The mechanics of neutrophils: synthetic modeling of three experiments

Much experimental data exist on the mechanical properties of neutrophils, but so far, they have mostly been approached within the framework of liquid droplet models. This has two main drawbacks: 1), It treats the cytoplasm as a single phase when in reality, it is a composite of cytosol and cytoskeleton; and 2), It does not address the problem of active neutrophil deformation and force generation. To fill these lacunae, we develop here a comprehensive continuum-mechanical paradigm of the neutrophil that includes proper treatment of the membrane, cytosol, and cytoskeleton components. We further introduce two models of active force production: a cytoskeletal swelling force and a polymerization force. Armed with these tools, we present computer simulations of three classic experiments: the passive aspiration of a neutrophil into a micropipette, the active extension of a pseudopod by a neutrophil exposed to a local stimulus, and the crawling of a neutrophil inside a micropipette toward a chemoattractant against a varying counterpressure. Principal results include: 1), Membrane cortical tension is a global property of the neutrophil that is affected by local area-increasing shape changes. We argue that there exists an area dilation viscosity caused by the work of unfurling membrane-storing wrinkles and that this viscosity is responsible for much of the regulation of neutrophil deformation. 2), If there is no swelling force of the cytoskeleton, then it must be endowed with a strong cohesive elasticity to prevent phase separation from the cytosol during vigorous suction into a capillary tube. 3), We find that both swelling and polymerization force models are able to provide a unifying fit to the experimental data for the three experiments. However, force production required in the polymerization model is beyond what is expected from a simple short-range Brownian ratchet model. 4), It appears that, in the crawling of neutrophils or other amoeboid cells inside a micropipette, measurement of velocity versus counterpressure curves could provide a determination of whether cytoskeleton-to-cytoskeleton interactions (such as swelling) or cytoskeleton-to-membrane interactions (such as polymerization force) are predominantly responsible for active protrusion.     

A Ser/Thr kinase required for membrane-associated assembly of the major sperm protein motility apparatus in the amoeboid sperm of Ascaris

Leading edge protrusion in the amoeboid sperm of Ascaris suum is driven by the localized assembly of the major sperm protein (MSP) cytoskeleton in the same way that actin assembly powers protrusion in other types of crawling cell. Reconstitution of this process in vitro led to the identification of two accessory proteins required for MSP polymerization: an integral membrane phosphoprotein, MSP polymerization-organizing protein (MPOP), and a cytosolic component, MSP fiber protein 2 (MFP2). Here, we identify and characterize a 34-kDa cytosolic protein, MSP polymerization-activating kinase (MPAK) that links the activities of MPOP and MFP2. Depletion/add-back assays of sperm extracts showed that MPAK, which is a member of the casein kinase 1 family of Ser/Thr protein kinases, is required for motility. MPOP and MPAK comigrated by native gel electrophoresis, coimmunoprecipitated, and colocalized by immunofluorescence, indicating that MPOP binds to and recruits MPAK to the membrane surface. MPAK, in turn, phosphorylated MFP2 on threonine residues, resulting in incorporation of MFP2 into the cytoskeleton. Beads coated with MPAK assembled a surrounding cloud of MSP filaments when incubated in MPAK-depleted sperm extract, but only when supplemented with detergent-solubilized MPOP. Our results suggest that interactions involving MPOP, MPAK, and MFP2 focus MSP polymerization to the plasma membrane at the leading edge of the cell thereby generating protrusion and minimizing nonproductive filament formation elsewhere.     

Localized depolymerization of the major sperm protein cytoskeleton correlates with the forward movement of the cell body in the amoeboid movement of nematode sperm.

The major sperm protein (MSP)-based amoeboid motility of Ascaris suum sperm requires coordinated lamellipodial protrusion and cell body retraction. In these cells, protrusion and retraction are tightly coupled to the assembly and disassembly of the cytoskeleton at opposite ends of the lamellipodium. Although polymerization along the leading edge appears to drive protrusion, the behavior of sperm tethered to the substrate showed that an additional force is required to pull the cell body forward. To examine the mechanism of cell body movement, we used pH to uncouple cytoskeletal polymerization and depolymerization. In sperm treated with pH 6.75 buffer, protrusion of the leading edge slowed dramatically while both cytoskeletal disassembly at the base of the lamellipodium and cell body retraction continued. At pH 6.35, the cytoskeleton pulled away from the leading edge and receded through the lamellipodium as its disassembly at the cell body continued. The cytoskeleton disassembled rapidly and completely in cells treated at pH 5.5, but reformed when the cells were washed with physiological buffer. Cytoskeletal reassembly occurred at the lamellipodial margin and caused membrane protrusion, but the cell body did not move until the cytoskeleton was rebuilt and depolymerization resumed. These results indicate that cell body retraction is mediated by tension in the cytoskeleton, correlated with MSP depolymerization at the base of the lamellipodium.     

细胞运动、细胞迁移与细胞骨架研究进展

细胞定向运动与细胞骨架的动态循环密切相关。运动细胞在其伪足前沿依靠细胞骨架的不断聚合推动细胞膜的前进,在基部靠近细胞体部位通过细胞骨架的不断解聚收缩拖拉细胞体向前运动,细胞骨架的聚合与解聚通过伪足与支撑表面的吸附与解吸附而偶连。肌动蛋白组成的微丝骨架是大多数运动细胞的主要成分。外界刺激引起微丝细胞骨架动态变化的信号通路已逐步明了。线虫精子细胞的运动行为与阿米巴变形运动相似,但是在线虫精子细胞中没有肌动蛋白,而是以精子主要蛋白为基础形成细胞骨架驱动精子细胞的运动。与肌动蛋白不同,精子主要蛋白没有分子极性、ATP结合位点和马达蛋白。通过比较研究以上两种运动体系将有助于在分子水平上进一步阐明细胞运动的机理。     

Force generation by actin polymerization II: the elastic ratchet and tethered filaments

The motion of many intracellular pathogens is driven by the polymerization of actin filaments. The propulsive force developed by the polymerization process is thought to arise from the thermal motions of the polymerizing filament tips. Recent experiments suggest that the nucleation of actin filaments involves a phase when the filaments are attached to the pathogen surface by a protein complex. Here we extend the "elastic ratchet model" of Mogilner and Oster to incorporate these new findings. We apply this "tethered ratchet" model to derive the force-velocity relation for Listeria and discuss relations of our theoretical predictions to experimental measurements. We also discuss "symmetry breaking" dynamics observed in ActA-coated bead experiments, and the implications of the model for lamellipodial protrusion in migrating cells.     

Dephosphorylation of Major Sperm Protein (MSP) Fiber Protein 3 by Protein Phosphatase 2A during Cell Body Retraction in the MSP-based Amoeboid Motility of Ascaris Sperm

The crawling movement of nematode sperm requires coordination of leading edge protrusion with cell body retraction, both of which are powered by modulation of a cytoskeleton based on major sperm protein (MSP) filaments. We used a cell-free in vitro motility system in which both protrusion and retraction can be reconstituted, to identify two proteins involved in cell body retraction. Pharmacological and depletion-add back assays showed that retraction was triggered by a putative protein phosphatase 2A (PP2A, a Ser/Thr phosphatase activated by tyrosine dephosphorylation). Immunofluorescence showed that PP2A was present in the cell body and was concentrated at the base of the lamellipod where the force for retraction is generated. PP2A targeted MSP fiber protein 3 (MFP3), a protein unique to nematode sperm that binds to the MSP filaments in the motility apparatus. Dephosphorylation of MFP3 caused its release from the cytoskeleton and generated filament disassembly. Our results suggest that interaction between PP2A and MFP3 leads to local disassembly of the MSP cytoskeleton at the base of the lamellipod in sperm that in turn pulls the trailing cell body forward.     

Reconstitution in vitro of MSP-based filopodium extension in nematode sperm

The major sperm protein (MSP) motility system in nematode sperm is best known for propelling the movement of mature sperm, where it has taken over the role usually played by actin in amoeboid cell motility. However, MSP filaments also drive the extension of filopodia, transient organelles composed of a core bundle of MSP filaments, that form in the late in sperm development but are not found on crawling cells. We have reconstituted filopodial extension in vitro whereby thin bundles of MSP filaments, each enveloped by a membrane sheath at their growing end, elongated at rates up to 17 microm/min. These bundles often exceeded 500 microm in length but were comprised of filaments only 1 microm long. The reconstituted filopodia assembled in the same cell-free sperm extracts that produced MSP fibers, robust meshworks of filaments that exhibit the same organization and dynamics as the lamellipodial filament system that propels sperm movement. The filopodia and fibers that assembled in vitro both had a membranous structure at their growing end, shared four MSP accessory proteins, and responded identically to agents that alter MSP-based motility by modulating protein phosphorylation. However, filopodia grew three- to four-fold faster than fibers. The reconstitution of filopodial extension shows that, like the actin cytoskeleton, MSP filaments can adopt two architectures, bundles and meshworks, each capable of pushing against membranes to generate protrusion. The reconstitution of both forms of motility in the same in vitro system provides a promising avenue for understanding how the forces for membrane protrusion are produced.     

Progress in protrusion: the tell-tale scar.

The crawling movement of a cell involves protrusion of its leading edge, in coordination with the translocation of its cell body, and depends upon a cytoplasmic machinery able to respond to signals from the environment. Protrusion is now understood to be driven by actin polymerization, and signalling from membrane receptors to actin has been shown to be mediated by the Rho family of GTPases. However, a major gap in our understanding of regulated motility has been how to connect the signalling pathway to the motile machinery itself. Recent structural, biochemical and genetic studies have identified some of the missing links and provided a strong working model for the pathways and mechanisms by which the signals are interpreted and implemented.     

On the edge: modeling protrusion

Actin-based protrusion is the first step in cell crawling. In the last two decades, the studies of actin networks in the lamellipodium and Listeria's comet tail advanced so far that the last goal of the reductionist agenda - reconstitution of protrusion from purified components in vitro and in silico - became viable. Earlier models dealt with growth of and force generation by a single actin filament. Modern models of tethered ratchet, autocatalytic branching, end-tracking motor action and elastic- and nano- propulsion have recently helped to elucidate dynamics and forces in complex actin networks. By considering these models, their limitations and their relationships to recent biophysical data, progress is being made toward a unified model of protrusion.     

Evidence for phosphorylation in the MSP cytoskeletal filaments of amoeboid spermatozoa

Nematode spermatozoa are highly specialized cells that lack flagella and, instead, extend a pseudopod to initiate motility. Crawling spermatozoa display classic features of amoeboid motility (e.g. protrusion of a pseudopod that attaches to the substrate and the assembly and disassembly of cytoskeletal filaments involved in cell traction and locomotion), however, cytoskeletal dynamics in these cells are powered exclusively by Major Sperm Protein (MSP) rather than actin and no other molecular motors have been identified. Thus, MSP-based motility is regarded as a simple locomotion machinery suitable for the study of plasma membrane protrusion and cell motility in general. This recent focus on MSP dynamics has increased the necessity of a standardized methodology to obtain C. elegans sperm extract that can be used in biochemical assays and proteomic analysis for comparative studies. In the present work we have modified a method to reproducibly obtain relative high amounts of proteins from C. elegans sperm extract. We show that these extracts share some of the properties observed in sperm extracts from the parasitic nematode Ascaris including Major Sperm Protein (MSP) precipitation and MSP fiber elongation. Using this method coupled to immunoblot detection, Mass Spectrometry identification, in silico prediction of functional domains and biochemical assays, our results indicate the presence of phosphorylation sites in MSP of Caenorhabditis elegans spermatozoa.     

Dissection of the Ascaris sperm motility machinery identifies key proteins involved in major sperm protein-based amoeboid locomotion

Although Ascaris sperm motility closely resembles that seen in many other types of crawling cells, the lamellipodial dynamics that drive movement result from modulation of a cytoskeleton based on the major sperm protein (MSP) rather than actin. The dynamics of the Ascaris sperm cytoskeleton can be studied in a cell-free in vitro system based on the movement of plasma membrane vesicles by fibers constructed from bundles of MSP filaments. In addition to ATP, MSP, and a plasma membrane protein, reconstitution of MSP motility in this cell-free extract requires cytosolic proteins that orchestrate the site-specific assembly and bundling of MSP filaments that generates locomotion. Here, we identify a fraction of cytosol that is comprised of a small number of proteins but contains all of the soluble components required to assemble fibers. We have purified two of these proteins, designated MSP fiber proteins (MFPs) 1 and 2 and demonstrated by immunolabeling that both are located in the MSP cytoskeleton in cells and in fibers. These proteins had reciprocal effects on fiber assembly in vitro: MFP1 decreased the rate of fiber growth, whereas MFP2 increased the growth rate.     

Polarization and Movement of Keratocytes: A Multiscale Modelling Approach

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3.In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte.     

Regulation of actin dynamics in rapidly moving cells: a quantitative analysis

We develop a mathematical model that describes key details of actin dynamics in protrusion associated with cell motility. The model is based on the dendritic-nucleation hypothesis for lamellipodial protrusion in nonmuscle cells such as keratocytes. We consider a set of partial differential equations for diffusion and reactions of sequestered actin complexes, nucleation, and growth by polymerization of barbed ends of actin filaments, as well as capping and depolymerization of the filaments. The mechanical aspect of protrusion is based on an elastic polymerization ratchet mechanism. An output of the model is a relationship between the protrusion velocity and the number of filament barbed ends pushing the membrane. Significantly, this relationship has a local maximum: too many barbed ends deplete the available monomer pool, too few are insufficient to generate protrusive force, so motility is stalled at either extreme. Our results suggest that to achieve rapid motility, some tuning of parameters affecting actin dynamics must be operating in the cell.     

The polymerization ratchet model explains the force-velocity relation for growing microtubules

The polymerization of filamentous proteins generates mechanical forces which drive many cellular processes. Dogterom and Yurke measured the force-velocity relation generated by a single microtubule. They found that the force is generally in the range predicted by the “polymerization ratchet” mechanism, but the force-velocity relationship decreased faster than that theory predicted. Here we generalize the polymerization ratchet model to take into account the “subsidy effect” that arises because a microtubule consists of 13 protofilaments. With this generalization the model fits the experimental data well. The biological implications of the polymerization ratchet model are discussed. Received: 18 May 1998 / Revised version: 4 November 1998 / Accepted: 30 November 1998     

Hydrostatic Pressure Shows That Lamellipodial Motility in Ascaris Sperm Requires Membrane-associated Major Sperm Protein Filament Nucleation and Elongation

Sperm from nematodes use a major sperm protein (MSP) cytoskeleton in place of an actin cytoskeleton to drive their ameboid locomotion. Motility is coupled to the assembly of MSP fibers near the leading edge of the pseudopod plasma membrane. This unique motility system has been reconstituted in vitro in cell-free extracts of sperm from Ascaris suum: inside-out vesicles derived from the plasma membrane trigger assembly of meshworks of MSP filaments, called fibers, that push the vesicle forward as they grow (Italiano, J.E., Jr., T.M. Roberts, M. Stewart, and C.A. Fontana. 1996. Cell. 84:105–114). We used changes in hydrostatic pressure within a microscope optical chamber to investigate the mechanism of assembly of the motile apparatus. The effects of pressure on the MSP cytoskeleton in vivo and in vitro were similar: pressures >50 atm slowed and >300 atm stopped fiber growth. We focused on the in vitro system to show that filament assembly occurs in the immediate vicinity of the vesicle. At 300 atm, fibers were stable, but vesicles often detached from the ends of fibers. When the pressure was dropped, normal fiber growth occurred from detached vesicles but the ends of fibers without vesicles did not grow. Below 300 atm, pressure modulates both the number of filaments assembled at the vesicle (proportional to fiber optical density and filament nucleation rate), and their rate of assembly (proportional to the rates of fiber growth and filament elongation). Thus, fiber growth is not simply because of the addition of subunits onto the ends of existing filaments, but rather is regulated by pressure-sensitive factors at or near the vesicle surface. Once a filament is incorporated into a fiber, its rates of addition and loss of subunits are very slow and disassembly occurs by pathways distinct from assembly. The effects of pressure on fiber assembly are sensitive to dilution of the extract but largely independent of MSP concentration, indicating that a cytosolic component other than MSP is required for vesicle-association filament nucleation and elongation. Based on these data we present a model for the mechanism of locomotion-associated MSP polymerization the principles of which may apply generally to the way cells assemble filaments locally to drive protrusion of the leading edge.     

An adhesion-dependent switch between mechanisms that determine motile cell shape

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.     

Structure of MFP2 and its function in enhancing MSP polymerization in Ascaris sperm amoeboid motility

The simplicity and specialization of the cell motility machinery of Ascaris sperm provides a powerful system in which to probe the basic molecular mechanism of amoeboid cell motility. Although Ascaris sperm locomotion closely resembles that seen in many other types of crawling cell, movement is generated by modulation of a cytoskeleton based on the major sperm protein (MSP) rather than the actin present in other cell types. The Ascaris motility machinery can be studied conveniently in a cell-free in vitro system based on the movement of plasma membrane vesicles by fibres constructed from bundles of MSP filaments. In addition to ATP, MSP and a plasma membrane protein, reconstitution of MSP motility in this cell-free extract requires cytosolic proteins to orchestrate the site-specific assembly and bundling of MSP filaments that generates locomotion. One of these proteins, MFP2, accelerates the rate of movement in this assay. Here, we describe crystal structures of two isoforms of MFP2 and show that both are constructed from two domains that have the same fold based on a novel, compact beta sheet arrangement. Patterns of conservation observed in a structure-based analysis of MFP2 sequences from different nematode species identified regions that may be putative functional interfaces involved both in interactions between MFP2 domains and also with other components of the sperm motility machinery. Analysis of the growth of fibres in vitro in the presence of added MFP2 indicated that MFP2 increases the rate of locomotion by enhancing the effective rate of MSP filament polymerization. This observation, together with the structural data, suggests that MFP2 may function in a manner analogous to formins in actin-based motility.     

Quantification of Cell Edge Velocities and Traction Forces Reveals Distinct Motility Modules during Cell Spreading

Actin-based cell motility and force generation are central to immune response, tissue development, and cancer metastasis, and understanding actin cytoskeleton regulation is a major goal of cell biologists. Cell spreading is a commonly used model system for motility experiments – spreading fibroblasts exhibit stereotypic, spatially-isotropic edge dynamics during a reproducible sequence of functional phases: 1) During early spreading, cells form initial contacts with the surface. 2) The middle spreading phase exhibits rapidly increasing attachment area. 3) Late spreading is characterized by periodic contractions and stable adhesions formation. While differences in cytoskeletal regulation between phases are known, a global analysis of the spatial and temporal coordination of motility and force generation is missing. Implementing improved algorithms for analyzing edge dynamics over the entire cell periphery, we observed that a single domain of homogeneous cytoskeletal dynamics dominated each of the three phases of spreading. These domains exhibited a unique combination of biophysical and biochemical parameters – a motility module. Biophysical characterization of the motility modules revealed that the early phase was dominated by periodic, rapid membrane blebbing; the middle phase exhibited continuous protrusion with very low traction force generation; and the late phase was characterized by global periodic contractions and high force generation. Biochemically, each motility module exhibited a different distribution of the actin-related protein VASP, while inhibition of actin polymerization revealed different dependencies on barbed-end polymerization. In addition, our whole-cell analysis revealed that many cells exhibited heterogeneous combinations of motility modules in neighboring regions of the cell edge. Together, these observations support a model of motility in which regions of the cell edge exhibit one of a limited number of motility modules that, together, determine the overall motility function. Our data and algorithms are publicly available to encourage further exploration.     

Redundant mechanisms for stable cell locomotion revealed by minimal models

Crawling of eukaryotic cells on flat surfaces is underlain by the protrusion of the actin network, the contractile activity of myosin II motors, and graded adhesion to the substrate regulated by complex biochemical networks. Some crawling cells, such as fish keratocytes, maintain a roughly constant shape and velocity. Here we use moving-boundary simulations to explore four different minimal mechanisms for cell locomotion: 1), a biophysical model for myosin contraction-driven motility; 2), a G-actin transport-limited motility model; 3), a simple model for Rac/Rho-regulated motility; and 4), a model that assumes that microtubule-based transport of vesicles to the leading edge limits the rate of protrusion. We show that all of these models, alone or in combination, are sufficient to produce half-moon steady shapes and movements that are characteristic of keratocytes, suggesting that these mechanisms may serve redundant and complementary roles in driving cell motility. Moving-boundary simulations demonstrate local and global stability of the motile cell shapes and make testable predictions regarding the dependence of shape and speed on mechanical and biochemical parameters. The models shed light on the roles of membrane-mediated area conservation and the coupling of mechanical and biochemical mechanisms in stabilizing motile cells.     

Modeling cell protrusion predicts how myosin II and actin turnover affect adhesion-based signaling

Orchestration of cell migration is essential for development, tissue regeneration, and the immune response. This dynamic process integrates adhesion, signaling, and cytoskeletal subprocesses across spatial and temporal scales. In mesenchymal cells, adhesion complexes bound to extracellular matrix mediate both biochemical signal transduction and physical interaction with the F-actin cytoskeleton. Here, we present a mathematical model that offers insight into both aspects, considering spatiotemporal dynamics of nascent adhesions, active signaling molecules, mechanical clutching, actin treadmilling, and nonmuscle myosin II contractility. At the core of the model is a positive feedback loop, whereby adhesion-based signaling promotes generation of barbed ends at, and protrusion of, the cell’s leading edge, which in turn promotes formation and stabilization of nascent adhesions. The model predicts a switch-like transition and optimality of membrane protrusion, determined by the balance of actin polymerization and retrograde flow, with respect to extracellular matrix density. The model, together with new experimental measurements, explains how protrusion can be modulated by mechanical effects (nonmuscle myosin II contractility and adhesive bond stiffness) and F-actin turnover.