Intracellular elasticity and viscosity in the body, leading, and trailing regions of locomoting neutrophils

Masaru Yanai1, James P. Butler1,2, Tomoko Suzuki1,3, Akio Kanda1, Masashi Kurachi3, Hideo Tashiro3, and Hidetada Sasaki1

1 Department of Geriatric and Respiratory Medicine, Tohoku University School of Medicine, Sendai 980-8574; 3 Laboratory for Photo-biology, Photodynamics Research Center, Institute of Physical and Chemical Research (RIKEN), Sendai 980-0868, Japan; and 2 Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02115


    ABSTRACT
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MATERIALS AND METHODS
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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.

cytoskeleton; biomechanics; pseudopodia


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INTRODUCTION
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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.

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
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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 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 (beeswax-lanolin-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 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 phi  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 sinphi (note that for the granule lagging behind the trap motion, phi  < 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
&phgr; = sin<SUP>−1</SUP>(<IT>x<SUB>z</SUB></IT>/<IT>x</IT><SUB>0</SUB>) (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 eta . 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 eta  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 time-dependent 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 eta 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 eta 1 and the desired material descriptors G and eta  described below. Because the granule and 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 = <IT>G</IT><SUB>1</SUB><IT>x</IT> + &eegr;<SUB>1</SUB><IT><A><AC>x</AC><AC>˙</AC></A> = k</IT>(<IT>a − x</IT>) (2)
where the overdot denotes differentiation with respect to time.

In the complex Fourier domain, the trap and granule displacements can be written as
<IT>a</IT> = <IT>a</IT><SUB>0</SUB> cos(ω<IT>t</IT>) = Re(<IT>a</IT><SUB>0</SUB><IT>e</IT><SUP><IT>iωt</IT></SUP>)
<IT>x</IT> = Re(<IT><A><AC>x</AC><AC>˜</AC></A>e</IT><SUP><IT>iωt</IT></SUP>) (3)
where omega  is the angular frequency, i = <RAD><RCD>−1</RCD></RAD>, x~ is the complex displacement, and t is time. The equation of motion then simplifies to the algebraic expression
(<IT>G</IT><SUB>1</SUB> + <IT>k + i</IT>ω&eegr;<SUB>1</SUB>)<IT><A><AC>x</AC><AC>˜</AC></A> = ka</IT><SUB>0</SUB> (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
<IT>T</IT> = <FR><NU><IT><A><AC>x</AC><AC>˜</AC></A></IT></NU><DE><IT>a</IT><SUB>0</SUB></DE></FR> = <FR><NU><IT>k</IT></NU><DE><IT>k + G</IT><SUB>1</SUB> + <IT>i</IT>ω&eegr;<SUB>1</SUB></DE></FR> = ‖<IT>T</IT>‖<IT>e<SUP>i&phgr;</SUP></IT> (5)
where
‖<IT>T</IT>‖ = <IT>x</IT><SUB>0</SUB>/<IT>a</IT><SUB>0</SUB>
&phgr; = arg <IT>T</IT> = sin<SUP>−1</SUP> (<IT>x<SUB>z</SUB></IT>/<IT>x</IT><SUB>0</SUB>) (6)
The spring constant of the trap, k, is proportional to the laser power P; thus
<IT>k</IT>/<IT>k</IT><SUB>90</SUB> = <IT>P</IT>/<IT>P</IT><SUB>90</SUB> (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 omega , 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
<IT>T</IT><SUP>−1</SUP> − 1 = <IT>G</IT><SUB>1</SUB>/<IT>k + i</IT>&eegr;<SUB>1</SUB>ω/<IT>k</IT> (8)
Having made measurements at various frequencies omega  and at various laser powers (and hence various values of k), we finally estimate G1 and eta 1 from this expression as follows. With T-1 - 1 taken to be the dependent variable and 1/k and omega /k independent variables, G1 and eta 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 omega /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 eta : F = 6pi eta ru. This is the same as writing the damping force as F = eta 1&xdot;, from which we make the immediate identifications
&eegr; = &eegr;<SUB>1</SUB>/6&pgr;<IT>r</IT>
<IT>G = </IT><IT>G</IT><SUB>1</SUB>/6&pgr;<IT>r</IT> (9)
for the viscosity and, by analogy, the stiffness modulus. The SEs for these parameters also scale like 1/6pi 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 two-way ANOVA. Statistical significance was assessed a priori at P < 0.05, but posterior significances were found to be much stronger.


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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.

                              
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Table 1.   Regional and treatment distribution of measured granules

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.


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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 phi . Note that phi  < 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.

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.


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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)].

As described in MATERIALS AND METHODS, the transfer function can be used to estimate the uniaxial elastic modulus G1 and viscosity eta 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 proportionality 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 omega /k, where the slope is an estimate of the uniaxial viscosity eta 1 (from the imaginary part of Eq. 8).


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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 omega /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. omega /k. Slopes are estimates of the different uniaxial viscosities in these regions.

Figure 4 shows a bar graph representation (means ± SE) of the values of the material properties G (Fig. 4A) and eta  (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 eta , there was no significant difference between the body and trailing regions. Surprisingly, neither cytochalasin D nor nocodazole had any effect on either G or eta  in these regions. By contrast, both G and eta  are significantly lower in the leading region under all conditions when compared with either the body or trailing region. Interestingly, G and eta  in the leading region were not significantly different between control and nocodazole treatment conditions, whereas both G and eta  in the cytochalasin D group (while less than the corresponding values in the body or trailing region) were significantly higher than G and eta  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.



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Fig. 4.   Bar graph showing the material stiffness G and viscosity eta  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 eta . Comparisons that showed significance here are the same as in A.


    DISCUSSION
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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 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 observations 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 mixing) 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 eta  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 tau , defined by tau  = eta /G, is a convenient parameter that describes the extent to which fluidlike behavior can be quantified. Thus a purely elastic medium is characterized by tau  = 0, whereas a purely fluid medium is characterized by tau  = infinity . We find, for the body, trailing region, and the leading region, that tau (body) = 0.34 s, tau (trailing region) = 0.48 s, and tau (leading region) = 1.71 s. The observation that the rheological time constant is longer in the leading region 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.

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 techniques, such as cell aspiration, involve large-scale deformation of the entire cell. It is not surprising, therefore, that they should show sharp decreases in stiffness when the actin filaments or microtubules are disrupted; these observations are thus consistent with our own, following the above interpretation.

In contrast to our observations in the body or trailing regions, we observed no change in the stiffness or viscosity in the leading region with nocodazole treatment. This suggests few microtubules in the flowing core of the pseudopod, or at least a much diminished biochemical and mechanical interaction with pseudopodial granules. This is consistent with a flowing fluid core and is supported by histochemical studies (13). On the other hand, with cytochalasin D treatment, both stiffness and viscosity (while less than in the body or trailing region) in fact increased over values seen common to both control and nocodazole groups. The origin of this surprising result is less clear, but some speculative ideas deserve mention. The network of F-actin is almost certainly necessary for any development of intracellular pressure. To the extent that an increased intracellular pressure is necessary to drive pseudopodial protrusion, any disruption of the network, such as an assembly inhibition by cytochalasin D, would imply a corresponding drop in intracellular pressure. This in turn would decrease the normal separation of fluid from the cytoskeleton as the protrusion progresses, and F-actin fragments [similar to the phenomena reported by Safiejko-Mroczka and Bell (14)] could be dragged into the much more slowly developing pseudopod seen in cytochalasin D-treated cells. Indeed, even if intracellular pressure were unchanged, the presence of short F-actin polymers flowing into the pseudopod would increase the apparent stiffness and viscosity compared with control or nocodazole treatment conditions. We must emphasize that these ideas remain speculative, insofar as we did not measure the F-actin concentrations in any of these experiments and cannot yet conclude that cortical tension and increased intracellular pressure are the causal agencies effecting pseudopodial protrusion.

In conclusion, we have found that, first, in normal locomoting neutrophils, the intracellular granules appear to behave as two distinct populations. In the body and trailing region of the cell, those in the majority fixed population were stiffer than can be measured by displacements with a 90-mW optical trap, whereas those in the minority free population were easily oscillated. This was in striking contrast to the virtual absence of any fixed granules in the leading region of the neutrophils. Second, the free granules in the pseudopodial core showed a substantial drop in both stiffness and viscosity when compared with the body or trailing regions (the body and trailing region were not significantly different). Third, neither cytochalasin D nor nocodazole caused a significant drop in stiffness or viscosity in the body or trailing region of the cell. Taken together, these results suggest the presence of a discrete filament lattice to which the fixed granules are 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.


    ACKNOWLEDGEMENTS

We are grateful to C. M. Doerschuk for very helpful advice, suggestions, and critique of this work.


    FOOTNOTES

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.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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: myan{at}geriat.med.tohuku.ac.jp).

Received 8 February 1999; accepted in final form 21 May 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
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Am J Physiol Cell Physiol 277(3):C432-C440
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