Choosing orientation: influence of cargo geometry and ActA polarization on actin comet tails

Networks of polymerizing actin filaments can propel intracellular pathogens and drive movement of artificial particles in reconstituted systems. While biochemical mechanisms activating actin network assembly have been well characterized, it remains unclear how particle geometry and large-scale force balance affect emergent properties of movement. We reconstituted actin-based motility using ellipsoidal beads resembling the geometry of Listeria monocytogenes. Beads coated uniformly with the L. monocytogenes ActA protein migrated equally well in either of two distinct orientations, with their long axes parallel or perpendicular to the direction of motion, while intermediate orientations were unstable. When beads were coated with a fluid lipid bilayer rendering ActA laterally mobile, beads predominantly migrated with their long axes parallel to the direction of motion, mimicking the orientation of motile L. monocytogenes. Generating an accurate biophysical model to account for our observations required the combination of elastic-propulsion and tethered-ratchet actin-polymerization theories. Our results indicate that the characteristic orientation of L. monocytogenes must be due to polarized ActA rather than intrinsic actin network forces. Furthermore, viscoelastic stresses, forces, and torques produced by individual actin filaments and lateral movement of molecular complexes must all be incorporated to correctly predict large-scale behavior in the actin-based movement of nonspherical particles.     

Geometry-Driven Polarity in Motile Amoeboid Cells

Motile eukaryotic cells, such as leukocytes, cancer cells, and amoeba, typically move inside the narrow interstitial spacings of tissue or soil. While most of our knowledge of actin-driven eukaryotic motility was obtained from cells that move on planar open surfaces, recent work has demonstrated that confinement can lead to strongly altered motile behavior. Here, we report experimental evidence that motile amoeboid cells undergo a spontaneous symmetry breaking in confined interstitial spaces. Inside narrow channels, the cells switch to a highly persistent, unidirectional mode of motion, moving at a constant speed along the channel. They remain in contact with the two opposing channel side walls and alternate protrusions of their leading edge near each wall. Their actin cytoskeleton exhibits a characteristic arrangement that is dominated by dense, stationary actin foci at the side walls, in conjunction with less dense dynamic regions at the leading edge. Our experimental findings can be explained based on an excitable network model that accounts for the confinement-induced symmetry breaking and correctly recovers the spatio-temporal pattern of protrusions at the leading edge. Since motile cells typically live in the narrow interstitial spacings of tissue or soil, we expect that the geometry-driven polarity we report here plays an important role for movement of cells in their natural environment.     

Actin filament attachments for sustained motility in vitro are maintained by filament bundling

We reconstructed cellular motility in vitro from individual proteins to investigate how actin filaments are organized at the leading edge. Using total internal reflection fluorescence microscopy of actin filaments, we tested how profilin, Arp2/3, and capping protein (CP) function together to propel thin glass nanofibers or beads coated with N-WASP WCA domains. Thin nanofibers produced wide comet tails that showed more structural variation in actin filament organization than did bead substrates. During sustained motility, physiological concentrations of Mg(2+) generated actin filament bundles that processively attached to the nanofiber. Reduction of total Mg(2+) abolished particle motility and actin attachment to the particle surface without affecting actin polymerization, Arp2/3 nucleation, or filament capping. Analysis of similar motility of microspheres showed that loss of filament bundling did not affect actin shell formation or symmetry breaking but eliminated sustained attachments between the comet tail and the particle surface. Addition of Mg(2+), Lys-Lys(2+), or fascin restored both comet tail attachment and sustained particle motility in low Mg(2+) buffers. TIRF microscopic analysis of filaments captured by WCA-coated beads in the absence of Arp2/3, profilin, and CP showed that filament bundling by polycation or fascin addition increased barbed end capture by WCA domains. We propose a model in which CP directs barbed ends toward the leading edge and polycation-induced filament bundling sustains processive barbed end attachment to the leading edge.     

Actin-myosin network reorganization breaks symmetry at the cell rear to spontaneously initiate polarized cell motility

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.     

In Silico Reconstitution of Listeria Propulsion Exhibits Nano-Saltation

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein–protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our “in silico reconstitution” produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes, in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.     

Biophysical parameters influence actin-based movement, trajectory, and initiation in a cell-free system

Using a biochemically complex cytoplasmic extract to reconstitute actin-based motility of Listeria monocytogenes and polystyrene beads coated with the bacterial protein ActA, we have systematically varied a series of biophysical parameters and examined their effects on initiation of motility, particle speed, speed variability, and path trajectory. Bead size had a profound effect on all aspects of motility, with increasing size causing slower, straighter movement and inhibiting symmetry-breaking. Speed also was reduced by extract dilution, by addition of methylcellulose, and paradoxically by addition of excess skeletal muscle actin, but it was enhanced by addition of nonmuscle (platelet) actin. Large, persistent individual variations in speed were observed for all conditions and their relative magnitude increased with extract dilution, indicating that persistent alterations in particle surface properties may be responsible for intrinsic speed variations. Trajectory curvature was increased for smaller beads and also for particles moving in the presence of methylcellulose or excess skeletal muscle actin. Symmetry breaking and movement initiation occurred by two distinct modes: either stochastic amplification of local variation for small beads in concentrated extracts, or gradual accumulation of strain in the actin gel for large beads in dilute extracts. Neither mode was sufficient to enable spherical particles to break symmetry in the cytoplasm of living cells.     

In silico reconstitution of Listeria propulsion exhibits nano-saltation

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein–protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our “in silico reconstitution” produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes, in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.     

Mesoscopic Model of Actin-Based Propulsion

Two theoretical models dominate current understanding of actin-based propulsion: microscopic polymerization ratchet model predicts that growing and writhing actin filaments generate forces and movements, while macroscopic elastic propulsion model suggests that deformation and stress of growing actin gel are responsible for the propulsion. We examine both experimentally and computationally the 2D movement of ellipsoidal beads propelled by actin tails and show that neither of the two models can explain the observed bistability of the orientation of the beads. To explain the data, we develop a 2D hybrid mesoscopic model by reconciling these two models such that individual actin filaments undergoing nucleation, elongation, attachment, detachment and capping are embedded into the boundary of a node-spring viscoelastic network representing the macroscopic actin gel. Stochastic simulations of this ‘in silico’ actin network show that the combined effects of the macroscopic elastic deformation and microscopic ratchets can explain the observed bistable orientation of the actin-propelled ellipsoidal beads. To test the theory further, we analyze observed distribution of the curvatures of the trajectories and show that the hybrid model''s predictions fit the data. Finally, we demonstrate that the model can explain both concave-up and concave-down force-velocity relations for growing actin networks depending on the characteristic time scale and network recoil. To summarize, we propose that both microscopic polymerization ratchets and macroscopic stresses of the deformable actin network are responsible for the force and movement generation.     

Characterization of in vitro motility assays using smooth muscle and cytoplasmic myosins

We have used two in vitro motility assays to study the relative movement of actin and myosin from turkey gizzards (smooth muscle) and human platelets. In the Nitella-based in vitro motility assay, myosin-coated polymer beads move over a fixed substratum of actin bundles derived from dissection of the alga, Nitella, whereas in the sliding actin filament assay fluorescently labeled actin filaments slide over myosin molecules adhered to a glass surface. Both assay systems yielded similar relative velocities using smooth muscle myosin and actin under our standard conditions. We have studied the effects of ATP, ionic strength, magnesium, and tropomyosin on the velocity and found that with the exception of the dependence on MgCl2, the two assays gave very similar results. Calcium over a concentration of pCa 8 to 4 had no effect on the velocity of actin filaments. Phosphorylated smooth muscle myosin propelled filaments of smooth muscle and skeletal muscle actin at the same rate. Phosphorylated smooth muscle and cytoplasmic myosin monomers also moved actin filaments, demonstrating that filament formation is not required for movement.     

Cooperative symmetry-breaking by actin polymerization in a model for cell motility

Polymerizing networks of actin filaments are capable of exerting significant mechanical forces, used by eukaryotic cells and their prokaryotic pathogens to change shape or to move. Here we show that small beads coated uniformly with a protein that catalyses actin polymerization are initially surrounded by symmetrical clouds of actin filaments. This symmetry is broken spontaneously, after which the beads undergo directional motion. We have developed a stochastic theory, in which each actin filament is modelled as an elastic brownian ratchet, that quantitatively accounts for the observed emergent symmetry-breaking behaviour. Symmetry-breaking can only occur for polymers that have a significant subunit off-rate, such as the biopolymers actin and tubulin.     

Deformations in actin comets from rocketing beads

The mechanical and dynamical properties of the actin network are essential for many cellular processes like motility or division, and there is a growing body of evidence that they are also important for adhesion and trafficking. The leading edge of migrating cells is pushed out by the polymerization of actin networks, a process orchestrated by cross-linkers and other actin-binding proteins. In vitro physical characterizations show that these same proteins control the elastic properties of actin gels. Here we use a biomimetic system of Listeria monocytogenes, beads coated with an activator of actin polymerization, to assess the role of various actin-binding proteins in propulsion. We find that the properties of actin-based movement are clearly affected by the presence of cross-linkers. By monitoring the evolution of marked parts of the comet, we provide direct experimental evidence that the actin gel continuously undergoes deformations during the growth of the comet. Depending on the protein composition in the motility medium, deformations arise from either gel elasticity or monomer diffusion through the actin comet. Our findings demonstrate that actin-based movement is governed by the mechanical properties of the actin network, which are fine-tuned by proteins involved in actin dynamics and assembly.     

Mammalian twinfilin sequesters ADP-G-actin and caps filament barbed ends: implications in motility

Twinfilins are conserved actin-binding proteins composed of two actin depolymerizing factor homology (ADF-H) domains. Twinfilins are involved in diverse morphological and motile processes, but their mechanism of action has not been elucidated. Here, we show that mammalian twinfilin both sequesters ADP-G-actin and caps filament barbed ends with preferential affinity for ADP-bound ends. Twinfilin replaces capping protein and promotes motility of N-WASP functionalized beads in a biomimetic motility assay, indicating that the capping activity supports twinfilin's function in motility. Consistently, in vivo twinfilin localizes to actin tails of propelling endosomes. The ADP-actin-sequestering activity cooperates with the filament capping activity of twinfilin to finely regulate motility due to processive filament assembly catalyzed by formin-functionalized beads. The isolated ADF-H domains do not cap barbed ends nor promote motility, but sequester ADP-actin, the C-terminal domain showing the highest affinity. A structural model for binding of twinfilin to barbed ends is proposed based on the similar foldings of twinfilin ADF-H domains and gelsolin segments.     

Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G'(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G'(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.     

Clamped-filament elongation model for actin-based motors.

Although actin-based motility drives cell crawling and intracellular locomotion of organelles and certain pathogens, the underlying mechanism of force generation remains a mystery. Recent experiments demonstrated that Listeria exhibit episodes of 5.4-nm stepwise motion corresponding to the periodicity of the actin filament subunits, and extremely small positional fluctuations during the intermittent pauses [S. C. Kuo and J. L. McGrath. 2000. Nature. 407:1026-1029]. These findings suggest that motile bacteria remain firmly bound to actin filament ends as they elongate, a behavior that appears to rule out previous models for actin-based motility. We propose and analyze a new mechanochemical model (called the "Lock, Load & Fire" mechanism) for force generation by means of affinity-modulated, clamped-filament elongation. During the locking step, the filament's terminal ATP-containing subunit binds tightly to a clamp situated on the surface of a motile object; in the loading step, actin.ATP monomer(s) bind to the filament end, an event that triggers the firing step, wherein ATP hydrolysis on the clamped subunit attenuates the filament's affinity for the clamp. This last step initiates translocation of the new ATP-containing terminus to the clamp, whereupon another cycle begins anew. This model explains how surface-tethered filaments can grow while exerting flexural or tensile force on the motile surface. Moreover, stochastic simulations of the model reproduce the signature motions of Listeria. This elongation motor, which we term actoclampin, exploits actin's intrinsic ATPase activity to provide a simple, high-fidelity enzymatic reaction cycle for force production that does not require elongating filaments to dissociate from the motile surface. This mechanism may operate whenever actin polymerization is called upon to generate the forces that drive cell crawling or intracellular organelle motility.     

Study of bovine sperm motility in shear-thinning viscoelastic fluids

To elucidate the process whereby sperm arrive at an egg in the female reproductive organs, it is essential to investigate how rheological properties of the fluid around mammalian spermatozoa affect their motility. We examined the motility and flagellar waveform of bovine sperm swimming in a fluid with similar rheological properties as mammalian cervical mucus. The results indicated that the surrounding rheological properties largely affected the flagellar waveform of mammalian spermatozoa; in particular, shear-thinning viscoelastic fluid increased the progressive motility of the sperm. To investigate the influence of flagellar waveform on sperm motility in more detail, the waveform was expressed as a function and the progressive thrust of the sperm was calculated based on the empirical resistive force theory. The results of this study showed that the progressive thrust increased with the curvature of the flagellar tip. Moreover, we calculated the thrust efficiency of motile sperm. Results showed that the thrust efficiency in shear-thinning viscoelastic fluids was larger than that in Newtonian fluids, regardless of viscosity. This suggests that motile sperm in cervical mucus move efficiently by means of a motion mechanism that is suited to their surrounding environment.     

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.     

Silanized surfaces for in vitro studies of actomyosin function and nanotechnology applications

We have previously shown that selective heavy meromyosin (HMM) adsorption to predefined regions of nanostructured polymer resist surfaces may be used to produce a nanostructured in vitro motility assay. However, actomyosin function was of lower quality than on conventional nitrocellulose films. We have therefore studied actomyosin function on differently derivatized glass surfaces with the aim to find a substitute for the polymer resists. We have found that surfaces derivatized with trimethylchlorosilane (TMCS) were superior to all other surfaces tested, including nitrocellulose. High-quality actin filament motility was observed up to 6 days after incubation with HMM and the fraction of motile actin filaments and the velocity of smooth sliding were generally higher on TMCS than on nitrocellulose. The actomyosin function on TMCS-derivatized glass and nitrocellulose is considered in relation to roughness and hydrophobicity of these surfaces. The results suggest that TMCS is an ideal substitute for polymer resists in the nanostructured in vitro motility assay. Furthermore, TMCS derivatized glass also seems to offer several advantages over nitrocellulose for HMM adsorption in the ordinary in vitro motility assay.     

Actin filament elasticity and retrograde flow shape the force-velocity relation of motile cells

Cells migrate through a crowded environment during processes such as metastasis or wound healing, and must generate and withstand substantial forces. The cellular motility responses to environmental forces are represented by their force-velocity relation, which has been measured for fish keratocytes but remains unexplained. Even pN opposing forces slow down lamellipodium motion by three orders of magnitude. At larger opposing forces, the retrograde flow of the actin network accelerates until it compensates for polymerization, and cell motion stalls. Subsequently, the lamellipodium adapts to the stalled state. We present a mechanism quantitatively explaining the cell's force-velocity relation and its changes upon application of drugs that hinder actin polymerization or actomyosin-based contractility. Elastic properties of filaments, close to the lamellipodium leading edge, and retrograde flow shape the force-velocity relation. To our knowledge, our results shed new light on how these migratory responses are regulated, and on the mechanics and structure of the lamellipodium.     

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.     

Turnover of branched actin filament networks by stochastic fragmentation with ADF/cofilin

Cell motility depends on the rapid assembly, aging, severing, and disassembly of actin filaments in spatially distinct zones. How a set of actin regulatory proteins that sustains actin-based force generation during motility work together in space and time remains poorly understood. We present our study of the distribution and dynamics of Arp2/3 complex, capping protein (CP), and actin-depolymerizing factor (ADF)/cofilin in actin "comet tails," using a minimal reconstituted system with nucleation-promoting factor (NPF)-coated beads. The Arp2/3 complex concentrates at nucleation sites near the beads as well as in the first actin shell. CP colocalizes with actin and is homogeneously distributed throughout the comet tail; it serves to constrain the spatial distribution of ATP/ADP-P(i) filament zones to areas near the bead. The association of ADF/cofilin with the actin network is therefore governed by kinetics of actin assembly, actin nucleotide state, and CP binding. A kinetic simulation accurately validates these observations. Following its binding to the actin networks, ADF/cofilin is able to break up the dense actin filament array of a comet tail. Stochastic severing by ADF/cofilin loosens the tight entanglement of actin filaments inside the comet tail and facilitates turnover through the macroscopic release of large portions of the aged actin network.