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Particle-TrackingMicrorheology of LivingCells: Principles andApplicationsDenis WirtzDepartment of Chemical and Biomolecular Engineering and Institute forNanoBioTechnology, Johns Hopkins University, Baltimore, Maryland 21218;email: wirtz@jhu.edu

Annu. Rev. Biophys. 2009. 38:301–26

The Annual Review of Biophysics is online atbiophys.annualreviews.org

This article’s doi:10.1146/annurev.biophys.050708.133724

Copyright c© 2009 by Annual Reviews.All rights reserved

1936-122X/09/0609-0301$20.00

Key Words

cell mechanics, nanorheology, viscosity, elasticity, LINC complex,laminopathies, emerin

AbstractA multitude of cellular and subcellular processes depend critically onthe mechanical deformability of the cytoplasm. We have recently in-troduced the method of particle-tracking microrheology, which mea-sures the viscoelastic properties of the cytoplasm locally and withhigh spatiotemporal resolution. Here we establish the basic principlesof particle-tracking microrheology, describing the advantages of thisapproach over more conventional approaches to cell mechanics. Wepresent basic concepts of molecular mechanics and polymer physicsrelevant to the microrheological response of cells. Particle-tracking mi-crorheology can probe the mechanical properties of live cells in experi-mentally difficult, yet more physiological, environments, including cellsembedded inside a 3D matrix, adherent cells subjected to shear flows,and cells inside a developing embryo. Particle-tracking microrheologycan readily reveal the lost ability of diseased cells to resist shear forces.

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Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . 302BASIC CONCEPTS OF

MOLECULAR CELLMECHANICS . . . . . . . . . . . . . . . . . . . . 305Working Definitions of Stress,

Viscosity, Elasticity,and Compliance . . . . . . . . . . . . . . . . 305

A Model System: A Solutionof Actin Filaments . . . . . . . . . . . . . . 306

BASIC PRINCIPLES OFPARTICLE-TRACKINGMICRORHEOLOGY . . . . . . . . . . . . . 308Particle-Tracking Microrheology

of a Viscous Liquid. . . . . . . . . . . . . . 308Particle-Tracking Microrheology

of an Elastic Solid . . . . . . . . . . . . . . . 312Particle-Tracking Microrheology

of a Viscoelastic Material . . . . . . . . 313Dynamic Viscosity Versus

Shear Viscosity . . . . . . . . . . . . . . . . . 314Creep Compliance from

Particle-TrackingMeasurements . . . . . . . . . . . . . . . . . . 314

PARTICLE-TRACKINGMICRORHEOLOGY OF CELLS . 315Interstitial Viscosity Versus

Mesoscale Viscoelasticityof the Cytoplasm . . . . . . . . . . . . . . . 315

Active Versus PassiveMicrorheology. . . . . . . . . . . . . . . . . . 316

Advantages of Particle-TrackingMicrorheology Over CurrentMethods. . . . . . . . . . . . . . . . . . . . . . . . 317

Illustrative Example ofParticle-Tracking Microrheologyof Living Cells . . . . . . . . . . . . . . . . . . 319

INTRODUCTION

Many cellular and subcellular processes dependcritically on the mechanical deformability ofthe cytoplasm. For example, the translocationof organelles (e.g., nucleus, mitochondria, andendoplasmic reticulum) within the cytoplasm

is partly controlled by their frictional drag andtherefore by the local viscoelastic properties ofthe cytoplasm (54, 55, 59, 68). Migrating cellsat the edge of a wound significantly increase thestiffness of their cytoplasm to enable dendriticfilamentous actin (F-actin) assemblies to pro-duce net protruding forces against the plasmamembrane (50, 80). Axonal elongation dependsdirectly on the highly regulated intracellularviscosity of the growth cone (72). Cells need toadapt their intracellular physical properties tothe physical properties of their extracellular mi-lieu to grow, differentiate, and migrate (20, 22,78). Moreover, changes in the mechanical prop-erties of cells often correlate with disease state(14, 34, 58). For instance, cells derived frommouse models of progeria (premature aging) ormuscular dystrophy display significantly softer(i.e., less elastic) cytoplasm (55) than wild-typecontrols. This affects the ability of these cellsto resist shear forces and to migrate to the edgeof a wound (60).

We have recently introduced the method ofparticle-tracking microrheology (102) to mea-sure the viscoelastic properties of the cytoplasmlocally and with high spatiotemporal resolution.In this approach, fluorescent beads of less than1 μm in diameter are injected directly into thecytoplasm of live cells (Figure 1). These beadsrapidly disperse throughout the cytoplasm andare subsequently tracked by fluorescence mi-croscopy (102). The recorded movements ofthe beads are analyzed in terms of viscosityand elasticity of the cytoplasm. We and oth-ers have exploited particle-tracking microrhe-ology to probe the viscoelastic properties ofvarious types of cells in a wide range of con-ditions (12, 37, 45, 57, 60, 61, 67, 73, 77, 85,92, 95, 103). These measurements have re-vealed important new mechanistic insights intohow the physical properties of the cytoplasmadapt to various chemical and physical stimuli,how they can control basic cell functions, andhow these properties can be significantly alteredin diseased cells. Below, we briefly describedifferent cell biological questions, which havebeen recently addressed using particle-trackingmicrorheology.

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a

b

c d e

f

(x1,y1)

(x2,y2)

2 2

1

1

3

3

Figure 1Particle-tracking microrheology. (a) Submicron fluorescent beads are dialyzed. (b, c) These beads are spread on a grid, which is placedinside a ballistic injection machine. After ballistic injection, the beads disperse rapidly within the cytoplasm. (d ) The cells are placedunder a high-magnification fluorescence microscope. The random spontaneous movements of the beads are monitored with highspatial and temporal resolution. The numerals 1, 2, and 3 refer to the order of steps in which particle-tracking is conducted. (e) Usingthe appropriate software, the time-dependent (x, y) coordinates of the beads are mathematically transformed into mean squareddisplacements (MSDs). ( f ) The time lag-dependent MSDs of the beads are subsequently transformed into local values of either thefrequency-dependent viscoelastic moduli, G′(ω) and G′ ′(ω), or the creep compliance, �(t), of the cytoplasm. Modified with permissionfrom Reference 76.

Particle-tracking microrheology (also callednanorheology) shows that the cytoplasm of ad-herent cells at rest, such as endothelial cellsand fibroblasts on planar substrates, is typi-cally more elastic than viscous (i.e., these cellsshow a rheological behavior which is akin tothat of a solid) for timescales between 0.1 and∼10 s (102). However, at timescales greaterthan 10–20 s, these cells show a predominantlyviscous response to shear forces: The cyto-plasm behaves like a liquid (102). In general,the viscoelastic properties of adherent cells aredominated by the actin filament cytoskeleton.Indeed pharmacological treatment inducingthe disassembly of actin filaments elimi-nates the deformability of the cytoplasm andrenders the cytoplasm mostly viscous at alltimescales (107, 116). Moreover, the levelof elasticity in the cell correlates with thelocal concentration of F-actin present inthe cytoplasm: The actin-rich cell periph-ery (i.e., the lamella) is significantly stifferthan the perinuclear region, which con-tains less actin. Serum-starved cells, which

show little organized F-actin, have both alow viscosity and a low elasticity. However,when suddenly subjected to a shear flowsimilar to that present in blood vessels, the cy-toplasm of serum-starved cells displays rapid as-sembly of actin filaments into organized struc-tures (61, 76). Particle-tracking microrheologyreveals that flow-induced actin filament assem-bly is accompanied by a rapid rise in cyto-plasmic stiffness, followed by an equally rapiddecrease in stiffness (61). This transient in-crease in cytoplasmic stiffness correlates withthe transient activation of the Rho/Rho ki-nase (ROCK) pathway and the associated as-sembly and transient contraction of the actinfilament network by myosin II. These resultssuggest that when an adherent cell is subjectedto shear stresses, its first action is to prevent de-tachment from its substratum by greatly stiff-ening the cytoplasm through enhanced actinfilament assembly and Rho-kinase-mediatedcontractility.

During migration at the edge of a wound,cells polarize their overall morphology and

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position the microtubule organizing center(MTOC) toward the cell’s leading edge (31, 59).Particle-tracking microrheology indicates thatthe mechanical properties of the cytoplasm be-come spatially polarized as well: The cytoplasmis much stiffer at the leading edge than at thetrailing edge of the migrating cell, i.e., the re-gion near the nucleus that is positioned nearthe back of the cell (50). MTOC repositioningat the edge of the wound is abrogated in cellstransfected with a dominant-negative mutant ofthe small GTPase Cdc42 (98). Similarly, cellswith deactivated Cdc42 show no spatial polar-ization in their mechanical properties. Theseresults suggest that a differential distributionof subcellular mechanical microenvironmentsis essential for directed cell migration and iscoordinated through microtubules (50).

Particle-tracking microrheology has alsoshown that the elasticity of the cytoplasm ismuch lower than that of the nucleus in the samecell. The nucleus is also more elastic than vis-cous, which reveals that the intranuclear regiondisplays an unexpectedly strong solid-like be-havior (103). Indeed, when cells move though adense extracellular matrix, a rate-limiting stepin the 3D migration process is the squeezingof the nucleus by the pores of the matrix,not the deformation of the cytoplasm (6, 56).Measurements of the mean shear viscosity andthe elasticity of the intranuclear region deter-mine a lower bound of the propulsive forces(3–15 pN) required for nuclear organellessuch as the promyelocytic leukemia bodyto undergo processive transport within thenucleus by overcoming the friction forces setby the intranuclear viscosity. Dynamic analysisof the spontaneous movements of submicronbeads embedded in the nucleus also reveals thepresence of transient nuclear microdomains ofmean size 290 nm that are mostly absent in thecytoplasm (32, 103). The strong elastic charac-ter and the micro-organization of the intranu-clear region revealed by particle-tracking anal-ysis may help the nucleus preserve its structuralcoherence. This study highlights the differencebetween the low interstitial nucleoplasmic vis-cosity, which controls the transport of nuclear

proteins and molecules, and the much highermesoscale viscosity, which affects the diffusionand the directed transport of nuclear organellesand reorganization of interphase chromosomes(103).

Finally, particle-tracking microrheology hasshown that when human endothelial cells areplaced inside a 3D matrix, their cytoplasmis much softer than when the same cells areplaced on a thin planar layer of the same ma-trix (77). Vascular endothelial growth factor(VEGF) treatment, which enhances endothelialmigration in the 3D matrix, increases the de-formability of the cytoplasm of endothelial cellsin the matrix. This VEGF-induced softeningresponse of the cytoplasm is abrogated by spe-cific ROCK inhibition. These results suggestthat ROCK plays an essential role in the regu-lation of the intracellular mechanical responseto VEGF of endothelial cells in a 3D matrix.

The above measurements could only havebeen achieved thanks to particle-trackingmicrorheology, which can reveal the me-chanical properties of live cells in experi-mentally difficult—yet more physiological—environments. For instance, particle-trackingmicrorheology is the only cell mechanicsmethod that can probe the mechanical proper-ties of individual cells deeply embedded insidea 3D matrix and their mechanical response toagonists and/or drug treatments (77), monitorchanges in cytoskeleton elasticity in cells sub-jected to shear flows (61), or measure in vivothe local viscoelastic properties of a Caenorhab-ditis elegans embryo embedded in an impenetra-ble shell (16). Cells in these more physiologi-cal environments cannot be probed by existingmethods of cell mechanics, such as atomic forcemicroscopy (AFM), because these cells are inac-cessible to direct physical contact and can onlybe probed at a distance.

This review describes basic concepts ofmolecular mechanics and polymer physicsapplied to cells and introduces the funda-mental principles underlying particle-trackingmicrorheology and its advantages over tradi-tional cell mechanics methods. This review alsoshows how particle-tracking microrheology can

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readily reveal the lost ability of diseased cells toresist shear forces.

BASIC CONCEPTS OFMOLECULAR CELL MECHANICS

Working Definitions of Stress,Viscosity, Elasticity, and Compliance

Because different experimental methods mea-sure different (but often related) rheologicalquantities, the intracellular mechanics of aliving cell is best characterized by multiplerheological parameters, including viscosity,elasticity, and creep compliance. These rheo-logical parameters simply describe the mechan-ical response of a material (such as the cell’scytoplasm) subjected to a force and how it mea-sures the resulting deformation and, vice versa,the mechanical response of a material subjectedto a deformation and how it measures the forcerequired to produce the deformation. The rhe-ological response of the cytoplasm can be eitherpredominantly viscous or elastic, depending onthe time of application and the magnitude ofthe force. These forces can be externally appliedas in the case of endothelial cells subjected toblood flow (61), result from internal tension asin the case of actomyosin contractility, or both(49).

The shear viscosity of a liquid measures itspropensity to flow under random or appliedforces. The shear viscosity generates the dragforces that slow down the motion of organellesand protein complexes in the cytoplasm and nu-cleus. A simple way to measure the viscosity ofa material or liquid is to use a falling-ball vis-cometer. Here the speed at which heavy metal-lic beads fall through the probed material de-pends on an effective viscosity. This method ishighly approximate due to the uncontrolled in-teractions between the beads and the material,the inherent difficulty to measure the terminalvelocity of the beads, and the assumptions thatneed to be made to compute this viscosity. Al-ternatively, the material can be subjected to asteady shear deformation of controlled rate us-ing a rheometer. Here, the material is placed

between two parallel plates or between a coneand plate. The viscosity is the ratio of the stress(force per unit area) induced in the material bythe imposed deformation to the rate of sheardeformation. In cells, the viscosity of the cyto-plasm predominantly governs the transport andmovements of subcellular organelles and cy-toskeleton structures at long timescales. A ma-terial that is only viscous (and not elastic), suchas water, cannot resist mechanical stresses; it canonly slow down its deformation by the imposedmechanical stress. Upon cessation of the stress,the material or liquid has lost all memory ofits original shape and location. Below, we showhow the viscosity of a material or a liquid can beobtained by tracking the random movements ofsubmicron beads embedded in the material.

The elasticity (also called the elastic modu-lus) of a material measures its stretchiness. Elas-ticity measures the ability of cytoplasmic struc-tures to resist forces and store energy caused bydeformation. A material that is only elastic (andnot viscous) can deform under stress but can-not flow. As no viscous dissipation occurs dur-ing its deformation, the elastic material snapsback to its original shape upon cessation of thestress. Elasticity typically governs the responseof the cytoplasm to mechanical stresses at shorttimescales.

Some materials, such as Silly Putty®, can beboth viscous and elastic. Silly Putty can bounceas it deforms upon impact, but quickly regainsits shape, which means it is elastic. It is alsoviscous, as Silly Putty rolled into a ball will par-tially flatten due to its own weight when left on aflat surface. These simple observations indicatethat Silly Putty is elastic at short timescales (i.e.,during impact) and viscous at long timescales.Similarly, the cytoplasm of living cells is bothviscous and elastic, i.e., it is viscoelastic.

Instead of working in the time domain, rhe-ologists tend to work in the frequency do-main. The frequency-dependent elastic mod-ulus of a material, G′(ω), can be obtainedby subjecting it to oscillatory deformations ofcontrolled frequency ω and constant (small)amplitude. When an oscillatory deformation isapplied and is given by a sine function of time,

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γ(t) = γ0 sin ωt, the stress, τ, induced withinthe material by this deformation will typi-cally have both sine and cosine components.Specifically, the stress can be decomposed intoa sine (in-phase) component and a cosine(out-of-phase) component: τ(t) = τ′ sin ωt +τ′ ′ cos ωt = γ0(G′ sin ωt + G′ ′ cos ωt). Theelastic modulus of the material, G′, is equalto the in-phase component of the frequency-dependent stress divided by the amplitude ofthe oscillatory deformation, i.e., G′(ω) = τ′/γ0.The viscous modulus of the same material,G′ ′(ω), can be obtained during the same mea-surement by extracting the out-of-phase com-ponent of the frequency-dependent stress anddividing by the amplitude of the oscillatory de-formation, i.e., G′ ′(ω) = τ′ ′/γ0 (24). If the ma-terial is an elastic solid (no or little viscosity),such as rubber, then the induced stress is ex-actly in phase with the input deformation andτ(t) = τ′ sin ωt. In this case, G′ ′ = 0. If thematerial is a viscous liquid (no elasticity), suchas water or glycerol, then the induced stress isout of phase with the input deformation, andτ(t) = τ′ ′ cos ωt. In this case, G′ = 0.

Typical biological materials, such as cells andtissues, have rheological properties that dependon the rate of deformation, ω, i.e., both G′ andG′ ′ depend on ω. At low frequencies, the cyto-plasm has the time to reorganize its cytoskele-ton polymers and it can flow, behaving as a vis-cous liquid. At high frequencies, the cytoplasmdoes not have the time to reorganize and the cy-toplasm behaves as an elastic solid, which resiststhe deformation. This underlies the importanceof measuring the full frequency-dependent re-sponse of cells and tissues, which undergo bothslow and rapid movements. However, the rhe-ology of individual cells cannot be measuredwith a macroscopic device, such as a rheometer.Moreover, even if a microscopic rheometer ex-isted, measuring the full frequency-dependentrheological response of the cytoplasm to oscil-latory deformations would be tedious, as this re-sponse would have to be probed one frequencyat a time over a wide range of frequencies.Below, we show that the frequency-dependentviscous and elastic moduli of a cell can be ob-

tained in ∼10 s from the dynamic movementsof submicron probe beads embedded in thecytoplasm, without subjecting the cell to anyexternal force or deformation.

A material that is only viscous and has noelasticity, such as water, is a liquid and G′ = 0.A material that is only elastic and has no or littleviscosity, such as rubber or Jell-O, is a solid andG′ ′ ≈ 0. A material that is more viscous thanelastic, i.e., G′ ′(ω) > G′(ω), is a viscoelastic liq-uid; a material that is more elastic than viscous,G′(ω) > G′ ′(ω), is a viscoelastic solid.

Finally, the creep compliance of the cyto-plasm refers to its deformability. Experimen-tally, it is measured by the deformation of thecytoplasm resulting from an applied mechan-ical stress (applied force). A high complianceindicates that a material has a low propensityto resist mechanical deformation following ap-plication of a shear stress; a low complianceindicates that it can resist such stress. Whenthe material is only viscous or only elastic andnot both, the creep compliance of the mate-rial is inversely proportional to its viscosity orelasticity, respectively. Below, we show how thetime-dependent creep compliance of the cyto-plasm can be obtained directly from trackingthe movements of submicron probe beads em-bedded in the cytoplasm, without subjecting thecell to any external force.

Viscoelastic moduli (G′ and G′ ′) and creepcompliance of the cytoplasm are related. In-deed, it is possible to compute the time-dependent cytoplasmic creep compliance fromthe frequency-dependent viscoelastic parame-ters and, vice versa, the viscoelastic moduli ofthe cytoplasm can be computed from the time-dependent creep compliance. The shear viscos-ity can also be estimated from the frequency-dependent viscous and elastic moduli.

A Model System: A Solutionof Actin Filaments

To obtain a more intuitive understanding of therheological concepts defined above, we con-sider the simple (but not trivial) system ofa concentrated solution of actin filaments. A

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key contributor to cytoplasmic stiffness is thecytoskeleton, which is composed of three ma-jor filamentous proteins: F-actin, microtubules,and intermediate filaments (92). The cytoskele-ton provides the cytoplasm with its structureand shape. In the cell, actin monomers as-semble into semiflexible F-actin polymers thatreadily form entangled networks (30, 97, 108)whose viscoelastic properties can be controlledby either altering the local density of actin fil-aments or the cross-linking/bundling activityof F-actin-binding proteins, such as α-actininor filamin (43, 113). In most cells, F-actin andintermediate filaments are the primary contrib-utors to cytoplasmic stiffness (92).

The cytoplasm of adherent cells is rheolog-ically complex: It typically behaves as a vis-coelastic liquid when sheared either slowly orfor a long time, and as a viscoelastic solid whensheared either rapidly or for a short time. Thisrheological complexity can be captured by a

solution of entangled actin filaments in vitroin the absence of motor or cross-linking pro-teins (3, 47). Below a threshold concentrationof ∼0.2 mg/ml, actin filaments cannot resistshear deformations; their global rheological re-sponse is viscous, with a viscosity equal to thatof buffer, with a small additional correction dueto the presence of the filaments (17). However,past this threshold concentration, the actin fil-aments in suspension begin to form entangle-ments. Because these filaments are rigid (30),they form entanglements more readily thanflexible polymers that have the same contourlength. These entanglements form topologicalobstacles in the network that impede the lat-eral bending motion of the filaments, but nottheir longitudinal movements. These polymerentanglements render the solution of actin fil-aments elastic.

At short timescales, the filaments onlyundergo thermally driven lateral fluctuations

Slow longitudinal back-and-forth fluctuations (τ > τe)

Fast lateral fluctuations (τ > τe)

Cytoskeleton polymer

Time lag (s)

a bbb c

τR

τe

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an

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Γ(t) ~ <Δr2(t)>

~t~ t3/4

~t~t3/4

Cre

ep

co

mp

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nce

Γ(t

)

Time lag

τR

τe

Figure 2Physical origin of the displacements of beads in the cytoplasm. (a) Ballistically injected beads are lodged within the cytoskeleton.The size of the beads is larger than the average mesh size of the cytoskeleton network, which is ∼50 nm in fibroblasts. (b) Thespontaneous movements of the cytoskeleton filaments that surround each bead induce displacements of the beads. At short timescales,the displacements of the beads are predominantly induced by the fast lateral bending fluctuations of the cytoskeleton filaments. Atlong times, the displacements of the beads are predominantly induced by the slow longitudinal back-and-forth lateral fluctuations of thecytoskeleton filaments. Finally, filaments move sufficiently to allow beads to escape the cage to move to the next cage. (c) Accordingly,the mean squared displacements (MSDs) of the beads show a t3/4 power-law dependence at short timescales, a quasi plateau valueat intermediate timescales between τe and τR, and a linear dependence at long times caused by the slow viscous diffusion of the beads.(Inset) The deformability of the cytoplasm [creep compliance, �(t)] is proportional to the MSD of the beads, 〈�r2(t)〉. See text for details.

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(Figure 2). These fluctuations are fast, as theyinvolve small sections of the filaments betweennetwork entanglements. A fast camera showseach actin filament undergoing lateral fluc-tuations within a confining tube-like regionformed by the surrounding filaments (17, 18,46). At intermediate timescales that are longerthan the time for the lateral fluctuations tobegin to hit the walls of the tube region,the back-and-forth longitudinal movements ofthe filament in the network can take place(Figure 2). These longitudinal motions areslow because they involve the entire filament.But these back-and-forth movements resultin no net displacement of the filaments: Themovements of the filaments are effectivelycurved 1D random walks. Finally, at timescaleslonger than a characteristic terminal relaxationtime of the network, which depends on thelength of the filament, the filament can finallyescape the tube-like region (39, 70).

This description of the timescale-dependentmovements of individual filaments in a densenetwork can be redescribed in rheological termsfor the whole filament network following deGennes’ original concept (17). Consider anactin filament network subjected to a con-stant stress (force per unit area) of relativelysmall magnitude. At short timescales, the fil-aments can only relax the energetically unfa-vorable distortions, which are created in thepolymer network by the externally appliedstress, through lateral fluctuations (70). Thecreep compliance—or the deformation of thenetwork—increases as a function of time ast3/4 (114) (Figure 2c). The exponent 3/4 re-flects the lateral bending fluctuations of thefilaments (70, 74). At longer timescales, thenetwork cannot relax anymore because no netfilament motion occurs at these timescales.Accordingly, the creep compliance of the fila-ment network becomes approximately constant(or a quasi plateau, Figure 2c) and the networkbehaves mostly as an elastic gel, as the elasticmodulus becomes much larger than the viscousmodulus. A stably cross-linked actin filamentnetwork behaves similarly, but at all timescales(44). At long timescales, the filaments can finally

diffuse out of their confining tubes, the networkcan relax the stress, and the creep compliancegrows linearly with time, a proportionality thatreflects viscous diffusion (21). The network be-comes a viscoelastic liquid, for which the viscousmodulus is much larger than the elastic modu-lus (24). If the actin filament network is stablycross-linked, the polymer cannot undergo thisterminal relaxation and the plateau value of thecompliance persists indefinitely. Often the tran-sition from the plateau region to the terminalrelaxation is not sharp because actin filamentshave a wide distribution of lengths, which de-fine a broad distribution of relaxation times.

A permanently cross-linked actin filamentnetwork provides cells with structural stabilitybut does not allow them to readily soften to al-low for cell shape changes that are, for instance,required during intravasation and extravasationof cancer cells in and out of blood vessels (110).To circumvent this problem and allow for a stiffbut malleable cytoskeleton, cells have evolvedan ingenious mechanism. This mechanism doesnot require dynamic disassembly and reassem-bly of the filaments themselves to modulate themechanical properties of the network. InsteadF-actin networks exploit dynamic cross-linkingproteins, such as filamin or α-actinin (25, 99,109, 110). When such a network is shearedmore slowly than the lifetime of binding of thecross-linking protein, the network can flow andbehaves mostly as a liquid. When sheared ata rate faster than the inverse binding lifetimeof the cross-linking protein, the actin filamentnetwork behaves as an elastic gel and cannotflow (109, 110, 115).

BASIC PRINCIPLES OFPARTICLE-TRACKINGMICRORHEOLOGY

Particle-Tracking Microrheologyof a Viscous Liquid

To understand how the viscoelastic propertiesof the cytoplasm of cells can be obtained bytracking the movements of beads embedded init, we consider first the simpler limit case of

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submicron beads suspended in a viscous liquid(no elasticity). These beads are smaller than 1μm so that they undergo Brownian motion, asinertial forces (gravity) are negligible. If activetransport of the nanoparticles is also negligible,only two types of forces act on the beads insidethe cytoplasm:

� The small random force produced bythe random bombardment of watermolecules generated by the thermal en-ergy kBT and the movements of other cy-toplasmic structures, such as cytoskeletonfilaments and other organelles (102).

� The counteracting frictional force, whichresults from the movement of the beadsdriven by thermal energy. The frictionalforce is proportional to the velocity of thebead and the bead’s friction coefficient,which depends on the viscoelastic prop-erties of the cytoplasm and the size of thebead.

Because we neglect inertia and directed mo-tion, the mathematical equation describing themotion of a bead simply states that the sum ofthese two forces is zero. This resulting equa-tion is not deterministic, but stochastic, be-cause the force that powers the bead move-ments is random in amplitude and direction.

The solution of this stochastic equation, i.e., thetime-dependent coordinates of the bead, is theconventional random walk (5). Therefore, onaverage, the bead remains at the same posi-tion. However, the standard deviation of thedisplacements or the mean squared displace-ment (MSD) of the bead, 〈�r2〉, is not zero.

In a liquid of unknown shear viscosity,η, the submicron bead undergoes Brownianmotion driven by the thermal energy kBT. Eachtime the bead takes a step in a random direc-tion, it loses all memory of where it just camefrom. The next step occurs in an uncorrelateddirection. Einstein showed that, in these con-ditions, the bead undergoes a random walk andits time-averaged MSD is simply 〈�r2〉 = 4Dt(Figure 3a). Here t is time lag, 〈...〉 indicatestime-averaging, and D is the diffusion coeffi-cient of the bead. The linear dependence of theMSD on time lag is a signature of pure vis-cous diffusion of the bead (81). Equivalently,the square-root dependence of the root MSDwith time,

√〈�r2〉 = √

4Dt ∼ t1/2, is a sig-nature of viscous diffusion (5). For a sphericalbead, the diffusion coefficient is given by therelation D = kB T/ξ (Stokes-Einstein relation),where ξ = 6πηa is the friction coefficient ofthe bead in the liquid and a is the radius of thebead. After rearrangements, one finds that the

Time lag (t)

a b

dis

pla

cem

en

t <

Δr2

(t)>

Time dependent Time independent

Figure 3Particle-tracking microrheology of a viscous liquid and an elastic solid. (a) The mean squared displacement(MSD) of beads immersed in a viscous liquid (such as water or glycerol) grows linearly with time lag, with aslope inversely proportional to the viscosity of the liquid and the radius of the bead. (b) The MSD of beadsembedded in an elastic solid (such as rubber) is independent of time lag. The plateau value is inverselyproportional to the elasticity of the solid.

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viscosity of the liquid can be estimated as soonas the MSD of the bead is measured (114):

η = 2kB T3πa

t〈�r2(t)〉 . 1.

This expression explains how one can esti-mate the viscosity of a liquid merely by sus-pending small beads in that liquid, subsequentlytracking their thermally excited random mo-tion using fluorescence light microscopy andappropriate particle-tracking software, and fi-nally computing the MSD from the trajectoriesof the beads.

In practice, tens to hundreds of beads needto be tracked to ensure adequate statistical av-eraging. In this case, the ensemble-averagedMSD, 〈〈�r2(t)〉〉, which is the means of all mea-sured MSDs, is used instead of 〈�r2〉. If the sus-pending fluid is indeed a liquid, then t/〈�r2(t)〉should be a constant independent of t (seeEquation 1), which is a stringent test of viscousdiffusion. If t/〈�r2(t)〉 is nonconstant, it usuallyindicates that the suspending fluid is a viscoelas-tic material instead of a viscous liquid (65).

We consider a 100-nm-diameter bead sus-pended in corn syrup, which has a shear viscos-ity close to that of the cytoplasm of fibroblasts,η = 20 P = 2 Pa.s (typical values of viscos-ity are listed in Table 1). The thermal energyis kBT ≈ 4.2 pN.nm (where T = 37◦C) andthe diffusion coefficient of the bead is D ≈0.0022 μm2/s. By comparison, the diffusion ofthe same bead in water is 4.4 μm2/s. There-fore, the value of the time-averaged MSD of thebead after t = 0.1 s, 1 s, and 10 s of trackingis ≈0.00088 μm2 (or 88 nm2), 0.0088 μm2, and0.088 μm2, respectively. This result indicatesthat the average size of the region crisscrossedby the Brownian movements of the bead afterthe same times is

√〈�r2〉 = √

4Dt ≈ 30, 94,and 300 nm, respectively. This result suggeststhat high-resolution tracking is required to ob-tain good measurements of MSDs of 100-nmbeads in a highly viscous liquid within a 10-s-long tracking time.

The prefactor 4 in the expression 〈�r2〉 =4Dt stems from the fact that microscopyprobes the 2D projection of an intrinsically 3D

movement of the bead. This is correct onlyif the material in the proximity of the beadis isotropic, i.e., this material or liquid hasthe same physical properties in all three (x,y, and z) directions. To test whether this islikely to be true without tracking the move-ments of the beads in all three directions (19),one can compute the MSDs of the bead inthe x and y directions independently. Indeed,from the measured time-dependent coordi-nates of the bead, x(t) and y(t), the MSD is givenby 〈�r2(t)〉 = 〈[x(t) − x(0)]2 + [y(t) − y(0)]2〉,where x(0) and y(0) correspond to the initialposition of the bead. If the material is isotropic,then 〈[x(t) − x(0)]2〉 = 〈[y(t) − y(0)]2〉 andtherefore 〈�r2(t)〉 = 2〈[x(t) − x(0)]2〉 =2〈[y(t) − y(0)]2〉. If the MSDs of the beadin the x and y directions are indeed Brow-nian (corresponding to two independent1D random walks), then 〈[x(t) − x(0)]2〉 =〈[y(t) − y(0)]2〉 = 2Dt. Hence, 〈�r2(t)〉 = 4Dt,and therefore it is likely that the MSDs ofthe bead in the z direction are also Brownianand equal to those in the x and y directions,which indicates that the viscoelastic propertiesof the cytoplasm in the vicinity of the bead areisotropic (38).

In the case of a viscous liquid, the elasticmodulus of the liquid is of course zero, G′ = 0,and it can be shown that the viscous modulus issimply G′ ′ = ηω. Here ω is the frequency (orrate) of deformation in an oscillatory mode ofdeformation and is equal to the inverse of thetime lag t, ω = 1/t. This means that if this liq-uid were placed in a rheometer and subjectedto oscillatory deformations, then the elasticmodulus would be negligible and the viscousmodulus would increase linearly with the inputfrequency ω. Equivalent to the linear depen-dence of the MSD with time, that the viscousmodulus of a given material increases linearlywith the rate of deformation indicates that thismaterial is a viscous liquid. This rheological re-sponse, i.e., G′ ≈ 0 and G′ ′ = ηω, is for instancethat of an unpolymerized G-actin solution invitro or that of the cytoplasm of a cell treatedwith an actin-depolymerizing drug (e.g., latrun-culin A or cytochalasin D).

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Table 1 Elasticity and shear viscosity of the cytoplasm of different types of cells measured by particle-trackingmicrorheologya

Cell type and condition; values of viscoelasticparameters

Averageviscosity (poise)

Average elasticityat 1 Hz (dyne/cm2) Reference

Serum-starved Swiss3T3 fibroblastb 10 ± 3 50 ± 20 (49)Serum-starved Swiss 3T3 fibroblast treated with LPAc 95 ± 20 120 ± 30 (49)Serum-starved Swiss3T3 fibroblast subjected to shear flowd 300 ± 40 600 ± 50 (61)Swiss 3T3 fibroblast at the edge of a wounde 45 ± 15 330 ± 30 (50)Swiss 3T3 fibroblast treated with bradykininf 22 ± 13 90 ± 20 (50)Swiss 3T3 fibroblast treated with PDGFg 24 ± 8 190 ± 30 (50)Mouse embryonic fibroblast (Lmna+/+ MEF)h 18 ± 2 140 ± 30 (60)MEF treated with latrunculin Bi NA 80 ± 4 (60)MEF treated with nocodazolej NA 50 ± 4 (60)MEF deficient in lamin A/C (Lmna−/− MEF) 8 ± 1 60 ± 4 (60)HUVEC on a planar 2D peptide matrixk 17 ± 1 130 ± 10 P. Panorchan, J.S.H. Lee,

D. Wirtz, unpublisheddata

HUVEC on a planar 2D peptide matrix and treated withVEGFl

8 ± 1 100 ± 5 P. Panorchan, J.S.H. Lee,D. Wirtz, unpublisheddata

HUVEC inside a 3D peptide matrixk 14 ± 1 55 ± 4 (77)HUVEC inside a 3D peptide matrix treated with VEGFl 18 ± 1 40 ± 3 (77)HUVEC inside a 3D fibronectin matrix NA 58 ± 6 (117)HUVEC inside a 3D fibronectin matrix treated withinhibiting FN peptide

NA 20 ± 4 (117)

Single-cell C. elegans embryom 10 ± 1 Negligible (16)Interphase nucleus of Swiss 3T3 fibroblastn 520 ± 50 180 ± 30 (103)

aParticle-tracking microrheology was used to study the mechanical properties of many varieties of cells under a wide range of conditions. Unless stated, allvalues of viscosity and elasticity in the table are for the cytoplasm. The elasticity was evaluated at a shear frequency of 1 s−1 (1 s−1 = 1 Hz) and the shearviscosity was estimated as the product of plateau modulus and the relaxation time. The plateau modulus is the value of the elastic modulus at intermediatefrequencies where it reaches a quasi plateau value. The relaxation time is the inverse of the frequency where elastic and viscous moduli are equal. Allmeasurements are mean ± sem. Unit conversions are 1 dyne/cm2 = 0.1 Pa = 0.1 N/m2 = 0.1 pN/μm2. Pa, Pascal; pN, piconewton; NA, not available.bCells placed on 50 μg/ml fibronectin deposited on glass were serum starved for 48 h before measurements.cSerum-starved cells placed on 50 μg/ml fibronectin deposited on glass were treated with 1 μg/ml lysophosphatidic acid (LPA), which activatesRho-mediated actomyosin contractility. LPA was applied 15 min before measurements.dCells were grown on 20 μg/ml fibronectin for 24 h and exposed to shear flow (wall shear stress, 9.4 dyne/cm2) for 40 min before measurements.eCells in complete medium and grown on 50 μg/ml fibronectin to confluence were wounded to induce migration. Measurements were conducted 4 h afterwounding.fCells in complete medium and grown on 50 μg/ml fibronectin were treated with 100 ng/ml bradykinin for 10 min before measurements.gCells in complete medium and grown on 50 μg/ml fibronectin were treated with 10 ng/ml platelet-derived growth factor (PDGF) for 10 min beforemeasurements.hCells in complete medium were grown on glass.iLmna+/+ mouse embryonic fibroblasts (MEFs) in complete medium grown on glass were treated with 5 μg/ml actin-filament disassembly druglatrunculin B.jLmna+/+ MEFs in complete medium and grown on glass were treated with 5 μg/ml microtubule disassembly drug nocodazole.kCells in complete medium were placed in a 0.5% puramatrix gel. HUVEC, human umbilical vein endothelial cell.lCells in complete medium were placed in a 0.5% puramatrix gel and treated with 4 ng/ml vascular endothelial growth factor (VEGF) for 24 h prior to themeasurements.mYoung Caenorhabditis elegans eggs were obtained by cutting gravid hermaphrodites from worms in egg salts. The nanoparticles were then microinjectedinto the syncytial gonads of gravid hermaphrodites.nCells in complete medium.

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If the probed system were in equilibriumand perfectly uniform, tracking one bead fora long time (e.g., 1000 s) and dividing this timespan into 100 equal time spans of 10 s shouldbe equivalent to tracking 100 beads each for 10s. Although it is impractical to track a singlebead for a long time even in in vitro systemsbecause of drift problems, this equivalency iscorrect for liquids such as water and glycerol, asignature of ergodicity. But it is incorrect in sus-pensions of actin filaments in vitro and in livecells, which are systems far from equilibriumand highly spatially heterogeneous (100, 104).Indeed, beads well dispersed in the cytoplasmshow a wide distribution in MSDs (102).

We note that individual trajectories of thebeads, even in water, are typically highly asym-metric in shape (38). Even the overall shape ofa computer-generated random walk is highlyasymmetric (5, 87), i.e., it is not a circle. Theshape of the object encompassing an individualtrajectory of a single bead in a liquid is an el-lipse in the 2D space (e.g., a protein diffusingwithin the plasma membrane) and an ellipsoidin the 3D space (e.g., GFP diffusing in the cyto-plasm) (36). However, when these trajectoriesare ensemble-averaged and the trajectories aresuperimposed, the object encompassing theseindividual trajectories is a circle in 2D and asphere in 3D.

Particle-Tracking Microrheologyof an Elastic Solid

The second limit example involves the samebead, but this time embedded in a highly elasticmaterial of negligible viscosity, such as rubber.Each time the bead is driven by the thermalenergy in a random direction, the surroundingmaterial pushes back instantaneously with equalforce in the opposite direction. Therefore, theMSD of the bead is finite but constant: 〈�r2〉 =K at all timescales (Figure 3b). The indepen-dence of the MSD with time is a signature ofpurely elastic solid behavior. The viscous mod-ulus of this elastic solid is of course G′ ′(ω) = 0.The elastic modulus of an elastic solid is sim-ply G′(ω) = 2kB T/3πa〈�r2〉 = 2kB T/3πa K ,

which is a constant independent of ω, i.e., theelastic modulus of an elastic solid is inverselyproportional to the MSD of the beads embed-ded in it. This expression shows that one cancompute the elastic modulus of an elastic solidfrom particle-tracking measurements of 〈�r2〉without imposing any oscillatory deformation.The fact that the elastic modulus of a given ma-terial is independent of the rate of deforma-tion or frequency, ω, is a signature of purelyelastic behavior. This would be the rheologicalresponse of a permanently cross-linked actinfilament network (75) or Jell-O, where G′ isapproximately a constant independent of fre-quency and G′ ′ is much smaller than G′.

Let us consider a 100-nm-diameterbead suspended in a stiff elastic material offrequency-independent elasticity of G′ =10 Pa = 100 dyne/cm2. Typical values ofelasticity are given in Table 1. Then, the time-averaged MSD of the bead in this materialat all timescales is 〈�r2〉 = 2kB T/3πaG′ ≈0.002 μm2, which can readily be measuredby fluorescence microscopy and appropriateparticle-tracking software.

These two examples—viscous liquid andelastic solid—illustrate how the time depen-dence of the MSD of beads inside a given mate-rial can help rapidly diagnose key physical prop-erties of the material, including whether it is aliquid (then, 〈�r2〉 ∼ t or 〈�r2〉/t is a constant)or an elastic solid (then, 〈�r2〉 is a constant).

The results above indicate that to estimatethe viscosity of a liquid, a spatial resolutionof at least 30 nm is required when tracking100-nm-diameter beads for 10 s using a camerathat collects images at a rate of 10 frames persecond. In practice, the spatial resolution onthe displacements of the beads must be anorder of magnitude better, approximately 3 nmfor a 100-nm-diameter fluorescent bead. Sucha high, subpixel spatial resolution can beobtained by using either quadrant detection orfluorescence video microscopy. The advantageof quadrant detection is its superior detectioncapability (<1 nm) (93), but quadrant detectioncan only track one or two beads at a time (28,29, 116). This is a serious problem when it is

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desirable to monitor simultaneously the vis-coelastic properties of various locations withinthe cell. When using high-magnification,high-numerical-aperture lenses (11), video mi-croscopy allows one to track hundreds of beadsat the same time (13, 86, 102) but has a maxi-mum resolution of the order of 3–10 nm, de-pending on the experimental setup. The spatialresolution of the measurements will vary fromone instrument to another as it also depends onthe stability of the microscope system used totrack the beads. For a material that is essentiallyelastic and with a maximum spatial resolutionof 3 nm, the highest elasticity that can stillbe measured with accuracy using particle-tracking microrheology is approximatelyG′

max = 2kB T/3πa(3 nm)2 ≈ 1,900 Pa ≈19,000 dyne/cm2 (88, 89), which is muchhigher than typical values of the elasticity of thecytoplasm. Therefore, using video microscopyand high-resolution tracking allows for themeasurements of highly elastic materials.

Particle-Tracking Microrheologyof a Viscoelastic Material

The rheological behavior of the cytoplasm ora reconstituted actin filament network is inter-mediate between the two limit behaviors of aviscous liquid and an elastic solid, as describedabove. Indeed, the cytoplasm is predominantlyviscous at long timescales (t > τR) or low ratesof shear, G′ ′(ω) G′(ω) for ω < ωR, and pre-dominantly elastic at short timescales or highrates of shear, G′ ′(ω) G′(ω) for ω > ωR,where ωR is the inverse of the relaxation timeof the cytoskeleton network, τR (Figure 4). Athigh frequencies, ω > ωe, both G′ and G′ ′ areproportional to ω3/4, a power-law dependencethat reflects the bending lateral fluctuations ofthe semiflexible filaments in the network (40,90). The exponent would be 1/2 if the polymersconstituting the cytoskeleton were flexible (21),but intermediate filaments, actin filaments, andmicrotubules in live cells are semiflexible (1).The frequency ωe is approximately equal to the

Softer

Stiffer

Relaxation time: τR

= 1 ωR

–1

Shear viscosity: η ≈ G'pτ

R

ωe

ωR

Frequency (ω)Time lag (t)

Cre

ep

co

mp

lia

nce

Γ(t

)

Vis

coe

last

ic m

od

uli

G’(

ω),

G’’(

ω)

G'p

a b

τR

τe

Figure 4Creep compliance and viscoelastic moduli of the cytoplasm. (a) Typical creep compliance of the cytoplasm measured by thespontaneous displacements of beads embedded in the cytoplasm of a living cell (see also the inset in Figure 2c). The creep compliancedefines two characteristic timescales, τe and τR. (b) The frequency-dependent elastic (or storage) modulus, G′(ω), and viscous (or loss)modulus, G′ ′(ω), of the cytoplasm can be approximately computed from the mean squared displacement of the beads or equivalentlyfrom the time-dependent creep compliance shown in panel a. In general, the cytoplasm behaves as a viscoelastic liquid at lowfrequencies (corresponding to long timescales, t > τR): G′ ′(ω) > G′(ω) for ω < ωR. The cytoplasm behaves as a viscoelastic solid atintermediate frequencies: G′(ω) > G′ ′(ω) for ωe > ω > ωR. Finally, the cytoplasm behaves again as a viscous liquid at highfrequencies: ω > ωe, for which G′(ω) ∼ G′ ′(ω) ∼ ω3/4.

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inverse of the time required for lateral fluctua-tions to begin to touch the walls of the confiningtube-like region (Figure 4).

In particle-tracking microrheology of livingcells, the size of the probing beads is largerthan the average mesh size of the cytoskeleton,typically 50 nm for fibroblasts (62, 63). Hereagain, without applying oscillatory deforma-tions or mechanical stresses to the cytoplasm ofthe cells, the frequency-dependent elastic mod-ulus and viscous modulus can be computed fromthe MSDs of embedded beads. In this case, theviscoelastic moduli can be obtained from theso-called complex modulus, G∗(ω), as (66)

G∗(ω) = 2kB T3πaiωFu[�r2(t)]

, 2.

where Fu[〈�r2(t)〉] is the unilateral Fouriertransform of 〈�r2(t)〉. The above equation canbe solved analytically (65), if we allow thefrequency-dependent elastic modulus to be cal-culated algebraically using the following rela-tionship:

G′(ω) = |G∗(ω)| cos[

πα(ω)2

], 3.

and the amplitude can be approximated as

|G∗(ω)| ≈ 2kB T3πa〈�r2(1/ω)〉�[1 + α(ω)]

. 4.

Here α is the local logarithmic slope of〈�r2(t)〉 estimated at the frequency of interestand � is the gamma function.

Dynamic Viscosity VersusShear Viscosity

The viscous modulus (also called the loss mod-ulus), G′ ′(ω), or alternatively the dynamic vis-cosity, η′ ′(ω) = G′ ′(ω)/ω, and the shear vis-cosity, η, of a material ought not to be confusedwith each other. G′ ′(ω) has units of pressure(Pa or dyne/cm2) and represents the fraction ofthe energy induced by the imposed deforma-tion, which is lost by viscous dissipation as op-posed to stored elastically by the material. In arheometer, it is computed by imposing an oscil-latory deformation of controlled frequency andmeasuring the out-of-phase component of the

frequency-dependent stress induced in the ma-terial. In contrast, the shear viscosity η has unitsof Pa.s and is measured by imposing a steadydeformation of constant rate. It is the ratio ofthe stress induced in the material to the rate ofdeformation.

Here again without applying any externalforces to the cytoplasm, one can compute anapproximate value of its shear viscosity η fromthe frequency-dependent viscoelastic moduli,G′(ω) and G′ ′(ω):

η ≈ G′PτR, 5.

where G ′P is the plateau value of the elastic

modulus G′(ω) at intermediate frequencies (be-tween ωe and ωR), and τR is the inverse of thefrequency ωR at which G′(ω) and G′ ′(ω) areequal (see definitions in Figure 4a,b). Typicalvalues of shear viscosity of the cytoplasm aregiven in Table 1.

Particle-tracking microrheology not onlyshows that the rheology of the cytoplasmis timescale dependent, but also that thefrequency-dependent viscoelastic moduli de-fine a single crossover frequency, ωR, at lowfrequencies (Figure 4b). Below this frequency,the cytoplasm behaves essentially as a viscousliquid. Equivalently, in the time domain, if thecytoplasm were subjected to a step deforma-tion, the time-dependent stress induced in thecytoplasm would adopt a plateau value at inter-mediate timescales, crossing over at a charac-teristic time τR ( = 1/ωR) to a terminal viscousrelaxation at long timescales (15).

Creep Compliance fromParticle-Tracking Measurements

From a rheological point of view, the cy-toplasm is a viscoelastic material. As sug-gested above, the mathematical transformationof the measured time-dependent MSD intofrequency-dependent elastic and viscous mod-uli, G′(ω) and G′ ′(ω), is not trivial (65, 66)(see Equations 2–4). This transformation in-volves Fourier/Laplace integrals that presumethe knowledge of the MSD over an infiniterange of timescales. Therefore, large errors can

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be introduced into the computation of G′(ω)and G′ ′(ω) at low and high frequencies, corre-sponding to the maximum time of capture (atlong timescales) and the rate of image capture ofthe camera for the MSD (at short timescales),respectively. However, the MSD of a bead isproportional to the creep compliance, �(t), ofthe material in which the bead is embedded(114) (Figures 2c and 4a):

�(t) = 3πa2kB T

〈�r2(t)〉. 6.

The creep compliance of a material isits deformability and, in classical rheologicalmeasurements, is obtained by imposing a steadymechanical stress of constant magnitude andmeasuring the resulting deformation of the ma-terial. Here we can compute the creep com-pliance from particle-tracking measurementswithout imposing any deformations.

If we return to the examples of vis-cous liquid and elastic solid described above,then simple substitution of the expressions of〈�r2〉, 〈�r2〉 = (2kB T/3πaη)t and 〈�r2〉 = Kin Equation 6 indicates that the creep compli-ance of a viscous liquid is �(t) = t/η, while thecreep compliance of a highly elastic solid (neg-ligible viscosity) is �(t) = (3πa K/2kB T ) =constant. Therefore, the creep compliance of aviscous liquid is inversely proportional to theshear viscosity, �(t) ∼ 1/η, and the creep com-pliance of an elastic solid is the inverse of thematerial’s elasticity, � = 1/G′, where G′ is aconstant.

All the rheological information about thecytoplasm or the material in which the prob-ing beads are embedded is contained in boththe time dependence of creep compliance andits magnitude (94) (Figure 4a). To illustratethis, we return to the relatively simple exampleof a concentrated suspension of uncross-linkedactin filaments, in which 100-nm-diameterbeads have now been embedded. This beadis larger than the mesh size of the network.Hence the bead is in intimate physical con-tact with the filaments that, for a time, forma cage that confines the bead (Figure 2a). Atshort timescales, the motion of the bead is

dictated by the lateral fluctuations of the fil-aments in contact with the bead (Figure 2b).Hence the MSD of the bead grows with timeas t3/4 (Figure 2c). An ultrafast camera wouldshow that the bead undergoes random, small-magnitude, rapid displacements created by thelateral fluctuations of the confining filaments.At intermediate timescales, the bead does notundergo net motion anymore. A camera cap-turing images at that rate would not captureany net motion of the bead because, at in-termediate timescales, the filaments surround-ing it cannot get out of their confining tube-like region. Finally, at long timescales, thefilaments surrounding the bead can escape theirtube-like regions through large-magnitude lon-gitudinal motion (Figure 2b). Accordingly, thefilamentous cage that was confining the beaddisappears because its constitutive filamentshave moved out of the way. A slow camerawould capture the bead going from cage to cage,undergoing a random walk—albeit at a slowpace set by the high viscosity of the actin fil-ament solution. The MSD of the bead growsproportionally with time, a signature of viscousdiffusion.

PARTICLE-TRACKINGMICRORHEOLOGY OF CELLS

Interstitial Viscosity Versus MesoscaleViscoelasticity of the Cytoplasm

The viscosity of the intracellular space dependscritically on the length scale being probed. Atsmall length scales, the viscosity of the cyto-plasm is essentially that of water [more pre-cisely, 1.2–1.4 times the viscosity of water (27)]or approximately 0.01 P (64, 91). It can be mea-sured by monitoring the diffusion of GFP orsmall fluorescently labeled DNA fragments inthe cell. This interstitial viscosity is a key pa-rameter that controls the transport of smallglobular proteins and it varies slightly for vari-ous cell conditions.

At length scales larger than the effectivemesh size of the cytoskeleton meshwork, theapparent viscosity is much higher, typically

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>10 P, or 1000 times the viscosity ofwater. This effective mesh size can be mea-sured by probing the diffusion of fluorescentlylabeled dextran or DNA inside the cell. Thediffusion of dextran polymers with a gyrationradius of <50 nm within the cytoplasm (of fi-broblasts) is largely unhindered, whereas poly-mers with a gyration radius of >50 nm be-come immobilized (63, 64, 91). At length scaleslarger than the effective mesh size of the cyto-plasm, the viscoelastic moduli and creep com-pliance computed from particle-tracking mea-surements should be independent of the size ofthe probe beads used in the experiments. Thisis readily seen from the expression in Equation1 in the limit case of a viscous liquid: The creepcompliance depends linearly on both bead sizeand MSD, which itself depends inversely onbead size.

The above discussion about how viscoelas-tic parameters of the cytoplasm can be obtainedfrom particle-tracking measurements assumesthat the probing beads are larger than the effec-tive mesh size of the cytoplasm or the networkbeing probed (Figure 4a). We call this viscos-ity mesoscale viscosity, as it describes the rheo-logical properties at length scales intermediatebetween small globular proteins in the inter-stitial space and the whole cell. The mesoscaleviscosity controls the rate of movements of mi-tochondria (53), nuclei (59), and phagosomes(96), as well as viruses, bacteria, and engineereddrug delivery microcarriers (96), because theseentities are larger than the effective mesh size ofthe cytoskeleton. The mesoscale viscosity of thecytoplasm also controls the rates of cell spread-ing and migration (35).

Active Versus Passive Microrheology

Direct injection of the beads into the cyto-plasm (102), as opposed to passive engulfmentof the beads inside the cytoplasm, circum-vents the endocytic pathway and therefore theengulfment of the beads in vesicles tetheredto cytoskeleton filaments by motor proteins(96). These vesicles move toward the nucleus;therefore, the probe beads undergo directed

motion. Although interesting in their ownright, such directed displacements prevent thecomputation of the viscoelastic parameters ofthe cytoplasm from MSDs.

Nevertheless, even in the absence of directedmotion, actomyosin contractility could affectthe movements of beads. Recent work with re-constituted actin filament networks containingmyosin II has shown that in this in vitro sys-tem the movements of beads can be affected10-fold, and even more at long timescales bythe activity of motor proteins (69). Even with-out producing a net movement of the filaments,motor proteins enhance the random move-ments of the beads, akin to an effective >10-fold increase in the temperature of the sys-tem (69). These enhanced movements allow forfaster relaxation of mechanical stresses. Thisresult obtained with purified proteins suggeststhat particle-tracking measurements of the me-chanical properties of the cytoplasm signif-icantly underestimate the values of the vis-coelastic properties of the cytoplasm in livecells.

However, our unpublished results suggestthat reducing or eliminating actomyosin con-tractility in a live cell using either blebbistatin,which blocks the myosin heads in a complexwith low actin affinity (52), or ML-7, whichspecifically inhibits MLCK (myosin light chainkinase), which normally phosphorylates myosinII, has no significant effect on the magnitudeof the displacements of the beads comparedwith control cells. This absence of effect mayresult because myosin II molecules are mostlylocalized to the contractile actin stress fiberslocalized to the ventral side of the cell andthe leading edge and are not present in largequantities in the body of the cell (108), wherebeads used for particle-tracking microrheologyare lodged. Therefore, a direct extrapolation ofresults obtained in vitro with purified proteins,although often instructive of the more complexbehavior of cytoskeleton in cells (79), can bemisleading.

The movements of the cell itself can addan additional contribution to the overall move-ments of the probing beads. The speed of

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adherent cells (7) is typically much lower thanthe speed of the probing beads embeddedin the cytoplasm. Therefore, the movementsof the cell will be felt by the beads embeddedin the cytoplasm only when they are monitoredfor a long time. The contribution of cell move-ments to the overall movements of the beadscan readily be detected by the curvature of theMSDs of the embedded beads. To illustrate thiseffect, we consider the simple case of a viscousliquid. If an overall movement is added to thethermally driven random motion of the bead,then the MSD can be rewritten as (81)

〈�r2〉 = 4Dt + v2t2, 7.

where v is the overall speed of the suspendingliquid. The first term in this expression corre-sponds to the random thermally driven motionof the bead, and the second term correspondsto the motion of the bead imposed by the over-all movement of the liquid. At short timescales,the second term is negligible and we recover〈�r2〉 ≈ 4Dt, i.e., bead movements are domi-nated by viscous diffusion. At long timescales,the second term dominates, 〈�r2〉 ≈ v2t2, cor-responding to a quadratic dependence on time,which is readily observed at long timescales inthe MSD profile. The timescale at which thecrossover between these two regimes occurs(when 4Dt = v2t2) is t = 4D/v2. For instance,for a 100-nm-diameter bead in a 20 P viscousliquid, D ≈ 0.0022 μm2/s, moving at a constantspeed of 5 μm/h (a typical speed for a culturedadherent cell), the crossover time is equal tot = 4D/v2 = 1.3 s, which is readily detectedwhen tracking a bead for 10 s.

Advantages of Particle-TrackingMicrorheology Over Current Methods

Particle-tracking microrheology can measuredirectly the mechanical properties of thecytoplasm because of the intimate contactbetween the probing beads and subcellularstructures (103). In contrast, most currentsingle-cell mechanics methods rely on adirect contact between the cell surface and aphysical probe. For example, AFM probes the

mechanical properties of cells using softcantilevers (41); magnetocytometry (106,111) measures cell mechanics by subjectinglarge beads coated with extracellular matrixmolecules bound to cell receptors to rotationalmovements. These methods cannot distinguishthe contribution of the plasma membrane fromthe combined response of the nucleus and thecytoplasm without making drastic assumptions.If two elastic elements of different stiffness areconnected to one another (here the nucleusand the cytoskeleton), their total response isdominated by the stiffer element. Therefore,methods such as AFM, magnetocytometry,or micropipette suction probe the combinedresponse of the nucleus and cytoplasm, evenwhen the probe is positioned far away fromthe nucleus. In contrast, particle-trackingmicrorheology, which relies on the smallestenergy possible—thermal energy—is a highlylocalized measurement inside the cytoplasm.

Unlike most other approaches to cell me-chanics, particle-tracking microrheology mea-sures frequency-rate-dependent viscoelasticmoduli, G′(ω) and G′ ′(ω). This is particu-larly crucial for the cytoskeleton, which be-haves like a liquid at long timescales (or lowrates of shear) and like an elastic solid atshort timescales (or high rates of shear). Thefrequency-dependent mechanical response ofthe cytoplasm of a live cell can be measured inabout 10 s by particle-tracking microrheology,at least for timescales relevant to cell motility. Incontrast, AFM measurements may take up to 1 hfor high-resolution mechanical measurements(82). Such time-consuming measurements can-not capture fast subcellular dynamics and areunsuitable for motile cells.

Particle-tracking microrheology requiresshort times of data collection, typically 10–20 s,to measure frequency-dependent viscoelasticmoduli over two decades in frequency (ortimescales). This is not the case for otherparticle-tracking methods for which the cor-related motion between two particles is usedinstead of the motion of individual parti-cles as a probe of local cytoplasmic rheology(13). These methods are inappropriate for the

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measurement of the mechanical properties oflive cells because they incorrectly assume thatthe intracellular milieu is homogeneous andstatic. Furthermore, to obtain statistically sig-nificant data, measurement times are on the or-der of 30–60 min, timescales for which migrat-ing cells cannot be assumed to be stationary.

By tracking multiple beads simultaneously,microrheology can measure simultaneously themicromechanical responses to stimuli in vari-ous parts of the cell. This is particularly im-portant because the viscoelastic properties canvary by more than 2 orders of magnitudewithin the same cell (51, 102, 103). By usingvideo-based, multiple-particle tracking insteadof laser-deflection particle tracking (65, 116),hundreds of beads embedded in the cytoplasmcan be tracked at the same time.

Particle-tracking microrheology measure-ments of the cytoplasm of live cells are typi-cally conducted using carboxylated polystyrenebeads or polyethylene glycol (PEG)-coatedbeads. The rheology of reconstituted actin fil-ament networks or DNA solutions measuredby particle-tracking microrheology and usingthese beads is quantitatively similar to thatmeasured by rheometry (75, 114). This indi-cates that the presence of the beads in poly-mer networks does not affect the global me-chanical properties of the networks. Moreover,our unpublished results show that carboxy-lated polystyrene beads or PEG-coated beadsyield the same frequency-dependent viscoelas-tic moduli for the cytoplasm of fibroblasts, butnot for amino-modified beads (102). Finally,the proximity of some of the beads to theplasma membrane will not significantly affectthe movements of the beads because hydrody-namic interactions caused by the movements ofthe beads and reflecting off the membrane areeffectively screened by the cytoskeleton mesh(21, 116). Subcellular organelles can also beused as probing particles (40, 86, 116). How-ever, because their interactions with subcellu-lar structures are ill-defined, only the frequencydependence of the viscoelastic moduli is mean-ingful, at least at high frequency, not the abso-lute value of moduli.

Microrheological measurements are abso-lute and compare favorably with traditionalrheometric measurements of standard fluids ofknown viscosity and elasticity (2, 65, 112, 114).This is not the case of some single-cell ap-proaches that rely on a direct physical contactbetween the cell surface and the probe (suchas a cantilever or a macroscopic bead). For in-stance, the apparent viscoelastic moduli mea-sured by magnetocytometry and AFM dependgreatly on the type of ligands coated on themagnetic beads or the AFM cantilever. Extra-cellular matrix ligands—including fibronectinor RGD peptide—coated onto magnetic beadsand AFM cantilevers lead to vastly different val-ues of (apparent) cell stiffness. Therefore, themeasurements of viscoelastic properties of stan-dard materials using these methods cannot bereadily compared with those obtained using arheometer. Furthermore, particle-tracking mi-crorheology measures both elasticity and vis-cosity, whereas many other approaches cannotdirectly distinguish the elastic response fromthe viscous response of the cell.

Importantly, values of shear viscosity andelastic moduli of the cytoplasm in live cellsmeasured by particle-tracking microrheology(Table 1) are similar to those measured inreconstituted actin filament networks in thepresence of cross-linking/bundling proteins(Table 2). The elasticity of live cells, such asmouse embryonic fibroblasts or human umbili-cal vein endothelial cells (HUVECs), which arecommonly used as models of cell biology, andof reconstituted actin filament networks are onthe order of tens of Pascal (hundreds of dyneper cm2). This is in striking contrast to valuesof cell elasticity obtained using AFM, whichis of the order of hundreds and even thou-sands of Pascal (82). To our knowledge, no actinfilament network reconstituted in vitro thatcontains a physiological concentration of actinpolymerized in the presence of cross-linkingand bundling proteins and under mechanicaltension (which can further increase the networkelasticity) reaches these high levels of elastic-ity (99). The discrepancy between values of cellelasticity measured by AFM and those obtained

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Table 2 Viscosity and elasticity of common liquids and cytoskeletal filament networks measured bya cone-and-plate rheometer

Type of material; values ofviscoelastic parameters Average viscosity (poise)

Average elasticity at1 rad/s (dyne/cm2) Reference

Water 0.01 0 –Blood 0.1 Negligible –Glycerol ∼1 Negligible –Corn syrup ∼20 Negligible –Ketchup ∼500 Negligible –Jell-O Negligible 1,000 –Polyacrylamide gel – 500 (26)F-actin network – 8 ± 3 (113)F-actin + filamin – 450 ± 60 (99)F-actin + α-actinin – 120 ± 20 (113)F-actin + Arp2/3 complex/WASp – 60 ± 15 (105)F-actin + fascin – 80 ± 10 (101)F-actin + fimbrin – 300 ± 30 (48)Vimentin network – 14 ± 2 (23)

aMeasurements are mean ± sem. The elasticity was measured at a shear amplitude of 1% and a shear frequency of 1 rad/s.Shear viscosity of the F-actin and vimentin networks was not measured because these filaments break under continuousshear.bThe concentrations of actin and vimentin solutions are 24 μM. The concentrations of α-actinin, fascin, fimbrin, andfilamin in solutions are 0.24 μM. The concentration of the Arp2/3 complex is 0.12 μM and that of its activator WASp is0.06 μM. The concentration of acrylamide and bis-acrylamide in the polyacrylamide gel is 0.04% and 0.05%, respectively.Unit conversions are 1 P = 0.1 Pa.s; 1 dyne/cm2 = 0.1 Pa.

with actin filament networks by conventionalrheometry or particle-tracking microrheologyremains unexplained.

Applications of particle-tracking microrhe-ology discussed in the Introduction were ren-dered possible thanks to the replacement ofmanual microinjection of beads into cells withballistic injection (61, 76, 77). In a single bal-listic injection, the number of injected cellsamenable to measurements increases 1000-fold compared with conventional microinjec-tion (61, 77). With a large sample size percondition (typical number of probed cells is∼30), particle-tracking microrheology resultsbecome more precise and significant. Ballis-tic transfer of beads to the cytoplasm coupledwith particle tracking (named ballistic injectionnanorheology, or BIN) provides a more preciseand consistent value for global and local vis-coelastic properties.

Illustrative Example ofParticle-Tracking Microrheologyof Living Cells

In typical measurements of cell mechanics (e.g.,AFM) (82–84), it is assumed that the nucleusand the cytoplasm contribute independently toglobal cell stiffness. This assumption is an over-simplification that overlooks the existence ofcritical functional links between the nucleus andthe cytoskeleton. These connections are estab-lished by specific linker proteins located at thenuclear envelope, including the LINC complex(10), and they physically connect the filamen-tous nuclear lamina underneath the nuclear en-velope to the actin/microtubule/intermediatefilament cytoskeleton in the cytoplasm. Thesephysical connections between nucleus and cy-toskeleton are as important to cell mechanics asthe intrinsic mechanical properties of the nu-cleus and the cytoskeleton themselves. Indeed,

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when these functional links are disrupted, theelasticity of the cytoplasm is drastically reduced;the magnitude of this reduction is as importantas when the actin cytoskeleton is completelydisassembled with drugs (60).

Particle-tracking microrheology shows thatthe loss of the LINC complex dramatically af-fects the ability of cells to resist mechanicalshear forces (95). Mutations scattered alongLmna, which encodes A-type lamins, have been

associated with a broad range of human diseasescollectively called laminopathies (4, 8, 9, 33,42, 71). These diseases involve either specificor combined pathologies of neurons, muscle,and bone tissue (4, 42). Cytoplasmic fragilityas measured by particle-tracking microrheol-ogy correlates with the loss of the LINC com-plex from the nuclear envelope in cells derivedfrom mouse models of laminopathy (37, 60, 95)(Figure 5).

10–2

10–3

b10–1

MS

D <

Δr2

(τ)>

(μ

m2)

c Healthy cell Laminopathic cell

Softness detected

Defunctnucleocytoskeletalconnection

Cytoplasm

Nucleus

Actin

No resistance

Force

Stiffness detected

Resistance

Force

MAF WT

MAF LmnaL530P/L530P

10–2 10–1 100 101

Time lag τ(s)

MAF LmnaL530P/L530PMAF WT

20 μm

0.1 μm

a

Figure 5Intracellular microrheology of laminopathic fibroblasts. (a) Fluorescent 100-nm-diameter polystyrene beads are ballistically injectedinto wild-type (WT) (left panel ) and LmnaL530P/L530P (right panel ) mouse adult fibroblasts (MAFs), derived from a mouse model ofprogeria. Fluorescent micrographs of beads (outlined in white circles) are superimposed onto phase-contrast micrographs of cells.Representative trajectories of nanoparticles are shown at the top right of each micrograph (inset). (b) Ensemble-averaged mean squareddisplacements (MSDs) of the beads embedded in the cytoplasm of WT (blue curve) and LmnaL530P/L530P (red curve) MAFs are shown.(c) Model for the intracellular mechanics of healthy and laminopathic cells. Healthy cells in which the nucleocytoskeletal connectionsare intact can resist forces of large magnitude, whereas laminopathic cells cannot resist such forces because of defunctnucleocytoskeletal connections. Modified with permission from Reference 37.

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SUMMARY POINTS

1. The viscoelastic properties of the cytoplasm and nucleoplasm control key cell functions,including cell motility, cell adhesion, and the regulated movements of organelles.

2. Particle-tracking microrheology can measure the viscoelastic properties of living cellswithout subjecting them to applied forces. In this approach, fluorescent submicron beadsare injected directly into the cytoplasm of live cells. These beads rapidly disperse through-out the cytoplasm and are subsequently tracked by fluorescence microscopy. Analysis ofthe recorded movements of the beads transforms the MSDs of the beads in terms ofeither viscosity and elasticity or the compliance of the cytoplasm.

3. Particle-tracking microrheology can reveal the micromechanical properties of cells inmore physiological environments, such as a 3D extracellular matrix or inside an embryo,better than traditional approaches to cell mechanics.

4. Particle-tracking microrheology measurements, which are fast, acknowledge that themechanical properties of the cytoplasm are spatially variable and depend on timescale.

5. Particle-tracking microrheology reveals the reduced ability of cells from mouse modelsof laminopathies to resist mechanical shear forces.

FUTURE ISSUES

1. The levels of viscosity, elasticity, and compliance of the cytoplasm, as measured byparticle-tracking microrheology, should be tested to determine whether they can serveas reliable diagnostic markers of disease, in particular cancer and laminopathies.

2. To circumvent the need of beads to probe cytoplasmic microrheology, exogenous beadsshould be rationally replaced with endogenous subcellular markers.

3. Researchers should assess quantitatively the role of motor proteins (e.g., myosins) onthe movements of beads lodged in the cytoskeleton of living cells and therefore thecomputation of viscoelastic parameters.

4. Can the wide range of phenotypes associated with human laminopathy be explained bythe differential mechanical response at the cellular level?

5. A high-throughput device based on particle-tracking microrheology would allow themethod to become a diagnostic tool for human disease.

6. Particle-tracking microrheology should be extended to in vivo measurements.

DISCLOSURE STATEMENT

The author is not aware of any biases that might be perceived as affecting the objectivity of thisreview.

ACKNOWLEDGMENTS

The author thanks Yiider Tseng, Thomas P. Kole, Jerry S.H. Lee, Porntula Panorchan, Brian R.Daniels, and Melissa S. Thompson for key contributions to the development of particle-tracking

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microrheology and its applications in cell biology, as well as Didier Hodzic, Christopher M. Hale,Shyam B. Khatau, Philip Stewart-Hutchinson, and Colin L. Stewart, who contributed to the workon nucleocytoskeleton protein linkers. The author also thanks members of the Wirtz group forreading and editing the manuscript. Work in the author’s laboratory is supported by the NationalInstitutes of Health (NIGMS, NIBIB, and NCI), the Howard Hughes Medical Institute, and theAmerican Heart Association.

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Annual Review ofBiophysics

Volume 38, 2009Contents

FrontispieceSunney I. Chan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �xii

A Physical Chemist’s Expedition to Explore the Worldof Membrane ProteinsSunney I. Chan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Crystallizing Membrane Proteins for Structure Determination:Use of Lipidic MesophasesMartin Caffrey � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �29

Advances in Imaging Secondary Ion Mass Spectrometryfor Biological SamplesSteven G. Boxer, Mary L. Kraft, and Peter K. Weber � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �53

Controlling Proteins Through Molecular SpringsGiovanni Zocchi � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �75

Electron Crystallography as a Technique to Study the Structureon Membrane Proteins in a Lipidic EnvironmentStefan Raunser and Thomas Walz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �89

Nuclear Envelope Formation: Mind the GapsBanafshé Larijani and Dominic L. Poccia � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 107

The Interplay of Catalysis and Toxicity by Amyloid Intermediateson Lipid Bilayers: Insights from Type II DiabetesJames A. Hebda and Andrew D. Miranker � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 125

Advances in High-Pressure Biophysics: Status and Prospectsof Macromolecular CrystallographyRoger Fourme, Eric Girard, Richard Kahn, Anne-Claire Dhaussy,

and Isabella Ascone � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 153

Imaging Transcription in Living CellsXavier Darzacq, Jie Yao, Daniel R. Larson, Sébastien Z. Causse, Lana Bosanac,

Valeria de Turris, Vera M. Ruda, Timothee Lionnet, Daniel Zenklusen,Benjamin Guglielmi, Robert Tjian, and Robert H. Singer � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 173

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A Complex Assembly Landscape for the 30S Ribosomal SubunitMichael T. Sykes and James R. Williamson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 197

Mechanical Signaling in Networks of Motor and Cytoskeletal ProteinsJonathon Howard � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 217

Biochemical and Structural Properties of the Integrin-AssociatedCytoskeletal Protein TalinDavid R. Critchley � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 235

Single-Molecule Approaches to Stochastic Gene ExpressionArjun Raj and Alexander van Oudenaarden � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 255

Comparative Enzymology and Structural Biology of RNASelf-CleavageMartha J. Fedor � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 271

Particle-Tracking Microrheology of Living Cells: Principlesand ApplicationsDenis Wirtz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 301

Bioimage Informatics for Experimental BiologyJason R. Swedlow, Ilya G. Goldberg, Kevin W. Eliceiri, and the OME Consortium � � � � 327

Site-Directed Spectroscopic Probes of ActomyosinStructural DynamicsDavid D. Thomas, David Kast, and Vicci L. Korman � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 347

Lessons from Structural GenomicsThomas C. Terwilliger, David Stuart, and Shigeyuki Yokoyama � � � � � � � � � � � � � � � � � � � � � � � � � 371

Structure and Dynamics of Membrane Proteins by Magic AngleSpinning Solid-State NMRAnn McDermott � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 385

Index

Cumulative Index of Contributing Authors, Volumes 34–38 � � � � � � � � � � � � � � � � � � � � � � � � � � � 405

Errata

An online log of corrections to Annual Review of Biophysics articles may be found athttp://biophys.annualreviews.org/errata.shtml

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erso

nal u

se o

nly.