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* Department of Chemical and Biomolecular Engineering,
Department of Materials Science and Engineering,
Howard Hughes Medical Institute Graduate Program, The Johns Hopkins University, Baltimore, Maryland
Correspondence: Address reprint requests to Denis Wirtz, Dept. of Chemical and Biomolecular Engineering, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218. Tel.: 410-516-7006; Fax: 410-516-5510; E-mail: wirtz{at}jhu.edu.
| ABSTRACT |
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| INTRODUCTION |
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We have introduced and refined the method of particle tracking microrheology, whereby the Brownian displacements of individual submicron particles embedded in a complex fluid (such as the cytoplasm of living cells) are monitored simultaneously with high spatial and temporal resolution (7
10
). The extent and time lag-dependence of the mean squared displacements (MSDs) of the nanoparticles directly reflect the local micromechanical properties of the viscoelastic milieu in the vicinity of each nanoparticle (11
). The method of particle tracking microrheology has been used to probe the intracellular mechanical response of living cells exposed in vitro to migratory cues (12
), the topical addition of actin filament cross-linkers (10
), shear flow stimuli (13
), and agonists of actomyosin contractility (14
).
Although this approach does not require direct contact between the cell and the probe, its current form does not make it readily amenable to probe the microrheology of cells in vivo. Indeed, to circumvent the endocytic pathway involving the directed motion of nanoparticles in endocytic vesicles, nanoparticles must be introduced directly (usually via microinjection) into the cytoplasm of the cells, which is not immediately possible. Here, we adapt the method of particle tracking microrheology to probe, for the first time, the mechanical properties of the cytoplasm of individual cells in vivo. To establish a proof of principle, we determine the local time-dependent viscoelastic properties of the cytoplasm of developing Caenorhabditis elegans zygotes undergoing polarization. C. elegans, a small free-living nematode, is used extensively as a model organism in many areas of current biological research, notably cellular polarization. Probing the viscoelastic properties of a viable, developing C. elegans embryo is challenging, as it is enclosed in an impermeable shell throughout its early development, making it impossible to probe using conventional biophysical methods. The biophysical properties therein have implications in many aspects of the polarization process from mitotic spindle positioning to the transport of subcellular organelles.
Cellular polarization is a highly regulated process marked by the asymmetric distribution of intracellular constituents. The ability to attain a polarized state is essential for the proper function of virtually all differentiated cells and operates under highly conserved mechanisms. Despite the importance and diverse context of cell polarity, relatively little is known about the physical phenomena that mediate this phenomenon. The C. elegans zygote represents a popular model system for the study of natural cellular polarization due to the fact that the first few polarized cleavages determine the ultimate body axes of the adult organism (15
). Furthermore, the relative ease of genetic manipulations, such as gene transgenic expression and gene silencing via RNAi (16
), provide the opportunity to explore the roles of individual genes in the polarization process.
The polarization of the C. elegans embryo is initiated upon fertilization by a cue from the incoming sperm, whose point of entry determines the ultimate posterior pole of the embryo (17
). The embryo becomes polarized along the anterior/posterior (A/P) axis by cytoskeletal-mediated mechanisms (18
20
). Asymmetric contractility of the cortical actin meshwork generates large-scale cytoplasmic flow, whereby internal cytoplasm flows toward the posterior pole and cortical cytoplasm flows reciprocally toward the anterior pole of the embryo, resulting in both cortical and cytoplasmic reorganization before the first cell cleavage (20
,21
). Several constituents of the cytoplasm, including members of the Par family of proteins (22
,23
) and germ granules (24
,25
), are asymmetrically segregated during distinct polarization phases (26
). Subsequent cytokinesis at the eccentrically positioned mitotic spindle generates two daughter cellsa somatic blastomere at the anterior and a germline progenitor at the posterior, which differ in size, cellular endowment, and differentiation potential (15
,27
).
Asymmetric cell division is crucial for the generation of cell diversity in developing organisms. During anaphase of the initial mitosis in the C. elegans embryo, the mitotic spindle elongates asymmetrically, whereby the anterior spindle pole remains relatively stationary and the posterior spindle pole is displaced posteriorly as it oscillates transversely (28
). Cytokinesis about the asymmetric spindle results in a posterior blastomere smaller than that of the anterior. In previous studies, the mitotic spindle was severed by various methods and the resultant motion of the spindle poles was monitored (29
). These studies revealed the striking effect that the posterior spindle pole traveled through the embryonic cytoplasm at a higher peak velocity than its anterior counterpart. Possible explanations for this phenomenon include either a difference in the net force acting on each spindle pole, a difference in the viscoelastic properties of the cytoplasm through which each spindle pole travels, or both. To address these possibilities, the viscoelastic properties of the C. elegans embryo were characterized using in vivo particle tracking microrheology.
Results from the in vivo microrheology studies presented here indicate that the embryonic cytoplasm behaves as a highly viscous liquid with negligible elasticity. Despite large morphological changes and continuous cytoskeleton reorganization, the properties of the cytoplasm of the C. elegans embryo remain spatially uniform throughout the embryo from fertilization until the two-cell stage. Due to the fact that migrating subcellular structures of equivalent size and shape encounter equal viscous drag, the results safely rule out the possibility that differences in viscoelastic properties mediate physical asymmetries present in the first embryonic division. Therefore, our results support the hypothesis that the asymmetric positioning of the mitotic spindles derives from the asymmetric distribution of forces, as opposed to asymmetric viscoelastic properties within the zygote (30
). Furthermore, using the absolute value of the cytoplasmic viscosity determined from in vivo particle tracking microrheology, we estimate the force exerted by a single elementary force generator to be in the single-piconewton scale, supporting the hypothesis that the mitotic spindles are pulled cortically by minus end-directed dynein motor proteins (31
).
| MATERIALS AND METHODS |
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Light microscopy
Young C. elegans eggs were obtained by cutting gravid hermaphrodites worms in egg salts (118 mM NaCl, 121 mM KCl in H2O) with the help of a dissecting microscope and transferred to 3% agarose pads (Invitrogen, Carlsbad, CA) sealed by capillary action underneath cover slips (VWR, West Chester, PA). Eggs were viewed by DIC optics using a Nikon TE300 epifluorescence microscope with a 60x DIC oil-immersion lens (N.A. 1.4, Nikon, Melville, NY) and an Orca II charge-coupled device camera (Hamamatsu; Bridgewater, NJ). All image collection was performed at 25°C.
Preparation of PEG-coated nanoparticles
To probe the micromechanical properties of live embryos, we used primarily polyethylene glycol (PEG) coated (PEGylated) 100-nm diameter nanoparticles, which were prepared as described (33
). Briefly, 5 mg/ml amine-terminated PEG (diamino-PEG, average MW 3400) (Shearwater, Huntsville, AL) in 50 mM MES (pH = 6.0) was mixed at 1:1 ratio with 2% w/v aqueous suspension of carboxylate-modified polystyrene nanoaparticles (Molecular Probes, Eugene, OR) and incubated for 15 min at room temperature. Then 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDAC) was added to a final concentration of 4 mg/mL and the pH was adjusted to 6.5. The resulting solution was incubated overnight. 100 mM glycine was added to quench the reaction and the mixture was incubated for 30 min at room temperature. PEGylated microspheres were obtained by centrifugation (3,300 g for 15 min) and washed three times with PBS.
Incorporation of nanoparticles in C. elegans embryos
A colloidal suspension of fluorescent polystyrene nanoparticles was dialyzed against ddH2O overnight at room temperature. The nanoparticles were surface-modified with the hydrophilic polymer PEG to ensure that the nanoparticles did not interact directly with subcellular structures. Microneedles (World Precision Instruments, Sarasota, FL) pulled on a vertical micropipette puller (Sutter Instruments, Novato, CA) (34
) were filled by capillary action with the nanoparticle suspension. The needles were mounted on a microinjector controlled by a micromanipulator (Eppendorf 5170, Hamburg, Germany) mounted on a Zeiss Axiovert 10 inverted microscope (Zeiss, Germany). The nanoparticles were microinjected into the syncytial gonads of gravid hermaphrodites according to the protocol developed for transformation (35
). After injection, worms were immersed in recovery buffer (20% glucose, 1M KCl, 5M NaCl, 1M MgCl2, 1M CaCl2, 1M HEPES pH 7.2 in H2O) for at least 15 min and then transferred to M9 buffer (22mM KH2PO4, 42mM Na2HPO4, 85mM NaCl, 1mM MgSO4 in H2O) for at least 1 h before being incubated at 25°C for
4 h before image acquisition.
Particle-tracking intracellular microrheology
The motion of fluorescent nanoparticles embedded in the cytoplasm of embryos was recorded at a rate of 30 frames/second using a silicon-intensifier target (SIT) camera (VE-100 Dage-MTI, Michigan City, IN) mounted on a Nikon TE300 epifluorescence microscope with a 60x DIC oil-immersion lens (N.A. 1.4, Nikon). DIC images of the embryos were acquired with an Orca II charge-coupled device camera (Hamamatsu) between acquisitions movies of nanoparticle movements. Image acquisition was performed at 25°C.
Movies of nanoparticle motion were analyzed using Metamorph software (Universal Imaging, West Chester, PA) and custom software designed to transform MSD into rheological parameters describing the viscoelastic properties of the cytoplasm (14
). The displacement of the intensity-weighted centroid of each nanoparticle was tracked with a resolution of
10 nm. This spatial resolution on displacement was measured independently by tethering nanoparticles to a glass cover slip and measure their apparent displacement, as described (9
). The coordinates of the centroids were transformed into time-averaged mean squared displacements MSDs:
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Here t is the elapsed time and
is the time lag. We verified that
[x(t +
) x(t)]2
=
[y(t +
) y(t)]2
, which indicates that the embryos were locally isotropic. The two-demensional MSD in a viscous medium (i.e., no elasticity) depends linearly on time lag:
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, by the Stokes-Einstein relationship (36
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Further details about the multiple-particle tracking and microrheology analysis, including effects of particle sizes and surface chemistry, have been presented previously (10
,37
).
| RESULTS |
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Trajectories of the centroids of nanoparticles embedded within the anterior and posterior cytoplasm of early C. elegans embryos were monitored with 10-nm spatial resolution and 33-ms temporal resolution for 20-s intervals (Fig. 3, A and B). The dependence of particle mean squared displacements (MSDs) on the time-lag,
, was used to infer the local viscoelastic properties of cytoplasmic cytoplasm. The MSD, 
r2(
)
, of a spherical particle undergoing thermal motion in a complex fluid exhibits a dependence on time-lag modeled as 
r2(
)

. In a simple viscous fluid,
= 1 and the MSD exhibits a linear dependence on the time lag. In a fluid that exhibits elasticity, particle motion becomes restricted and demonstrates subdiffusive behavior, described by
< 1 and a MSD that grows more slowly with time lag. Conversely, the MSDs of particles experiencing convective flow grow more rapidly with time, described by
> 1. For example, in the presence of a linear velocity field with constant velocity, v, the displacement of a particle over a time-lag,
, is described by r = v
, resulting in a MSD of 
r2(
)
= (v
)2, where
= 2. However, due to the fact that velocity fields in biological systems are often transient and nonuniform, MSDs rarely attain
-values as high as 2. The slope of a log-log plot of MSDs as a function of time-lag indicates the
-value.
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> 1s), indicating directed motion presumably due to bulk embryonic reorganization. There was also a considerable lack of subdiffusive particles, making the elasticity of the cytoplasm too small to measure. MSDs in both the anterior and posterior cytoplasm had narrow distributions about the mean (Fig. 3, E and F), indicating that the viscoelastic properties of the embryonic cytoplasm were largely uniform throughout the embryo. The difference between the MSDs of nanoparticles in the anterior and posterior was not statistically significant (unpaired student t-test, P > 0.5). The viscoelastic character of the embryonic cytoplasm did not vary with time, but remained constant throughout the first cell cycle (data not shown).
To directly compare the viscoelastic properties of the anterior and posterior regions, we determined the time-dependent ensemble averaged MSDs of each population (Fig. 4, A and B). These global averages showed that the viscoelastic character of the cytoplasm in each region was virtually identical over all time-lags considered. Because the nanoparticles behaved as colloidal spheres undergoing Brownian motion in a simple viscous fluid, their two-dimensional ensemble averaged MSDs can be described by 
r2(
)
= 4D
, where D is the effective diffusion coefficient. This relationship provided an excellent fit for both sets of data (R2 > 0.98 for anterior and posterior). The diffusion coefficients in the anterior and posterior regions were determined to be 0.0041 ± 0.0002 and 0.0040 ± 0.0002, respectively (mean ± SE) (Fig. 4 C). The diffusion coefficient of the beads in the anterior cytoplasm was
3% greater than those in the posterior, within the range of experimental error.
|

a, which relates the mean diffusion coefficient of a spherical Brownian particle to the viscosity of its suspending medium (Fig. 4 A), we determined that the mean shear cytoplasmic viscosity in the anterior and posterior regions of C. elegans early embryos to be
= 10.3 ± 0.8 Poise and 10.7 ± 0.8 Poise, respectively (mean ± SE; 1 Poise = 0.1 Pascal x s) (Fig. 4 D). Here kB is Boltzmann's constant, T is the absolute temperature, and a = 50 nm is the radius of the nanoparticle. Therefore, the viscosity of the early embryo is
3 orders of magnitude greater than that of water (0.01 Poise) and similar to that of glycerin. | DISCUSSION |
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Using Stokes' law, fe =
ve, where
= 6
R is the viscous drag coefficient, to model the viscous drag encountered by centrosomes fragments, we calculated the elementary force, fe, to be
5 piconewtons (pN). This force is
5x greater than the elementary force generated by dynein, a microtubule motor protein (31
). However, it is likely that fragment sizes, R, measured by fluorescence microscopy, were overestimated by at least the same factor (S.W. Grill, personal correspondence). Therefore, our findings support the model in which minus-end-directed dyneins mediate spindle positioning in the early embryo.
The absolute magnitude of the cytoplasmic viscosity may be used to determine the force necessary to transport subcellular organelles and macromolecular complexes, such as pronuclei or germ granules, through the cytoplasm during embryonic reorganization and patterning. Because migrating organelles must, at the very least, overcome the viscous drag encountered due to their motion, the viscosity effectively sets a lower bound for the force transduction necessary for such motion. However, the
-values that exceed 1 at increasing time-lags indicate the presence of convection within the cytoplasm, presumably due to cytoplasmic streaming. Subcellular organelles and macromolecular structures may depend on this flow rather than molecular motors as a means of migration. It should be noted, however, that despite the presence of these cytoplasmic velocity fields, the inert nanoparticles remained uniformly dispersed throughout the embryos (Fig. 2, A and B), indicating that cytoplasmic flow is not sufficient to segregate submicron particles.
Together, these results show the new possibility of probing single-cell mechanics in vivo, where the physical properties of individual cells are probed in live animals. Another possible approach to measure cell mechanics in embryos would consist in injecting magnetic beads, instead of inert nanoparticles, into the gonad of C. elegans. Upon incorporation of the magnetic beads in the cytoplasm of embryo, its viscoelastic properties could be measured using magnetic tweezers (41
,42
), but this approach remains to be demonstrated.
| ACKNOWLEDGEMENTS |
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This work was funded by the National Aeronautics and Space Administration grant NAG9-1563, the National Institutes of Health grants GM065835 and GM075305, and a Howard Hughes Medical Institute graduate training grant in nanobiotechnology at Johns Hopkins.
Submitted on December 30, 2005; accepted for publication February 24, 2006.
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