Alexandra Levtchenko
email: alexandra.levtchenko@geeps.centralesupelec.fr

Raphaël Lachaume

Jérôme Michallon

Stéphane Collin

José Alvarez

Sylvain Le Gall

Zakaria Djebbour

Jean-Paul Kleider

Coupling Optical and Electrical Modelling for the study of a-Si:H-based nanowire Array Solar Cells

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Coupled optical/electrical simulations have been performed on a p-i-n radial nanowire arrays based on crystalline p-type silicon (c-Si) core/hydrogenated amorphous silicon (a-Si:H) shell heterojunction. Three-dimensional (3D) optical calculations based on Rigorous Coupled Wave Analysis (RCWA) are firstly performed and then coupled to a semiconductor device simulator that exploits the radial symmetry of the nanowires. By varying either the doping concentration of the c-Si core, or the work function of the Aldoped ZnO (AZO) back contact we can separate and originally highlight the contribution to the cells performance of the nanowires themselves (the radial junction) from the planar part in between the nanowires (the planar junction). We show that the short-circuit current density (J sc ) only depends on the doping of the c-Si core indicating that it is mainly influenced by the radial junction. Whereas the open-circuit voltage (V oc ) is strongly affected by the back contact conditions (AZO work function), revealing an important impact of the interspacing between the nanowires on the characteristics of the entire nanowire array. We explain this strong influence of the back contact conditions by the fact that it determines the band-bending in the a-Si:H absorber shell touching the AZO, i.e. in the planar part. Therefore, it directly impacts the potential drop (V bi ) in the same area. For low work functions, the dark current density (J dark ) is increased in the planar region, where V bi is lower, which degrades the V oc of the entire cell.

Introduction

Recently, many researches have been focused on the development of nanowire arrays for microelectronic and photovoltaic applications [1,2]. In the context of photovoltaics, optical modelling has been used to demonstrate light absorption enhancement in nanowire arrays as compared with planar cells [3][4][5]. However, in order to reduce the costs of such a structure, a promising design would consist in a nanowire with a thin-film absorber. Experimentally, significant improvements of nanowire growth and material properties have been reported for radial heterojunctions based on thin c-Si cores and a-Si:H absorber shells [6][7][8]. However, to determine their ideal design it is necessary to resort to numerical simulations. Previous modelling work focused either only on their optical light harvesting properties [7,9,10] or only on their electrical performance without taking into account the light enhancement effects of nanostructuration [11,12]. Besides, a study of both optical and electrical properties of c-Si/a-Si:H radial heterojunctions has already been proposed for a c-Si absorber [13], therefore it is now mandatory to couple optical models to electrical simulations to assess the carrier collection efficiency of nanowires based on a-Si:H absorbers. In this study we first performed optical modelling to determine the photogeneration rate distribution in nanowires as well as the available photocurrent. Then the photogeneration was imported into a semiconductor device simulator [START_REF]User's manual for ATLAS from Silvaco International[END_REF] to show the impact on electrical performance of the planar junction located in the interspacing between nanowires.

Modelling methods

Simulated structure

Figure 1 shows the structure of interest. The array of nanowires has been designed from experimental achievements [6][7][8]. For the modelling, a periodic square mesh arrangement was considered and the period was calculated from the density of nanowires determined by SEM images for the best cell performance, namely 2.6 ×10 8 cm -2 (see Fig. 1a) [6] Each nanowire, described in Fig. 1b, consists in a radial p-i-n junction with 20 nm p-type crystalline silicon core, (p)c-Si, covered by 100 nm of intrinsic hydrogenated amorphous silicon absorber, (i)a-Si:H, surrounded by n-type hydrogenated amorphous silicon shell, (n)a-Si:H of 10 nm. The 1 µm long (p)c-Si core allows the radial collection of holes which then flow to the back contact made of aluminium doped zinc oxide (AZO). Radial collection of electrons is ensured by indium tin oxyde (ITO). In addition to the radial junction of nanowires, there is a planar junction in between the nanowires for which the back contact acts as a hole collector.

Optical modelling

Photogeneration in the nanowire array was calculated with 3D Rigorous Coupled Wave Analysis (RCWA) method. Optical indices of materials were directly extracted from ellipsometry measurements. Photogeneration profile of a single nanowire is then extracted and flattened to a 2D plane. This photogeneration profile is then implemented into a semiconductor device simulator based on the finite volume method that exploits the radial symmetry of the nanowires (see Fig. 3).

Electrical modelling

Electrical parameters of the materials are gathered in Table 1. Amorphous silicon was modelled with defects density of states (DOS) as described in Fig. 2a for (n)a-Si:H and 2b for (i)a-Si:H. The doping of c-Si was varied in a large range: from 10 17 to 8×10 18 cm -3 , while the doping of (n)a-Si:H was set to 1.7×10 19 cm -3 leading to a position of the fermi level of 0.16 eV under the conduction band with the introduced defects. The fermi level of (i)a-Si:H is located at 0.85 eV from the conduction band. The work function of ITO was chosen to meet flat band conditions at the ITO/(n)a-Si:H interface in order to study only the influence of the AZO contact. The reported work function of AZO depends on the measurement technique as well as on the material synthesis conditions [START_REF] Jaramillo | [END_REF], therefore in this study it was varied of ±500 meV around 5 eV. Interfaces between the different layers are considered ideal (no recombination). At the contacts, surface recombination velocities were taken infinite for both types of carriers as in [16].

Results and discussion

Photogeneration and ideal current

Figure 3a shows the sketch of the electrically modelled structure (nanowire and the surrounding planar part) which takes into account the rotational symmetry of the nanowires around z-axis. The corresponding photogeneration rate (G) distribution, calculated by RCWA, is represented in Fig. 3b. It shows that in the designed array the light is mostly concentrated at the top of the core of the nanowire. The resulting ideal current density (J opt ) corresponds to the case in which all the photogenerated carriers are collected, and is expressed as:

𝐽 𝑜𝑝𝑡 = 𝑞.∭ 𝐺(𝑟,𝜃,𝑧).𝑑𝑟.𝑑𝜃.𝑑𝑧 𝑆 , (1)
where r, θ and z are respectively radial, angular and longitudinal components of cylindrical coordinates, q is the electric charge and S is the area of a mesh, namely the square of the distance between two nanowires.. The global J opt of the structure is 15.3 mA/cm². It is divided into 14 mA/cm² for the radial part (91.5 %) and 1.3 mA/cm² for the planar part (8.5 %).

Carrier collection efficiency

When considering J sc , modelling the planar part allows to take into account an enhancement of 1.2 mA/cm² to the total J sc thanks to its good carrier collection efficiency (J sc /J opt ) of 92.3 %. The nanowire part has also a good carrier collection efficiency (83.6 %) meaning that the main way of improving the efficiency of the array is to optimize the absorption via the geometry of the nanostructuration and the optical properties of materials.

As shown in Fig. 3a, the studied structure has two types of junctions: a radial one in the nanowires, and a planar one related to the interspacing between these nanowires. The two parameters that influence their respective effects on the cell's performance are the doping of the c-Si core and the back contact (AZO) work function, as they determine the band-bending in the absorber material (i)a-Si:H.

Figure 4a shows the short-circuit current density (J sc ) as a function of doping concentration of c-Si for three different work function values. We notice a strong dependence on the doping of c-Si while it only slightly depends on the AZO work function. The major increase of J sc with doping occurs between 5×10 17 cm -3 and 5×10 18 cm -3 with an enhancement of 11%. Then it saturates at a value of 12.9 mA/cm² for the best case. This harvesting can be explained by the increase of the electric field in both junctions: when the doping of (p)c-Si, or the AZO work function, increases the band-bending in the absorber gets stronger, resulting in a larger electric field. However, as the photogeneration rate in the radial part is much more important than in the planar one, there is a larger possibility of carrier collection enhancement by field effect there.

The work function of AZO has a strong impact on the open-circuit voltage as shown in Fig. 4b. This is also due to the variations of the band-bending in (i)a-Si:H. Figures 4c and4d depict the 1D electronic band diagrams of both planar (r-axis cutline on Fig. 3a) and radial (zaxis cutline on Fig. 3a) junctions for work function values of 4.8 eV and 5.2 eV, respectively. The blue curve with circle markers and the green one with square markers correspond to the planar junction : (n)a-Si:H/(i)a-Si:H/AZO, while the purple curve with triangle markers corresponds to the radial one: (n)a-Si:H/(i)a-Si:H/(p)c-Si. It is important to notice that the potential drop, or built-in potential (V bi ), in the absorber is different for each junction. When V bi is larger in the radial part (see Fig. 4c), namely for work functions up to 5 eV, V oc depends only on the planar junction contact. When V bi is lower in the radial part (see Fig. 4d), V oc also depends on the radial contact.

The expression of V oc can be written as:

𝑉 𝑜𝑐 = 𝑛𝑘𝑇 𝑞 ln � 𝐽 𝑠𝑐 𝐽 𝑑𝑎𝑟𝑘 �, (2)
where n is the ideality factor of the diode, k is the Boltzmann constant, T is the temperature, q is the electric charge, J sc the short-circuit current density, and J dark the current density in the dark. Considering that J sc does not vary consequently with the AZO work function, as shown in Fig. 4a, the variations of V oc directly depend on those of J dark . When increasing the work function, J dark also rises as depicted in Fig. 5a. When looking at the distribution of J dark at V oc (i.e. for the same total current density value) at different work functions (see Fig. 5b, 5c and 5d) it appears that it increases in the planar region when its V bi is smaller than the radial one.

It then starts to flow to the radial junction when increasing the work function, therefore making the planar region more resistive. Depending on the structure's parameters, the planar junction can drastically affect the performance of the full cell: for low work functions, the planar region degrades the V oc of the entire cell.

Conclusions

In this paper we performed coupled optical/electrical modelling of c-Si core / a-Si absorber-shell radial heterojunction nanowires array. We showed the importance to take into account the region between the nanowires as it consists in a planar junction which influences the performance of the entire cell. The efficiency is determined by the work function of the back contact through the V oc which is degraded when the dark current density is concentrated in the planar region.

Figure 1

 1 Figure 1 (a) Geometry of the simulated nanowire array. (b) Detailed structure of a single nanowire and the planar junction interspacing that has been modelled.

Figure 2

 2 Figure 2 Density of defect states in (a) n-type a-Si:H (b) intrinsic a-Si:H.

Figure 3

 3 Figure 3 (a) Sketch of the radial symmetry of nanowires with the surrounding planar part. (b) Corresponding photogeneration rate distribution calculated by RCWA.

Figure 4

 4 Figure 4 Parameters influencing J sc and V oc . (a) Variation of the short-circuit current density (J sc ) as a function of doping concentration of c-Si for three different work function values (black square symbol: 5.5eV; blue line: 5.2 eV and orange triangle: 4.8 eV). (b) Open-circuit voltage (V oc ) as a function of AZO work function for two doping concentration values (blue star: 1×10 18 cm -3 and green cross: 8×10 18 cm -3 ). (c) and (d) represent the 1D band diagrams of both junctions for respectively AZO work function of 4.8 eV (c) and 5.2 eV (d). The blue curve with circle markers and the green one with square markers correspond to the planar junction : (n)a-Si:H/(i)a-Si:H/AZO, while the purple curve with triangle markers corresponds to the radial one: (n)a-Si:H/(i)a-Si:H/(p)c-Si.

Figure 5

 5 Figure 5 (a) Dark current density dependence on bias for N a =8×10 18 cm -3 . Map of J dark distribution in the entire structure at V oc for different AZO workfunctions (b) 4.8 eV, (c) 5.0 eV and (d) 5.2eV.

Table 1

 1 Electrical parameters of materials at 300K

		(p) c-Si	(i) a-Si:H	(n) a-Si:H
	E g (eV)	1.12	1.7	1.7
	χ (eV)	4.05	3.8	3.8
	ε r	11.9	11.9	11.9
	µ n (cm²/(V.s)) 1300	20	20
	µ p (cm²/(V.s)) 491	4	4
	N c (cm -3 )	2.8×10 19	5×10 20	5×10 20
	N v (cm -3 )	1.04×10 19	5×10 20	5×10 20

Acknowledgements

This work has been supported by the French Research National Agency -project SOLARIUM (ANR-14-CE05-0025).


Keith Burridge
email: keith_burridge@med.unc.edu

Christophe Guilluy
email: christophe.guilluy@univ-nantes.fr

Focal adhesions, stress fibers and mechanical tension

Keywords: Myosin II, RhoA, Integrins, Substratum rigidity

come

Focal adhesions, stress fibers and mechanical tension

Introduction

Growing in culture many cell types, particularly those of me-senchymal origin, display prominent bundles of filamentous actin (F-actin) associated with myosin II, α-actinin and several other cytoskeletal proteins. These structures, known as stress fibers (SFs) occur in several distinct forms. Frequently, they are associated at one or both ends with adhesions to the underlying matrix, known most commonly as focal adhesions (FAs). For over 40 years there has been considerable interest in the functions of these structures, their role in cell migration, and how they assemble and disassemble. Much evidence has indicated that these structures are mechanosensitive [START_REF] Burridge | Are stress fibres contractile?[END_REF][START_REF] Geiger | Exploring the neighborhood: adhesion-coupled cell mechanosensors[END_REF][START_REF] Hoffman | Dynamic molecular processes mediate cellular mechanotransduction[END_REF][START_REF] Case | Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch[END_REF][START_REF] Burridge | The tension mounts: stress fibers as force-generating mechanotransducers[END_REF] and it was concluded earlier that mechanical tension contributes to their assembly [START_REF] Burridge | Are stress fibres contractile?[END_REF][START_REF] Riveline | Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism[END_REF][START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF]. However, several recent studies have challenged this view and demonstrated a more complex situation [START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motorindependent manner[END_REF][START_REF] Stricker | Spatiotemporal constraints on the forcedependent growth of focal adhesions[END_REF][START_REF] Oakes | Tension is required but not sufficient for focal adhesion maturation without a stress fiber template[END_REF][START_REF] Thievessen | Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth[END_REF]. Here, we consider the role of mechanical force in the assembly of SFs and FAs.

It is often forgotten, even by those who study FAs and SFs, that these structures are not needed for cell migration [START_REF] Burridge | Are stress fibres contractile?[END_REF][START_REF] Herman | Relation between cell activity and the distribution of cytoplasmic actin and myosin[END_REF]. Many cells (e.g. leukocytes) do not develop FAs or SFs but migrate highly effectively. Indeed, the presence of FAs can hinder cell migration due to excessive adhesion. Nevertheless, many migratory cells do display FAs and SFs. In these cells there must be a dynamic coupling of adhesion strength and traction force for cells to move forward. It is important that both adhesion and traction at the front are stronger than at the rear, and so mechanisms must exist for modulating these. Force at the front of migrating cells derives from both retrograde actin flow and myosin-generated tension [START_REF] Case | Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch[END_REF].

For many years, the term stress fiber was most commonly applied to the large bundles of Factin that traverse much of the cell and that are anchored at both ends by FAs. However, it was readily apparent that a variety of structures were often referred to as stress fibers. In 1998, Small and colleagues distinguished 2 types of SF: ventral SFs, which are anchored at each end by a FA, and dorsal SFs, which are anchored only at one end by a FA close to the cell front. Dorsal SFs extend back toward the nucleus and upwards toward the dorsal cell surface. They also discussed "arcs", convex bundles of F-actin that form behind the leading edge of migrating or spreading cells and which move rearwards below the dorsal surface [START_REF] Small | Assembling an actin cytoskeleton for cell attachment and movement[END_REF]. Subsequent studies have included arcs, often referred to as transverse arcs, as a form of SF [START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF]. Arcs contain many of the same proteins, but unlike other types of SF, they are not directly anchored by adhesions to the matrix. However, arcs can give rise to ventral SFs and will be considered here as a form of SF.

One complicating factor in the relationship between mechanical tension and the assembly of FAs and SF is that the three types of filament bundle collectively referred to as SFs differ in their genesis, behavior, and relationship to FAs. Additionally, different models have been used to study how SFs and FAs assemble.

Systems for analyzing SF and FA assembly

Most studies have examined the assembly and disassembly of these structures as cells spread and migrate on coverslips coated with extracellular matrix (ECM) (most commonly fibronectin) [START_REF] Case | Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch[END_REF][START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF][START_REF] Webb | FAK-Src signalling through paxillin, ERK and MLCK regulates adhesion disassembly[END_REF][START_REF] Burnette | A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells[END_REF][START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF]. This system is well suited to analyzing adhesion dynamics and actin organization as cells migrate. The second experimental model for examining FA and SF assembly was pioneered by Ridley and Hall [START_REF] Ridley | The small GTP-binding protein rho regulates the assembly of focal adhesions and actin stress fibers in response to growth-factors[END_REF]. They exploited the observation that some cells lose their SFs and FAs when deprived of serum to become quiescent. Upon re-addition of serum or other factors that activate RhoA, FAs and SFs rapidly reassemble. It should be noted that these cells are usually in a non-migratory state and often confluent. This system was used to identify RhoA as a key regulatory protein controlling the assembly of these structures. It was also the system used to show that RhoA-induced assembly of FAs and SFs was blocked by a variety of inhibitors of myosin activity and contractility. This led to the conclusion that RhoA-stimulated myosin activity drives the assembly of SFs and FAs [START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF]. The bundling of F-actin to form a SF was attributed not only to the tension generated by myosin but also to myosin's crosslinking of F-actin [START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF][START_REF] Burridge | Focal adhesions, contractility, and signaling[END_REF]. Contractility inhibitors available at the time of these experiments were relatively non-specific. However, subsequent studies using blebbistatin and Y27632, which inhibit the activities of myosin II and ROCK respectively, have also shown that inhibiting myosin activity blocks the formation of most FAs and SFs [START_REF] Pasapera | Myosin II activity regulates vinculin recruitment to focal adhesions through FAK-mediated paxillin phosphorylation[END_REF][START_REF] Even-Ram | Myosin IIA regulates cell motility and actomyosin-microtubule crosstalk[END_REF]. Similarly, knockout or knockdown of myosin II expression prevented maturation of nascent adhesions into FAs [START_REF] Even-Ram | Myosin IIA regulates cell motility and actomyosin-microtubule crosstalk[END_REF][START_REF] Vicente-Manzanares | Regulation of protrusion, adhesion dynamics, and polarity by myosins IIA and IIB in migrating cells[END_REF]. In one study this was found for both myosin IIA and IIB [START_REF] Vicente-Manzanares | Regulation of protrusion, adhesion dynamics, and polarity by myosins IIA and IIB in migrating cells[END_REF], whereas in another this was dependent on knockout of myosin IIA but not IIB [START_REF] Even-Ram | Myosin IIA regulates cell motility and actomyosin-microtubule crosstalk[END_REF] This second model system (stimulation of quiescent cells with serum or Rho-activating factors) was well suited to microinjection of constitutively active or dominant negative constructs. In addition, it has the advantage of allowing synchronous assembly of FAs and SFs to be studied in many cells. However, many cell types are resistant to serum-starvation; they either maintain FAs and SFs, or show only a slight decrease in these structures when deprived of serum. Another disadvantage is that this system does not recapitulate the events that occur as cells migrate and engage the ECM at new sites.

Cell migration involves a series of transitions that affect both the adhesions and organization of the actin cytoskeleton. As the lamellipodium extends, driven by Arp2/3 complexmediated actin polymerization, initial adhesions form as integrin receptors engage the underlying matrix [START_REF] Case | Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch[END_REF][START_REF] Vicente-Manzanares | Adhesion dynamics at a glance[END_REF]. Such "nascent adhesions" are often transient and many rapidly disassemble. Maturation of adhesions that are not disassembled occurs at the transition between the lamellipodium and lamella, where retrograde actin flow changes from being driven by actin polymerization to myosin-based contraction. Whereas actin is organized in the lamellipodium as a branching dendritic network, in the lamella it is often bundled into the different SF types [START_REF] Ponti | Two distinct actin networks drive the protrusion of migrating cells[END_REF]. The maturing adhesions elongate in the direction of retrograde actin flow and retard the rate of rearward movement of actin [START_REF] Alexandrova | Comparative dynamics of retrograde actin flow and focal adhesions: formation of nascent adhesions triggers transition from fast to slow flow[END_REF]. They act as "molecular clutches" that couple the force of retrograde flow into forward extension of the lamellipodium [START_REF] Case | Integration of actin dynamics and cell adhesion by a three-dimensional, mechanosensitive molecular clutch[END_REF]. Consistent with this clutch-like function, it was observed that in stationary cells FAs are often pulled toward the nucleus, whereas in migrating cells they are stationary [START_REF] Smilenov | Focal adhesion motility revealed in stationary fibroblasts[END_REF]. The small maturing adhesions are often referred to as "focal complexes" [START_REF] Nobes | Rac, and Cdc42 GTPases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamelli-podia, and filopodia[END_REF]. Some continue enlarging to become classical "focal adhesions". However, the different types of adhesion are poorly defined and it is often difficult to distinguish one type from another. In general, FAs are dependent on RhoA activity, whereas focal complexes are dependent on active Rac1 or Cdc42 [START_REF] Nobes | Rac, and Cdc42 GTPases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamelli-podia, and filopodia[END_REF].

Hotulainen and Lappalainen used live cell imaging to analyze assembly of the different SF types in migrating osteosarcoma cells [START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF]. They observed dorsal SFs initiating at small adhesions forming behind the leading edge. As the cell front extended away from the adhesion, dorsal SFs elongated. This SF growth was inhibited by depleting cells of the formin mDia1. Alpha-actinin was incorporated into the growing SF. Recruitment of myosin II into the dorsal SF was a relatively late event. A subsequent study using higher resolution imaging concluded that little if any myosin II is incorporated into dorsal SFs [START_REF] Burnette | A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells[END_REF]. Transverse arcs arose behind the lamellipodium from the combination of short myosin filaments plus actin filaments generated at the leading edge by the Arp2/3 complex. In this system, ventral SFs developed most commonly from the fusion of each end of an arc with a dorsal SF. The annealing of two dorsal SFs growing from opposite sides of a cell also gave rise to ventral SFs, again anchored at each end by FAs. A subtype of ventral SFs (discussed later) is the perinuclear "actin cap", where ventral SFs wrap over nuclei and anchor to elongated FAs [START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF]. The different SF types are illustrated in Fig. 1.

Burnette and colleagues used the same cells to explore the factors that maintain the lamella flat as cells migrate [START_REF] Burnette | A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells[END_REF]. They determined that dorsal SFs, which they found contained little to no myosin II, acted as struts connecting the ventral adhesions with the dorsal contractile actin meshwork. Their analysis revealed that contraction of transverse arcs generated tension on dorsal SFs, and this caused the dorsal SFs to pivot, thereby flattening the lamella [START_REF] Burnette | A contractile and counterbalancing adhesion system controls the 3D shape of crawling cells[END_REF].

The role of myosin and tension in the development of stress fibers and focal adhesions

Besides the evidence that blocking Rho-mediated myosin activity inhibited ventral SF and FA assembly in quiescent cells [START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF], support for mechanical tension stimulating assembly comes from several observations. For example, shear stress at levels equivalent to that experienced in arteries induced endothelial cells in culture to develop SFs [START_REF] Franke | Induction of human vascular endothelial stress fibres by fluid shear stress[END_REF]. Direct evidence for mechanical tension stimulating growth of FAs came from Riveline and colleagues who applied force directly to individual cells with a glass rod. They observed growth of adhesions by IRM optics and incorporation of fluorescently labeled FA proteins [START_REF] Riveline | Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism[END_REF]. Adhesion growth was blocked by inhibiting RhoA activity, but this could be rescued by expression of the constitutively active formin, mDia1, which is normally activated by RhoA. It was concluded that FA growth requires both tension and actin polymerization, with each being driven by active RhoA. Supporting this idea that growth of FAs reflects the tension applied to them, Geiger's group used traction force microscopy to reveal a close correlation between the size of FAs and the force that is transmitted across them [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. [see comments[END_REF][START_REF] Schwarz | Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization[END_REF].

If mechanical force promotes the growth and maturation of FAs, one prediction is that new components will be recruited to FAs in response to force. This is indeed what was seen both when individual components such as vinculin were examined [START_REF] Galbraith | The relationship between force and focal complex development[END_REF], as well as when the FA proteome was analyzed [START_REF] Kuo | Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for beta-Pix in negative regulation of focal adhesion maturation[END_REF][START_REF] Schiller | Quantitative proteomics of the integrin adhesome show a myosin II-dependent recruitment of LIM domain proteins[END_REF]. Examining the composition of isolated FAs, many proteins were found to be recruited to FAs in the presence, but not the absence of active myosin [START_REF] Kuo | Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for beta-Pix in negative regulation of focal adhesion maturation[END_REF][START_REF] Schiller | Quantitative proteomics of the integrin adhesome show a myosin II-dependent recruitment of LIM domain proteins[END_REF]. The idea that tension stimulates FA growth and maturation is also supported by experiments using beads coated with integrin ligands to apply force to cells. Reinforcement of the adhesion made to beads has been observed in multiple studies [START_REF] Galbraith | The relationship between force and focal complex development[END_REF][START_REF] Choquet | Extracellular matrix rigidity causes strengthening of integrin-cytoskeleton linkages[END_REF][START_REF] Wang | Mechanotransduction across the cell surface and through the cytoskeleton[END_REF][START_REF] Matthews | Cellular adaptation to mechanical stress: role of integrins, Rho, cytoskeletal tension and mechanosensitive ion channels[END_REF][START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF]. FA proteins are recruited to the bead adhesion sites under tension [START_REF] Galbraith | The relationship between force and focal complex development[END_REF], again consistent with force contributing to adhesion assembly.

What is the basis for the stiffening or reinforcement that occurs when tension is applied exogenously on integrins? One of the signaling pathways activated in response to tension on integrins is the RhoA pathway [START_REF] Matthews | Cellular adaptation to mechanical stress: role of integrins, Rho, cytoskeletal tension and mechanosensitive ion channels[END_REF][START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF][START_REF] Zhao | Force activates smooth muscle alpha-actin promoter activity through the Rho signaling pathway[END_REF]. Not only will this lead to increased actin polymerization via the RhoA-activated formin mDia1 [START_REF] Watanabe | p140mDia, a mammalian homolog of Drosophila diaphanous, is a target protein for Rho small GTPase and is a ligand for profilin[END_REF], but it will also promote the stability of actin filaments by inhibiting the severing activity of cofilin (via ROCK4 LIMK4 phosphorylation of cofilin). Additionally, the activation of myosin II by ROCK [START_REF] Amano | Phosphorylation and activation of myosin by Rho-associated kinase (Rho-kinase)[END_REF][START_REF] Kimura | Regulation of myosin phosphatase by Rho and Rho-Associated kinase (Rhokinase)[END_REF] will lead to a positive feedback loop increasing tension. Just as importantly, activated myosin II that has assembled into bipolar filaments is a multivalent cross-linker and bundler of F-actin [START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motorindependent manner[END_REF][START_REF] Burridge | Focal adhesions, contractility, and signaling[END_REF]. Additionally, F-actin reveals enhanced affinity for myosin II when under tension [START_REF] Uyeda | Stretching actin filaments within cells enhances their affinity for the myosin II motor domain[END_REF]. Similarly, in response to tension, F-actin binds less cofilin and is more resistant to severing by cofilin [START_REF] Hayakawa | Actin filaments function as a tension sensor by tensiondependent binding of cofilin to the filament[END_REF].

How might force on a FA lead to recruitment of new components? One way may involve exposure of tension-sensitive cryptic protein binding sites (illustrated in Fig. 2A). Originally demonstrated for fibronectin [START_REF] Zhong | Rho-mediated contractility exposes a cryptic site in fibronectin and induces fibronectin matrix assembly[END_REF], this has also been shown for proteins at the cytoplasmic face of FAs, such as talin. Applying tension to single talin molecules exposed previously buried vinculin binding sites [START_REF] Del Rio | Stretching single talin rod molecules activates vinculin binding[END_REF]. Similarly, other proteins may expose sites that become modified, thereby facilitating new interactions [START_REF] Tamada | Activation of a signaling cascade by cy-toskeleton stretch[END_REF]. For example, mechanically stretching p130cas exposed multiple tyrosines that could be phosphorylated by Src [START_REF] Sawada | Force sensing by mechanical extension of the Src family kinase substrate p130Cas[END_REF].

SFs have also been shown to undergo reinforcement in response to strain. First demonstrated when cells experience cyclic stretch or shear stress [START_REF] Yoshigi | Mechanical force mobilizes zyxin from focal adhesions to actin filaments and regulates cytoskeletal reinforcement[END_REF], zyxin shuttles from FAs to zones of tension within SFs and triggers local recruitment of α-actinin and vasodilator-stimulated phosphoprotein (VASP) that thickens and reinforces SFs [START_REF] Yoshigi | Mechanical force mobilizes zyxin from focal adhesions to actin filaments and regulates cytoskeletal reinforcement[END_REF][START_REF] Colombelli | Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization[END_REF]. Zyxin-dependent SF reinforcement has also been observed in cells that are not subjected to external mechanical stress. This repair mechanism serves to limit SF elongation and breakage at sites of excessive strain [START_REF] Smith | A zyxinmediated mechanism for actin stress fiber maintenance and repair[END_REF]. Interestingly, zyxin targeting to SFs depends on MAPK activation. Although the mechanism involved is not fully understood, multiple models have been proposed and hinge on tension-dependent conformational changes in SF-associated proteins to expose new docking sites for zyxin [START_REF] Smith | A zyxinmediated mechanism for actin stress fiber maintenance and repair[END_REF].

Little is known about how the bonds between particular proteins in FAs respond to mechanical tension. However, in some cases "catch" bonds, which strengthen in response to tension [START_REF] Evans | Forces and bond dynamics in cell adhesion[END_REF], have been identified, for example, for the fibronectin-binding integrin α5β1 [START_REF] Friedland | Mechanically activated integrin switch controls alpha5beta1 function[END_REF][START_REF] Kong | Demonstration of catch bonds between an integrin and its ligand[END_REF]. We suspect that more catch bonds will be identified operating in FAs. We anticipate that some of the signaling associated with mechanical tension will modify protein interactions, converting slip bonds into catch bonds, thereby facilitating tension-induced stabilization. Conversely, the conversion of catch bonds into slip bonds may contribute to the disassembly of adhesions at the rear of migrating cells.

Evidence against tension playing a dominant role in FA and SF assembly

In contrast to the above studies, several have challenged the importance of myosin-generated tension in FA and SF assembly. Some of the different conclusions may reflect that different types of SF and FAs assemble through different mechanisms. So, for example, in the study by Hotulainen and Lappalainen, inhibiting myosin activity rapidly blocked formation of transverse arcs, but had little initial effect on dorsal SFs and the small adhesions that anchor them [START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF]. Tension was also important in the conversion of transverse arcs into ventral SFs, following their fusion with dorsal SFs. The role of myosin in dorsal SF assembly seems minimal. In several ways, dorsal SFs resemble filopodia. Both structures consist of narrow bundles of F-actin anchored either in a tip complex (filopodium) or nascent adhesion (dorsal SF). The filaments within these bundles all appear initially to have a single polarity, with polymerization occurring at the membrane attachment site, i.e. the filopodial tip or matrix adhesion. Because myosin II cannot generate contractile force on bundles of F-actin with a single polarity, whenever myosin II incorporates into these structures (such as when dorsal SFs are fusing with transverse arcs), then the polarity of the actin filaments must be broken so that the bundle contains F-actin of opposite polarities. Little is known about how this polarity transition occurs, although some possibilities have been suggested [START_REF] Burridge | The tension mounts: stress fibers as force-generating mechanotransducers[END_REF][START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF].

Tension generated within stress fibers is transmitted across FAs as demonstrated by studying traction forces at a subcellular scale [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. [see comments[END_REF][START_REF] Plotnikov | Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration[END_REF][START_REF] Beningo | Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts[END_REF][START_REF] Tan | Cells lying on a bed of microneedles: an approach to isolate mechanical force[END_REF][START_REF] Gardel | Traction stress in focal adhesions correlates biphasically with actin retrograde flow speed[END_REF] and shown most directly using a vinculin tension sensor [START_REF] Grashoff | Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics[END_REF]. As mentioned above, Geiger and his colleagues correlated the magnitude of force generated at a FA with the cross-sectional area of the FA [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. [see comments[END_REF]. A very different conclusion was reached by Beningo and colleagues who found that small adhesions at the front of a migrating cell developed greater tractional force than the larger adhesions further away from the front [START_REF] Beningo | Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts[END_REF]. Similar results were reported by Stricker et al. [START_REF] Stricker | Spatiotemporal constraints on the forcedependent growth of focal adhesions[END_REF]. A key difference in these studies is that these last two groups examined FAs in migrating cells, whereas the study reporting a positive correlation between FA size and tension used stationary cells [START_REF] Balaban | Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. [see comments[END_REF]. Another study found that for larger FAs their size was proportional to the force being transmitted, but for small adhesions the correlation broke down [START_REF] Tan | Cells lying on a bed of microneedles: an approach to isolate mechanical force[END_REF]. Since small adhesions are usually at the cell front, a potential explanation is that the additional force experienced by these small adhesions arises from retrograde actin flow and from transverse arcs that transmit tension to the matrix via dorsal SFs. However, this does not explain why these small adhesions do not enlarge in response to the high force being applied, which would be predicted by the Riveline study [START_REF] Riveline | Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism[END_REF].

Choi and colleagues investigated the role of myosin II in nascent adhesion maturation [START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motorindependent manner[END_REF]. Initial adhesion assembly occurred within the lamellipodium independently of myosin II on a template, the dorsal SF. The rate of assembly was proportional to the rate of protrusion of the lamellipodium. Template formation required α-actinin, indicating the importance of Factin crosslinking. The subsequent maturation of these nascent adhesions into FAs was blocked by knockdown of myosin IIA expression. Strikingly, the cells depleted of myosin IIA could be rescued by inactive motor mutants of myosin IIA that were unable to generate force. However, these mutants maintained their actin-binding ability. It was concluded that myosin's crosslinking function is more important than its tension-generating function for maturation of nascent adhesions [START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motorindependent manner[END_REF].

Some of the strongest arguments against tension driving assembly of FAs have come from

Gardel and her colleagues. They demonstrated that in migrating cells up to 60% of the force exerted on the substratum is generated by the lamellar actin network rather than by SFs [START_REF] Aratyn-Schaus | Dynamic and structural signatures of lamellar actomyosin force generation[END_REF]. Using blebbistatin wash-out as a trigger for inducing myosin activity, they showed that the assembly of SFs lagged temporally behind the development of traction forces. They also noted that FA growth rate remained constant under a range of different tensions [START_REF] Stricker | Myosin II-mediated focal adhesion maturation is tension insensitive[END_REF]. Titrating the level of myosin activity by varying the concentration of inhibitors led them to conclude that tension is necessary but not sufficient for FA maturation [START_REF] Oakes | Tension is required but not sufficient for focal adhesion maturation without a stress fiber template[END_REF]. They also concluded that the dorsal SF was critical as a structural template [START_REF] Oakes | Tension is required but not sufficient for focal adhesion maturation without a stress fiber template[END_REF].

Waterman's group found that FA growth was fast in cells lacking vinculin but that these cells exerted low traction on the substratum [START_REF] Thievessen | Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth[END_REF]. They concluded that vinculin when present couples retrograde actin flow to integrins and acts as a molecular clutch. Their finding that vinculin promotes the transmission of force to the substratum but results in slower growth of FAs runs counter to the idea that force itself contributes to FA growth.

Reconciling the differences

How can these seemingly different conclusions be reconciled? Some of the differences may come from the use of the different systems, migrating cells versus quiescent stationary cells. Other differences surely derive from grouping together the different types of SF and adhesion that are seen in migrating cells. The organization and behavior of dorsal SFs is different from transverse arcs and ventral SFs. The former seem largely independent of myosin-generated contractility whereas myosin is important for both transverse arcs and ventral SFs. However, myosin is needed for the maturation of adhesions, particularly its crosslinking function as shown by Choi and colleagues [START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motorindependent manner[END_REF].

In the original model of tension driving SF and FA assembly, actin polymerization was relatively minor [START_REF] Chrzanowska-Wodnicka | Rho-stimulated contractility drives the formation of stress fibers and focal adhesions[END_REF]. The pulling together and alignment of pre-existing filaments, already attached to integrins, was more important than nucleation of new filaments. This was supported by limited actin polymerization as SFs and FAs assembled in the quiescent cell model [START_REF] Machesky | Role of actin polymerization and adhesion to extra-cellular matrix in Racand rho-induced cytoskeletal reorganization[END_REF]. However, it is clear that actin polymerization is essential for the development of SFs and FAs in migrating cells [START_REF] Oakes | Tension is required but not sufficient for focal adhesion maturation without a stress fiber template[END_REF][START_REF] Hotulainen | Stress fibers are generated by two distinct actin assembly mechanisms in motile cells[END_REF]. One possibility is that mechanical tension may stimulate formin-mediated actin polymerization at FAs. Such a mechanism was suggested in the Rive-line study [START_REF] Riveline | Focal contacts as mechanosensors: externally applied local mechanical force induces growth of focal contacts by an mDia1-dependent and ROCK-independent mechanism[END_REF], in which they observed that tension-dependent adhesion growth was dependent on mDia. Consistent with this, Schiller and colleagues recently observed that actomyosin contractility was necessary to recruit mDia to adhesions [START_REF] Schiller | Beta1-and alphav-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments[END_REF]. Using a proteomic approach, they discovered that β1 and αv integrins cooperate to activate RhoA during adhesion to fibronectin but that downstream of RhoA the pathways diverged. Unexpectedly, β1 integrins were coupled to ROCK and activation of myosin II, whereas αv was coupled to activation of mDia and actin polymerization. However, in response to myosin II activity and high tension, αv integrin was recruited along with mDia to the adhesions. They concluded that cooperation between these fibronectin-binding integrins and their RhoA signaling pathways (Fig. 2B) contributed to adhesion maturation [START_REF] Schiller | Beta1-and alphav-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments[END_REF].

Stress fibers, focal adhesions and rigidity of the substratum

It has long been recognized that SFs are more prominent in cells growing on plastic or glass surfaces than they are in the same cells in their native tissue environment or growing in 3D systems [START_REF] Burridge | Are stress fibres contractile?[END_REF]. Is the prominence of SFs and FAs in cells growing in vitro due to the two dimensional nature of the substratum, to its rigidity, or both? Fibroblasts cultured in three dimensional collagen gels rarely develop SFs. Fibroblasts will actively contract free-floating gels, but if the gels are anchored to prevent contraction to a smaller volume, the cells develop isometric tension and develop SFs [START_REF] Mochitate | Stress relaxation of contracted collagen gels: disruption of actin filament bundles, release of cell surface fibronectin, and down-regulation of DNA and protein synthesis[END_REF][START_REF] Grinnell | Fibroblasts, myofibroblasts, and wound contraction[END_REF][START_REF] Tomasek | Fibroblast contraction occurs on release of tension in attached collagen lattices: dependency on an organized actin cytoskeleton and serum[END_REF]. Release of the gels from their attachments to the culture dish results in rapid contraction of the gels and disassembly of the SFs [START_REF] Mochitate | Stress relaxation of contracted collagen gels: disruption of actin filament bundles, release of cell surface fibronectin, and down-regulation of DNA and protein synthesis[END_REF][START_REF] Grinnell | Fibroblasts, myofibroblasts, and wound contraction[END_REF][START_REF] Tomasek | Fibroblast contraction occurs on release of tension in attached collagen lattices: dependency on an organized actin cytoskeleton and serum[END_REF].

The role of substrate rigidity in SF and FA assembly was examined directly by Pelham and Wang, who discovered that assembly of these structures was inhibited on soft substrata [START_REF] Pelham | Cell locomotion and focal adhesions are regulated by substrate flexibility[END_REF]. How might this occur? With the recognition that active RhoA drives formation of these structures [START_REF] Ridley | The small GTP-binding protein rho regulates the assembly of focal adhesions and actin stress fibers in response to growth-factors[END_REF], this raised the question whether adhesion to a rigid substratum stimulates RhoA activity. Measuring RhoA activity revealed that RhoA is activated in cells grown on rigid substrata [START_REF] Wozniak | ROCK-generated contractility regulates breast epithelial cell differentiation in response to the physical properties of a three-dimensional collagen matrix[END_REF][START_REF] Paszek | Tensional homeostasis and the malignant phenotype[END_REF]. Experimentally applying tension to engaged integrins was also found to activate RhoA [START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF][START_REF] Zhao | Force activates smooth muscle alpha-actin promoter activity through the Rho signaling pathway[END_REF]. Dissecting the pathway, Guilluy and colleagues identified both GEF-H1 and LARG as guanine nucleotide exchange factors (GEFs) responding to tension applied to fibronectin-coated beads [START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF]. GEF-H1 was activated downstream from FAK, Ras and the MEK/ERK pathway, whereas LARG was activated via the tyrosine kinase Fyn. Keely's group also found GEF-H1 was activated in cells adhering to rigid substrata, but in their case this was attributed to the release of GEF-H1 from microtubules [START_REF] Heck | Microtubules regulate GEF-H1 in response to extra-cellular matrix stiffness[END_REF]. Using proteomic approaches two groups have observed both GEF-H1 and mDia being recruited to adhesions in response to actomyosin contractility, suggesting that mechanical tension activates a GEF-H1/RhoA/mDia pathway that may promote adhesion growth [START_REF] Kuo | Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for beta-Pix in negative regulation of focal adhesion maturation[END_REF][START_REF] Schiller | Beta1-and alphav-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments[END_REF].

High resolution traction force microscopy revealed that traction generated at one FA was often independent of the traction being generated by an adjacent FA within the same cell [START_REF] Plotnikov | Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration[END_REF]. The force transmitted by an adhesion was either stable over time or it fluctuated. In situations where it fluctuated, this "tugging" at FAs was dispensable for their maturation, as well as for directional migration in response to chemotactic or haptotactic cues. However, it was needed for durotaxis, the migration up a stiffness gradient [START_REF] Plotnikov | Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration[END_REF]. The authors concluded that fluctuating tension at FAs provides a mechanism by which a cell senses the stiffness of the substratum.

Connections to the nucleus

It has long been known that tension exerted on the cell surface is transmitted to the nucleus and that multiple connections link the nucleus to the cytoskeleton [START_REF] Maniotis | Demonstration of mechanical connections between integrins, cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure[END_REF]. Indeed, mechanical force exerted on cells has profound effects on gene transcription [START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF][START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF][START_REF] Mcbeath | Cell shape, cytoskeletal tension, and RhoA regulate stem cell lineage commitment[END_REF][START_REF] Wang | Mechanotransduction at a distance: mechanically coupling the extracellular matrix with the nucleus[END_REF], and tension exerted via SFs impacts nuclear structure and function [START_REF] Swift | Nuclear lamin-A scales with tissue stiffness and enhances matrix-directed differentiation[END_REF][START_REF] Guilluy | Isolated nuclei adapt to force and reveal a mechanotransduction pathway in the nucleus[END_REF]. The nesprin family of proteins span the outer nuclear membrane, connecting the different filament systems to proteins spanning the inner nuclear membrane such as SUN 1 and 2 [START_REF] Wang | Mechanotransduction at a distance: mechanically coupling the extracellular matrix with the nucleus[END_REF][START_REF] Lombardi | The interaction between nesprins and sun proteins at the nuclear envelope is critical for force transmission between the nucleus and cytoskeleton[END_REF][START_REF] Starr | Interactions between nuclei and the cytoskeleton are mediated by SUN-KASH nuclear-envelope bridges[END_REF]. These proteins connecting the nucleus with the cytoskeleton have been referred to as the Linker of nucleoskeleton and cytoskeleton (LINC) complex [START_REF] Crisp | Coupling of the nucleus and cytoplasm: role of the LINC complex[END_REF].

Investigating the relationship of the centrosome and nucleus to signals driving directional fibroblast migration, Gundersen's group observed that the nucleus was pulled rearwards by actin filaments, such that the centrosome came lie in front of it [START_REF] Gomes | Nuclear movement regulated by Cdc42, MRCK, myosin, and actin flow establishes MTOC polarization in migrating cells[END_REF]. Pursuing this further, they identified bundles of actin filaments (dorsal actin cables) moving rearward over the nucleus and forming aligned arrays with the LINC complex. These transmembrane actinassociated nuclear lines (TAN lines) appear closely related to arcs that arise near the cell front and move backwards via retrograde flow [START_REF] Luxton | Linear arrays of nuclear envelope proteins harness retrograde actin flow for nuclear movement[END_REF]. However, once these arcs pass over the nucleus, they engage and align the LINC complex. The rearward movement of nuclei and TAN lines is closely correlated. Disrupting the LINC complex disrupts TAN lines and prevents nuclear movement in response to migration signals [START_REF] Luxton | Linear arrays of nuclear envelope proteins harness retrograde actin flow for nuclear movement[END_REF]. Depletion of emerin, an inner nuclear membrane protein involved in the interaction of the LINC complex with the nuclear lamins, caused the TAN lines to slip over immobile nuclei [START_REF] Chang | Emerin organizes actin flow for nuclear movement and centrosome orientation in migrating fibroblasts[END_REF].

Examining the relationship between cell and nuclear shape, Wirtz's group identified a subset of ventral SFs that wrap over the nucleus. These SFs connect to the nucleus via the LINC complex and form a perinuclear "actin cap". These SFs were implicated in determining nuclear shape, which was observed to be elongated in the direction of cell migration in moving cells, but round in stationary cells [START_REF] Khatau | A perinuclear actin cap regulates nuclear shape[END_REF]. Like other ventral SFs, the SFs of the actin cap are anchored by FAs at each end. However, these FAs and their associated SFs are distinctive in several respects. The FAs have a larger area and are more elongated than the FAs associated with other ventral SFs [START_REF] Kim | Actin cap associated focal adhesions and their distinct role in cellular mechanosensing[END_REF]. Together with the SFs of the actin cap, they are more susceptible to disassembly by the actin depolymerizing drug Latrunculin B. They are also more dynamic, with several FA components having shorter half-lives. Strikingly, the FAs associated with the actin cap were the first to disassemble after adhesion to soft substrata, leading to the conclusion that these FAs are more mechanosensitive than most FAs [START_REF] Kim | Actin cap associated focal adhesions and their distinct role in cellular mechanosensing[END_REF]. One has to wonder whether these actin cap-associated FAs are the same as those described by Waterman's group, i.e. fluctuating in tension to "sense" the stiffness of the substratum [START_REF] Plotnikov | Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration[END_REF]. Persistent migration was associated with an actin cap, whereas this disassembled when cells paused to change direction. Experimentally disrupting the actin cap inhibited persistent cell migration [START_REF] Kim | Tight coupling between nucleus and cell migration through the perinuclear actin cap[END_REF].

The above results raise the question of what the role of the nucleus is in cell migration, a topic beyond the scope of this brief review. However, numerous studies have observed that disrupting the LINC complex and hence the connections between the nucleus and the cytoskeleton have major effects on cell migration [START_REF] Starr | Interactions between nuclei and the cytoskeleton are mediated by SUN-KASH nuclear-envelope bridges[END_REF][START_REF] Jaalouk | Mechanotransduction gone awry[END_REF]. Whereas the nucleus appears important in cell migration, it should also be remembered that cells lacking a nucleus are capable of migrating [START_REF] Goldman | Preservation of normal behavior by enucleated cells in culture[END_REF][START_REF] Verkhovsky | Self-polarization and directional motility of cytoplasm[END_REF].

Concluding remarks

Our knowledge of the structure and organization of SFs and FAs has increased greatly in the last few years. Although there are still components that need to be identified, much of the analysis is moving toward the biophysical and attempting to understand how these structures that generate and transmit tension are organized by the forces that they are experiencing. One area that will be important in the future is characterizing which protein interactions within SFs and FAs are governed by catch bonds. Another area concerns how cells respond to different strain rates and the effect of different force regimes. Already some important results have been obtained. For example, Fletcher's group found that the rate of application of force impacts a cell's response [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF]. A step displacement causing the height of a 12 mm tall cell to increase by 1 mm resulted in immediate increase in tension followed by a rapid viscoelastic relaxation to a new baseline above the previous steady-state level. However, when the same change in height was imposed at a rate of 0.1 mm/min, there was just a gradual increase in steady-state tension to a new level that was below the value eventually achieved by the step increase in height. There was also no viscoelastic relaxation. When the height was increased ten times faster (by 1 mm/min), there was a much greater increase in steady-state tension, but again no viscoelastic relaxation [START_REF] Webster | Tensional homeostasis in single fibroblasts[END_REF]. High rates of strain have also been found to lead to fluidization of the cytoskeleton [START_REF] Trepat | Universal physical responses to stretch in the living cell[END_REF][START_REF] Krishnan | Reinforcement versus fluidization in cytoskeletal mechanoresponsiveness[END_REF]. Reconciling the different responses to force, i.e. reinforcement versus fluidization will be important. Although this may partly reflect differences in experimental conditions, ultimately it will involve understanding how the different protein interactions respond to different force regimes and whether slip or catch bonds are involved. Mechanical tension activates signaling pathways at adhesion sites. a. Exposure of cryptic sites. Tension can affect protein conformation to expose protein binding sites (e.g. talin) or sites for kinases or other protein modifications (e.g. p130cas). b. RhoA regulation of adhesion maturation through Rock and mDia. Adhesion to fibronectin activates RhoA through p115 RhoGEF and LARG [START_REF] Dubash | A novel role for Lsc/p115 RhoGEF and LARG in regulating RhoA activity downstream of adhesion to fibronectin[END_REF], leading to Rock-mediated myosin stimulation. In response to tension, GEF-H1, LARG and mDia are recruited [START_REF] Kuo | Analysis of the myosin-II-responsive focal adhesion proteome reveals a role for beta-Pix in negative regulation of focal adhesion maturation[END_REF][START_REF] Guilluy | The Rho GEFs LARG and GEF-H1 regulate the mechanical response to force on integrins[END_REF] and promote actin polymerization. B1 (1) and αv (2) integrin subtypes cooperate to regulate RhoA signaling and adhesion maturation [START_REF] Schiller | Beta1-and alphav-class integrins cooperate to regulate myosin II during rigidity sensing of fibronectin-based microenvironments[END_REF].

Fig. 1 .

 1 Fig. 1. Types of stress fiber in migrating cells. Schematic representation of SFs in motile cells, (a) top and (b) side views. Four categories of SFs are observed: dorsal SFs, transverse arcs, ventral SFs and the perinuclear actin cap.

Fig. 2 .

 2 Fig. 2.

Exp Cell Res. Author manuscript; available in PMC 2017 April 10.

Acknowledgments

We thank Erika Wittchen for valuable comments on the manuscript. KB is supported by the Kenan Foundation and by NIH grants (GM029860, GM103723 and HL114388). CG is supported by grants from the Agence National de la Recherche (ANR-13-JSV1-0008), from the European Union Seventh Framework Programme (Marie Curie Career Integration n°304162).