The shape of motile cells is determined by many dynamic processes spanning several orders of magnitude in space and time, from local polymerization of actin monomers at subsecond timescales to global, cell-scale geometry that may persist for hours. Understanding the mechanism of shape determination in cells has proved to be extremely challenging due to the numerous components involved and the complexity of their interactions. Here we harness the natural phenotypic variability in a large population of motile epithelial keratocytes from fish (Hypsophrys nicaraguensis) to reveal mechanisms of shape determination. We find that the cells inhabit a low-dimensional, highly correlated spectrum of possible functional states. We further show that a model of actin network treadmilling in an inextensible membrane bag can quantitatively recapitulate this spectrum and predict both cell shape and speed. Our model provides a simple biochemical and biophysical basis for the observed morphology and behaviour of motile cells.Cell shape emerges from the interaction of many constituent elements-notably, the cytoskeleton, the cell membrane and cellsubstrate adhesions-that have been studied in great detail at the molecular level 1-3 ; however, the mechanism by which global morphology is generated and maintained at the cellular scale is not understood. Many studies have characterized the morphological effects of perturbing various cytoskeletal and other cellular components (for example, ref. 4); yet, there have been no comprehensive efforts to try to understand cell shape from first principles. Here we address this issue in the context of motile epithelial keratocytes derived from fish skin. Fish keratocytes are among the fastest moving animal cells, and their motility machinery is characterized by extremely rapid molecular dynamics and turnover [5][6][7][8] . At the same time, keratocytes are able to maintain nearly constant speed and direction during movement over many cell lengths. Their shapes, consisting of a bulbous cell body at the rear attached to a broad, thin lamellipodium at the front and sides, are simple, stereotyped and notoriously temporally persistent 9,10 . The molecular dynamism of these cells, combined with the persistence of their global shape and behaviour, make them an ideal model system for investigating the mechanisms of cell shape determination.The relative simplicity of keratocytes has inspired extensive experimental and theoretical investigations into this cell type 5-17 , considerably advancing the understanding of cell motility. A notable example is the graded radial extension (GRE) model 12 , which was an early attempt to link the mechanism of motility at the molecular level with overall cell geometry. The GRE model proposed that local cell extension (either protrusion or retraction) occurs perpendicular to the cell edge, and that the magnitude of this extension is graded from a maximum near the cell midline to a minimum towards the sides. Although this phenomenological model has been shown experimentally ...

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.

Crawling locomotion of eukaryotic cells is achieved by a process dependent on the actin cytoskeleton1: protrusion of the leading edge requires assembly of a network of actin filaments2, which must be disassembled at the cell rear for sustained motility. Although ADF/cofilin proteins have been shown to contribute to actin disassembly3, it is not clear how activity of these locally acting proteins could be coordinated over the whole-cell distance scale. Here we show that nonmuscle myosin II plays a direct role in actin network disassembly in crawling cells. In moving fish keratocytes, myosin II is concentrated in regions at the rear with high rates of network disassembly. Activation of myosin II by ATP in detergent-extracted cytoskeletons results in rear-localized disassembly of the actin network. Inhibition of myosin II activity and stabilization of actin filaments synergistically impede cell motility, suggesting the existence of two disassembly pathways, one of which requires myosin II activity. Our results establish the importance of myosin II as an enzyme for actin network disassembly; we propose that gradual formation and reorganization of an actomyosin network provides an intrinsic destruction timer, enabling long-range coordination of actin network treadmilling in motile cells.

We have analyzed the spontaneous symmetry breaking and initiation of actin-based motility in keratocytes (fish epithelial cells). In stationary keratocytes, the actin network flow was inwards and radially symmetric. Immediately before motility initiation, the actin network flow increased at the prospective cell rear and reoriented in the perinuclear region, aligning with the prospective axis of movement. Changes in actin network flow at the cell front were detectable only after cell polarization. Inhibition of myosin II or Rho kinase disrupted actin network organization and flow in the perinuclear region and decreased the motility initiation frequency, whereas increasing myosin II activity with calyculin A increased the motility initiation frequency. Local stimulation of myosin activity in stationary cells by the local application of calyculin A induced directed motility initiation away from the site of stimulation. Together, these results indicate that large-scale actin–myosin network reorganization and contractility at the cell rear initiate spontaneous symmetry breaking and polarized motility of keratocytes.