Intracellular Microrheology as a Tool for the Measurement of the Local Mechanical Properties of Live Cells

CHAPTER 3

Intracellular Microrheology as a Tool for the Measurement of the Local Mechanical Properties of Live Cells Thomas P. Kole,* Yiider Tseng,* and Denis Wirtz*,{ *Department of Chemical and Biomolecular Engineering The Johns Hopkins University Baltimore, Maryland 21218 {

Graduate Program in Molecular Biophysics The Johns Hopkins University Baltimore, Maryland 21218

I. Introduction A. Background B. Methods for the Measurement of the Viscoelastic Properties of Living Cells C. Intracellular Microrheology II. Materials and Instrumentation A. Preparation of Probe Nanospheres for Intracellular Microrheology B. Cell Culture and Microinjection of Probe Nanospheres C. Video-Based Live-Cell Intracellular Microrheology III. Procedures A. Preparation of Probe Nanospheres for Intracellular Microrheology B. Cell Culture and Microinjection of Probe Nanospheres C. Video-Based Intracellular Microrheology IV. Pearls and Pitfalls V. Concluding Remarks References

METHODS IN CELL BIOLOGY, VOL. 78 Copyright 2004, Elsevier Inc. All rights reserved. 0091-679X/04 $35.00

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I. Introduction A. Background The cytoskeleton is an extremely dynamic and highly interconnected network of filamentous proteins that extend throughout the cytoplasm and provide cells with a structural framework. The cytoskeleton is composed of three major classes of structural filamentous proteins (microtubules, microfilaments, and intermediate filaments), which are categorized according to their constituent protein subunits and filament diameters. Accessory proteins that bind, bundle, and/or cross-link these proteins in globular or filamentous form control the dynamic mechanical properties and organization of the cytoskeleton and determine the morphology, intracellular architecture, and mechanics of the cell (Coulombe et al., 2000; Heidemann and Wirtz, 2004; Howard, 2001). Because of their aspect ratio and internal architecture (Steinmetz et al., 1997), actin filaments behave as semiflexible polymers (Gittes et al., 1993), which facilitate their entanglements and the formation of highly elastic networks even at low polymer concentrations (Morse, 1998). The complex viscoelastic properties of actin filament networks (Hinner et al., 1998; Palmer et al., 1999) are believed to be required to orchestrate the mechanical behavior that shapes cells and provides them with the ability to move and resist external stresses. Much like conventional polymer networks (Ferry, 1980), cross-linking and/or bundling of actin filaments has profound eVects on the organization and mechanical properties of the actin cytoskeleton (Borisy and Svitkina, 2000; Pollard et al., 1994). Actin networks containing actin-binding proteins respond to chemical and physical changes in the cytoplasmic environment, including changes in pH, ionic strength, concentration of regulatory proteins, as well as rates of mechanical stress to locally regulate the mechanical properties of the cell (Sato et al., 1985, 1987; Tseng et al., 2004). Like F-actin, one of the primary functions of intermediate filaments (IFs) is to provide mechanical strength to cells (Coulombe et al., 2000). Most of what we know about the physical properties of IFs has been gathered by use of purified proteins. IFs also form semiflexible polymers in vitro. This means that the persistence length of IFs (
1
m) is on the same order of magnitude as their contour length (
2.5
m) (Mucke et al., 2004). Unlike F-actin, IFs have a natural propensity to self-interact and form bundled/cross-linked structures, a property that depends on pH, ionic strength, and pairwise interactions (Yamada et al., 2002). A mechanical signature of this behavior is that the stiVness of IF networks is mostly independent of the rate of deformation (Janmey et al., 1991; Ma et al., 1999; Yamada et al., 2003): IFs in entangled networks cannot diVuse readily and therefore cannot relax mechanical stresses. IFs behave like cross-linked networks in standard assembly conditions in vitro. In vitro rheological studies that use purified cytoskeletal proteins suggest molecular mechanisms of regulation of cytoskeleton mechanics (Heidemann and Wirtz, 2004). The mechanical behavior of F-actin and IFs and their tight regulation by

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auxiliary proteins and environmental conditions seem to be closely correlated with key cellular processes that are mechanical in nature, including cell shape changes during mitosis, the separation of daughter cells by the contractile ring during cytokinesis, cell–cell and cell–matrix interactions, transmembrane signaling, endocytosis, secretion, and motility (Schmidt and Hall, 1998). However, the mechanical behavior of living cells and the molecular signaling pathways by which it is regulated remain largely unknown. In particular, how the unique physical properties of IFs are exploited by cells to shape their plasma membrane, promote cell– cell interactions, and participate to produce the propulsive forces required for wound healing remains largely unknown. This is largely due to the absence of noninvasive methods that measure unambiguously the local mechanical properties of the intracellular milieu. Here we detail a new method to measure cytoskeleton networks in vitro and in vivo, which can be implemented within an existing light microscope relatively easily. B. Methods for the Measurement of the Viscoelastic Properties of Living Cells There have been numerous attempts to quantify the mechanical properties of the cytoskeleton of living cells; however, most current methods cannot readily measure local mechanical parameters (Heidemann and Wirtz, 2004). Light and electron microscopy have been used successfully to gain insight into the spatial distribution of cytoskeleton arrays and their auxiliary proteins in cells (Schoenenberger et al., 1999; Svitkina and Borisy, 1998, 1999). However, microscopy does not constitute a functional assay as such and does not measure the physical properties of cells such as cytoplasmic viscosity and elasticity. Magnetic tweezers and magnetic microspheres embedded within the cytoplasm of live cells have been used to probe the frequency-dependent viscoelastic moduli of live cells (Bausch et al., 1999; Crick and Hughes, 1950). However, this approach typically requires the use of large magnetic beads (>1
m), which can distort their local subcellular environment to reach suYciently high probing forces. Moreover, specific and nonspecific interactions between the (phagocytosed) beads and subcellular structures are diYcult to assess. Finally, the slow response time of the probe renders the approach inapplicable to examine the temporal response of a cell to extracellular stimuli. By monitoring the diVusion of small, inert tracer particles by means of fluorescence microscopy, Ragsdale and colleagues (1997) probed the micromechanical properties of fibroblasts. However, in its present form, many hypotheses are required to compute the cytoplasmic elasticity, and no global cellular response is obtained. Scanning probe microscopy (SPM), a technique derived from atomic force microscopy (AFM), has been used to quantify the local mechanical properties of stationary and motile fibroblasts (Haga et al., 2000; Nagayama et al., 2001). By measuring local cell properties, AFM acknowledges the regional variations of the cytoskeleton architectures observed under light microscopy. But AFM presents the central problem of measuring cytoplasmic mechanics by probing the cell from the outside. Therefore, mechanical parameters

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reported by AFM are ill-defined composites of the plasma membrane tension and the viscoelasticity of the underlying cytoskeleton. Moreover, the type of deformation caused by the AFM tip (shear, stretch, or both) is unknown. This is a serious problem, because complex viscoelastic fluids can respond diVerently when sheared or stretched. Magnetocytometry uses magnetic microspheres coated with extracellular matrix (ECM) components such as fibronectin (FN) or arginineglycine-aspartic acid (RGD) peptides to apply calibrated torques to the surface of live cells (Cai et al., 1998; Wang et al., 1993). Although local in nature, this approach does not provide local information, because measurements are averaged over many cells in culture and hundreds of probes. Moreover, the ECM-coated beads promote actin polymerization and the formation of actin-rich focal adhesion complexes underneath the plasma membrane. Hence major reorganization of the cytoskeleton is caused by the probing beads, a problem that makes magnetocytometry highly invasive. Furthermore, the surface area of contact between the cell surface and the beads is not controlled. This makes magnetocytometry ambiguous, because an apparent increase or decrease in cytoplasmic stiVness may be due to a change in plasma membrane tension or a change in the avidity/aYnity of the cell surface receptors for the ECM-coated beads. Finally, this approach has not been tested with standard fluids; positive controls are missing. Other methods have been used to assess cell mechanics. These include parallel microplates (Beil et al., 2003; Thoumine and Ott, 1997), micropipette manipulation (Merkel et al., 2000; Paulitschke et al., 1995) and calibrated microneedles (Heidemann et al., 1999; Rahman et al., 2002). All these methods suVer from some of the same drawbacks detailed previously. These methods attempt to measure cytoplasmic mechanics from the cell exterior, they apply ill-defined mechanical deformations, they do not measure frequency-dependent viscoelastic parameters, and they often cannot directly distinguish viscosity from elasticity. Most importantly, all these methods overlook the central fact that the cytoplasm is highly heterogeneous and warrants a local physical probe. C. Intracellular Microrheology To address these shortcomings, we have introduced the method of intracellular microrheology (ICM) to extract the local viscoelastic properties of live cells (Tseng et al., 2002). This work extends previous work from our group on the microrheology of reconstituted cytoskeletal filament networks (Apgar et al., 2000; Ma et al., 2001; Palmer et al., 1998; Tseng et al., 2002; Xu et al., 1998); DNA solutions (Goodman et al., 2002; Mason et al., 1997a), engineered protein polymers (Petka et al., 1998; Xu et al., 2002), and live cell microrheology with organelles used as local cytoplasmic probes (Yamada et al., 2000). ICM consists of introducing fluorescent nanoprobes (<0.2
m) into the cytoplasm of living cell by use of microinjection and then statistically analyzing their thermally excited motion to extract the local mechanical properties of the cytoskeletal network surrounding the particle. Particles embedded in the cytoplasm of living cells are equivalent to

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nanoscale rheometers that impose a time-averaged constant stress in the surrounding fluid on the order of kBT/a3 where kB is the Boltzmann constant, T is the absolute temperature, and a is the particle radius. The resulting deformation is measured as the particle displacement and can be directly related to the viscoelastic properties of the surrounding fluid (Fig. 1). Intracellular microrheology avoids most of the limitations of current cellmechanics methods. ICM measures intracellular mechanical properties, both locally and globally. It can readily be combined with fluorescence/bright field microscopy to correlate cytoskeleton architecture and cell organization with local intracellular mechanics in single live cells. ICM measures both elasticity and viscosity and has been tested against standard fluids of known viscoelasticity with traditional mechanical rheometers (Mason et al., 1997b; Xu et al., 1998). It measures frequency-dependent viscoelastic parameters; moreover, it measures viscoelastic parameters of cytoplasm in the linear regime of small deformations (Tseng et al., 2002). These two qualities allow for a direct, comprehensive comparison of live-cell viscoelastic parameters with those displayed by reconstituted cytoskeleton networks in vitro. ICM measurements are rapid and can probe the spatiotemporal mechanical response of a cell a stimulus in real time (Kole et al., 2004). Moreover, because ICM probes mechanics from the inside of the cell, for the first time it allows measurement of the mechanics of cells embedded in threedimensional networks. Fluorescent nanospheres are prepared by dialysis against injection buVer and then microinjected into the cytoplasm of live cells (Fig. 2A–C). Microinjected cells containing fluorescent particles are placed on the stage of a microscope at 37  C. Movies of the fluctuating fluorescent nanospheres are then recorded onto the

Fig. 1 Brownian motion of a submicron particle entangled in a filamentous protein network. Thermal energy creates a random force on each probe nanosphere of order-of-magnitude kBT/a3, where a is the radius of the nanosphere. This force creates a local deformation of the viscoelastic medium in the vicinity of the particle, which is observed and measured as the particle’s displacement by video-based particle nanotracking.

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Fig. 2 Schematic of intracellular microrheology (ICM). (A) Particles are first prepared by dialysis against microinjection buVer. (B) Dialyzed particles are then microinjected into the cytoplasm of adherent cells and become embedded in the cytoskeletal network (C). (D) The Brownian displacements of particles injected into the cell are monitored by video-based particle tracking with highmagnification fluorescence microscopy. (E) The time-dependent x and y coordinates of recorded particles are tracked by measurement of intensity-weighted centroid displacements. (F) Mean-squared displacements are calculated for each particle and used to evaluate the frequency-dependent viscoelastic moduli of the cell (G).

random-access memory of a personal computer by a silicon-intensifier target (SIT) camera (VE-100 Dage-MTI, Michigan City, IN) mounted on an inverted epifluorescence microscope (Eclipse TE300, Nikon, Melville, NY) at a frame rate of 30 Hz by use of the Metavue software (Universal Imaging Corp., West Chester, PA). A high magnification 100 Plan Fluor oil-immersion objective (N.A. 1.3) is used for particle tracking, which permits approximately 5-nm spatial resolution over a 120
m  120
m field of view, as assessed by monitoring the apparent displacement of nanospheres firmly attached to a glass coverslip with the same microscope and camera settings as used during live-cell experiments. The displacements [x(t),y(t)], where t is the elapsed time of the particles centroids, are simultaneously monitored in the focal plane of the microscope for 20 seconds (Fig. 2D,E). The same multiple-particle tracking approach has recently been used to track the multistep transport process of gene carriers from the plasma membrane to the nucleus of live cells (Suh et al., 2003) and the micromechanical properties of the interphase nucleus (Tseng et al., 2004).

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Movies of fluctuating nanospheres are analyzed by a custom particle tracking routine incorporated into the Metamorph imaging suite (Universal Imaging Corp.) as described (Tseng and Wirtz, 2001). Individual time-averaged mean square displacements (MSDs), h
r2 ðÞi ¼ h½xðt þ Þ  xðtÞ 2 þ ½yðt þ Þ  yðtÞ 2 i, where  is the time scale, are calculated from the two-dimensional trajectories of the centroids of the nanospheres (Fig. 2F). All control experiments are described in Tseng and Colleagues (2002), including eVects of particle size and surface chemistry. For a particle in a perfectly viscous fluid undergoing diVusive motion, the power law slope of the MSD will approach a value of one, whereas a particle embedded in a perfectly elastic solid will yield an MSD with a slope of zero. This implies that a complex viscoelastic fluid will result in power law slopes of the MSD between zero and one. The shear creep compliance can be related to the MSD through the following relationship (Xu et al., 1998): ðÞ ¼

3kB T h
r2 ðÞi 2a

ð1Þ

The creep compliance is a measure of the deformability of the cell and shares all of the same features as the MSD (Xu et al., 1998). All the mechanical information is contained in the amplitude and the time scale dependence of the creep compliance. However, by use of the generalized form of the Stokes Einstein relationship (Mason et al., 1997b) ˜ GðsÞ ¼

2kB T 3as
h˜r 2 ðsÞi

ð2Þ

˜ (s), where s is the Laplace frequenwe can approximate the viscoelastic spectrum G 2 cy, from h
rr˜ ðsÞi, the unilateral Laplace transform of h
r2 ðÞi. With this expression, we can calculate the traditional frequency-dependent elastic modulus G0 (!) and loss modulus G00 (!) from time scale-dependent MSDs as described (Mason, 2000; Mason et al., 1997b) (Fig. 2G). The viscoelastic moduli G0 (!) and G00 (!) are the real and imaginary parts, respectively, of the complex modulus G*(!), ˜ (s) in Fourier space, and they obey Kramers–Kronig which is the projection of G relationships (Mason et al., 1997b). In addition, the diVusion coeYcient, D, of a nanosphere of radius a can be calculated from the Stokes–Einstein relationship (Berg, 1993; Chandrasekhar, 1943; Einstein, 1905; Qian et al., 1991): D¼

kB T 6a

ð3Þ

where  is the viscosity of the fluid surrounding the particle. In the case of a viscoelastic fluid, such as the cytoplasm of a living cell,  is not a constant and is time scale–dependent, therefore giving rise to a time scale–dependent diVusion coeYcient. We can, however, instead approximate  as the shear viscosity s, which is the product of the relaxation time (the time scale at which the viscous

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to elastic crossover occurs, see Fig. 2G) and the plateau value of the elastic modulus (Eckstein et al., 1998). It is important to note that the diVusion coeYcient calculated from two-dimensional particle trajectories can be approximated as the three-dimensional diVusion coeYcient, assuming that the local environment surrounding each nanosphere is isotropic in three dimensions. This is a valid approximation, even in regions of the cell where long-range interactions between nanospheres and the cell membrane could occur by way of hydrodynamic interactions, because those interactions are screened to within a mesh size of the surrounding network, which is approximately 50 nm. If the cell thickness were similar or smaller than the particle diameter, they would be mostly excluded from those (too thin) areas. Through the use of ICM, we have found that the mechanical properties of the cell are highly heterogeneous and spatially coordinated (Fig. 3A-C) (Kole et al., 2004; Tseng et al., 2002, 2004). Serum-starved Swiss 3T3 fibroblasts treated with LPA exhibit significant increases in both cytoplasmic elasticity and viscosity. Our results showed that that the mechanical response of Swiss 3T3 cells to Rho activation by lysophosphatidic acid (LPA) is time-dependent and follows the time-dependent profile of Rho activation. This mechanical response is not instantaneous, and the delay between Rho activation and stiVening of the cell may be attributed to the slow gelation kinetics of the actin cytoskeleton. Comparison of the observed micromechanical trends in control cells treated with LPA with fluorescent micrographs of the actin cytoskeleton showed that there was little correlation between F-actin structures and their mechanical function. Although LPA elicited rapid formation of actin stress fibers and global stiVening of the cell, micromechanical relaxation of the cell was not accompanied by disassembly of stress fibers and other organized F-actin structures. We also observed a key distinction between intracellular stiVness and intracellular tension that is generated by myosin-based contraction of the actin cytoskeleton. Treatment of Swiss 3T3 cells with the contractile inhibitor Y-27632 resulted in the increase of intracellular stiVness to levels that are almost twice that of untreated cells. Recently, using wounded fibroblast monolayers, we have demonstrated that the leading edge of motile cells is much stiVer than the perinuclear region. Particles toward the leading edge exhibit more confined motions than those closer to the nucleus (Fig. 3A,B). Examination of the ensemble-averaged creep compliances of both migrating and quiescent 3T3 fibroblasts revealed that the overall mechanical properties of the cell dramatically changed on the initiation of migration. Cells along the edge of a wounded fibroblast monolayer were significantly less deformable than quiescent fibroblasts and possessed an increased frequency range of elastically dominant mechanical responses to strain. This more solidlike behavior makes migrating cells better able to elastically rebound under mechanical stress and, therefore, potentially less prone to mechanical failure, which may be important in vivo where cells are migrating through dense tissue networks and/or against venus/arterial shear flow.

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Fig. 3 Application of intracellular microrheology. (A) Local mapping of the mechanical properties of a migrating cell at the edge of a wounded fibroblast monolayer. Here we only show tracked particles and have neglected aggregates that violate assumptions made in the generalized Stokes–Einstein relationship. Each particle position was color coded, corresponding to the local value of the creep compliance at that position in the cell. The color indicators at each particle position do not reflect the size of the particle (100 nm). Indicator size was increased to aid visual presentation. The time-dependent trajectory of a particle close to the nucleus (1) is much more confined than a particle toward the leading edge (2). (B) The mean-squared displacements (MSDs) of particles depicted in (A) together with the ensemble averaged MSD of all particles within the cell. The MSD of the particle close to the nucleus (1) is much larger than a particle toward the leading edge (2), suggesting that the leading edge of migrating cells is much stiVer than the perinuclear region. (C) Distribution of the MSDs of particles embedded within the cytoplasm of the cell shown in (A). The mechanical properties of the cell are highly heterogeneous, thus illustrating the necessity of local measurements within the cell.

II. Materials and Instrumentation A. Preparation of Probe Nanospheres for Intracellular Microrheology One hundred nanometer–diameter fluorescent carboxylate modified nanospheres (Cat. No. F8803) from Molecular Probes, Inc. were used as local probes of the mechanical properties of live cells. Particles were prepared by dialysis against

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Dulbecco’s phosphate-buVered saline (DPBS, Cat. No. 14040-133) from Invitrogen with 300,000 MW Spectra/Por Cellulose Ester dialysis membrane tubing (Cat. No. 131447) from Spectrum Laboratories, Inc. Polyethylene glycol (PEG)–coated particles were prepared with 3.4-kDa amine-terminated PEG (Cat. No. 2V2V0F22) from Shearwater Corp dissolved in 2-[N-morpholino]ethanesulfonic acid (MES, Cat. No. M-8250) from Sigma-Aldrich. Sodium hydroxide (NaOH, Cat. No. 3722-05) was purchased from J. T. Baker. 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide (EDAC, Cat. No. E-2247) was purchased from Molecular Probes, Inc. B. Cell Culture and Microinjection of Probe Nanospheres Swiss 3T3 mouse fibroblasts (Cat. No. CCL-92), Dulbecco’s modified eagle medium (DMEM, Cat. No. 30-2002), and bovine calf serum (BCS, Cat. No. 30-2030) were from American Type Tissue Culture (ATCC). Fibronectin (Cat. No. 341631) was from Calbiochem. Hank’s balanced salt solution (HBSS, Cat. No. 14170-112) and 0.25% trypsin–1 mM ethylenediamine tetraacetic acid (EDTA) (Cat. No. 25200-056) were from Invitrogen; 35-mm Poly-d-lysine–coated glass bottom dishes (Cat. No. P35GC-0-14-C) were from MatTek Corp., and 500nm inner diameter prepulled glass capillary microneedles (Cat. No. TIP05TW1) were from World Precision Instruments. Microneedle back-loading pipette tips (Cat. No. 930001007), Transjector 5246 microinjection device (Cat. No. 5246000.010), and Micromanipulator 5171 (Cat. No. 5171000.019) were from Brinkmann Instruments; 10X Tris-buVered saline (TBS), pH. 7.4 (Cat. No. 351086-101), was from Quality Biological Inc. Alexa Fluor 488 10,000-MW fluorescent dextran (Cat. No. D22910) is from Molecular Probes, Inc. C. Video-Based Live-Cell Intracellular Microrheology Live cell ICM experiments were conducted on a Nikon TE300 or Nikon TE2000E inverted epifluorescent microscope with a Nikon PlanFluor 100 oil immersion lens (N.A. 1.3). Movies of fluctuating fluorescent nanospheres were recorded onto the random-access memory of a PC computer with a siliconintensifier target (SIT) camera (VE-100 Dage-MTI, Michigan City, IN) at a frame rate of 30 Hz with the software Metavue (Universal Imaging Corp., West Chester, PA). The time-dependent spatial coordinates of the fluorescent particles were obtained by use of particle tracking routines built into Metamorph Imaging Suite (Universal Imaging Corp.).

III. Procedures A. Preparation of Probe Nanospheres for Intracellular Microrheology Carboxylate modified polystyrene nanospheres (100 nm) were purchased as a 2% (w/v) suspension containing 0.1% sodium azide. Fluorescent nanospheres that are to be used for microinjection must first be dialyzed against DPBS injection

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buVer and adjusted to a suitable particle concentration. Optionally, particles can be passively or covalently surface coated to specifically control particle interactions within the cell. Protein-resistant PEG-coated particles are obtained by covalently coupling amine-terminated PEG to the surface of carboxylate-coated nanospheres by means of the carbodiimide method.

1. Preparation of Carboxylate-Modified Nanospheres a. Steps 1. Stock nanospheres (1 ml) are pipetted into a 2-cm piece of dialysis tubing sealed at one end and prewet with DPBS. 2. The preceding is dialyzed against 4 L of DPBS with gentle stirring at 4  C for 12–16 hours. This is repeated three times with fresh DBPS. 3. The particle solution from step 2 is carefully transferred into a sterile 50-ml conical tube. 4. DPBS is added to a final volume of 20 ml and stored at 4  C.

2. Preparation of Polyethylene Glycol–Coated Nanospheres a. Solutions 1. 50 mM MES buVer, pH 6.0 2. 1 M NaOH b. Steps 1. Five milligrams of amine-terminated PEG is dissolved in 1 ml of MES buVer in a glass vial. 2. One milliliter of particle solution is added from step 3 earlier and oral incubated at room temperature for 15 minutes. 3. EDAC (8 mg) is added and mixed thoroughly. 4. The pH of the reaction mixture is adjusted to 6.5 with NaOH and incubated with gentle rocking at room temperature for 2 hours. 5. Glycine (15 mg) is added to quench the reaction and incubated at room temperature for 30 minutes. 6. The reaction mixture is carefully pipetted into a 3-cm piece of dialysis tubing sealed at one end and prewet with DPBS and dialyzed against 4 L of DPBS at 4  C for 12–16 hours. This is repeated five times with fresh DPBS. 7. The particle solution from step 6 is carefully transferred into a sterile 50-ml conical tube. DPBS is added to a final volume of 20 ml and it is stored at 4  C.

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B. Cell Culture and Microinjection of Probe Nanospheres Particles are now ready to be microinjected into the cytoplasm of live cells and used as local probes of the intracellular mechanical properties of the cell. Immediately before injection, cells are diluted in injection buVer and centrifuged to remove aggregates that may clog the injection needle. Adherent cells are plated on extracellular matrix (ECM)-coated glass-bottom dishes marked with an x at the center with a carbide tipped pen. Cultures are then serum-starved overnight, microinjected with fluorescent particles dispersed in DPBS, and subsequently used for live cell ICM.

1. Plating of Cells for Microinjection a. Solutions 1. cDMEM: Dulbecco’s modified Eagle’s medium containing 10% bovine calf serum. 2. Fifty micrograms per milliliter fibronectin in DPBS. b. Steps 1. With a carbide-tipped pencil, an x is inscribed on the bottom center of sterile 35-mm poly-d-lysine–coated glass-bottom culture dishes. The dishes are coated with bovine plasma fibronectin by incubating with a 50
g/ml fibronectin solution in DPBS for 45–60 minutes at room temperature. 2. Medium from a T-75 tissue culture flask containing 70%–80% confluent layer of Swiss 3T3 fibroblasts or another type of adherent cell is aspirated. 3. The mixture is washed with 10 ml of HBSS. 4. Trypsin-EDTA (2 ml) is added and the flask is carefully rotated to cover the entire bottom surface of the flask. This is incubated at 37  C for 5 minutes or until cells are visually detached from the surface of the flask. 5. cDMEM (8 ml) is added and pipetted up and down to mix thoroughly. 6. The cell suspension is transferred to a 15-ml conical centrifuge tube and pellet cells at 1100 rpm for 5 minutes. The supernatant is aspirated and the pellet is carefully resuspended in 10 ml of cDMEM. 7. The cell density is measured, and 1  104 cells/ml suspension in cDMEM is prepared. 8. The fibronectin solution is gently aspirated from the 35-mm glass-bottom dishes and washed once with HBSS. Two milliliters of suspension is added from step 7 to each dish. Cells are allowed to adhere overnight at 37  C and 5% CO2.

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2. Microinjection of Fluorescent Nanospheres a. Solutions 1. Particle solution prepared in step 3 (preparation of carboxylate-modified nanospheres) or step 7 (preparation of polyethylene glycol–coated nanospheres). 2. 1 TBS.

b. Steps 1. Previously prepared 35-mm culture dishes are serum starved by washing three times with HBSS and replacing complete media (cDMEM) with DMEM. Cells are allowed to incubate for 24 hours. 2. Twenty microliters of solution 1 are pipetted into 980
l of DPBS in a sterile 1.5-ml centrifuge tube and spun at 16,000g for 15 minutes. Optionally, particle solution can be briefly sonicated for 5 minutes before centrifugation. 3. The top 100
l of the centrifuged particle solution is carefully pipetted oV and transferred to a new sterile 1.5-ml centrifuge tube. This is the microinjection suspension containing approximately 3.6  1010 particles/ml. Optionally, fluorescently labeled dextran can be added to the microinjection suspension to a final concentration of 2 mg/ml to facilitate visualization of microinjected cells. 4. Previously serum-starved cells are placed on the stage of a microscope equipped with a 37  C and 5% CO2 incubator and a suitable microinjection system. Four microliters (4
l) of microinjection suspension are backloaded from step (3) into a microinjection needle and immediately mounted onto micromanipulator; the tip is immersed into the media of the 35-mm culture dish. 5. The center of the dish marked by an x is located at 10 magnification and then the tip of the microinjection needle is centered over the x. A higher power objective (60) is used, and the tip of the microneedle is positioned over the perinuclear region of a cell near the x on the bottom of the coverslip. 6. The microneedle is lowered until the tip begins to deform the cell, and this height is set as the injection plane. The microneedle is raised 5–10
m above the cell and the cell is injected. This procedure is repeated for every cell within a 1-mm radius of the x. 7. The cells are immediately washed three times with TBS and the media are replaced with DMEM. Cells are allowed to incubate for 12–24 hours to facilitate spreading of particles throughout the cytoplasm.

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C. Video-Based Intracellular Microrheology After a 12–24-hour incubation period, microinjected cells are ready to be used in live cell ICM experiments. Experiments are performed with high-magnification objectives in a climate-controlled environment. After initial particle tracking, the procedure can be repeated for more cells, the culture can be fixed for subsequent labeling with fluorescent antibodies, or the culture may be stimulated with an exogenous stimulus and then remeasured to examine the intracellular mechanical eVects of the applied stimulus. Movies of fluctuating nanospheres are analyzed by a custom particle tracking routine incorporated into the Metamorph imaging suite (Universal Imaging Corp.) as described (Tseng and Wirtz, 2001). Individual time-averaged MSDs, h
r2 ðÞi ¼ h½xðt þ Þ  xðtÞ 2 þ ½yðt þ Þ  yðtÞ 2 i, where  is the time scale, are calculated from the two-dimensional trajectories of the centroids of the nanopheres.

1. Acquisition of Moving Particle Video a. Steps 1. The previously microinjected cell culture is placed on the stage of an epifluorescent microscope surrounded by an air-curtain incubator maintained at 37  C and 5% CO2. 2. The center of the dish is located and marked by an x at low (10) magnification and then switched to a high N.A. objective. With a combination of fluorescence and bright field illumination, the microinjected cells are identified within a 1-mm radius of the x. 3. One cell is chosen and with fluorescence microscopy, 20–100 seconds of streaming video are obtained through a SIT camera controlled by Metavue acquisition software. High-resolution bright-field and fluorescence still images of the cell are immediately captured with a CCD camera also controlled by Metavue acquisition software. The movie of the fluctuating particles is saved as an STK file and the still images as TIFF files.

2. Analysis of Movies of Fluctuating Particles a. Steps 1. An STK file of fluctuating nanospheres is opened in the Metamorph image analysis software. Pixel distances are calibrated with calibration files previously made with a stage micrometer. 2. By use of the track objects command, regions around each particle are created. Regions around aggregated particles are not created. These particles violate assumptions made in our constitutive viscoelastic equations and therefore cannot be used in our analysis. 3. For each particle, the inner region is adjusted so that it extends just beyond the edge of the particle. Similarly, the outer region is adjusted so that it

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encompasses an area large enough so that in the subsequent frame no part of the particle will be outside this area. An image of the initial frame with labeled regions visible is duplicated and saved as a TIFF file. 4. The particles are tracked, and the particle number, frame number, and the time-dependent coordinates, [x(t),y(t)], are logged for each frame. These data are saved as an Excel spreadsheet.

3. Calculation of Mean Squared Displacement, Creep Compliance, and Viscoelastic Moduli From the time-dependent coordinates, [x(t),y(t)], the MSD for each particle is calculated with the following formulas (Qian et al., 1991): MSDX ðÞ

¼

N X ðxðti þ Þ  xðti ÞÞ2 =ðN þ 1Þ i¼1

MSDY ðÞ ¼

N X ðyðti þ Þ  yðti ÞÞ2 =ðN þ 1Þ

ð4Þ

i¼1

and MSDðÞ ¼ MSDX ðÞ þ MSDY ðÞ

ð5Þ

The creep compliance is then calculated using Eq. (1) and the results from Eq. (5). Individual particle MSDs and/or creep compliances can be ensemble averaged to obtain a ‘‘bulk’’ mechanical measurement and then used to calculate viscoelastic moduli. To obtain classical frequency-dependent viscoelastic moduli as measured ˜ (s) from by conventional mechanical rheometers, the complex shear modulus G Eq. (2) must first be transformed into the time domain and then Fourier transformed into frequency space. However, because data for h
r2 ðÞi are only measured over a limited time range at discrete times, this method can introduce significant numerical errors at extreme frequencies and requires numerically intensive computations. Alternatively, Eq. (2) can be continued into the Fourier domain by a simple substitution of s ¼ i ! to obtain: G ð!Þ ¼

kB T ai!Ju fh
r2 ðÞig

ð6Þ

where Ju fh
r2 ðtÞig is the Fourier transform of the time-dependent MSD Ju fh
r2 ðtÞig can be estimated algebraically using a wedge assumption (Mason, 2000; Mason et al., 1997b):   i!Iu h
r2 ðÞi  h
r2 ð1=!Þi ½1 þ ð!Þ i ð!Þ ð7Þ where ð!Þ ¼ d ln h
r2 ðÞi=d ln j¼1=! is the local logarithmic slope of h
r2 ðÞi at the frequency of interest ! ¼ 1/. The frequency-dependent elastic and viscous

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moduli, G0 and G00 , respectively, can then be calculated algebraically by use of the following relationships: G0 ð!Þ ¼ jG ð!Þjcosð ð!Þ=2Þ

ð8Þ

G00 ð!Þ ¼ jG ð!Þjsinð ð!Þ=2Þ

ð9Þ

where jG ð!Þj ¼

2kB T 3ah
r2 ð1=!Þi ð1 þ ð!ÞÞ

ð10Þ

IV. Pearls and Pitfalls The data generated from ICM are critically dependent on the ability to accurately measure the spatial fluctuations of Brownian particles; therefore, it is critical to maintain a precisely aligned microscope. Misalignments may cause particle displacements along the optical axis to be mistaken as lateral displacements, which will greatly diminish the spatial resolution of particle displacements. It is also important to note that each instrument will have its own resolution, which depends not only on the quality of the optics (lens, N.A., and magnification) and quality of microscope alignment, but also on the mechanical stability of the microscope. The very small displacements such as those measured with microinjected particles in crowded areas of the cytoplasm require the highest possible resolution. Therefore, placing the microscope on an air-floated optical table is highly recommended. The resolution of the ICM optical setup can be obtained by measuring the root mean square diameter (r.m.s.d) of particles firmly attached to the surface of a glass coverslip. In our system, the r.m.s.d. of a fixed 0.1-
m particle is approximately 5 nm. This implies that the upper limit for elasticity measurements with our system is approximately 1.1 kPa. The derivation of Eq. (2) neglects an inertial term that becomes significant only at high (1 MHz) frequencies, so it is important to avoid frame acquisition rates higher than 106 frames/sec. However, this is currently outside the range available to video microscopy. Because of the relatively similar sizes of particles microinjected into the cell and the inner diameter of microinjection needles, needles can easily become clogged. It is therefore extremely important to apply a slight compensation pressure to the microinjection needle so that there is always a constant flow out of the needle. In the event of a clogged needle, apply a large cleansing pressure to try and pass the clog, or gently chip the tip of the needle on the coverslip until particles begin to flow again. It is extremely important to wash cells immediately after microinjection to remove any particles that may be floating in the media, which on contact with a cell may be endocytosed. Endocytosed particles spend most of their lifetime within

3. ICM to Measure Mechanical Properties of Live Cells

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the cell under the influence of directed motor proteins. The nonrandom component of this motion cannot be accounted for by the equations of motion derived here, and, therefore, endocytosed particles may not be used for the measurement of the local viscoelastic properties of the cell by use of ICM. Particles moving under the influence of nonrandom forces will yield MSDs with power-law slopes greater than unity. Vertical drifting of the culture dish on the microscope stage during particle tracking can occur from heating the oil in between the coverslip and the objective. To prevent this, we suggest placing a weight on top of the dish. Similarly, inverted microscope objective assemblies have a tendency to sink over time. Even in the course of a 20-second experiment, vertical drifting of the objective assembly may be significant. Therefore, it is critical to tighten the focus control to its maximum setting or to implement a laser-monitored control system to maintain a constant objective position. Our particle tracking technique measures the two-dimensional displacements of an essentially three-dimensional motion. But this has little consequence on the evaluation of the MSD and cell mechanics parameters. Here, we probe the passive motion of inert particles in a locally isotropic medium. Therefore, the MSD in two dimensions, Eq. (5), is simply two thirds of the MSD in three dimensions, because the projections of the random movements along the x-, y-, and z-axes are uncorrelated. This would not be true if the purpose were to track directed motion.

V. Concluding Remarks Intracellular microrheology is a powerful technique that allows us for the first time to probe the mechanical properties of the cytoskeleton in its natural environment. ICM oVers numerous advantages over other techniques that have been developed to quantify the mechanical properties of living cells (Gittes et al., 1997; Mason et al., 1997b; Yamada et al., 2000). ICM is able to provide simultaneous local measurements as well as a global picture of the local stiVness of a single cell (Fig. 3), a feat that cannot be achieved by any other method. Furthermore, ICM measures frequency-dependent mechanical properties and, as such, has revealed the highly dynamic nature of cytoskeletal filament organization and cross-linking. Through the use of ICM, we have shown that the mechanical properties of the cell are highly heterogeneous and spatially coordinated (Kole et al., 2004; Tseng et al., 2002, 2004). Moreover, we have identified key molecules and molecular mechanisms that are involved in the regulation of the mechanical properties of the cell (Kole et al., 2004). Combined with existing methods such as transmission electron microscopy (TEM), ICM will be used to provide greater insight into the correlation of cytoskeleton structure with mechanical function. It has been widely suggested that the mechanical properties of cytoskeleton filaments play a critical role in many cellular processes (Heidemann and Wirtz, 2004). We are now in a

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position to test these hypotheses with careful studies that use a multidisciplinary approach combining ICM, molecular biology, and cell biology. Acknowledgments This work was supported by a National Institutes of Health and National Aeronautics and Space Administration grant (NAG9-1563, D. Wirtz and Y. Tseng) and a National Science Foundation grant (NES/NIRT CTS0210718, D. Wirtz). T. P. Kole was supported by a National Aeronautics and Space Administration training grant (NGT965).

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