. Specifically, the fraction of fixed granules was substantial
(65%) in the body and trailing regions of the control
group and fell sharply in the two treatment groups to
⬍20% and ⬍40%, respectively.
These observations, taken together, suggest the following interpretation. In control cells, there is a free
granular population that interacts only weakly with
the cytoskeleton, perhaps only through restriction of
large-scale displacements. Similarly, there is the complementary fixed population that interacts strongly with
the cytoskeleton, through chemical or mechanical interactions. If the only effects of cytochalasin D and nocodazole are on the extent of polymerization of the F-actin
and microtubule components of the cytoskeleton, then
one might expect that the sole effect of drug treatment
would be a sharp decrease in the fraction of fixed versus
free granules and that, furthermore, the free granules
in the control case would exhibit the same rheological
properties as in the drug treatment groups. This is
precisely what we observed. By contrast, other tech-
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compared with the body and trailing region is then a
quantification of the statement that the leading region
is more fluidlike. Note that the rheological time constant is an independent descriptor of the material. For
example, honey is more fluidlike than Jello, in this
sense of time constant, despite having a larger viscosity. Our experiments thus show that the leading edge of
locomoting neutrophils is more fluidlike in both the
sense of a lower viscosity and stiffness as well as in the
shift of time constant along the solid/fluid continuum.
Mechanisms responsible for pseudopod formation
have been extensively investigated; some are still controversial, but all lean toward one or the other of two
distinct hypotheses. One is that cortical contraction
generates an increase in intracellular hydrostatic pressure or in gel osmotic pressure and associated solation,
which causes a protrusion of the anterior region to form
a pseudopod (9, 10, 11, 26). The other is that polymerization and cross-linking of actin at the anterior tip push
the cell membrane forward as the pseudopod grows (5,
6, 12, 17). In support of the first hypothesis, contractility of the cortical layer in motile cells has been widely
demonstrated. In vitro studies show that contraction
coupled to solation occurs with changes in Ca2⫹ concentration or pH in a gel from amoebae extracts (9) or in an
actin gel mixed with myosin and gelsolin (10). Histochemical colocalization of actin and myosin at the
pseudopodial base in Dictyostelium amoebae (13) has
been observed. Finally, cortical contraction is consistent with direct measurements of intracellular pressure in Amoeba proteus (25).
Support for the second hypothesis has largely come
from histochemical studies showing that heavy condensation of F-actin exists in the lamellipodia of D. amoebae (6), fibroblasts (18), fish keratocytes (20), or neutrophils especially chemotactically stimulated (2). Both of
these modes of pseudopod protrusion may exist in
amoeboid cells; which mechanism is involved in any
given circumstance may depend on the cell type or
conditions of chemotactic induction.
The leading region itself may also be regionally
heterogeneous, particularly the streaming cytoplasmic
core versus the pseudopodial tip. All of our stiffness and
viscosity measurements in the leading region were
done at sites where intracellular granules flowed into
the lamellipod. The absence of granules at the very tip
of the pseudopod prevented any rheological measurements there, and thus we cannot compare the tip with
the core. At least two possibilities may be suggested.
First, continued pseudopodial growth may be associated with simple pressure forces, even at the pseudopodial tip, which is supported by evidence of decreased
F-actin in the protruding pseudopod (4, 11, 14). Second,
even with a fluid core, the pseudopod may grow through
actin polymerization at its tip, being further anchored
by the cytoskeleton to the substrate. This is supported
by observations of increased pseudopodial F-actin (16,
17, 23). Which of these mechanisms underlies pseudopodial protrusion is no doubt cell type dependent and
remains open.
RHEOLOGY OF LOCOMOTING NEUTROPHILS
bound, within which the free granules sample the
cytosolic phase and which is essentially absent in the
flowing core of a protruding pseudopod. Furthermore,
the uniform drop in stiffness and viscosity measured
with free granules in the pseudopod strongly supports
the hypothesis that the pseudopodial core is more
fluidlike than the cytosolic component of the body or
trailing region of the neutrophil and that the pseudopod does not protrude secondary to a continuously
polymerizing actin assembly throughout the entire
pseudopod.
We are grateful to C. M. Doerschuk for very helpful advice,
suggestions, and critique of this work.
This study was partly supported by grants provided by the
Ministry of Education, Japan (nos. 08559015 and 10670529), and by
National Heart, Lung, and Blood Institute Grant HL-33009.
Address for reprint requests and other correspondence: M. Yanai,
Dept. of Geriatric and Respiratory Medicine, Tohoku University
School of Medicine, 1–1 Seiryo-machi, Aoba-ku, Sendai 980-8574,
Japan (E-mail: [email protected]).
Received 8 February 1999; accepted in final form 21 May 1999.
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