physics of cellular movements - supplementary info

7/31/2019 Physics of Cellular Movements - Supplementary Info

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Physics of CellularMovements

Erich Sackmann,1,2,

Felix Keber,2 andDoris Heinrich2

1Physics Department, Institute for Biophysics E22,Technische Universita t Mu nchen, D-85748 Garching,

Germany; email: [email protected] t fu r Physik and Center for NanoScience (CeNS),

Ludwig-Maximilians-Universita t Mu nchen, D-80539 Munich,Germany; email: [email protected],

[email protected]

Annu. Rev. Condens. Matter Phys. 2010. 1:25776

First published online as a Review in Advance onMay 21, 2010

The Annual Review of Condensed Matter Physics is

online at conmatphys.annualreviews.org

This articles doi:10.1146/annurev-conmatphys-070909-104105

Copyright 2010 by Annual Reviews.All rights reserved

1947-5454/10/0810-0257$20.00

Corresponding author.

Key Words

cell adhesion, microtubule-actin-crosstalk, actin polymerizationwaves, cell locomotion, intracellular transport

Abstract

The survival of cells depends on perpetual active motions, includ-

ing (a) bending excitations of the soft cell envelopes, (b) the bidi-

rectional transport of materials and organelles between the cell

center and the periphery, and (c) the ongoing restructuring of

the intracellular macromolecular scaffolds mediating global cell

changes associated with cell adhesion locomotion and phagocyto-

sis. Central questions addressed are the following: How can this

bustling motion of extremely complex soft structures be character-

ized and measured? What are the major driving forces? Further

topics include (a) the active dynamic control of global shape

changes by the interactive coupling of the aster-like soft scaffold of

microtubules and the network of actin filaments associated withthe cell envelope (the actin cortex) and (b) the generation of pro-

pulsion forces by solitary actin gelation waves propagating within

the actin cortex.

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INTRODUCTION

It is fascinating to look at our blood cells through a phase contrast microscope and see with

our own eyes that cells are really living. In the large white blood cells, we see intercellular

organelles moving around in the cytoplasmic space in a seemingly irregular fashion, remi-

niscent of random walks. The nucleus-free erythrocytes (simple cell envelopes filled with

hemoglobin solution) show pronounced thickness fluctuation as if driven by magic forces.

Some white blood cells crawl over the surface as shown in the famous movie Crawling

neutrophil chasing bacteria that can be downloaded from YouTube.

Until a decade ago, physicists were mainly studying the static physical properties of the

erythrocyte. Much of our present knowledge on the physical basis of the self-organization

of cell membranes is due to comparative studies of erythrocyte envelopes and model mem-

branes. These studies led to the curvature elasticity concept of cell shape changes (reviewedin Reference 1), and the thermomechanical control of microstructures in cell envelopes and

of cell adhesion (reviewed in References 1 and 2).

In the past decade, nucleated cells became a topic of interest for physicists. Most studies

concentrated on the mechanics and microviscoelasticity of cells. Comparative studies of

cells and of in vitro models of intracellular macromolecular scaffolds, made up of semi-

flexible actin filaments and microtubules (MTs), provided valuable insight into correla-

tions between the molecular architecture of cells and their mechanical properties (3, 4).

Experiments provided evidence that the rheological properties of cells show typical univer-sal features of soft glassy materials, which is reflected by similar behavior of in vitro

models of actin networks (reviewed in References 3, 5). The glass-like behavior can explain

the astonishing robustness of cells against removal of proteins by mutations. The physics of

cells was further stimulated by recent studies showing that cells can sense forces (68), and

thereby adjust their mechanical impedance to that of the environment by reorganization of

the actin cortex. Moreover, the mechanical properties of the tissue or bones can stimulate

the differentiation of stem cells into specific cells, such as muscle cells. Mechanical forces

also control the development of nerve connections by synapses during the development of

embryos (9).

During the past few years, physicists became interested in the tremendously complex

problem of cell dynamics and its key role in numerous vital processes, such as cell migra-

tion, immunological processes (10, 11), or the engulfment of bacteria (discussed below).

The elucidation of the hierarchy of motions in complex soft materials, such as cells, is a

great future challenge for physicists working in the field of soft materials.

In this article, we describe the intrinsic motions of cells driven by thermal and activerandom and directed forces mediated by molecular motors, solitary actin gelation (or

polymerization) waves (SAGWs), and the dynamic coupling of the soft star-like scaffold

of MTs to the actin cortex of the composite cell envelope.

We focus on three topics: (a) the optimized exploration of the cytoplasmatic space by

internalized objects (endosomes) through alternating random and directed local forces,

(b) the dynamic control of the global mechanical stability of cells via actin-microtubule

crosstalk, and (c) the quasi-random crawling of cells over surfaces by nucleation and

growth of actin networks.Special emphasis is placed on the control of the structure and the physical properties

and the function of the composite cell envelopes by numerous actin-binding proteins

acting as actuators (effectors), the activity of which is controlled by biochemical switches

Cell shape changes:changes of the globalshape of cells, such asdiscocyte-to-sphere

transitions of redblood cells(erythrocytes)

MT: microtubule

Solitary actin gelation

(or polymerization)wave (SAGW):propagating

accumulation of actingel mediated bypolymerisation atthe front anddecomposition atthe end

Solitary wave:a self-reinforcingsingle wave packet

propagating withconstant velocitywhile maintainingits shape

Composite cellenvelope: stratifiedouter shell ofeukaryotic cells

composed of thelipid-protein bilayer(PM), the glycocalix,and the actin cortex

Actin-microtubulecrosstalk: interactionof microtubules withthe actin cortexresulting in the

interactiverestructuring ofthe actin cortexA

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actuated by external signals, local forces, and cell adhesion. The physical basis of the

membrane-bending undulations and their biological role is summarized in Supplemental

Appendix G (follow the Supplemental Material link from the Annual Reviews home page

at http://www.annualreviews.org).

We focus on studies of the amoeboid cells of the slime mold Dictyostelium discoideum(abbreviated as Dictyostelium cells). It is a prototype of a highly mobile cell that can be

observed under the microscope for days. It is extremely robust against the knockout of

proteins by mutation. Comparative studies showed that Dictyostelium cells and animal

cells share many common features and differ mostly in the time scale of dynamic processes.

The main difference between these cells is that the animal cells possess a third type of

macromolecular scaffold that is composed of semiflexible macromolecules called interme-

diate filaments.

MICROANATOMY AND DYNAMICS OFTHE COMPOSITE CELL ENVELOPE

Because many motional processes and mechanical properties are controlled by cell enve-

lopes, we first summarize the microanatomy of this stratified soft shell (see Figure 1). It

consists of two subshells: the plasma membrane (PM) and the associated macromolecular

network. The PM is a multicomponent lipid-protein alloy containing a stunning multitudeof functional proteins, including ion channels, enzymes, hormone amplifiers, and several

families of proteins mediating cell-adhesion, called cell adhesion molecules (CAMs) (1, 2).

The simplest composite cell envelope is that of the erythrocyte. Its intracellular scaffold

consists of a two-dimensional macromolecular network, and the microanatomy and

dynamics of this shell has been extensively reviewed (2).

In nucleated cells (such as the Dictyostelium cells or white blood cells), the mem-

brane-associated network is formed by the actin cortex. It consists of a 0.20.5-mm-thick

shell made up of slightly cross-linked actin filaments. These semiflexible macromoleculesare locally coupled to the intracellular domains of integral membrane proteins by spe-

cific actin-membrane linkers. A frequent linker is talin, which anchors actin to CAMs

(as shown in Figure 1c). The attachment of phosphate groups to tyrosine side chains of

the protein (called tyrosine phosphorylation) triggers the binding of talin (12). This is

mediated by specific enzymes (called tyrosine kinases), which can be switched on by

biochemical signals, external forces, or cell adhesion. In this way, the structure and the

elasticity of the cell envelope can be modified within seconds by external forces or

chemical signals, such as hormones or chemoattractants (see Figure 1b and Supplemen-

tal Appendix B).

As shown in Figure 1d, the actin cortex can undergo a series of phase transitions, from

homogeneous networks to heterogels composed of tightly coupled bundles or branched

networks (12, 13). Transitions between different states of the actin cortex can be controlled

by activation of specific actin cross-linkers and the density of the actin network, which is

essential for the dynamic reorganization of the actin cortex (14, 15).

The lipid-protein bilayer is extremely soft with respect to shearing and bending, but it isnearly incompressible with respect to lateral extensions. The softness is most impressively

demonstrated by the pronounced bending excitations of many cell types, resulting in a

dynamic roughness of cell surfaces of 10 nm (1618). The entropic disjoining pressure

mediated by the dynamic surface roughness plays a key role for the dynamics of cell

PM: plasmamembrane; lipidbilayer of the cellenvelope

Cell adhesion mole-cule (CAM): cellsurface receptorsmediating celladhesion

Supplemental Material

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Receptorb

Activation(kinase)

CAM activated CAM inactive

Inhibition

(phosphatase)

PLinker

P

dc

cc

I

II

III

IV

CAM cluster

P-3,4,5-P3-coupled protein

Talin

Actin

Plasma

membrane:

4nm

+

Arp2/3

Arp2/3

ActinActin

aPS CAM

CAM

Glycocalix:40nm

Actin

cortex

:400nm

GL

Cross-linker

Cross-linker+++

+

=

Actin flament

Filamin

Myosin

Figure 1

(a) Diagram of the three-layered composite shell of nucleated cells, composed of the central lipid-protein bilayer (called plasmamembrane, PM), the glycocalix (G) facing the extracellular space, and the actin cortex. The glycocalix is formed by the head groupsof cell adhesion molecules (CAMs), receptors binding polysaccharides (PSs) of the extracellular matrix, and glycolipids (GLs). Notethat the actin filaments (diameters $8 nm) are slightly thicker than the lipid-protein bilayer ($5 nm) (not shown to scale).(b) Illustration of the activation of the actin-membrane linker by phosphorylation. The activation and deactivation are mediated

by the antagonistic pair of enzymes: the phosphate-coupler (kinase) and the phosphate-decoupler (phosphatase) (see SupplementalMaterial A, follow the Supplemental Material link from the Annual Reviews home page at http://www.annualreviews.org).(c) Simplified model of coupling between subshells of nucleated cells. Actin filaments are coupled to intracellular domains of celladhesion molecules (such as integrins) via talin after activation of this actin-membrane linker by phosphorylation. Note that CAMsthat are not clustered and linked to talin (such as that on the right side) are only very weakly binding to tissues. The network canextend in the third dimension by coupling of other actin filaments via cross-linkers. The right side of the image shows the coupling ofextrinsic proteins to the membrane through the lipid anchor PI-4,5-P2, assisted by electrostatic binding of positively charged aminoacids to acidic lipids. This coupling plays a key role for the dynamic restructuring of the actin cortex (see Figure 5). (d) Manifold ofgel states in actin networks. With increasing density of cross-linkers (increasing ratio e Dcc/x of the distance between cross-linkersDcc and the mesh sizex), the homogeneous network in the center can undergo transitions into a manifold of heterogeneous gel states.These include condensed networks interconnected by thin bundles (I); actin bundles generated by myosin microbundles, which formpercolated networks (II); and branched networks formed by the cross-linker Arp2/3 (III). The heterogels may coexist with theslightly linked homogeneous networks. Such coexisting networks are formed for instance by the cross-linker filamin (IV). The typeof network formed depends on the structure and the binding kinetics of the cross-linkers. The branched network is only formed bythe cross-linker Arp2/3. Bundles may be generated by molecular motors of the myosin family, generating micromotors.

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adhesion, as well as the adhesion-induced formation of microdomains (19), which is

discussed in more detail in Supplemental Appendix G (also see Reference 1).

THE GLOBAL MECHANICAL DESIGN OF CELLSThe global shape and mechanical stability of the simple shell of erythrocytes and of the

envelopes of intracellular organelles are determined by the minimum elastic energy of the

shells. In many cases, the shape is determined by the minimum bending energy. It can

therefore be controlled by varying the area-to-volume ratio of the shell or by introducing

spontaneous curvatures (2, 20). More complex and asymmetric shapes of the soft shells

can be generated by lateral phase separation within the plasma membrane or by introduc-

ing shear elasticity. The shape is then determined by the ratio of the shear elastic modulusto the bending modulus of the shell (21, 22).

The situation is much more complex for nucleated cells, as shown in Figure 2 for

Dictyostelium cells. The mechanical stability of the cytoplasmic space is determined by

Fex(t)

FR2

F R2

F R1

Talin

Bead

CAM

Actin-cortex

MT-actincoupler

+

+

+

C

MT

End

PM

Figure 2

Projected image of an adhering cell showing its mechanical stabilization by the fraction of tensedmicrotubules (MTs) that are fixed to the centrosome (C) with their minus end, and to the viscoelasticactin cortex with their plus end. Note that some MTs may also form thin bundles. The large arrowpointing to the left indicates a strong external force Fex(t) acting on a bead bound to an MT, which isbalanced by the tensil forces (FRX) evoked in the MT. The forces FRX are balanced by shear stresses (s)in the actin cortex, which are coupled to the plasma membrane (PM) by talin (as shown in the inset andFigure 1a). Inset, upper left: Model of coupling of the MT plus-end to the intracellular side of the actincortex, which can be mediated by various coupling proteins, including dynactin, a 37-nm-long rodcarrying Dynein, a minus-end-directed motor (see Supplemental Material B). The experiments leadingto this model of soft cells are summarized in Supplemental Material G.


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the aster-shaped scaffold of MTs. These 25-nm-thick nanotubes are fixed with their minus

ends to the centrosome, an organelle located near the nucleus that acts as global cell

organizer. Some MTs are anchored with their plus end at the actin cortex by specific

linkers, thus mediating a mechanical link between the two networks (23, 24).

The buckling forces of the MTs (with a bending stiffness of B % 5 1028 Nm) are inthe piconewton range. Therefore, these filaments can only transmit tensions, and therefore

the cytoplasmic space is viscoplastic. Strong external forces have to be balanced by inter-

play of the traction forces in the MT network and the shear stress in the viscoelastic actin

cortex exhibiting shear moduli of approximately 103 Pa (4).

It is important to emphasize that only a fraction ($10%) of the MTs is fixed to theactin cortex, whereas the rest is mobile and subjected to continuous shrinking and

growth, resulting in the turnover of all MTs within one hour (23, 24). In fact, free

(nonadhering) cells exhibit mostly MTs with free dangling plus ends, whereas the frac-

tion of fixed filaments increases when the cells adhere to surfaces or move on surfaces.

The stable MT fraction may also help to maintain the global mechanical tension in long

axons, which has been shown to be required for the accumulation of presynaptic vesicles

at the axon endings (9).

The above model on the smart mechanical design of cells is suggested by two groups of

experiments: first, by analysis of the quasi-random motions of colloidal probes within the

cell (25, 26) and, second, by magnetic tweezer microrheology studies of the cell cytoplasm(27). In the latter type of experiment, superparamagnetic microparticles (DynabeadsW) are

transferred into the cells by phagocytosis. The engulfed beads are wrapped by the PM,

which exposes its inner leaflet. The beads are treated by the cell as intracellular compart-

ments and are shuffled around within the cytoplasmic space. Therefore, engulfed colloidal

beads are ideal probes for systematic studies of the intracellular dynamics or for measuring

the viscoelastic impedances or active forces.

OPTIMIZATION OF EXPLORATION OF THE INTRACELLULAR SPACEBY INTERMITTENT RANDOM AND DIRECTED MOTION OFORGANELLES AND ENDOSOMES

Colloidal probes engulfed by cells exhibit four types of motions in the cytoplasmic space:

(a) random walks, (b) unidirectional local motions (with velocities $0.5 to 1.5 mm s1)along the MT that are mediated by MT-associated motors, (c) quasi-random sweeping

(or flagella-like) motions of the MTs (with v % 0.5 mm s1

) attributed to the active movementof the plus end of the MTs parallel to the actin cortex, and (d) occasional very fast deflections

over micrometer distances with ultrafast velocities of up to $10 mm s1.Because the movements of the endosomes consist of random and directed motions, it is

useful to characterize the motions in terms of local velocity distributions [P(v)] and the

conventional mean square displacement (MSD) as a function of time. Systematic measure-

ments of the local velocities showed that they can be best characterized in terms of very

broad log normal distributions of the random variable (v):

Pv 1vffiffiffiffiffiffi

2pp

s2exp log v

2

2s2

n o, 1:

comprising velocities between 0.005 (the lower limit of measurement) and 2 mm s1, with a

maximum at v % 0.3 mm s1. The low-velocity regime of the distribution is attributed to

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the effective velocity of the random walk. The center of P(v) is dominated by the MT

angular motion (with typical velocities of 0.5 mm s1) and the regime from the center of

P(v) to velocities of 2 mm s1 by the active transport of the beads along the MT.

Superimposed on these motions are long velocity tails ranging up to 10 mm s1. These

ultrafast motions are rare events. They are attributed to the sudden release of strain energystored in microtubules, which are prestressed by the actin cortex. These abrupt motions are

reminiscent of earthquakes driven by mechanical instabilities of Earths crust.

The velocity distributions provide valuable insights into subtle changes in the intracel-

lular transport caused by modifications of changes to the cytoskeleton composition due to

mutations, hormones, or drugs. Examples are the decomposition of the MT network by

benomyl (a fungi-killing poison) and of the actin cortex by latrunculin A (a toxin that

sequesters actin monomers and inhibits its polymerization). In both cases, the fast motions

with v > 1 mm s1 are abolished. Removal of myosin II motors results in a decrease of the

maximum of P(v) corresponding to an apparent increase in the viscosity of the cytoplasm.

However, the ultrafast motions are not affected (27), and are thus not driven by molecular

motors. Both experiments are consistent with the assumption that the ultrafast motions are

caused by the release of prestress due to the coupling of the microtubules to the actin

cortex.

The conventional way of analyzing the intracellular motions of the pseudo endosomes is

to measure the MSD of the colloidal probes (25, 2830):

DRt2 DRt t Rt2E: 2:

Microrheological experiments show that the MSD in the intracellular space of cells follows

a power law of the form

DRt2 const ta: 3:Here, the exponent a is larger than 1 in all cells studied (Dictyostelium, fibroblasts) anddepends on the bead radius (R) and the measuring time. It varies from a % 1.3 for R %0.5 mm to a % 1.5 for R % 2 mm in fibroblasts (29) and approaches the value for randomwalks ofa % 1 with decreasing size of the particles.

The subdiffusive behavior is a consequence of the general Einstein law for the MSD in

complex fluids (25, 31),

Dxt

2E 2Dt 2kBT

zt t 4:

with a time-dependent friction coefficient z / tb. This deviation from the random walkbehavior is thus a consequence of the viscoelasticity of the cytoplasmic space and has been

used extensively to measure viscoelastic impedance of the cytoplasm (25, 26).

More detailed information is obtained by measuring the directional persistence of the

bead motion. It is defined as the MSD of the fluctuation of the velocity vector according to

Dft2

jft t ftj2D E

, 5:

where f is the angular direction of the velocity vector. Df(t) varies between 0 for directed

and 2p for random motion. Below we summarize some pertinent results characteristic for

Dictyostelium cells (27).

Intracellular transport:actively and passivelydriven motion ofinternalized objects or

intracellularorganelles in thecytoplasm

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1. By measuring the mean square values DR(t)2 and Df(t)2 as a function oft and averag-

ing over variable time intervals, one can distinguish between random motions [with

a % 1 and Df(t)2 $ 2p] and directed motions [with Df(t)2 % 0 and exponents varyingbetween a % 1.8 and a % 2.0]. The latter are attributed to the directed active motionsalong the MTs. The velocity distribution is asymmetric, with a maximum at v $0.3 mm s

1

(see Figure 3b). This could be interpreted in terms of the action of different numbers of

molecular motors or local variations of the cytoplasmic viscosity. In rheological studies

(27), we measured a power law z % 104 ffiffitp and an effective cytoplasmic viscosity ofZ $10 Pas. This would correspond to forces of f% 50 pN, requiring the concerted actionof up to 10 motors of the kinesin family.

2. The duration of the straight paths obeys an exponential distribution with a decay

time of t

%0.65 s, whereas the duration of the random walks obeys a log normal

distribution.

F(t)

Start

Endy-coordinate(m)

8

12

16

x-coordinate (m)

8 12 16

0.12

0.08

0.04

0.00

Pro

bability

1.00.60.2

v (ms1)

50

30

10

1

0.3

0.2

0.1

0.03.02.01.00.0

Time (s)

P(D)x103

D (mms1)

P()

a

b

c

600

450

300

150

0

Time (s) 102

10

4

Figure 3

(a) Example of quasi-random transport of colloidal probes in a Dictyostelium cell observed for about 10 min. The time course ofthe bead motion is indicated by a rainbow color code starting with red and ending with blue. The color-time relationship isshown in the inset to the right. Note that the motion consists of local, apparently random, walks and straight paths. In somecases, the bead moves very fast, exhibiting very large velocities of up to 5 mm s1. These earthquake-like motions are attributed tothe relaxation of prestressed microtubules. At some positions, strong force pulses (of 100 to 700 nN) were applied. Sometrajectories of the bead evoked by the force pulses are indicated by small arrows. Note that the bead is not deflected in thedirection of the external force (which is always directed toward the left, as shown in the inset to the left) but perpendicular ornearly opposite to it. (The trajectory was adopted from Reference 27.) (b) Distribution of velocities of straight bead motionsfulfilling the condition Df(t)2 % 0 and a % 2.0. Inset: Distribution of diffusion coefficients P(D) of the random walks. P(D) isplotted as a function of the logarithm of D. The Gauss-like distribution indicates a log normal distribution of D. ( c) DistributionP(t) of durations while the bead moves along nearly straight trajectories attributed to the transport along microtubules.

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3. The diffusion coefficients exhibit a broad distribution. It can be well represented

by a log-normal distribution showing that the random walks are not simple

Brownian motions. Such behavior is typical for diffusion in complex fluids with fractal

dimensionality.

There is another interesting interpretation. The average value of the diffusivity D %102 mm2 s1 would correspond to a viscosity of Z% kBT/6pRD % 101 Pas, which issmaller by two orders of magnitude than the measured values ($10 Pas). This leads to theconclusion that the random motion is driven by quasi-random forces mediated by the

actively driven motions in the cytoplasm, which could be interpreted in terms of an excess

temperature Tex, which is much higher than the physiological value (see also Reference 16).

In the cytoplasm, the combination of random and directed active motion exhibits two

advantages. By active motion along the MT alone, the endosomes would be mainlytransported between the periphery and the cell center in the radial direction. Random

walks alone could explore the whole space but would be very slow considering the high

viscosity of the cytoplasm. Because the two motions are independent, the MSD for a

straight motion and a subsequent random walk from one MT to a second one (in the

distance dd) would be of the order

hr2

i %6Dt

f D

kBT koff

2

, 6:

where f is the active force and the friction coefficient z has been replaced by D kBT/z.Equation 6 shows that the time t to reach a certain position at another MT would be t /6Dt and that the search for a specific target in the cytoplasm would be strongly

reduced by the combined modes of motion. A second advantage of the search strategy is

that the transition between two adjacent MTs is accelerated by the active sweeping

motions of the MTs (corresponding to a higher effective diffusion coefficient). The higher

efficiency of combined directed and random motions in cells has also been predicted bytheoretical studies (32, 33).

THE CROSSTALK BETWEEN THE ACTIN CORTEX ANDTHE MT-ASTER CONTROLS THE GLOBAL MECHANICALSTABILITY OF CELLS

A promising physical strategy to explore the crosstalk between the MT and the actin

network is magnetic tweezer microrheology. For this purpose, superparamagnetic beads(of 2.8 mm diameter) are transferred into the cells, and changes in their quasi-random

motion evoked by force pulses of $1 s duration are analyzed. The evaluation of severalhundred creep response functions obtained in Dictyostelium cells by force pulses of up to

1 nN provided the following insights (see Reference 27 and Supplemental Appendix F):

1. In most cases, the beads respond to forces below 100 pN in an unpredictable manner.

The deflections are delayed and often consist of several steps. Moreover, the direction of

deflection is seldom parallel to the force direction. This shows that the cytoplasmicspace of the cells does not behave as a passive viscoelastic system but rather as an active

viscoplastic body.

2. Above a threshold force of Fex ! 100 pN, the beads are deflected very fast (>5 mm s1)in a direction opposite or perpendicular to the applied force direction. The response


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time is tR % 0.2 s or smaller. Simultaneously, the centrosome moves in the samedirection, and its motion is correlated with that of the bead.

3. The nonlinear active response is also observed after knockout of the muscle type

myosin II, showing that this motor is not responsible for the active viscoplastic behavior

(see Figure 3b). It is abolished after dismantling either the actin network withlatrunculin A or the MT-aster with benomyl.

4. After the very fast response, the plus end of the MTs (and the centrosome) often return

close to the original position by diffusive motion with velocities of about 1 mm s1 or

smaller (see Reference 27 and Supplemental Figure 6). This behavior suggests that the

cells exhibit some mechanical short-term shape memory. It is lost when the cell starts to

crawl in a new direction by formation of a new pseudopod. The transient shape mem-

ory is determined by the balance of the tensile forces (FRX in Figure 2) in the MTand the

shearing (s in Figure 2) in the actin cortex.

The mechanical model can be considered as a special case of the famous Buckminster

Fuller design concept of tensional integrity (tensegrity) structures composed of alternating

arrangements of ropes and struts that are stabilized by appropriate prestresses [as postu-

lated by Ingber and coworkers (34)]. The cell is unique in the sense that the tension-bearing

elements are arranged as spikes in a wheel, whereas the compressions are balanced by the

hoop of the wheel (34).

The actin-MT connections play a key role for the separation of the two new sets ofchromosomes during cell division (cytokinesis) (35). Each set of chromosomes is coupled

to the plus ends of the MT emanating from one side of the centrosomes, whereas those

emanating from the opposite side couple to the actin cortex. The chromosomes are then

separated by movement of the centrosomes to opposite sides. This process is driven by the

movement of the two actin-MT assemblies to opposite poles of the cell until gobal mechan-

ical equilibrium between the two halves of the cell is reached. The underlying mechanism

of this process is not completely understood yet. One explanation is that it is driven by

actin-myosin II micromuscles because the two sets of chromosomes are not positioned

properly in mutants devoid of the motor protein (35, 36). The separation of the spindles

can, however, be driven by the SAGWs as described below. The actin-MT crosstalk may

also be responsible for the quasi-periodic oscillations of the centrosome observed occasion-

ally during the spindle positioning (36).

GLOBAL CELL MOTIONS AND CELLULAR SHAPE CHANGES

Cells Crawl on Surfaces by Pseudopod Spreading, thereby TransmittingPushing Forces Via Adhesion Domains

The most dramatic large-scale motions of cells occur during their crawling on surfaces by

cyclic spreading of broad protrusions (pseudopods) at the front followed by the active

retraction of the opposite end. In gradients of chemotactic signal molecules (e.g., c-AMP

in the case of Dictyostelium), the generation of pseudopods is triggered by binding of thechemoattractants to cell surface receptors. The cells polarize and generate protrusions in

the direction of the gradients. Elegant microfluidic experiments showed that the chemotac-

tic speed increases with the steepness of the gradient between a threshold of 103 nM mm1

and an upper limit of 10 nM mm1 (37).

Tensional integrity(tensegrity) structures:

mechanical structurescomposed of elements

that can either onlybalance tensions (suchas the MT) orextensional loads(such as the cellenevelope)

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However, the spontaneous generation of pseudopods at random sites is a basic activity

of vital cells even in the absence of external stimulations. The cells perform a specific kind

of random motion. It consists of persisting zig-zag-like motions for 1 to 2 min (over

distances of about 20 mm), which are followed by a change in direction (see Figure 4a and

References 38, 39).This saltatory motion is consistent with the dynamics of pseudopod spreading. They

protrude with constant velocity for about 5 mm and stop abruptly. Then the rear side is

retracted, and the cells unbind partially from the substrate, resulting in a reduction of the

contact area. Thereafter, a new direction is chosen. Thus, the locomotion is accompanied

by a cyclic variation of the contact area (e.g., between 20 and 200 mm2 on mica) with a

periodicity of 12 min. The velocity of pseudopod spreading varies from v % 0.1 mm s1 onsoft polymer cushions (38) to v

0.16 mm s1 on albumin-coated glass and 0.5 mm s1 on

freshly cleaved mica. This shows that the spreading velocity depends on the adhesionstrength.

In order to crawl, cells have to push the front of the pseudopod forward. Following

Reference 40, these forces can be determined by measuring the deformation of soft

substrates in front of the pseudopods by colloidal force microscopy, as shown in

Figure 4a. The forces depend on the stiffness of the substrate. For example, f % 1 nNfor a polymer film with an elastic modulus of 200 Nm2 on which the pseudopods

proceed at v 0.13m

m s

1

. To fulfill Newtons third law, the protrusion forces on thecell are balanced by opposite forces on the substrate at the rear of the protrusions, which

requires that the cell adheres on the substrate. The experiments also suggest that the

mechanical stability is maintained by a local dipolar stress field (see Figure 4a) as pre-

dicted theoretically (7).

The local pinning occurs through small ($1 mm diameter) adhesion domains, whichare formed by lateral segregation of CAMs binding to the surface of other cells or tissue

(as shown in Figure 3b). They are stabilized by anchoring the actin filaments to the

intracellular domains of the CAMs, which is mediated by talin or other actin-membranelinkers. The adhesion domains can become very large and are then called focal adhesion

complexes (41).

Model membrane studies suggest that cell adhesion occurs in two steps: First, the fast

generation of the domains of tight adhesion by lateral segregation of bound receptors, and

second, the stabilization of the domains by assembly of actin gels to the intracellular side of

the adhesion domains (2, 42, 43). The initial process exhibits typical features of first-order

wetting transitions, resulting in the formation of small adhesion domains enabling strong

adhesion with a small number of receptors (43). The adhesion strength of the domainsdepends on the bending stiffness and the lateral tension of the composite cell envelope and

is thus strongly increased by binding of the actin cortex to the adhesion domains (44).

The kinetics of the first stage of adhesion is determined by the pronounced thermally

and actively driven bending excitations, resulting in a dynamic surface roughness of about

10 nm, generating an entropic disjoining pressure pdisj (summarized in Supplementary

Appendix G and References 16 and 17). The dynamic surface roughness controls the

adhesion dynamics in two ways: It impedes adhesion, but it also provides the pushingforces that bring the receptors and ligands close enough for bond formation (18). There-

fore, the adhesion is initiated by a nucleation and growth process, and the adhesion

kinetics depend critically on the binding strength of the receptor-ligand-pairs (which varies

between 5 and 20 kBT) and the lateral density of the CAMs.


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CAM

CAM(integrin)

Myosina

c

b

Signal

VASP

ATP-Actin

Molecular switch (activated)

Molecularswitch

(inactive)

Arp2/3

ADP-Actin

P

Cappingprotein

Formin

Strainprobes

Soft tissue

x

y

z

+

20 m

60

120

180

240300

0

ATP

Proflin

Activated actin

F-actin

Filipod

ium

Mem

brane

InactiveRho X Active

+

Bead

Activation o scafolding protein

Mechanism o actin growth by ormin

Figure 4

(a) Quasi-random walk of a Dictyostelium cell crawling on freshly cleaved mica (on which cells adhere weakly). Thecell position was recorded every 10 s. The cell moves in one direction in a saltatory manner and changes the directionof motion about every 60 s by spreading a pseudopod in a new direction. (b) Measurement of protrusion forcesgenerated by polar actin growth at the front of the protrusion by analyzing the shear deformation field of softsubstrates using colloidal strain probes (following Reference 40). Protrusion forces are balanced by the shear deforma-tion of the substrate behind the adhesion domains mediating the mechanical coupling between the substrate and the cell

envelope (see Supplemental Appendix E). (c) Simplified treadmilling model of formation of two types of protrusions.Sharp protrusions (filipodia) generated by activated growth of actin bundles mediated by the actin growth promoterformin, and broad protrusions (pseudopods) generated by growth of branched network mediated by the cross-linkerArp2/3. The growth of the broad pseudopods is initiated by a large protein complex, such as vasolidator-stimulatedphosphoprotein (VASP), shown in the top right box. It acts as scaffolding proteins, which recruit the proteins requiredfor the polar growth of the actin gel, including the cross-linker Arp2/3 and ATP-actin to the front of the pseudopods.The activated ATP-actin monomer is provided by unbinding from the filaments at the minus ends, a process mediatedby the actin binding proteins cofilin (or coronin, see also Figure 5). The thick arrow indicates the flow of activatedactin monomers to the front of the pseudopod. The scaffolding protein is transformed from a sleeping state into anactive state. This step is triggered by a molecular switch of the GTPase family, such as Cdc42 (see Reference 47 andSupplemental Material B). In the bottom right box, the mechanism of actin growth by formin is illustrated (followingReferences 51 and 52).

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The adhesion domains ofDictyostelium cells can be visualized by fluorescence micros-

copy using labeled actin-membrane coupler talin (45). In mammalian cells, adhesion

is often mediated by receptors of the integrin family, a dimer of membrane-spanning chains

a and b, whereby the b-chain binds to talin. Recently, a CAM (spanning the membrane

with 9 helices) sharing common features with the integrin b-chain was discovered inDictyostelium cells (46). Thus, the adhesion of amoebae and mammalian cells may share

common features.

A Treadmilling Process Propels Pseudopod Spreading

A widely accepted model of the growth of pseudopods (illustrated in Figure 3b) suggests

that it is controlled by three processes: (a) unbinding of G-actin with bound ADP (ADP-

actin) from the minus end of matured actin filaments through the G-actin providerscofilin; (b) the activation of G-actin by ADPATP exchange mediated by profilin; and(c) the growth of actin gels (bundles or branched networks) at the front, pushing the

pseudopod forward. The last process is mediated by two types of actin growth pro-

moters together with actin cross-linkers: Pseudopod formation is accelerated by a scaf-

folding protein [such as vasolidator-stimulated phosphoprotein (VASP)], which helps to

recruit the proteins required for the actin growth, including the cross-linker Arp2/3 (see

Figure 3b and Supplemental Appendix D). A second class of growth promotors, namely

formin (and mDia 1), together with the cross-linker fascin, generates tube-like protru-

sions, called filipodia.

An impressive proof of the treadmilling process as force generator has been pro-

vided by the observation that bacteria propel themselves through cells by polar

growth of actin gels. These bacteria exhibit at their surface a specific protein (Act A)

that mimicks the function of VASP as scaffolding protein (47). It mediates the activa-

tion of Arp2/3, resulting in the generation of comet-like gels that drive the bacteria

forward with velocities of 0.07 mm s1

. The process can be reproduced in vitro bycovering colloidal beads with VASP and suspending them in solution containing

(a) actin filaments, (b) cofilin (which decouples G-actin from the F-actin), and (c) Arp2/3

and ATP (48, 49). Evidence has been provided that the motor acts as a Brownian

ratchet (50).

Another mechanism for generating the protrusion force that drives the propagation of

filipodia (see Figure 4) is based on the sequential attachment of actin monomers to the tip

of the actin bundle. The growth is mediated by the growth promoter formin. With this

mechanism, forces of up to 10 pN per filament can be generated (49, 51, 52). The speed ofadvancement is controlled by the generation of free volume between the tip of the actin

filaments and the membrane, suggesting that this force generator works as a Brownian

ratchet, too (49).

Solitary Actin Gelation Wave Model of Pseudopod Spreading

The treadmilling process can be described in terms of a SAGW that is generated by polar

growth of the actin network at the front and the decay of matured actin gel at the end of

the wave. The basic idea is that the polar growth of the actin network at the front is

mediated by localized recruitment of a supramolecular scaffolding protein complex (com-

posed of 5 proteins) to the inner leaflet of the adhering cell envelope. This scaffolding

Scaffolding proteins:protein complexes thatcan bind one or severaleffectors involved in

the activation ofsignaling pathways


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protein recruits the molecules required for the actin gelation, such as profilin, activated

ATP-actin, and Arp2/3. It resides as a sleeping (closed) form in the cytoplasm and is

activated by the binding of members of the Rho-family GTPases (Cdc42 in the case of

VASP). They act as molecular switches that open the closed conformation (see Supplemen-

tal Appendix B).The scaffold proteins of different cells share some common structural homologies but

are named differently in the literature. WAVE/Hem-1 predominately refers to leukocytes

(53), VASP/Ena to fibroblasts (24, 47), and CARMIL/Myosin-IB to Dictyostelium cells

(54, 55). Hem1, Ena, and myosin-IB are supposed to be the key actuators (effectors) that

drive actin growth. They are supposed to undergo cycles of activation (by binding to the

scaffold protein) and deactivation (by unbinding).

PI-3,4,5-P3

PI-4,5-P2 gradients act as a guidance field of cell locomotion. Although

the role of the scaffold protein and the components involved is well established, the mech-anism of triggering or propagation of the wave is still obscure. The present view is that the

SAGW is driven by a local enrichment of the signal molecule PI-3,4,5-P3 at the adhered

plasma membrane at the front of the cell, resulting in a gradient PI-3,4,5-P3PI-4,5-P2toward its rear end. The gradient is generated by the antagonistic pair of enzymes:

phosphoinositide-3-kinase (PI-3K), which couples phosphate groups to the 3-position of

the inositol head group, and the conjugate phosphatase (PI-3PH, often called PTEN),

acting as PI-3,4,5-P3 annihilator. Both enzymes bind to the phosphoinositides via specific

domains (called C2-domains; see Supplemental Apprendixes C and D). The gradient stim-

ulates the actin polymerization at the front and the subsequent retraction of the rear end of

cells during each cycle of crawling (53).

The role of the PI-3,4,5-P3/PI-4,5-P2 gradient for the cell polarization is demon-

strated by the following observation (56): If Dictyostelium cells are subjected to a

local gradient of a chemoattractant (cAMP), then the PI-3,4,5-generator (PI-3K) accu-

mulates at the front and the annihilator (PI-3PH) at the rear of the cell. The retrac-

tion of the rear end is driven by the activation of muscle myosin II motors and theformation of actin-myosin micromuscles. Myosin-II is known to be activated by the

GTPase Rho, whereas the actin polymerization at the front is activated by Cdc42.

The gradient is therefore attributed to the negative feedback between the two signal-

ing systems (53).

Several formal models of SAGW generation have been proposed, all based on the

idea that the waves are generated by three properties of the actin gelation machinery.

One model states that actin polymerization is triggered by recruitment of an actin

polymerization promoter (e.g., Hem-1 in the case of leukocytes and myosin I in the caseof Dictyostelium cells) from the cytosol to the adhering membrane (53, 54). A second

model is that the growth rate of actin decreases due to the depletion of the pool of

G-actin, which introduces a delay in the rate of gelation. A third model is that the

recruitment of the promoter is cooperative, implying that its rate of binding to the

membrane increases with the amount already bound (57, 58). This results in a pair of

coupled differential equations for the actin growth rate, which are similar to the tradi-

tional equations describing the propagation of flames or of action potentials along nerve

axons. However, these models do not consider the role of the adhering composite mem-

brane. The experiment described below suggests an important role for the adhesion-

induced aggregation of receptor-ligand pairs mediating the adhesion of cells to the

substrate.

CARMIL: Cappingprotein, Arp2/3,Myosin I Linker

PI-3,4,5-P3:

phosphatidylinositol3,4,5-triphosphate

PI-4,5-P2: phosphati-dylinositol-4,5-diphos-phate

Cell locomotion:creeping motion ofcells on surfaces

PI-3K (-PH):phosphoinositolkinase (phosphatase)


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SOLITARY ACTIN GELATION WAVES AS TRAVELING FORCEFIELD MOTORS

Frustrated Phagocytosis Driven by Solitary Actin Gelation Waves

A paradigm of a motional process propelled by actin gelation is phagocytosis, the internal-ization of large particles by cells. This process occurs in two steps. First, the cell envelope

spreads over the particle, with spreading velocities of $0.1 mm s1. Subsequently, theparticle is engulfed completely by fusion of the front rim of the cell lobe. The efficiency of

the primary process depends also on the participation of microtubules. Their dismantling

by poisons (e.g., colchicine) results in the slowing down of the process (but not in its

abolishment).

The experiment in Figure 5a shows that the engulfment of large particles by Dictyostelium

cells is propelled by actin gelation. The objects consist of elongated elevations (with rect-angular cross sections) fabricated on solid substrates [composed of poly-dimethylsiloxan

(PDMS), an inorganic polymer]. The cells spread over these objects with velocities

of $0.04 mm s1, but cannot engulf them. We thus deal with frustrated phagocytosis.The time evolution of newly polymerized actin can be visualized by LIM-proteins labeled

with red fluorescent protein (for a discussion of the function of LIM-proteins, see Supple-

mental Appendix B and References 54 and 59). Simultaneously, the function of the

actin monomer supplier coronin is observed by labeling these proteins with green fluorescent

proteins (GFPs).

The cells spread over one (or sometimes two) pillars, acting as phantom prey, and move

to the next elevation. This motion is accompanied by the formation of one or several knob-

like assemblies of actin gels, which form preferentially at the top edge and side walls of the

pillars. They propagate along the upper edge and side walls and appear to drive the cell

movement. In some cases, one observes the simple behavior shown in Figure 5a. Two actin

assemblies form on opposite sides of the pillar and slide in a coordinated way in one

direction, carrying the cell with them. The propagating actin assemblies are inwroughtwith coronin, which provides the reservoir of actin required for the actin growth.

Model of Traveling Force Field Motor Mediated byPropagating Gradient of Signaling Lipid PI-3,4,5-P3

Figure 5b shows a model of SAGW-driven phagocytosis, described below. The basic

assumption is that the polar growth of the actin gel is determined by the propagating PI-

3,4,5-P3/PI-4,5-P2 gradient in the adhering membrane. It is generated by interplay of thePI-3-kinase (a PI-3,4,5-P3 generator) and the PI-3-phosphatase (PTEN) (a PI-3,4,5-P3-

annihilator). PI-3,4,5-P3 is accumulated in the adhesion domains by recruitment of PI-3K,

as observed in Reference 57 (justified in Supplemental Apprendix A).

The polar growth of the gel is mediated by the actin polymerization promoter coronin

playing two roles (see, for example, Supplemental Appendix B). It removes small pieces of

F-actin at the trailing end and transfers them to the growing front. Here, the unique

capacity of coronin to bind strongly fragments of F-actin with bound ATP (and not to

monomeric ADP-actin, such as cofilin) comes into play.

The actin polymerization rate is controlled by CARMIL (60, 61), which recruits the

players involved in the polar growth of actin to the adhesion domains, including Arp2/3

and the motor protein myosin IB. The rate-limiting step is the unbinding of the capping

LIM-protein:polypeptide exhibitingone or more cystein-rich protein motifs

called LIM domains,which promote actinpolymerization andare characteristic foractin-networkregulating activity

GFP (RFP): green (red)fluorescent protein



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proteins at the plus end by CARMIL, enabling the attachment of fragments of F-actin

bound to coronin (62, see also Supplemental Appendix D).

The binding of CARMIL to the membrane can be mediated by myosin IB and by the

phosphoinositides (see Figure 5b). Myosin IB can bind to the PM either directly, by

electrostatically binding its long basic tail to the negatively charged lipid moiety of themembrane, or indirectly, by binding its tail domain to the actin filaments already anchored

to the adhesion domains via talin (as shown Figure 4b).

By the uncapping process via CARMIL, only assemblies of linear actin filaments can

be generated. Branched networks can be formed in a second step by activation of Arp2/3.

This can only occur after the coronin is phosphorylated. Evidence for the recruitment of

a

b

Talin

PI-4,5-P2

PI-3K

CARMIL

Myo-IB

K

Cap

Receptor(CAM)

PI-3PH

Arp2,3

G-Actin

F-Actin

PHK K

PI-3,4,5-P3

PH PH

PH

Contour

K

Coronin

Propagation

= = = =

=

45 51 57 63 69

Tissue

PM

RFP GFP

Figure 5

(a) Visualization of actin gelation waves by fluorescence microscopy of cells double labeled with red fluorescent protein (RFP)LIM and green fluorescent protein (GFP)-labeled coronin. The cell crawls over a rectangular elevation (6 21 5 mm3). Thebrownish rim defines the contour of the cell. For simplicity, only five snapshots of the contour of the cell and of the distribution offreshly polymerized actin and coronin at the time intervals (seconds) indicated are shown. Note: That the cell adheres only

slightly on top of the pillar (where only small actin gel patches are seen), and the propagating acting gelation wave (SAGW)moves the cell along the pillar. (b) Model of the cell motion as described in the text, showing the major molecular ingredientsinvolved in the SAGW generation. Note that the scaffolding protein complex CARMIL (Capping protein, Arp2/3, Myosin ILinker) can couple to the membrane via myosin IB or by binding to phosphoinositides (PI-3,4,5-P3 or PI-4,5-P2). Also note thatthe PI-3,4,5-P3-generating kinase PI-3K is recruited to the membrane after coupling of CAMs to the tissue (64).



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CARMIL by myosin IB and the delayed formation of branched networks is provided by the

following observation: At the front of the SAGW, the newly synthesized actin (as indicated

by LIM) and myosin IB appear simultaneously (e.g., within about 1 s after a sudden

generation of a gradient of chemoattractants cAMP). In contrast, the recruitment of Arp2/

3 to the front is delayed by 12 s (55).Concerning the propagation of the SAGW, we assume that the PI-3,4,5-P3/PI-4,5-P2

gradient is driven by the constant recruitment of PI-3K at the front of the spreading

pseudopod where the adhesion domains are constantly regenerated (63). At this site,

new CAMs are recruited that activate the PI-3K to generate new signaling lipids (Refer-

ence 64 and Supplemental Appendix A). Due to receptor clustering, the recruitment of the

CARMIL/myosin IB complex is a cooperative process.

The role of the MT network is still poorly understood, although it is well established

that it plays a regulatory role for global cell movements and propagation of cellular pro-trusions. Thus, MTs are required for effective phagocytosis because the particle uptake is

much slower if the MTs are removed. An established function of the MT is to recruit and

activate the PI-3,4,5-P3 generator PI-3K to membranes because concentration of the sig-

naling lipid in the membrane is lowered after MT decomposition (64). This mechanism

could also trigger the growth of actin assemblies at the poles of the dividing cell, mediating

the final positioning of the spindles (24) as suggested above.

CONCLUSION

SAGWs enable cells to generate nano-Newton forces, which propell cell locomotion or

global shape changes (e.g., phagocytosis). The protrusion forces are not generated by the

motion of motors but by propagating assemblies of the signal molecules PI-3,4,5-P3, which

mediate the local recruitment of the actuators (CARMIL and myosin IB), stimulating the

polar growth of the actin gel. With the SAGW-driven system, much larger forces can be

generated than with intracellular linear motors, although motions can only be generatedover small distances ($5 mm). For that reason, the persistent motions ofDictyostelium cellsconsist of zig-zag-like paths of about 5-mm step length (as shown in Reference 38 and

visualized in Figure 3b).

The propagation of the PI-3,4,5-P3 PI-4,5-P2 gradient is a membrane-bound processand shares common features with the diffusive transport of action potentials along nerve

axons. The action potential is generated by (electric fieldtriggered) cooperative opening of

many ion channels, but the propagation is driven by the local tangential transport of the

Na ions at the inner surface of the axon. The delayed opening of the K ions prevents thebackflow of the action potential. The role of Na channels appears to be played by the

accumulation of new PI-3,4,5-P3 lipids at the newly formed adhesion domains, whereas

the role of K ions is played by coronin, which dismantles the F-actin at the rear side.

SUMMARY POINTS

1. The cytoplasmic space of cells is an active viscoplastic body that is mechanically

stabilized by interactive crosstalk between the viscoelastic shell and the aster-like

array of microtubules embedded in the viscoplastic cytoplasmatic space.




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2. Freely swimming and adhering cells exhibit typical features of tensegrity struc-

tures, with microtubules acting as ropes, whereas the actin cortex plays the role of

a compressible strut.

3. The exploration of the intracellular space by organelles and phagosomes is opti-mized by superposition of random walks (driven mainly by nonthermal quasi-

random intracellular forces) and active motions along the microtubules.

4. Migrating cells explore the environment by Levy-like quasi-random walks com-

posed of persistent (zig-zag-like) paths and local reorientational motions. The

directed motion is driven by cyclic spreading of cell lobes (pseudopods) powered

by solitary acting gelation waves (SAGWs), followed by retraction of the rear of

the cell mediated by actin-myosin micromuscles.

5. SAGWs can act as traveling force-field motors that drive cells over local obstacles.The traveling force field is guided by the propagation of gradients of the signaling

lipids PI-3,4,5-P3 and PI-4,5-P2 (embedded in the adhering cell membrane),

which is possibly coupled to the migration of adhesion domains. The process is

reminiscent of the diffusive propagation of action potentials along nerve axons.

FUTURE ISSUES1. Development of micromechanical tools is needed for the measurement of abso-

lute viscoelastic moduli of cell envelopes and intracellular macromolecular scaf-

folds of living cells.

2. Investigation into cell signal processes triggered by mechanical forces from the

molecular level (such as force-induced control of enzyme functions and protein-

protein interaction) to the mesoscopic scale (such as the control of membrane

interactions by undulation-induced entropic forces) will provide more detailedinsights into the physical basis of cell movement.

3. The role of the interactive microtubule actin crosstalk in the polarization of

moving cells, in the sensing and balancing of external forces, and in the control

of cell-cell and cell-tissue adhesion should be clarified.

4. Theoretical concepts must be developed for the understanding and evaluation of

intracellular motions driven by quasi-random forces in systems far from thermo-

dynamic equilibrium.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings

that might be perceived as affecting the objectivity of this review.

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Annual Review of

Condensed Matter

Physics

Contents

Electron Transport in Carbon NanotubesShahal Ilani and Paul L. McEuen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

FeAs-Based Superconductivity: A Case Study of the Effects of

Transition Metal Doping on BaFe2As2Paul C. Canfield and Sergey L. Budko . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Scattering and Pairing in Cuprate Superconductors

Louis Taillefer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Spintronics

S.D. Bader and S.S.P. Parkin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Characterizing Graphene, Graphite, and Carbon Nanotubes by

Raman Spectroscopy

M.S. Dresselhaus, A. Jorio, and R. Saito . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Single-Molecule NanomagnetsJonathan R. Friedman and Myriam P. Sarachik . . . . . . . . . . . . . . . . . . . . 109

Fermi-Hubbard Physics with Atoms in an Optical Lattice

Tilman Esslinger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Nematic Fermi Fluids in Condensed Matter Physics

Eduardo Fradkin, Steven A. Kivelson, Michael J. Lawler,

James P. Eisenstein, and Andrew P. Mackenzie . . . . . . . . . . . . . . . . . . . . 153

The Coulomb Phase in Frustrated Systems

Christopher L. Henley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

First-Principles Calculations of Complex Metal-Oxide Materials

Karin M. Rabe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

X-Ray Diffraction Microscopy

Pierre Thibault and Veit Elser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

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Physics of Cellular Movements

Erich Sackmann, Felix Keber, and Doris Heinrich . . . . . . . . . . . . . . . . . . 257

Molecular Theories of Segmental Dynamics and Mechanical

Response in Deeply Supercooled Polymer Melts and Glasses

Kang Chen, Erica J. Saltzman, and Kenneth S. Schweizer . . . . . . . . . . . . . 277

Rheology of Soft Materials

Daniel T.N. Chen, Qi Wen, Paul A. Janmey, John C. Crocker, and

Arjun G. Yodh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

The Mechanics and Statistics of Active Matter

Sriram Ramaswamy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

The Jamming Transition and the Marginally Jammed SolidAndrea J. Liu and Sidney R. Nagel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Dynamics of Simple Cracks

Eran Bouchbinder, Jay Fineberg, and M. Marder . . . . . . . . . . . . . . . . . . . 371

Friction, Fracture, and Earthquakes

Eric G. Daub and Jean M. Carlson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Errata

An online log of corrections to Annual Review of Condensed Matter Physics

articles may be found at http://conmatphys.annualreviews.org/errata.shtml

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