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Cell Motility and the Cytoskeleton 3 5 3 3 1 3 4 4 (1996)
F-Actin Network Formation in Tethers and in
Pseudopods Stimulated by Chemoattractant
Doncho V. Zhelev, Abdullatif M. Alteraifi, and Robert M. Hochmuth
Department of Mechanical Engineering and Materials Science, Duke University,
Durham, North Carolina
Micropipets are used either to deliver a given concentration of the chemoattractant
N-formyl-methionyl-leucyl-phenylalanine(fh4LP) to a local region of a human
neutrophil or to create a membrane tether. Pseudopods, which have a cylindrical
shape and grow at a constant rate, are formed in either case. After reaching a
maximum extension, they retract, even in the presence of chemoattractant. As a
pseudopod grows, cell granules begin to penetrate the pseudopod region to a
“boundary” that defines a distance to the pseudopod’s leading edge that is almost
constant. The exclusion of granules from this domain indicates that it is filled with
a dense network. The formation of this network involves the plasma membrane
because pseudopod growth ceases when a membrane tether is pulled away from
the leading edge. The rate of pseudopod growth depends on fMLP concentration
just as the number of occupied N-formyl peptide receptors depends on this concentration. The experimental data are explained by assuming that F-actin network
is formed next to the plasma membrane. The newly formed network displaces the
membrane and the dominant process in the network region then becomes F-actin
depolymerization. The rate of pseudopod growth is determined by the rate of the
process leading to network formation. This process is apparently an enzymatic
type of reaction. It has a positive enthalpy change and, therefore, is endothermic. 0 1996 Wiley-Liss, Inc.
Key words: neutrophil, actin, cell activation, motility, MLP, receptor-ligandbinding
are observed at lower chemoattractant concentrations
than the cytotoxic responses [Omann et al., 1987; SnyNeutrophils migrate from the circulation to sites of
dennan and Uhing, 19921. In this work we study the
inflammation in response to cytokines. First, a circulatdependence of one of the migratory responses, namely
ing cell rolls and firmly adheres to the endothelium of the
the formation of a pseudopod, on the concentration of the
postcapillary venules. Then it transmigrates through the
chemoattractant N-formyl-methionyl-leucyl-phenylalagaps in the endothelium to the site of inflammation,
nine (fMLP).
where it releases enzymes and produces toxic oxygen
The migratory responses are mediated by adhesion
products. This process is highly regulated and involves
receptors [Hendey et al., 1992; Lawson and Maxfield,
many specialized molecules, such as adhesion receptors
199.51 and to a great extent by the rearrangement of the
[Springer, 19901, cytokine (or chemoattractant) receptors [Snyderman and Uhing, 19921, and cytoskeleton Received May 9, 1996; accepted August 13, 1996.
components [Stossel, 19931. The interaction between
these specialized molecules is mediated by not yet well- Address reprint requests to Doncho V. Zhelev, Department of Mecharacterized signal transduction pathways [Omann et chanical Engineering and Materials Science, Duke University,
al., 1987; Devreotes and Zigmond, 1988; Snyderman Durham, NC 27708-0300.
and Uhing, 19921. Regardless of the complexity of this A. M. Alteraifi’s present addresss is Department of Mechanical Enregulation, the neutrophil migratory and cytotoxic re- gineering, United Arab Emirates University, Al-ain, United Arab
sponse is dose dependent, where the migratory responses Emirates.
0 1996 Wiley-Liss, Inc.
Zhelev et al.
cytoskeleton [Stossel, 19931. The cytoskeleton rearrangement includes lamellipodium protrusion and/or
pseudopod formation, and cell body contraction
[Devreotes and Zigmond, 1988; Evans et al., 19931.
Lamellipodium protrusion is of particular interest because it is believed that under certain circumstances
(e.g., when cell motility is not altered by the rate of
detachment of the adhesion receptors), it determines the
rate of crawling [Zigmond, 19931. This protrusion is
strongly related to the formation of the F-actin network
[Stossel, 19931. The neutrophil’s F-actin has two pools:
one is triton soluble and the other is triton insoluble
[Watts and Howard, 19931. The triton soluble pool is not
stable and depolymerizes in seconds, while the triton
insoluble pool is relatively stable and does not depolymerize for tens of minutes. Two pools of F-actin are also
found in experiments of actin depolymerization in neutrophil lysates from passive and activated cells [Cano et
al., 19911. In this case, one of the pools contains fast
depolymerizing F-actin, while the F-actin of the other
pool is slow depolymerizing. The fast depolymerizing
F-actin is found in activated cells, where it provides almost all F-actin in the lamellipodium region [Cassimeris
et al., 19901. The presence of fast depolymerizing F-actin in the lamellipodium region provides conditions for
fast F-actin turnover. The turnover is essential for the
cytoskeletal rearrangement during cell crawling [Theriot
and Mitchison, 19911. However, while the F-actin turnover provides conditions for fast cytoskeleton rearrangement, it is the formation of the network that determines
the rate of lamellipodium protrusion and, therefore, the
rate of crawling.
The formation of F-actin network in human neutrophils stimulated by exposing a local region of the cell
body to the chemoattractant fMLP is studied in this
work. A new assay is introduced, where fMLP is delivered to a local region of the cell body by a small micropipet. The assay allows a precise measurement of the
geometry of the pseudopod region and measurement of
the rate of pseudopod extension. These two parameters
are used to relate the rate of pseudopod formation to the
N L P concentration at different temperatures. The experimental data are explained in terms of the proposed
“boundary polymerization model,” where: (1) F-actin
network forms at the boundary between the cytoplasm
membrane and the leading edge of the advancing network, (2) the newly formed filaments are trapped in the
pseudopod region as the boundary of polymerization advances, and (3) the trapped filaments depolymerize providing conditions for F-actin turnover [Theriot and
Mitchison, 19911. The chemoattractant stimulated
pseudopod protrusion is compared to network formation
in tethers [Zhelev and Hochmuth, 19951, which occurs in
the absence of chemoattractant.
Cell Preparation
The preparation of neutrophils has been described
elsewhere [Zhelev and Hochmuth, 19951. Briefly,
venous blood was drawn from healthy adult donors into
vacutainers containing EDTA as an anticoagulant. The
blood was centrifuged at 300g for 20 min and the blood
plasma collected. The cells from the buffy coat region,
which is observed on the top of the packed red cells,
were collected. The collected cells were resuspended in
the experimental solution. The experimental solution
was made of 50% autologous plasma from EDTA vacutainers with 50% Hank’s balanced salt solution (HBSS)
without Ca2+ (Sigma Chemical Co., St. Louis, MO).
Preparation of Beads and Small Pipets Filled
With Chemoattractant
Latex beads with immobilized secondary goat antimouse IgG (Sigma) were washed twice in phosphate
buffered saline (PBS), resuspended in PBS, vortexed,
and sonicated. The beads were incubated at room ternperature for 45 min in PBS containing 1 mg-ml-’ antiLFA- 1p (CD18) monoclonal antibody (mAb) (Becton
Dickinson, San Jose, CA). The beads were washed in
PBS and resuspended in HBSS. A drop of HBSS containing beads was put in the experimental chamber,
where single beads were selected and used for pulling
tethers from the neutrophil surface.
Small pipets with internal diameters between 1 and
2 pm were filled with a solution made of the solution used
in the chamber to which was added the chemoattractant N-formyl-methionyl-leucyl-phenylalanine( N L P ,
Sigma). The pipets were used to deliver the chemoattractant to a local region of the cell surface and in this way
to stimulate the formation of a pseudopod (Fig. 1). Using
a pipet allowed a precise control of the amount of
chemoattractant and the time of exposure.
The experimental chamber was 2 mm thick and
open from both sides to allow micromanipulation. The
bottom of the chamber was covered with a coverslip and
the top was covered with two parallel glass strips with a
1 mm thick gap. Thermostated water was allowed to
flow in the gap for temperature control. The cells were
observed with an inverted Leitz (Wetzlar, Germany) microscope with a 100 X oil immersion objective. Micropipets were made from 0.75 mm capillary glass tubing
pulled to a fine point with a vertical pipet puller and cut
to the desired diameter with a microforge. The pipets
were connected to a monometer system, with which the
pipet-chamber pressure difference could be controlled
between 0.5 and 100 Pa using the micrometer driven
F-Actin Network Formation
Fig. 1. Formation of a pseudopod stimulated by a local exposure of
the cell surface to fh4LP of given concentration. The small pipet is
filled with 1 X lo-’ M solution of MLP. A blowing pressure of 20
Pa is applied and the pipet is positioned close the cell surface. Fifteen
to 20 s later a pseudopod begins to grow. Both the area of the leading
edge and the diameter of the polymerized region remain almost constant as the pseudopod grows. After the pseudopod reaches a maximum extension it starts to retract even though the chemoattractant is
still present. The temperature is 22°C.
displacement of a water filled reservoir. Suction pressures as high as 40 kPa were obtained with a syringe. The
pressures were measured with a differential pressure
transducer (Validyne DP15-24). The pressure transducer
readings together with a time counter (Vista Electronics
Model 401, Vista Electronics, Ramona, CA) were multiplexed on the recorded images. The images were re-
corded using a Hamamatsu CCD camera. Distances were
measured on the recorded images by using video calipers
(Vista Electronics Model 305).
Two sets of experiments were performed for measuring the rate of rearrangement of the neutrophil cy-
Zhelev et al.
toskeleton: experiments where the formation of a
pseudopod was stimulated by blowing an FMLP solution
from a small pipet (Fig. 1) and experiments where a
tether was pulled from the cell surface (Fig. 2). In the
first set of experiments a single neutrophil was held in a
pipet. Then another pipet filled with a solution of FMLP
of a given concentration was positioned 1 to 2 pm from
the cell surface. A blowing pressure on the order of 20 Pa
was applied and the advancement of the polymerization
front for the pseudopod region was measured. The rate of
advancement was used to characterize the rate of cytoskeleton rearrangement stimulated by fMLP. During
cytoskeleton rearrangement the cortical tension of the
cell body changed, while it retained its liquid nature
[Evans and Yeung, 19891. This change in the cortical
tension was measured by using the holding pipet as described elsewhere [Zhelev and Hochmuth, 19951.
Briefly, the cell body was aspirated into the holding
pipet until it forms a near hemispherical projection. The
projection length of the cell inside the pipet was kept
constant by adjusting the pipet suction pressure. The cortical tension T, was calculated by [Evans and Yeung,
T, =
- hp
where h P was the pipet suction pressure, Rp was the
pipet radius, and R,,, was the cell radius outside the
pipet. In the presence of a pseudopod the shape of the
outside part of the cell body was not quite spherical (Fig.
1). In this case, R,,, represented the outside radius of
curvature next to the pipet orifice. This radius of curvature was measured from the recorded images. Usually
the pipet radius was significantly smaller than R,,,, so
that the imprecise values of R,,, from the recorded images did not affect significantly the calculated value for
the cortical tensions.
In the second set of experiments (Fig. 2) a single
neutrophil was held in a pipet. A bead with a monoclonal
antibody (mAb) for the CD18 adhesion receptor was
brought into contact with the cell surface for 3 to 5 s and
then withdrawn from the cell surface to a distance of 10
to 15 pm. During contact one or several CD18 receptors
bound to their antibodies on the bead surface. When the
bead is withdrawn, the bound CD18 receptors pulled the
membrane from the cell and one or several tethers were
formed. A polymer formed in the tether, beginning at the
cell body and spreading up the tether until a pseudopodlike structure was formed [Zhelev and Hochmuth, 19951.
The rate of advancement of the polymerization front
along the tether was used as a measure of the rate of
cytoskeleton rearrangement in the absence of chemoattractant. Only cells with single tethers were used in the
FMLP Stimulated Pseudopod Formation
In the experiment illustrated in Figure 1, the exposure of a local region of the cell surface to a fMLP
gradient induces the formation of a single pseudopod.
During this process the cell cytoplasm undergoes a dramatic change from a very viscous liquid to a highly
cross-linked rigid polymer structure made of F-actin.
This structure is dense enough to prevent granules from
entering it. The depth of penetration of the granules and
the leading edge of the pseudopod defines the apparent
boundaries of the polymer. Initially, the pseuodopod extends away from the cell body. After the pseudopod extends 3 to 5 pm, granules from the cell body begin to
penetrate into the pseudopod domain (Fig. 1). This defines the trailing boundary of the pseudopod. Both the
extension of the polymer network and the movement of
its trailing boundary proceed at a certain rate. This rate is
given by the slope of the plot of the measured position
vs. time of the two boundaries (see Fig. 3). It is seen
from Figure 3 that both rates are constant, which suggests that the processes related to these rates-namely ,
the process of network formation and the process of network degradation-proceed with the same rate.
The first event of fMLP induced pseudopod formation is the binding of the chemoattractant to its receptor
[Posner et al. , 19941. This binding leads to the formation
of a ternary complex and a release of activated G protein.
Even though the cascade of events following the release
of G protein is not well known, it is commonly observed
that the various cellular responses depend on the concentration of the chemoattractant [Omann et al., 19871.
Therefore, it is expected that the rate of network extension will be a function of fh4LP concentration in the
vicinity of the pseudopod’s leading edge. Because the
hydrodynamic conditions for fMLP delivery are similar
for all experiments, the fMLP concentration in the vicinity of the leading edge is proportional to its concentration
in the small pipet. Figure 4 shows the dependence of the
measured rate of network extension on the fMLP concentration in the small pipet for three different temperatures. The dependence of the rate of network extension
clearly depends on the fMLP concentration. The fMLP
concentration corresponding to the rate equal to half of
the measured maximum rate for a given temperature
(Fig. 4) corresponds to the apparent equilibrium dissociation constant. For 30°C the value of this constant
found from the data in Figure 4 is 5 x lo-’’ M. A
“saturation” of the measured rate is observed at high
F-Actin Network Formation
Fig. 2. Formation of a pseudopod-like structure in a tether. The tether
is formed as the bead coated with mAb to CD18 is touched to the cell
surface for 3 s and then withdrawn. Pulling a tether initiates the formation of a network. This network advances along the tether and
continues to distances up to 7 to 10 km, and then it starts to retract.
As the network advances it is followed by granules from the cell body.
The advancing granules and the leading boundary of the network
define the network region. The volume of the network region of the
pseudopod like structures is small compared to the same region of
fMLP stimulated pseudopods (see Figs. 1 and 10). The temperature is
fMLP concentrations. FMLP concentrations on the order
of lop7 M is the “saturation” concentration for the temperatures studied. The Arrhenius plot (Fig. 5) of the rates
at “saturation” is used to calculate the apparent activation energy of network formation. The apparent activation energy of network formation is found from the slope
of the line approximating the experimental data in Figure
5 multiplied by the gas constant. Its value is 36.6
kJ.mol-’ (8.7 kcal-mol-’).
The extent of the network during pseudopod formation always reaches a maximum. The maximum extension depends both on the fMLP concentration and the
temperature. Usually large maximum extensions are
measured at high temperatures. After the maximum extension is reached, two types of behavior are observed:
(1) the pseudopod starts to retract immediately, or (2) the
pseudopod maintains its maximum length for several
minutes-in some cases up to 10 min-and then retracts.
Different cells follow one or the other of the two path-
ways. In these experiments more than 90% of the observed cells follow the first pathway. [It is important to
note that fMLP is present in these experiments during
both the extension of the pseudopod and its retraction.
Modeling of the distribution of fMLP around the cell
surface (Alteraifi and Zhelev, unpublished results) shows
that 15 s after starting the flow of chemoattractant, its
distribution becomes constant and remains unchanged
(within 5%) for the next 20 to 30 min.] The rearrangement of the cytoskeleton in the pseudopod region is coupled with its contraction in the region of the main call
body. Figure 6 shows the measured apparent cortical
tension during fMLP-stimulated pseudopod formation. It
is seen that the extension of the pseudopod is coupled
with an increase in the cortical tension and its retraction
with a relaxation of the cortical tension. The increase of
the cortical tension usually begins after the initiation
of pseudopod growth. The delay between the initiation of
pseudopod growth and the increase of the cortical tension
Zhelev et al.
s c
t t '
o l = /'
Fig. 3. Distance vs. time of the leading (closed circles) and trailing
(open circles) boundary of the network region in a fMLP stimulated
pseudopod. The boundaries move with constant velocities and the
distance between them remains almost constant. The rate of advancement of the leading b o u n d q is on the order of 0.13 pms- The zero
time is when the cell is exposed to fMLP at a concentration of 1 X
M and the temperature is 22°C. The data are from the cell shown
in Fig. 10.
' ' " 1 1 ' '
1000/T (K-')
Fig. 5 . Arrhenius plot of the rates of network formation shown in
Figure 4 at fMLP concentrations equal to the concentration of saturation. The slope of the straight line found by the least square method is
-4.4-K. This slope multiplied by the gas constant R represents the
apparent activation energy of network formation. The calculated apparent activation enegy of network formation is 36.6 k.l*mol-'.
muth, 19951. After relaxation, the value for the cortical
tension usually is larger than its initial value.
Network Formation in Tethers
> 0.10
Time (s)
, , ,,,,,,
, , , ,,,,,,
, ,
WLP Concentration (M)
Fig. 4. Dependence of the rate of pseudopod extension (or network
formation) on the temperature and the concentration of fMLP in the
small pipet (see Fig. 1). Curve 1 is for 5"C, curve 2 for 22"C, and
curve 3 for 30°C. The concentrations for half of the measured maximum rate of extension for 5", 22", and 30°C are 2 X lo-', 2 X lop9,
and 5 x lo-'' M, respectively. When the fMLP concentration is on
M (concentration of saturation) or larger, the
the order of 1 x
measured rates are maximum.
measured from 13 cells is 26 & 13 s. The average maximum cortical tension is on the order of 0.15 mN-m-'.
The increase of the cortical tensions has a large deviation
from cell to cell and most probably is related to the state
of the cell cortex before stimulation [Zhelev and Hoch-
Pulling a tether from the neutrophil surface initiates
the formation of a pseudopod-like structure (Fig. 2).
Similar to the case of an fMLP-stimulated pseudopod,
the pseudopod-like structure in tethers advances along
the tether at a constant rate (Fig. 7) until it reaches its
maximum extension, and then it retracts. As in the case
of fMLP-stimulated pseudopods, the polymer network
advancing in the tether is bound between a leading and
trailing boundary. The rate of advancement of the two
network boundaries is similar, which provides an almost
constant thickness of the network region. The temperature dependence of the process of network formation in
tethers (Fig. 8) is similar to that in fMLP-stimulated
pseudopods (Fig. 5). This dependence is again used to
measure the apparent activation energy of network formation. This apparent activation energy is on the order of
34.9 kJ.mol-', which is similar to the apparent activation energy for the formation of fMLP-stimulated
Site of Network Formation
In the study of fMLP-stimulated pseudopod formation illustrated in Figure l , the length of the pseudopod
increases from 0 to 8 pm while its thickness remains
almost constant. Also, during pseudopod growth when
the pipet carrying fMLP is removed and the cell is
washed by moving it in the chamber, the pseudopod
F-Actin Network Formation
- 2
Time (s)
Fig. 6. Cell body contraction T, (open squares) during fMLP stimulated pseudopod growth (closed circles). The contraction of the main
cell body increases as the pseudopod extends and decreases when it is
about to retract. There is a delay of about 30 s between the start of
pseudopod growth and the increased contraction of the main cell body.
The zero time is the time when the cell is exposed to the chemoattractant and the temperature is 20°C.
0 1
Time (s)
Fig. 7. Polymerization and retraction cycles for network formation in
tethers. The leading (closed circles) and the trailing (open circles)
boundaries of the network are shown. The temperature is 22°C. In this
experiment, a single tether is pulled and the dynamics of formation of
a pseudopod-like structure is measured. Initially, the network extends
along the tether with almost constant velocity. When the leading
boundary of the network reaches a distance from the cell body of 10
to 15 pm, its growth ceases and the pseudopod-like structure starts to
“retract” (compare Fig. 2e and f ) in a process similar to pseudopod
retraction shown in Figure 3. The retraction proceeds until the pseudopod-like structure disappears almost completely (Fig. 2f), and then it
begins to grow all over again. This cyclic behavior is observed in
almost all experiments.
begins to retract (Fig. 9). This behavior suggests that
network formation occurs next to the leading boundary.
Then, it may be expected that proteins from the cytoplasm membrane are involved this process. If so, then
lOOOiT (K-’)
Fig. 8. Arrhenius plot of the rates of network advancement in tethers
for different temperatures. The slope is -4.2.K, which corresponds to
an apparent activation energy of network formation on the order of
34.9 kl.moI-’.
their “removal” from the network’s boundary is likely
to affect actin polymerization.
The cytoplasm membrane can be “stripped” from
the leading boundary of spontaneously formed pseudopods by pulling a tether (for details see Materials and
Methods) from the pseudopod’s leading boundary. [After the tether is pulled the pseudopod starts to retract
(Fig. 9)]. When the tether is pulled from the leading
boundary of a large lamellae, the network formation in
this region ceases, while in regions far from the disturbed
area it continues. The retraction of the pseudopod, after
pulling a tether from its leading boundary, suggests that
membrane proteins are crucial for network formation.
The formation of pseudopods in neutrophils can be
stimulated by soluble chemoattractants [Cassimeris and
Zigmond, 19901 as well as by ligands of the adhesion
receptors [Lofgren et al., 1993; Brennan et al., 1991;
Jaconi et al., 19911. This suggests that while pseudopod
formation does not require the presence of a surface
[Condeelis, 19931, the interaction of the cell with adjacent surfaces may alter its activation. To minimize the
effect of the adjacent surfaces, the neutrophils used in
this work are held with micropipets. This helps both to
minimize the effect of adhesion as well as to produce
highly oriented single pseudopods and pseudopod-like
structures (Figs. 1 and 2).
In the experiments on network formation in tethers,
the membrane at the tip of the tether is “attached”
through the binding of integrins to their antibody on the
bead surface. As mentioned already, the binding of in-
Zhelev et al.
" " ' " " " " " " ~ " " " ' " " " ' " ' ~
Average pseudopod length
tether pulled
Time (s)
Fig. 9. Network formation in spontaneously growing pseudopods and
retraction after tether formation. Two spontaneously growing pseudopods are shown (open and closed circles, respectively). The pseudopods extend linearly with time until they reach the average maximum
extension shown by the dashed line. When a tether is pulled from the
leading edge (arrows) of a growing pseudopod, the pseudopod starts to
retract. The retraction of the pseudopod starts a few seconds after
pulling the tether.
tegrins to their antibodies can result in cell stimulation.
To assure that receptor-antibody binding has a minimum
affect on the measured data, the rate of network advancement in tethers pulled by latex beads is compared to that
in tethers pulled by small pipets [Zhelev and Hochmuth,
19951. This comparison shows that for the same temperature and media, the measured velocities in both cases
are similar. The possibility of neutrophil stimulation by
the binding of adhesion receptors to their antibodies was
also explored by measuring calcium transients in the cell
cytoplasm. It is known that the crawling of neutrophils
on surfaces coated with vitronectin is coupled with the
occurrence of calcium transients [Marks and Maxfield,
19901. Vitronectin is a ligand for the integrin adhesion
receptors, so similar behavior is expected after the binding of CD18 to its monoclonal antibody. Indeed, after
keeping the cell and the bead in contact for 30 to 60 s,
calcium transients were measured by measuring the fluorescence from the calcium probe Fluo-3 (Alteraifi and
Zhelev, unpublished observations). However, when a
tether is pulled, both by using a latex bead and by using
a small pipet, calcium transients were not observed. (A
total of 15 cells was observed in two different experiments.) There were several factors that may have contributed to the negligible (if any) effect of the binding of
adhesion receptors at the tether tip to cell stimulation in
these experiments. First, the time of cell-bead contact
before pulling the tether was quite small, usually less
than 3 s, compared to the time of contact when calcium
transients were observed. Second, both during the initial
bead-cell contact and after the tether was pulled, there
were few receptors bound to antibodies. Third, these few
bound receptors provide few signal molecules for cell
stimulation. Fourth, the signal molecules have to
"travel" the distance along the tether by either diffusing
along the membrane or in the f-actin filled tether.
(Zhelev and Hochmuth [ 19951 have shown that 20 to 25
s after a tether is pulled it becomes stiff, probably because of the formation of crosslinked F-actin in its interior.) Whatever the factors leading to a negligible stimulation of the cell by the attached receptors at the tether
tip, they provide conditions for studying network formation in tethers pulled by latex beads instead of using
small pipets. The use of latex beads significantly simplified the experimental procedure and allowed many cells
in the same preparation to be studied on the same day.
The pseudopods produced using fMLP-filled pipets
are supported by F-actin network and are stiff, while the
main cell body maintains its liquid nature. The diameter
of the pseudopod region remains constant until the maximum extension is reached (Fig. 1). After that, the
pseudopod diameter increases both when the pseudopod
starts to retract (Fig. 1) or when it remains at maximum
extension (not shown). Another feature of these pseudopods is that they have a dense network located next to the
pseudopod's leading edge that excludes cell granules.
The apparent thickness of this network remains constant
while the pseudopod advances (Fig. 3). The same thickness for the pseudopod-like structure formed in a tether is
also constant (Fig. 7). Another important observation
giving an insight into network dynamics is the retraction
of the pseudopod after the "stripping" of the cytoplasm
membrane from its leading boundary (Fig. 9). All these
observations taken together suggest that the formation of
F-actin network in pseudopods and/or pseudopod-like
structures occurs at the network's leading boundary (Fig.
10B). This is consistent with the hypothesis of boundary
polymerization [Zhu and Skalak, 1988; Evans and
Dembo, 1990; Evans, 19931. The almost constant distance between the leading and the trailing boundary of
the network is consistent with the nucleation-release
model [Theriot and Mitchison, 1991; Zigmond, 19931.
There, new actin filaments are created near the leading
edge and remain trapped in their place as the leading
boundary of the network continues to advance. The
trapped filaments depolymerize until eventually they disappear. The depolymerized actin is transported to the
polymerization region and is partially consumed in the
polymerization process. This exchange of actin between
the polymerization region and the network volume is
known as F-actin turnover [Zigmond, 19931.
Another feature of the pseudopods studied in this
work is that the overall rate of their growth is almost
F-Actin Network Formation
-Network region
Trailing boundary
<g boundarjl
Network region-
Pseudopod region
Pseudopod region
Fig. 10. a: Formation of a thick pseudopod stimulated by a pipet
filled with fMLP. The penetration of granules into the pseudopod
region is more clearly seen in thick pseudopods than in thin pseudopods (compare to Fig. 1). Granule penetration determines the apparent
trailing edge of the F-actin network in the pseudopod region. The
distance between the trailing boundary and the leading edge of
the pseudopod is almost constant during the pseudopod growth. b:
Schematic of the boundary polymerization model. The F-actin network is formed in the boundary polymerization region, which is next
to the plasma membrane. The amount of polymerized actin is proportional to the number of occupied chemoattractant receptors in this
region. During pseudopod extension, the formed F-actin filaments
remain trapped in the network while the polymerization region continues to advance. The trapped filaments depolymerize until they
eventually disappear. Because F-actin filaments have different initial
lengths and because they are cross linked with different cross linking
proteins, some of the filaments depolymerize faster than others. This
provides conditions for the formation of vacancies in the network and
for the penetration of granules in this region. At the same time, slowly
depolymerizing filaments provide a support for the pseudopod shape.
The overall rate of pseudopod advancement is determined by the rate
of network formation.
constant. Pseudopod growth consists of the movement of
many “ruffles” that “appear” at the pseudopod leading
edge (see Figs. 1 and 10). Some of the “ruffles” advance more rapidly than others, then eventually these
“ruffles” slow down while others start to move more
rapidly. This difference in the movement of the “ruffles” contributes to the roughness of the shape of the
leading edge of the pseudopods observed in the experiments (see Figs. 1 and 10). However, regardless of the
different movement of individual ‘‘ruffles,’ ’ the overall
extension of the pseudopod region is almost constant (see
Figs. 3 and 9). Also constant, or nearly so, is the advancement of the network region in pseudopod-like
structures in tethers (Fig. 7). Similar to pseudopod ex-
tension, the movement of the trailing boundary of the
network region is almost constant (see Figs. 3 and 7).
The overall linearity of both pseudopod extension and
movement of the trailing boundary suggests that overall
the network formation is a steady-state process and the
amount of formed network per unit time equals the
amount of F-actin that is depolymerized during the same
time. In these experiments, the characteristic time for
F-actin turnover is of the order of 20 s, which is obtained
by dividing the typical 2 p,m thickness of the polymer
domain next to the leading edge by the characteristic
velocity of 0.1 p,m.s-’. The processes involved in network polymerization include: transport of actin to the site
of polymerization, the dissociation of actin monomers
Zhelev et al.
from their sequestering proteins, the formation of new
nucleation sites, and F-actin polymerization. The first
process has a physical nature, while the other three processes depend mainly on the rate of various chemical
reactions. Whether the rate-limiting process for network
formation has either a physical or chemical nature is
discussed below.
The physical process that may limit the rate of network formation is the transport of actin to the site of
polymerization. Because the rate of network formation is
constant and there is an F-actin turnover, this transport
can be diffusion limited. The diffusion in this case is a
steady state diffusion, where the characteristic time of
diffusion T~ of a given actin species to the polymerization region is calculated by
where ID is the diffusion distance and D is the diffusion
coefficent. The diffusing actin species that may provide
a pool of actin for polymerization are G-actin and non
attached F-actin filaments. The characteristic time of diffusion for these actin species is estimated in Appendix A.
From the estimate it is seen that the diffusion of G-actin
is much faster than the rate of pseudopod advancement,
while the diffusion of F-actin probably is much slower.
Therefore, it is likely that neither determines the rate of
pseudopod extension, unless both combine in some
unique way to produce the measured growth rates.
Something other than simple diffusion must be the ratelimiting process for pseudopod extension.
The data shown in Figure 4 show that the rate of
pseudopod extension depends on the chemoattractant
concentration in the small pipet. This dependence is similar to the binding of fMLP to its receptor [Sklar et al.,
19851. The chemoattractant concentration for observing
half of the maximum rate of pseudopod extension at
room temperature, calculated from the data in Figure 4,
is on the order of 2 X
M. This value is of the order
of the dissociation constant of fMLP [Tomhave et al.,
19941 and FNLPNTL [Sklar et al., 19851. All these data
taken together suggest that the rate of pseudopod extension is unlikely to depend on the transport of actin to the
site of polymerization. This rate most probably depends
on the rate of the chemical reactions triggered by the
binding of the chemoattractant to its receptor. These reactions include the formation of a ternary complex [Posner et al., 19941, release of activated G protein, activation of phospholipase C , production of the secondary
messengers inositol triphosphate and diacylglycerol, the
activation of protein kinase C , and a sequence of not yet
well-studied reactions that result in network formation
[Omann et al., 1987; Devreotes and Zigmond, 1988;
Snyderman and Uhing, 19921. Even though the exact
chemical reactions are unknown, the fact that the rate of
network formation is almost constant (Fig. 3) and that
this rate depends on the chemoattractant concentration
(Fig. 4) suggests that the involved reactions are steadystate reactions and are far from equilibrium. In the
boundary polymerization approximation used here (see
Fig. lOB), it is assumed that actin polymerizes at the
boundary (or the region) between the network and the
membrane. As the polymerization proceeds, the boundary is displaced from its previous position and depolymerization becomes the dominant feature of the network,
away from the boundary. Because of the movement of
the boundary the chemical reaction in the boundary polymerization region is far from equilibrium, while at the
same time it proceeds at a constant overall rate. These
characteristics suggest that network formation can be
modeled as an apparent “enzymne” reaction (see Appendix B). The calculated apparent Gibbs energy of this
reaction is on the order of 43 kJ.mol-’ (10 kcal.mol-’),
which is on the order of the Gibbs energy for ATP hydrolysis. The apparent Gibbs energy does not represent
the true Gibbs energy of the rate limiting reaction because it is not known how the rate constant k, is related
to the rate constants of the involved chemical reactions.
Even though the rate limiting reaction of network formation is unknown, the comparison of the Arrhenius plots
of network formation in fMLP stimulated pseudopods
and in tethers shows that the apparent activation energy
on both cases is similar. This similarity suggests that
both the process of chemoattractant-stimulated network
formation and the process of network formation in the
absence of chemoattractants share the same rate limiting
Pseuodpod formation stimulated by fMLP is coupled to an increase in the cortical tension of the main cell
body (Fig. 6). Because the neutrophil cortex forms an
apparent “shell” next to the cell surface [Zhelev et al.,
19941, the increase of the cortical tension leads to an
increase of the static pressure in the cell cytoplasm. It has
been suggested [Stossel, 1993, see also the reviews of
Codneelis, 1992, 19931 that the increase of the cytoplasm static pressure may be the driving force for cytoplasm flow and pseudopod extension. In previous work
on yeast phagocytosis [Evans et al., 19931 and mechanically stimulated cortical rearrangement [Zhelev and
Hochmuth, 19951, the increase of the cortical tension
was delayed until about 30 s after the initiation of cortical
rearrangement and cytoplasmic flow. This delay is also
observed here (see Fig. 6), where the delay between
initiation of pseudopod growth and cell body contraction
is on the order of 26 s. Therefore, the contraction of the
main cell body may account for the cytoplasm flow and
F-Actin Network Formation
cell shape changes only at the final stages of cortical Cassirneris, L., and Zigmond, S. H. (1990): Chemoattractant stimulation of polymorphonuclear leukocyte locomotion. Semin.
rearrangement. This observation is in accord with other
Cell Biol. 1:125-134.
biochemical studies [Condeelis, 19921 showing that it is
Cassirneris, L., McNeill, H., and Zigmond, S. H. (1990): Chemoatunlikely for the cell body contraction to be the major
tractant-stimulated polymorphonuclear leukocytes contain two
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Condeelis, J. (1992): Are all pseudopods created equal? Cell Motil.
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the network and the cytoplasm membrane. As the polyRev. Cell Biol. 4549-686.
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pied N-formyl peptide receptors in the membrane. The
J. Cell Biol. 122:1295-1300.
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This work was supported by a grant from the
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A.M.A., and a grant 5 R01 HL23728 from the National
Institutes of Health to R.M.H. Blood drawing was supported by grant MO 1-RR-30 from the National Institutes
of Health to the Rankin Clinical Research Unit of Duke
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309 -3 16.
Estimating the Characteristic Time of Diffusion
The characteristic time of diffusion of G-actin and
F-actin is calculated from Eq. 2. The diffusion distance
is on the order of the distance between the leading
boundary and the trailing boundary of the network. This
distance measured from the data in Figures 3 and 7 is of
the order of 1 to 3.5 pm. The diffusion coefficient in Eq.
2 is an apparent parameter. It depends on the cytoplasm
viscosity, network density, and the size of the diffusing
actin species. There are two actin species that may contribute to network formation--(;-actin and F-actin.
Among them G-actin diffuses faster and gives the lower
bound of the characteristic time of diffusion. The diffusion coefficient of G-actin has been measured in water
and is on the order of 7.1 x lo-” m2*s-l [Tait and
Frieden, 1982; Lanni and Ware, 19841. The value of the
diffusion coefficient when G-actin diffuses in the highly
viscous cytoplasm of the neutrophil is estimated below.
Measurements of the diffusion of fluorescent molecules and small beads in the cytoplasm of fibroblasts
and kidney cells show that these small molecules diffuse
up to five time slower than they do in water [Bicknese et
al., 1993; Luby-Phelps et al., 1993; Kao et al., 1993;
Berland et al., 19951. This slowing of the diffusion of
small molecules is a result of volume occlusion due to
the presence of the cell cytoskeleton [Kao et al., 19931.
Felder and Kam [1994] measured the diffusion of the
fluorescent probe BCECF in the cytoplasm of activated
human neutrophils and obtained a value of 4.3 X
m2*sP1[Felder and Kam, 19941. This value is 50 times
smaller than the diffusion coefficient of the same probe
in water and corresponds to more than 50% volume occlusion in the neutrophil cytoplasm [Kao et al., 19931.
The volume occlusion in the pseudopod region is difficult to measure because of F-actin turnover and the resulting gradient in network density. It can be estimated
from electron micrographs of triton X-100-extracted residues of human neutrophils [Stossel, 19931. From these
micrographs it is seen that the volume occlusion is less
than 50%. Therefore, the measured decrease of 50 times
in the BCECF diffusion in neutrophils by Felder and
Kam [19941 may give an overestimate of the value of the
diffusion coefficient for G-actin. In any case, the actual
value for the G-actin diffusion coefficient may be from
five [Bicknese et al., 1993; Luby-Phelps et al., 1993;
Kao et al., 1993; Berland et al., 19951 to fifty [Felder
and Kam, 19941 times smaller than the diffusion coefficient in water. However, because BCECF is similar in
size to G actin-I nm vs. 4 nm, respectively-the diffusion coefficient for G-actin is expected to be of the
same order of magnitude. Therefore, the minimum and
maximum apparent diffusion coefficients are on the order of 1.4 X lo-” m2-s-’ and 1.4 x
respectively. Then, the time of diffusion across a 2 km
dense network at the leading edge of the pseudopod region is on the order of 0.4 to 4 s. The later time is smaller
than the time of F-actin turnover, which is on the order
of 10 to 20s in our experiments and these of others [Cassimeris et al., 1990; Cano et al., 19911. It is seen that the
time of diffusion of G-actin is smaller than the time of
F-actin turnover and, thus, diffusion of G-actin is not the
rate-limiting process in network formation. However, if
F-Actin Network Formation
non attached F-actin filaments [Cano et al., 19911 provide a significant pool of actin for the polymerization
process, the characteristic time of actin diffusion can be
much slower [Simon et al., 19881 than that estimated for
G-actin. In this case (when non attached F-actin filaments rather than G-actin monomers provide a pool for
actin polymerization), actin diffusion could be a ratelimiting process in network formation.
Model for Network Formation in Pseudopods
Network dynamics in the pseudopod region is illustrated in Figure 10. The network filaments are formed
at the membrane boundary and depolymerize as this
boundary moves away. The rate limiting process for
boundary movement (or pseudopod extension) is the
slowest chemical reaction involved in network formation. Except for the slowest reaction, all other reactions
are at steady state. Also, just as it is for enzyme reactions, the amount of formed network [F] per unit time is
proportional to the concentration of at least one of the
chemical species involved in the slowest reaction. Therefore, because all reactions except the slowest one are
steady-state reactions, the concentration of this chemical
species is proportional to the number of occupied fMLP
receptors [E,] (or to the bulk concentration of fMPL as
shown in Fig. 3). Then, the apparent rate of network
formation is
(AII. 1)
where k, is an apparent rate constant.
The apparent rate k, can be estimated when the rate
of network formation -and the number of occupied
receptors [E,] are known. Unfortunately, the rate of network formation has not been measured in living cells,
and its value must be estimated. Instead of its actual
value, here its estimate is used. This estimate is found
from the amount of F-actin formed after the exposure of
the cells to a chemoattractant. In the experiments of
Can0 et al. [1991], neutrophils are exposed for 90 s to
0.02 p M fNLLP. After that time the amount of F-actin
has doubled relative to its amount in resting cells. The
total amount of actin in resting cells is about 100 pM and
from this only 30% is F-actin [Southwick et al., 19891.
Thus, the amount of freshly polymerized actin is on the
order of 30 pM. It is assumed that most of the polymerized actin remains in the pseudopod region and is exchanged during F-actin turnover. The time of F-actin
turnover is of the order of 20 s (Fig. 3). This gives for the
rate of network formation a value on the order of 1
pM.s-'. The rate of network formation can be converted
to the number of molecules added to the network per
second. This conversion is done by multiplying the
above rate by the cell volume and Avogadro's number.
The radius of a resting neutrophil is 4 pm. This gives for
liters. Then, the rate of
the cell volume 2.7 X
network formation calculated above converts to 1.6 x
lo5 s-l (molecules per second).
The other parameter, which is needed to calculate
k,, is the number of occupied N-formyl peptide receptors. At saturation, this number is equal to the number of
receptors in the leading edge of the pseudopod. The
number of N-formyl peptide receptors in the leading
edge is calculated by taking the fraction of the total
amount of receptors that reside in this region. This fraction is calculated from the ratio of the area of this region
to the total cell area. The diameter of the boundary polymerization region is of the order of 3 pm (see Fig. l),
which has a correspondingarea of 7 pm2. The area of the
neutrophil is of the order of 200 pm'. Then, the area of
the boundary polymerization region is 3.5% of the total
cell area. This is the fraction of N-formyl peptide receptors residing in the pseudopod's leading edge. The total
number of receptors on the membrane of a resting cell is
20,000 [Norgauer et al., 19911. Within the first 2 min
after cell activation, this number increases to reach a
total of 40,000 receptors, and then for the next several
minutes remains almost constant [Norgauer et al., 19911.
Considering the total number of receptors equal to
40,000, the number of receptors in the polymerization
region is on the order of 1,400. [In this calculation it is
assumed that N-fonnyl peptide receptors do not aggregate. This assumption is supported by the results from
our recent studies, where we characterize the binding of
fluorescent labeled ligands to the N-formyl peptide receptor during chemoattractantinduced pseudopod formation (Alteraifi and Zhelev, unpublished results)]. Using
the value of 1.6 X lo5 s-' for the rate of network formation and the value of 1,400 for the number of
N-formyl peptide receptors in the boundary polymerization region, the calculated apparent value of k, is 1.1 X
lo2 s-'.
The estimated value of k, is used to calculate the
apparent Gibbs energy of network formation AG+
[Glasstone et al., 19411. This is done by using
AG+ = AH+ - TAS+
where AH+ and AS+ are apparent enthalpy and entropy,
respectively, and T is the absolute temperature. The en-
thalpy is calculated from: AH+ = E, - RT, where E,
Zhelev et al.
is the activation energy of network formation given by
the slope of the Arrhenius plot in Figure 5 , and R is
the gas constant. The entropy is calculated from:
where h is the plank constant, and the
parameter Y is: Y = k,exp
The apparent en-
thalpy and entropy are 34 kl-mol-' (8 kcal-mol-') and
-30 J.mol-'.K-' (-7 cal-mol-'-K-'). The calculated
Gibbs energy for 37°C is on the order of 43 kJ-mol-' (10
kcal-molThe apparent enthalpy is positive, which
indicates that the process of network formation is endothermic.
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