the biophysics of 3d cell migration - johns hopkins university

BB47CH25_Wirtz ARI 21 April 2018 8:42

Annual Review of Biophysics

The Biophysics of3D Cell MigrationPei-Hsun Wu,1 Daniele M. Gilkes,1,2

and Denis Wirtz1,2,3

1Department of Chemical and Biomolecular Engineering, Johns Hopkins Physical Sciences inOncology Center, Institute for NanoBioTechnology, Johns Hopkins University, Baltimore,Maryland 21218, USA; email: [email protected], [email protected], [email protected] of Oncology, The Sidney Kimmel Comprehensive Cancer Center, Johns HopkinsUniversity School of Medicine, Baltimore, Maryland 21205, USA3Department of Pathology, Johns Hopkins University School of Medicine, Baltimore,Maryland 21205, USA

Annu. Rev. Biophys. 2018. 47:549–67

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

https://doi.org/10.1146/annurev-biophys-070816-033854

Copyright c© 2018 by Annual Reviews.All rights reserved

Keywords

3D migration, motility, focal adhesions, actin protrusions, random walk,extracellular matrices

Abstract

Three-dimensional (3D) cell culture systems have gained increasing interestnot only for 3D migration studies but also for their use in drug screening,tissue engineering, and ex vivo modeling of metastatic behavior in the fieldof cancer biology and morphogenesis in the field of developmental biology.The goal of studying cells in a 3D context is to attempt to more faith-fully recapitulate the physiological microenvironment of tissues, includingmechanical and structural parameters that we envision will reveal more pre-dictive data for development programs and disease states. In this review,we discuss the pros and cons of several well-characterized 3D cell culturesystems for performing 3D migration studies. We discuss the intracellularand extracellular signaling mechanisms that govern cell migration. We alsodescribe the mathematical models and relevant assumptions that can be usedto describe 3D cell movement.

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https://www.annualreviews.org/doi/full/10.1146/annurev-biophys-070816-033854


Contents

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550HOW IS 3D DEFINED FOR 3D MIGRATION STUDIES? . . . . . . . . . . . . . . . . . . . . . . 551EXTRACELLULAR DETERMINANTS OF 3D CELL MIGRATION. . . . . . . . . . . . 553CELLULAR DETERMINANTS OF CELL MIGRATION . . . . . . . . . . . . . . . . . . . . . . . 555

Focal Adhesion Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555Cytoskeleton Proteins, Lamina, Nucleus, and LINC Complexes . . . . . . . . . . . . . . . . . . 556Lamellipodium Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557

THE ROLE OF CELL DENSITY IN 3D CELL MIGRATION . . . . . . . . . . . . . . . . . . . 557ASSESSING CELL MOVEMENT IN 3D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

Analysis of 3D Cell Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560The Persistent Random Walk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560The Anisotropic Persistent Random Walk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

INTRODUCTION

Cell movement is a crucial physiological process involved in life and death events. During embry-onic development, motility is required to appropriately shape tissues and organs (61, 81, 85, 87)and is indispensable for wound healing (14, 70) and immune responses (35, 58, 65). In cancer, cellmovement drives the spread of cells from a primary tumor site throughout the body to distantorgans in a process termed metastasis (39, 82, 106, 110). Cell movement in development and dis-ease typically takes places in three-dimensional (3D) environments, which consist of either a 3Dextracellular matrix (ECM) (e.g., the stromal matrix that surrounds the primary tumor in cancer),a liquid (e.g., circulating tumor cells in blood), or other cells (e.g., glioblastoma multiform cellsinvading 3D brain tissues containing neurons and glial cells).

However, cell migration has historically been studied exclusively on two-dimensional (2D)tissue culture surfaces (Figure 1) (87). This is partly due to convenience: Two-dimensional culturedishes allow for the use of standard cell-biology imaging methods, including high-resolutionlight and electron microscopy of fixed and live cells, superresolution microscopy of labeled cells,atomic-force microscopy to probe cell mechanics, immunoblotting, quantitative polymerase chainreaction, and gene and RNA sequencing. Decades of cell-migration studies using 2D models haveunraveled the importance of molecules such as the small GTPase Rac1 and cell-division controlprotein 42 (Cdc42), which control activation of the actin nucleator Arp2/3 complex to form thebranched filamentous actin (F-actin) networks that result in lamellipodial protrusions (22, 57,68, 78, 99). Small clusters of integrin adhesion molecules coalesce at the extended lamellipodialtips and at the ventral side of adherent cells and are connected via the small GTPase RhoA(Ras homolog gene family, member A) to myosin-containing actin (actomyosin) stress fibers (23,109).

The study of migration in 3D is much more complex than studies in 2D (Figure 1) andtypically involves the design and utilization of 3D matrices as a scaffold for cell movement aswell as mathematical models to analyze cell movements. The realization that 3D migration, whilerequiring a similar repertoire of proteins, may be governed by an entirely different set of principleshas transformed the field of cell motility (30, 78).

550 Wu · Gilkes ·Wirtz

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a b

Figure 1Morphology and mode of migration of a mesenchymal cell placed (a) on a two-dimensional (2D) dish and (b) inside a filamentouscollagen matrix. Cells on a dish typically show a wide and thin lamellipodium at their leading edge and contain a dense actin filamentnetwork (112). The nucleus is located at the back of the cell (66). In the absence of chemotactic gradients, cells on dishes undergorandom migration with relatively high speed and short persistence (13). Cells inside a matrix display dendritic protrusions: thick motherprotrusions that prolong the centrally positioned nucleus and that are terminated by dendritic daughter protrusions that climb andretract dynamically along the collagen fibers to produce forces of migration (40). Actin-cap fibers, which are mechanically connected tothe nuclear envelope and lamina via LINC (linker of nucleoskeleton and cytoskeleton) complexes, provide mechanical support to themother protrusions and form a corona of parallel fibers that surround a core of densely packed parallel microtubules (10, 50, 51). In adense collagen matrix, the nucleus has to be actively squeezed to fit the small pores of the matrix (31, 111). In contrast to cells on a 2Ddish, cells in a collagen matrix undergo a highly persistent mode of migration at relatively low speed.

HOW IS 3D DEFINED FOR 3D MIGRATION STUDIES?

Mesenchymal cells in vivo typically are found in 3D matrices. A thin (50–200-nM) basementmembrane surrounds most epithelial cells and vasculature and provides an essential barrier layerseparating the epithelium from the interstitial matrix (101). The interstitial ECM is localizedbeyond the basement membrane and is composed predominantly of fibrillar collagens (such astype I collagen) supplemented by various proteoglycans and glycoproteins such as fibronectin,laminin, and tenascin (32, 44, 64, 79). Given the complex composition of the ECM in mammals,the investigation of cells migrating in their most native context, in vivo, could be considered as theoptimal choice to study cells and has been successfully used to image cells migrating on collagenfibers in vivo (33, 89). Imaging of live animals at microscopic resolution [intravital microscopy(IVM)] represents a powerful tool for addressing such questions. IVM can reveal cellular responsesover time and space and can be conducted under conditions closely approximating those of a naturalenvironment (80). In the early 1980s, zebrafish began to be utilized for in vivo imaging experiments(98). Zebrafish embryos develop quickly ex utero and are transparent, making them a perfectsubject to be studied with an optical microscopy such as confocal laser scanning microscopy anddifferential interference contrast (DIC) microscopy. Zebrafish provide an excellent model systemfor studies of genetics and embryogenesis. Individual cells can be labeled and followed during thecourse of development. Furthermore, unlike any other model organism, the zebrafish is particularlysuited for single-cell transplantation experiments that allow the properties of modified cells to bemonitored in their natural environment (48).

Progress in fluorescence labeling and detection—and the ability to image at greater depthsfor more extended periods of time and over larger tissue areas—has allowed the use of IVM inmice for the study of 3D migration. However, there are several issues that limit the utility of in-travital imaging experiments. First, intravital imaging experiments require expensive, specialized

www.annualreviews.org • The Biophysics of 3D Cell Migration 551

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equipment, including a dedicated confocal microscope with a multi-photon laser, long-distanceobjectives with high numerical apertures, and a stage top to house an anesthetized animal. More-over, the migrating cells of interest must be fluorescently tagged for in vivo monitoring (15, 117).Experimental parameters such as gene expression cannot easily be perturbed in a live mouse,making the mechanistic understanding of cell response to particular features of 3D environmentchallenging. No doubt, large-scale screening efforts cannot be conducted in this context (2, 47).These constraints and the need for high-throughput assays that have greater physiological rele-vance have resulted in the need for in vitro models that have increased complexity and that considerthe constituents and spatial constraints of cells in vivo.

To measure migration in a 3D environment, each cell should be fully embedded in a biocom-patible 3D material that is a semisolid (i.e., more elastic than viscous even at long timescales)but porous enough to allow access for nutrients from the cell culture medium to reach the cell(62). Additional considerations of the gel/matrix used for 3D motility studies include molecularcomposition, density, degree of fiber orientation, degree of cross-linking, and even the ability ofthe material to concentrate and/or present growth factors (41, 44). Table 1 describes the prosand cons of the most commonly reported 3D matrices used for 3D migration studies in vitro.In addition to the 3D culture systems described in Table 1, many laboratories utilize microflu-idic devices or microfabricated channels to model the confined spaces that cells encounter in the

Table 1 Three-dimensional matrices used for cell motility studies

Matrix Pros Cons

Collagen gels (<1 kPa) Widely used for 3D migration studiesCollagen is the major constituent of the ECMand is biocompatible with all cell types

Altering the gel stiffness can be achieved byadjusting the concentration of collagen

Somewhat tunable fiber orientationEnzymatically degradablePresents native cell adhesion ligands

Difficult to tune stiffness without modulatingporosity and the number of cellular binding sites

Difficult to distinguish the biomechanicalcontribution from biochemical affinity

Hyaluronic acid gel system(0.25–5 kPa)

HA is an ECM component in several tissue typesStiffness can be modulated independently ofadhesion strength by adjusting cross-linking

Wide variety and high degree of potentialchemical modification

Not compatible with all cell typesMust be modified with adhesive ligands to permitcell attachment

Gels feature a high density with minimal porescompared with a natural ECM

Polyethylene glycolhydrogels

Can be engineered to present different adhesiveligands and to degrade via passive, proteolytic,or user-directed modes

Stiffness can be easily tuned

Synthetic materialMaterial must be modified to incorporate MMPdegradation during migration

Basement membrane gels Derived from natural materialsMimics the basement membrane composition

Not readily manipulatedNot tunable and lacks a fibrillary architecture

Electrospun polymericnanofibers

Ability to generate micro-/nanoscale fibers Manufacturing challenges in controllingdiameter, spacing, and alignment

Cell-derived matrix Uses tissue-specific fibroblastsAllows the fibroblasts to assemble and deposittheir native ECM components

Fibrillary structure

Cells are not fully embedded in a true 3Dstructure

Abbreviations: 3D, three-dimensional; ECM, extracellular matrix; HA, hyaluronic acid; MMP, matrix metalloproteinase.


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0 min 60 min 120 min

x y

z

Figure 2Reconstructed three-dimensional (3D) views of MDA-MB-231 breast cancer cells embedded in 3D matrigelshow dynamic protrusions. MDA-MB-231 cells visualized by exogenous expression of green fluorescentprotein. Real-time volume imaging with size of 204 μm × 204 μm × 60 μm (x, y, and z direction) wasacquired using swept-field confocal microscopy. Speckles in images are coembedded 200-nm fluorescentbeads. Volume images of cell were deconvoluted and visualized by NIS-Elements software.

3D microenvironment. A recent review covers the use of microfluidics to assess cell motility inconfined environments (56).

Unless otherwise stated, the 3D migration studies discussed in this review have been conductedin collagen gels. Collagen is the primary organic constituent of native tissues. Type I collagen isthe most abundant protein in the ECM, making it an attractive choice for 3D migration studies(7, 107). Type I collagen is readily available from numerous vendors, including BD Biosciences,Advanced BioMatrix, and Flexcell. Important to note is that collagen used in hydrogels can bederived from solutions of acid- or pepsin-solubilized type I collagen sourced from rat tail tendon(27). Acid-extracted rat tail collagen retains the noncollagenous N- and C-terminal telopeptidedomains that allow cross-linking of lysine residues and the formation of fibrils that mimic theinterstitial matrix. Pepsin extraction of collagen causes the removal of telopeptide regions requiredfor fibrillary collagen formation. Therefore, gels derived from pepsin-extracted collagen lack afibrillar architecture that is typically found in the instrastitial matrix of mammalian tissue (26, 27).

To fully embed cells in a 3D collagen matrix (Figure 2), a common procedure is to mix cellswith acid-extracted collagen diluted in cell culture medium at a concentration of 1–5 mg/mL (30).Sodium hydroxide is quickly added to raise the pH of the mixture. The cells/collagen mixture isthen incubated at 37◦C to initiate collagen fibril self-assembly, which usually occurs within 30 min.Temperature can critically affect hydrogel architecture, with lower gelation temperatures leadingto the formation of larger fibrils (21, 31). Changes in hydrogel microstructure can significantlyinfluence cell behavior and in turn play a deterministic role in setting the pace and persistence of3D cell migration.

EXTRACELLULAR DETERMINANTS OF 3D CELL MIGRATION

Several key biophysical parameters of 3D type I collagen gels play a role in 3D migration, inparticular the mechanical properties (both viscous and elastic moduli), the pore size, the densityand orientation of RGD (Arg-Gly-Asp) ligands presented by the collagen fibers, and the localdirection of the fibers that make up the matrix. All these parameters have been implicated in 3Dcell migration (86). Recent work by several groups shows a correlation between cell-migrationspeed and pore size, which makes a priori physical sense: the smaller the pore size, the largerthe frictional steric resistance to cell movements and the more difficult it would be for the cell toproduce the necessary productive forces for net migration (22, 111). Work in several groups has alsoshown that, as in the 2D case (11), cancer-cell migration is positively correlated with the apparentstiffness of the tumor and associated stromal matrix (28, 36, 84). Clinical studies from breast cancer


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patients revealed a link between tissue density and the risk of breast cancer occurrence (6, 69). Usingatomic force microscopy, Weaver and colleagues (1) have also shown that the apparent stiffness offreshly obtained breast carcinoma tumors correlates with more invasive tumors and worse clinicaloutcomes. Recapitulation of 3D cell migration using biomimetic matrices composed of syntheticpolymers seems to confirm that cells migrate more rapidly in stiff matrices similarly to the 2Dcase (24, 60). Such synthetic matrices offer the advantage of eliminating possible confoundingfactors such as pore size and fiber alignment of reconstituted collagen matrices to focus on thepotential effect of matrix stiffness on 3D cell migration. Several groups have highlighted a role forintratumoral hypoxia (regions of low oxygen concentrations within the tumor) in promoting tumormatrix stiffness by enhancing collagen biogenesis through different mechanisms (17, 25, 36–38).

Recent work by Fraley et al. (31), however, reveals a more nuanced picture of the extracellulardeterminants of cell migration. The speed and persistence of migration of various types of cancercells were measured in matrices of increasing collagen content. Increasing collagen concentrationcan have many consequences besides increasing ligand presentation to the embedded cells. In-terestingly, cell speed and distance traveled (over a finite time) showed a U-shaped relationshipwith collagen content in the matrix: Cell speed is high at low and high collagen concentrationsbut low at an intermediate concentration. As expected, pore size steadily diminishes for increasingconcentrations. Hence, in a collagen matrix, the correlation between pore size and cell speed israther limited when probed over a wide range of concentrations. Moreover, matrix stiffness showsa highly nonlinear dependence with collagen concentration: The elasticity of the matrix is rela-tively high at low concentration and decreases and then re-increases for increasing concentration.This is due to the fact that a collagen I solution kept in soluble form on ice and subjected to a rapidthaw at 37◦C will induce the formation of a so-called frustrated polymer network system, at leastat high collagen concentrations. At low collagen concentrations, there are only few nucleationcenters, leading to the proper assembly of collagen I into long, thick fibers, which readily entangleto form a stiff network. At an intermediate collagen concentration, however, the multiplication ofnucleating centers leads to the formation of much shorter fibers and, therefore, of a (frustrated)soft polymer gel. At higher concentrations, despite a high number of nucleating centers, fibers canform and eventually align one another locally owing to nematic-like steric forces. These differentpolymer structures correspond to a stiffness that does not track cell speed. In other words, cellspeed displays a poor correlation with matrix stiffness.

The best predictor of cell speed in a pure collagen matrix is fiber alignment. Fiber alignmentcan be measured through Fourier analysis of confocal reflection micrographs with a thresholdsize equal to the size of the cell (3). This threshold is set up to take into account the fact thatpolymer alignment depends on the length scale of observation: Any reticulated network made ofentangled rigid polymer show high directionality (nonrandomness in orientation) at small lengthscales (smaller than the distance between polymer entanglements) and low directionality (i.e.,randomness in orientation) at larger length scales. Further validation, through the use of cross-linking proteins added to collagen I polymer solutions, strengthens the correlation between cellspeed and local fiber directionality and confirms the poor correlation between cell speed andpore size/matrix stiffness. Work by the Keely lab (16) indicates a strong correlation betweencollagen fiber alignment oriented perpendicular to the tumor boundary, as measured by secondharmonic generation imaging of the backscattered signal generated by collagen, and survival inbreast cancer patients. It is tempting to speculate that the aligned collagen at the tumor boundaryacts as a highway for cancer cells to invade adjacent normal tissue.

Matrix microstructure also profoundly influences the mode of migration of cells in a 3D matrix.At sufficiently low collagen concentrations, when the matrix pore size is larger than the nucleusof the migrating cell, matrix proteolysis by metalloproteinases (MMPs) is not critical and cells


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undergo an amoeboid mode of migration, whereby the cell moves through the matrix pores viashape changes (42, 111). At higher (more physiological) concentrations, the pore size is significantlysmaller than the nucleus of the cell. In this case, cell movements largely rely on local digestion ofcollagen I and undergo an amoeboid mode of migration. Accordingly, treatment of cells embeddedin a 3D matrix of low collagen content by MMP inhibitors does not significantly affect cellmigration, but blockade of MMPs will readily stop migration of the same cells in matrices of highcollagen content (31, 111).

CELLULAR DETERMINANTS OF CELL MIGRATION

In addition to the contributions imposed by the ECM in 3D cell migration, intracellular forcesalso play a major role. Integrins are α/β heterodimers that function to relay external forces intointernal signals. The role of integrin activation in focal adhesion (FA) assembly and in initiatingdownstream signaling has been extensively investigated (55, 108). FAs are integrin-containing,multi-protein structures that form mechanical links between intracellular actin bundles and theextracellular substrate in many cell types. In 3D substrates, actin protrusions form and drivemigratory behaviors. The section below discusses the role of important cellular proteins thatcontrol 3D migration.

Focal Adhesion Proteins

FAs are discrete protein complexes that form at the ventral surface of mesenchymal cells placedon culture dishes. They mediate adhesive connections between the underlying matrix and theactin cytoskeleton for fast signaling between the extracellular milieu and the genome throughLINC (linker of nucleoskeleton and cytoskeleton) complexes. LINC complexes are composed ofnesprins (nuclear envelope spectrin repeat proteins) that contain an actin-binding domain andSUN (Sad1 and UNC-84) proteins that bind the nuclear lamina, a dense polymer meshwork thatlies underneath the nuclear envelope. FAs contain tens of structural, scaffolding, and signalingproteins (74, 95). Through loss-of-function studies, a myriad of FA proteins, including talin,vinculin, FAK (focal adhesion kinase), p130Cas, and zyxin, have been implicated in the regulationof 2D cell migration, mechanosensing (ability of cells to sense different matrix stiffness), andmechanotransduction (the ability of cells to transduce mechanical forces to their genome) (30).Clustering of these FA proteins enhances cell adhesion to the ECM and signaling between thematrix and the cell, but the relationship between FA protein clustering and cell speed is nonlinear(52, 53). While FA shape and number do not predict cell migration, 2D cell speed and persistence,both, first increase and then decrease with the size of FAs.

Systematic depletion of FA proteins and assessment of cell behavior in a 3D matrix paint adifferent picture (30, 31). For instance, the depletion of zyxin decreases cell migration on dishes, butit induces remarkable periodic migratory excursions in a 3D matrix. Indeed, there is no correlationbetween 2D cell speed/persistence and 3D cell speed/persistence when FA proteins are depleted.Likewise, reducing the level of α5β1 integrin expression on the surface of breast carcinoma cellsusing a short hairpin RNA (shRNA)-mediated approach only modestly reduces migration on 2DFN-coated surfaces but has a major effect on migration in 3D collagen-fibronectin gels (46).Visualization of FA proteins, including integrins, in matrix-embedded cells suggests clustering ofFA proteins but in smaller and fewer FAs. However, the glass coverslip required for high-resolutionmicroscopy (high numerical aperture, short working distance) to visualize FAs can influence cellphysiology, as the cell can sense the presence of the coverslip through collagen-mediated tractionforces (67, 93).


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FA proteins readily regulate the ability of cells in a 3D matrix to form mother and daughterdendritic protrusions. The effect of FA protein depletion on dendritic branching of protrusionspredicts cell speed in a 3D collagen matrix (see more details in next section).

Cytoskeleton Proteins, Lamina, Nucleus, and LINC Complexes

Cells in a dense 3D collagen matrix form at their periphery hierarchically organized protrusionswhose morphology, molecular content, and role are distinct from those formed by the same cells in2D (77). These protrusions are dendritic: Mother protrusions prolong the nucleus and branch outinto thinner daughter protrusions, which further branch out into yet thinner protrusions, etc. (40).Using low-magnification phase-contrast microscopy, one readily detects up to 5–6 generations ofprotrusions. Dendritic protrusions form mostly at the front and the back of the cell, with the nu-cleus located in the middle of the cell. These thinner protrusions dynamically retract and pull whileclimbing along the length of the collagen fibers in actin- and microtubule-dependent ways (59).

Mother protrusions are mechanically supported by the nucleus, which is typically located inthe middle of the cell via highly contractile actomyosin fibers—perinuclear actin-cap fibers— thatare dynamically attached to the nuclear membrane through LINC complexes (10, 49–51). TheshRNA-mediated depletion of nesprin and SUN proteins that make up LINC complexes inducesthe collapse of mother and daughter protrusions. This prevents the cells from sensing and climbingalong collagen fibers, from actively squeezing the nucleus, and from producing the traction forcesrequired to migrate inside the 3D matrix. The same effect is observed when LINC complexes aredisrupted through the overexpression of the KASH (Klarsicht, ANC-1, Syne homology) domainof nesprins or when the main lamina component lamin A/C is genetically knocked out or depleted(49). While LINC proteins play only a marginal role in setting 2D migration speed and persistence(50), these structures that dynamically connect the nuclear lamina and the actin cytoskeleton playa central role in 3D cell migration.

Fluorescence microscopy reveals that the cross-section of mother protrusions is composed ofa dense core of parallel microtubules surrounded by a corona of parallel actin filaments (40, 63).Disassembly of either F-actin or microtubules via pharmacological treatments induces a collapseof these dendritic protrusions, preventing net migration in the matrix (40).

For a matrix of pore size significantly smaller than the size of the nucleus, the local digestionof the matrix via MMPs is warranted (111). Cells resolve the conundrum of both having to pullon a sufficiently stiff matrix for forces to be productive and creating enough space to move into(which in turn mechanically soften the matrix) by spatially segregating mechanical traction on thematrix from local digestion of the matrix (31). Local sensing of the matrix stiffness and ensuingtraction are generated by the daughter protrusions, while MMPs bound to the cell membranenear the nucleus (the larger part of the cell) locally digest the matrix. Cells migrating through a3D matrix typically form a channel whose diameter is quite smaller than the nucleus. Hence, cellsmechanically both pull and squeeze themselves by a combination of traction forces generated bythe daughter protrusions at the edge of the cell and anisotropic squeezing of the nucleus generatedby LINC-connected actin-cap fibers in the center of the cell.

Interestingly, the integrin- and MMP-regulated affinity of cells for the collagen matrix is high,and a mesenchymal cell will typically opt for the hard work of creating new channels in the 3Dmatrix, rather than exploiting the space it has previously created or channels formed by neighboringcells. Even in the absence of chemotactic gradients, cells in a 3D matrix tend to undergo long,persistent excursions (many hours, many cell lengths) before switching direction (29, 115). Theaffinity of cells for the matrix may explain (45) this: Once local symmetry of the matrix around thecell is created, cells will persist in that first direction.


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Lamellipodium Proteins

Close examination of the type of protrusions generated by cells that otherwise show lamellipodialprotrusions in 2D indicates that cells do not display these traditional thin (filopodium) or wide(lamellipodium) protrusions once embedded inside a 3D matrix. The formation of lammellipodialprotrusions in 2D is regulated by proteins that specifically localize to the lamellipodium, includ-ing the Arp2/3 complex and associated proteins WAVE1/2, N-Wasp, cortactin, and Rho-GTPaseCdc42 (75, 94). Hence, one can ask, What is the role of lamellipodium-specific proteins in theabsence of overt lamellipodial protrusions in a 3D matrix? Systematic depletion of these proteinsinduces significant reductions in the numbers of mother protrusions that prolong the nucleusand their daughter protrusions that dendritically stem from mother protrusions (40). Cell speedglobally correlates with daughter protrusions, which are regulated by FA proteins and lamel-lipodium proteins. This correlation explains results obtained by the Lauffenburger lab (72) thatalso found a strong correlation between lamellipodium production by cells on 2D dishes—but not2D cell-migration parameters—and cell speed in 3D matrices.

THE ROLE OF CELL DENSITY IN 3D CELL MIGRATION

Three-dimensional cell migration depends critically on cell density (i.e., the number of cells perunit volume in the matrix). Although typically not documented in cell-migration studies, 3D cellmigration is typically assessed for cells embedded at low density in collagen matrices—in otherwords, when the distance between well-dispersed individual cells in the matrix corresponds toseveral cell lengths (say, an intercellular distance of 500 μm compared to a cell size of 50–100 μm).

Recent work by Jayatilaka et al. (45), however, shows a striking dependence of cell speedand persistence of migration on the distance between the cells in the matrix. At low density(10,000 cells/mL, a low number of cells per unit volume of the matrix), corresponding to a dis-tance between cell centroids of ∼500 μm, human breast carcinoma MDA-MB-231 cells, whichare ubiquitously used to model metastatic breast cancer, do not move much over timescales thatare commensurate to their ∼24-h cell cycle in a 2-mg/mL collagen matrix. In contrast, the samecells show net migration at cell densities (100,000 cells/mL) corresponding to a cell-centroidinterdistance of 215 μm. Monitoring cell speed over several days (and therefore several cell di-visions) shows that as cell density increases, caused by the multiplication of cells in the matrix,cell speed increases >50% past a threshold density of 50 cells/mm3. Past that threshold density,cell-migration speed does not change. Importantly, this increase in cell migration occurs at celldensities for which cells do not touch one another. These observations suggest that cell prolifera-tion and cell migration—two key contributors to tumor progression—are functionally connectedto one another: As cells proliferate, cell density increases, which decreases the distance betweencells and in turn prompts cells to migrate significantly more rapidly.

This cell-density effect on cell migration is 3D specific: The same MDA-MB-231 cells pro-liferating on a 2D petri dish do not affect one another’s migration until cells reach confluencyon the dish, at which point cell migration becomes significantly impeded. Moreover, this 3Dphenomenon occurs only in metastatic cancer cells (e.g., metastatic carcinoma cells, fibrosarcomacells, and glioblastoma multiform cells) and does not occur in normal epithelial cells and fibroblastsor in nonmetastatic cancer cells.

Increases in 3D cell-migration parameters is mediated by the secretion of interleukins 6 and 8(IL-6, IL-8) and the corresponding activation of an autocrine Jak2/Stat3/Wasf3/Arp2–3 molecularpathway. The Arp2/3 complex, in turn, multiplies the number of dynamic dendritic daughter pro-trusions generated by the cells and therefore cell speed. Analysis based on the TCGA data indicates


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that overexpressions of Wasf3 and the Arp2/3 complex correlate with much worse clinical out-comes and longer metastasis-free survival. A stoichiometric mixture of IL-6 and IL-8 is necessaryand sufficient to observe cell-density-induced enhanced cell migration, a phenomenon observedonly in 3D matrices, not on 2D substrates. Increased cell density caused by proliferation on a 2Dculture dish does not induce the production of interleukins. Dual pharmacological blockade ofIL-6 and IL-8 receptors significantly blocks enhanced cell migration in vitro and slows down thespread of tumor cells from the breast to the lung, liver, and bones in orthotopic models in vivo.

Importantly, RNA-sequencing analysis indicates that gene expression of cells embedded in a3D matrix is significantly affected by cell density. The expression of hundreds of genes is down-and upregulated more than threefold by merely decreasing the distance between cell centroids,from 500 to 215 μm. Preliminary results indicate that, in particular, both the expression and theactivation of MMPs are greatly increased though increased cell density. Hence, in addition tomatrix microstructure (see previous section), cell density is another parameter that modulates theability of cells to invade and migrate, and blockade of MMPs critically depends on cell density.

ASSESSING CELL MOVEMENT IN 3D

The measurement of 3D cell migration is primarily accomplished via time-lapse imaging of cellsusing bright-field or fluorescence microscopy. Imaging fluorescently labeled cells can help betterresolve the cell edge and, hence, identify the geometric center of each cell. However, photobleach-ing and phototoxicity resulting from long-term fluorescent imaging and/or exogenous fluorescentprotein expression can negatively affect cellular behavior. Alternatively, imaging cells using bright-field microscopy does not require dyes or fluorescent proteins and has minimal phototoxicity.Phase contrast and DIC microscopy have often been used to visualize cells embedded in 3D ma-trices with enhanced contrast under bright-field imaging (30, 34, 102). In bright-field images,the movements of cells are obtained by tracking the centroid displacements between subsequentframes through pattern-recognition algorithms (Figure 3a), such as image cross-correlation, todetect the cell location with superior spatial resolution. Given that the edge of a cell is oftennot well defined in bright-field images, an initial cell location in the first frame of video mustbe prespecified and usually relies on manual input. In contrast, automated tracking with imageprocessing methods can be more readily achieved in time-lapse movies of fluorescently labeledcells. Detection and localization of fluorescently labeled cells are more straightforward, and sev-eral algorithms have been developed to compose trajectories of tracking objects from locations ofcells at different time points (Figure 3b) (4, 9).

Though cells embedded in 3D matrices can move freely in all x, y, and z dimensions, most 3Dmotility studies involve acquiring images based on observations in a fixed focal plane. Hence cellmovements in the z direction (orthogonal to the focal plane) are often not considered. Imagingof 3D cell migration at a fixed focal plane is valid with the assumption that cell movements areisotropic in all x, y, and z directions. Therefore, movements in each of the x, y, and z directionsare equivalent to one another. Hence, characteristics of cell movements in the z direction can bedirectly inferred from those in the x and y directions. For example, mean squared displacements(MSDs) are a common property used to characterize cell trajectories. The MSDs in the z directionare equivalent to MSDs in the x and y directions (i.e., MSDx = MSDy = MSDz). Thus, the MSD of3D cell movements can be described through the following formula: MSD3D = MSDx +MSDy +MSDz ∼= 3/2 MSD2D.

In some cases, the isotropic assumption may not be valid—for example, when scaffold fibersare aligned in a specific direction. In these cases, directly measuring the 3D trajectories of cellsis critical. To directly obtain real-time 3D cell movement trajectories in x, y, and z for cells


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0 18Time (h)

1.8 h 5.1 h 8.5 h 11.8 h 15.2 h

Cell trajectory[x(t), y(t)] 20 40 600 20 40100 101 102 103

100

101

102

103

104

Displacement (µm)

Occ

urre

nce

(a.u

.)

Time lag (min)

ACF

(a.u

.)

MSD

(µm

2 )

Time lag (min)

Speed,persistence time

PRW …

a

b 100

10–1

100

10–6

10–4

10–2

iAveragebehavior

iiStatistical

profile

iiiModelfitting

MSD(τ) = ⟨x(t + τ) – x(t)⟩2 + ⟨y(t + τ) – y(t)⟩2

MSD(τ) = nS2P2 (e– + – – 1)τP

APRW MSD2D(τ) = S2pP2

p (e– + – – 1)τPp

+ S2pP2

p (e– + – – 1) + 4σ 2τPs

Figure 3Typical method of data acquisition and analysis of three-dimensional (3D) cell migration. (a) Movements of live cells are imaged in realtime using video-based phase-contrast or fluorescence microscopy. Shown are human HT1080 fibrosarcoma cells moving in a2-mg/mL collagen I matrix. Trajectories of the centroids of the cells are obtained through analysis of the videos. (b) Characterization ofcell trajectories is most commonly conducted through three methods: (i ) measuring simple parameters, such as average cell speed,persistence time, and persistence distance traveled over time; (ii ) statistical profiling of cell trajectories, such as MSD, ACF, andprobability density function of speed; and (iii ) parameters derived from model fitting. The PRW model is commonly used in the studyof cell migration on 2D substrates. The APRW model is a recently proposed model to characterize cell migration in 3D matrices.Additional abbreviations: ACF, autocorrelation function; APRW, anisotropic persistent random walk model; MSD, mean squareddisplacement; PRW, persistent random walk.

embedded in 3D matrices requires imaging at different focal planes (z direction) with relativelyhigh speed (i.e., real-time volumetric imaging). In this case, imaging fluorescently labeled cellsis a more practical solution than performing bright-field imaging in terms of data analysis (43,54). Volumetric fluorescence imaging of cells significantly exposes cells with prolonged exposureof intense light, and hence temporal-resolution need largely decreases for reducing the adverseeffects from phototoxicity and photobleaching. Recent advances in light-sheet microscopy providean alternative solution for real-time 3D measurements of cell migration; light-sheet microscopyhas the advantage of minimized exposure of photons in biological systems and potentially can helpacquire 3D data sets (12, 91). Furthermore, the optical resolution in the z direction derived from


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optical microscopy, including confocal or wide-field fluorescence microscopy, is by default not asoptimal as in the x and y directions. Therefore, the positioning errors for cell locations are notequivalent between the lateral directions (x and y) and the z direction. Since the position errors ofcells can cause an overestimation of the cell speed and MSD (90, 113, 114), when cell movementsare in the range close to the position error, analyzing the anisotropic properties of cell trajectoriesneeds further consideration of the effect of positioning error.

Analysis of 3D Cell Migration

Random walks are ubiquitous in biology (5). The motility of cells in the absence of biochemicaland biophysical gradients has long been shown to display a great deal of randomness. Therefore,the analysis of cell motility is not a trivial task. Conventionally, the average speed and persistencetime of cell movement are often computed to characterize cell motility (75), yet the stochastic cellmovement generally makes cell speed time-lag dependent. Furthermore, cell-motility patternscan be complex and cell motility may not be fully represented by a single variable, such as cellspeed. Owing to the randomness of cell movements, statistical characterization is a reasonablefirst step to analyze motility.

There are several commonly used statistical profiles to characterize cell motility: (a) the MSD,(b) the autocorrelation function of cell velocities (ACF), (c) the probability density function of celldisplacements, (d ) the probability density function of angular displacements, and (e) the velocitypolarization profile. In general, obtaining the statistical profiles (MSD, ACF, etc.) of cell trajec-tories is applicable to all kinds of data sets to provide insightful information about cell migration(Figure 3b). These statistical profiles provide the quantitative outlook of cells’ migration strategieswithin the observation time window. To account for heterogeneity in cell migration over time, arecent study proposed a superstatistical approach to extract time-dependent statistical parametersfrom cell trajectories with a Bayesian method of sequential inference (71). Cell motility is alsocommonly interpreted through model-based analysis (5, 83, 92, 103, 104, 115, 118). Model-basedanalysis is aimed to provide characteristics of complex trajectories with a small set of meaningfulparameters (Figure 3).

The Persistent Random Walk Model

The persistent random walk (PRW) model has been widely used to characterize eukaryotic cellmotility on 2D substrates. The PRW model of cell motility is derived from the stochastic differ-ential equation describing the motion of a self-propelled cell:

dv

dt= − 1

Pv + S√

Pw, 1.

where t is time, v is the cell velocity, P is the persistent time, S is the speed, and w is a vector of aWiener process. A main characteristic of this model is that the MSD is

MSD (τ ) = nS2 P2(

e− τ

P + τ

P− 1

), 2.

where n is the dimension of space (1D, 2D, and 3D). The ACF of the cell velocity for this modelhas a single exponential decay—in other words,

v(τ )v(0) = nDP

e− tP . 3.


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The PRW model describes the trajectory of cells as a succession of uncorrelated movements ofduration equal to the persistence time. From fits of the MSDs of the cells with the PRW model(73, 96, 97, 103, 104), 2D motility would be fully characterized with just two parameters: cellspeed and persistence time. However, fits of MSDs do not rigorously test several key underlyingassumptions of the PRW model. These assumptions include a Gaussian distribution of cell ve-locities, a single-exponential decay of the velocity correlation function, an isotropic velocity field,and a flat distribution of angles between cell movements at long timescales (5). It has been shownthat cell movements on 2D substrates seem to exhibit a non-Gaussian-like velocity distribution inseveral studies for various types of cells, and, hence, several models have been proposed to accountfor such nonstandard behaviors (8, 19, 20, 92, 100).

A recent study found that the assumptions of the PRW model are quantitatively and qualitativelyerroneous for 3D cell migration: Cell migration in a 3D matrix is highly anisotropic. As a result,a new model, the anisotropic persistent random walk model (APRW), was proposed to bettercharacterize 3D cell migration (115).

The Anisotropic Persistent Random Walk Model

In the APRW model, cell motility is assumed to display different persistence and diffusivity alongtwo orthogonal axes—the primary migration axis and the secondary migration axis in the observed2D plane (115). The velocities of a cell along the primary ( p) and secondary (s) axes of migrationare governed by two Langevin equations:

dvp

d t= − 1

Ppvp + Sp√

Ppw , 4.

dvs

d t= − 1

Psvs + Ss√

Psw. 5.

The corresponding MSDs along the p and s axes are

MSDp (τ ) = Sp2 Pp

2(

e− τ

Pp + τ

Pp− 1

)+ 2σ 2, 6.

MSDs (τ ) = Ss2 Ps

2(

e− τ

Ps + τ

Ps− 1

)+ 2σ 2. 7.

Therefore, the total MSD of a cell is

MSD2D (τ ) = Sp2 Pp

2(

e− τ

Pp + τ

Pp− 1

)+ Ss

2 Ps2(

e− τ

Ps + τ

Ps− 1

)+ 4σ 2. 8.

The 2D cell diffusivity of the APRW model, Dtot, was calculated as Dtot = (Sp2 Pp + Ss

2 Ps )/4,and the diffusivity contributed from only the primary migration direction, Dp, is calculated asDP = (Sp

2 Pp )/4. The primary and secondary axes can be determined using the singular vectordecomposition on coordinates of cell trajectories. The anisotropic index, �, in the APRW model isdefined as the ratio between cell diffusivities along the primary and secondary migration axes—inother words,

� ≡ DP

Ds= Sp

2 Pp

Ss2 Ps

. 9.

Notably, when there is no anisotropy in the system (i.e., � = 1, Pp = Ps , and Sp = Ss ), the APRWmodel is equivalent to the PRW model. Hence, the APRW model covers behaviors described bythe PRW models. The APRW model has been used to characterize the migration of various types


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of cells embedded in 3D collagen matrices, as well as cells embedded in other composite 3Dmatrices systems, such as collagen mixtures with fibronectin (115, 116).

CONCLUDING REMARKS

In the past several years, tremendous effort has been put into the development of a variety of3D culture systems, as well as the adoption of 3D systems for use in drug discovery, cancer-cellbiology, stem-cell biology, engineered functional tissues for implantation, and other cell-basedanalyses. Yet much remains to be done, as current 3D models are still not realistic. Organ-on-the-chip technology coupled with quantitative pathology of tissues offers much promise for thedevelopment and application of more realistic 3D constructs.

While the forces driving 3D migration are being delineated, too little effort has been devotedto determining the molecular mechanisms and regulators of polarization in 3D migration, whichsets the direction of migration. Contractility-generated high-pressure lobopodial protrusions inhuman cells migrating in a 3D matrix and the nucleus of these cells can act as a piston thatphysically compartmentalizes the cytoplasm and increases the hydrostatic pressure between thenucleus and the leading edge of the cell to drive lamellipodia-independent 3D cell migration (76).This finding in part explained the anisotropic movement strategy deployed by migrating cells in3D ECM (115) and reveals that both cell-migration behaviors and regulatory mechanisms frommolecules to physical principles cannot be directly inferred from existing knowledge of cell 2Dmigration from the last few decades.

The visualization of protein expression patterns of cells in a 3D culture system is critical tostudy the molecular mechanisms that govern 3D cell migration. New technologies for improved3D imaging will be needed. Current fluorescence microscopy allows the identification of taggedmacromolecules and the analysis of their biological roles within living cells and tissues, but theability to directly obtain images that reveal fine structural details of cells in 3D is challenging owingto increased sampling depths required. One solution is light-sheet fluorescence microscopy, whichis a fluorescence microscopy technique that has intermediate optical resolution but good opticalsectioning capabilities and high speed. Electron microscopy offers much-improved resolution andultrastructural detail but at the expense of imaging a fixed sample with a restricted field of view.Emerging technologies such as 3D correlative light and electron microscopy hold promise fordetecting rare and dynamic events for structural analysis at high resolution and increased imagingdepths (88). Additionally, new techniques to monitor protein expression, localization, bindingaffinity, and activity of cells in 3D in both fixed and live specimens are becoming increasinglyrequired. For direct real-time monitoring of biological processes, one proposed method is theincorporation of biosensors. This is a direct extension of implantable biosensors for clinical appli-cations, such as the continuous monitoring of metabolites (105). Moreover, a recent review coversemerging technologies that enable spatially resolved transcriptomics that may soon have the po-tential to extend beyond transcriptomics to encompass spatially resolved genomics and proteomicstudies (18). As the complexity of 3D cell culture systems increases, so too will the emergingtechnologies needed to study cells in these complex microenvironments. The next decade willundoubtedly bring new and exciting technologies and unprecedented scientific discoveries.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.


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AKNOWLEDGMENTS

We would like to acknowledge all the researchers who have contributed to the field of 3D cellmigration. We apologize for any studies that we were not able to highlight owing to spaceconstraints. The authors would like to thank their funding sources for their support: U54-CA210173 (D.W., P.-H.W., D.M.G.), R00-CA181352, V Foundation, Susan G. Komen Foun-dation (CCR17483484), The Jayne Koskinas Ted Giovanis Foundation for Health and Policy,and the Breast Cancer Research Foundation (D.M.G.).

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BB47_FrontMatter ARI 11 April 2018 12:42

Annual Review ofBiophysics

Volume 47, 2018Contents

Structural Basis for G Protein–Coupled Receptor SignalingSarah C. Erlandson, Conor McMahon, and Andrew C. Kruse � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Collapse Transitions of Proteins and the Interplay Among Backbone,Sidechain, and Solvent InteractionsAlex S. Holehouse and Rohit V. Pappu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �19

Measuring Entropy in Molecular Recognition by ProteinsA. Joshua Wand and Kim A. Sharp � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �41

Assembly of COPI and COPII Vesicular Coat Proteins on MembranesJulien Bethune and Felix T. Wieland � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �63

Imaging mRNA In Vivo, from Birth to DeathEvelina Tutucci, Nathan M. Livingston, Robert H. Singer, and Bin Wu � � � � � � � � � � � � � � � � �85

Nanodiscs: A Controlled Bilayer Surface for the Study of MembraneProteinsMark A. McLean, Michael C. Gregory, and Stephen G. Sligar � � � � � � � � � � � � � � � � � � � � � � � � � � 107

The Jigsaw Puzzle of mRNA Translation Initiation in Eukaryotes:A Decade of Structures Unraveling the Mechanics of the ProcessYaser Hashem and Joachim Frank � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 125

Hemagglutinin-Mediated Membrane Fusion: A BiophysicalPerspectiveSander Boonstra, Jelle S. Blijleven, Wouter H. Roos, Patrick R. Onck,

Erik van der Giessen, and Antoine M. van Oijen � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 153

Cryo-EM Studies of Pre-mRNA Splicing: From Sample Preparationto Model VisualizationMax E. Wilkinson, Pei-Chun Lin, Clemens Plaschka, and Kiyoshi Nagai � � � � � � � � � � � � � � 175

Structure and Dynamics of Membrane Proteins from Solid-State NMRVenkata S. Mandala, Jonathan K. Williams, and Mei Hong � � � � � � � � � � � � � � � � � � � � � � � � � � � � 201

The Molecular Origin of Enthalpy/Entropy Compensation inBiomolecular RecognitionJerome M. Fox, Mengxia Zhao, Michael J. Fink, Kyungtae Kang,

and George M. Whitesides � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 223

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Modeling Cell Size Regulation: From Single-Cell-Level Statistics toMolecular Mechanisms and Population-Level EffectsPo-Yi Ho, Jie Lin, and Ariel Amir � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 251

Macroscopic Theory for Evolving Biological Systems Akinto ThermodynamicsKunihiko Kaneko and Chikara Furusawa � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 273

Photoreceptors Take Charge: Emerging Principles for Light SensingTilman Kottke, Aihua Xie, Delmar S. Larsen, and Wouter D. Hoff � � � � � � � � � � � � � � � � � � � � 291

High-Resolution Hydroxyl Radical Protein Footprinting: BiophysicsTool for Drug DiscoveryJanna Kiselar and Mark R. Chance � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 315

Dynamic Neutron Scattering by Biological SystemsJeremy C. Smith, Pan Tan, Loukas Petridis, and Liang Hong � � � � � � � � � � � � � � � � � � � � � � � � � � 335

Hydrogel-Tissue Chemistry: Principles and ApplicationsViviana Gradinaru, Jennifer Treweek, Kristin Overton, and Karl Deisseroth � � � � � � � � � � 355

Serial Femtosecond Crystallography of G Protein–Coupled ReceptorsBenjamin Stauch and Vadim Cherezov � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 377

Understanding Biological Regulation Through Synthetic BiologyCaleb J. Bashor and James J. Collins � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 399

Distinct Mechanisms of Transcription Initiation by RNAPolymerases I and IIChristoph Engel, Simon Neyer, and Patrick Cramer � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 425

Dynamics of Bacterial Gene Regulatory NetworksDavid L. Shis, Matthew R. Bennett, and Oleg A. Igoshin � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 447

Molecular Mechanisms of Fast Neurotransmitter ReleaseAxel T. Brunger, Ucheor B. Choi, Ying Lai, Jeremy Leitz, and Qiangjun Zhou � � � � � � � 469

Structure and Immune Recognition of the HIV Glycan ShieldMax Crispin, Andrew B. Ward, and Ian A. Wilson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 499

Substrate-Induced Formation of Ribosomal Decoding Center forAccurate and Rapid Genetic Code TranslationMichael Y. Pavlov and Mans Ehrenberg � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 525

The Biophysics of 3D Cell MigrationPei-Hsun Wu, Daniele M. Gilkes, and Denis Wirtz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 549

Single-Molecule View of Small RNA–Guided Target Searchand RecognitionViktorija Globyte, Sung Hyun Kim, and Chirlmin Joo � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 569

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Behavioral Variability and Phenotypic Diversityin Bacterial ChemotaxisAdam James Waite, Nicholas W. Frankel, and Thierry Emonet � � � � � � � � � � � � � � � � � � � � � � � � 595

Mechanotransduction by the Actin Cytoskeleton: ConvertingMechanical Stimuli into Biochemical SignalsAndrew R. Harris, Pamela Jreij, and Daniel A. Fletcher � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 617

The Physical Properties of Ceramides in MembranesAlicia Alonso and Felix M. Goni � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 633

The Physics of the Metaphase SpindleDavid Oriola, Daniel J. Needleman, and Jan Brugues � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 655

Indexes

Cumulative Index of Contributing Authors, Volumes 43–47 � � � � � � � � � � � � � � � � � � � � � � � � � � � 675

Errata

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

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the biophysics of 3d cell migration - johns hopkins university

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