A kinematic description of the trajectories of Listeria monocytogenes propelled by actin comet tails

Pushing boundaries: mechanisms enabling bacterial pathogens to spread between cells

For multiple intracellular bacterial pathogens, the ability to spread directly into adjacent epithelial cells is an essential step for disease in humans. For pathogens such as Shigella, Listeria, Rickettsia, and Burkholderia, this intercellular movement frequently requires the pathogens to manipulate the host actin cytoskeleton and deform the plasma membrane into structures known as protrusions, which extend into neighboring cells. The protrusion is then typically resolved into a double-membrane vacuole (DMV) from which the pathogen quickly escapes into the cytosol, where additional rounds of intercellular spread occur. Significant progress over the last few years has begun to define the mechanisms by which intracellular bacterial pathogens spread. This review highlights the interactions of bacterial and host factors that drive mechanisms required for intercellular spread with a focus on how protrusion structures form and resolve.

On the generation of force required for actin-based motility

The fundamental question of how forces are generated in a motile cell, a lamellipodium, and a comet tail is the subject of this note. It is now well established that cellular motility results from the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone around the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed, departing from the well-known theory of Larché-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.

Motility and swimming: universal description and generic trajectories

Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the ability of these entities to follow complex trajectories, ranging from straight, curved (circular, helical...), to random-like ones. The non-straight nature of these trajectories is often explained as a consequence of the asymmetry of the particle or the medium in which it moves, or due to the presence of bounding walls, etc... Here, we show that for a particle driven by a concentration field of an active species, straight, circular and helical trajectories emerge naturally in the absence of asymmetry of the particle or that of suspending medium. Our proof is based on general considerations, without referring to an explicit form of a model. We show that these three trajectories correspond to self-congruent solutions. Self-congruency means that the states of the system at different moments of time can be made identical by an appropriate combination of rotation and translation of the coordinate space. We show that these solutions are exhibited by spherically symmetric particles as a result of a series of pitchfork bifurcations, leading to spontaneous symmetry breaking in the concentration field driving the particle motility. Self-congruent dynamics in one and two dimensions are analyzed as well. Finally, we present a simple explicit nonlinear exactly solvable model of fully isotropic phoretic particle that shows the transitions from a non-motile state to straight motion to circular motion to helical motion as a series of spontaneous symmetry-breaking bifurcations. Whether a system exhibits or not a given trajectory only depends on the numerical values of parameters entering the model, while asymmetry of swimmer shape, or anisotropy of the suspending medium, or influence of bounding walls are not necessary.

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Ebola Virus Nucleocapsid-Like Structures Utilize Arp2/3 Signaling for Intracellular Long-Distance Transport

The intracellular transport of nucleocapsids of the highly pathogenic Marburg, as well as Ebola virus (MARV, EBOV), represents a critical step during the viral life cycle. Intriguingly, a population of these nucleocapsids is distributed over long distances in a directed and polar fashion. Recently, it has been demonstrated that the intracellular transport of filoviral nucleocapsids depends on actin polymerization. While it was shown that EBOV requires Arp2/3-dependent actin dynamics, the details of how the virus exploits host actin signaling during intracellular transport are largely unknown. Here, we apply a minimalistic transfection system to follow the nucleocapsid-like structures (NCLS) in living cells, which can be used to robustly quantify NCLS transport in live cell imaging experiments. Furthermore, in cells co-expressing LifeAct, a marker for actin dynamics, NCLS transport is accompanied by pulsative actin tails appearing on the rear end of NCLS. These actin tails can also be preserved in fixed cells, and can be visualized via high resolution imaging using STORM in transfected, as well as EBOV infected, cells. The application of inhibitory drugs and siRNA depletion against actin regulators indicated that EBOV NCLS utilize the canonical Arp2/3-Wave1-Rac1 pathway for long-distance transport in cells. These findings highlight the relevance of the regulation of actin polymerization during directed EBOV nucleocapsid transport in human cells.

Two-dimensional active motion

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

Stathmin recruits tubulin to Listeria monocytogenes-induced actin comets and promotes bacterial dissemination

The tubulin cytoskeleton is one of the main components of the cytoarchitecture and is involved in several cellular functions. Here, we examine the interplay between Listeria monocytogenes (Lm) and the tubulin cytoskeleton upon cellular infection. We show that non-polymeric tubulin is present throughout Lm actin comet tails and, to a less extent, in actin clouds. Moreover, we demonstrate that stathmin, a regulator of microtubule dynamics, is also found in these Lm-associated actin structures and is required for tubulin recruitment. Depletion of host stathmin results in longer comets containing less F-actin, which may be correlated with higher levels of inactive cofilin in the comet, thus suggesting a defect on local F-actin dynamics. In addition, intracellular bacterial speed is significantly reduced in stathmin-depleted cells, revealing the importance of stathmin/tubulin in intracellular Lm motility. In agreement, the area of infection foci and the total bacterial loads are also significantly reduced in stathmin-depleted cells. Collectively, our results demonstrate that stathmin promotes efficient cellular infection, possibly through tubulin recruitment and control of actin dynamics at Lm-polymerized actin structures.

Memory-Induced Transition from a Persistent Random Walk to Circular Motion for Achiral Microswimmers

We experimentally study the motion of light-activated colloidal microswimmers in a viscoelastic fluid. We find that, in such a non-Newtonian environment, the active colloids undergo an unexpected transition from enhanced angular diffusion to persistent rotational motion above a critical propulsion speed, despite their spherical shape and stiffness. We observe that, in contrast to chiral asymmetric microswimmers, the resulting circular orbits can spontaneously reverse their sense of rotation and exhibit an angular velocity and a radius of curvature that nonlinearly depend on the propulsion speed. By means of a minimal non-Markovian Langevin model for active Brownian motion, we show that these nonequilibrium effects emerge from the delayed response of the fluid with respect to the self-propulsion of the particle without counterpart in Newtonian fluids.

Micro-flock patterns and macro-clusters in chiral active Brownian disks

Chiral active particles (or self-propelled circle swimmers) feature a rich collective behavior, comprising rotating macro-clusters and micro-flock patterns which consist of phase-synchronized rotating clusters with a characteristic self-limited size. These patterns emerge from the competition of alignment interactions and rotations suggesting that they might occur generically in many chiral active matter systems. However, although excluded volume interactions occur naturally among typical circle swimmers, it is not yet clear if macro-clusters and micro-flock patterns survive their presence. The present work shows that both types of pattern do survive but feature strongly enhance fluctuations regarding the size and shape of the individual clusters. Despite these fluctuations, we find that the average micro-flock size still follows the same characteristic scaling law as in the absence of excluded volume interactions, i.e. micro-flock sizes scale linearly with the single-swimmer radius.

Transport of alignment active particles in funnel structures

We study the transport of alignment active particles in complex confined structures (an array of asymmetric funnels). It is found that due to the existence of the multiple pathways, the alignment interaction can enrich the transport behavior of active particles. In an array of asymmetric funnels, the purely nematic alignment always suppresses the rectification. However, the polar alignment does not always promote the rectification, the rectification is suppressed for large self-propulsion speed. In addition, we also found the existence of optimal parameters (the self-propulsion speed and the rotational diffusion coefficient) at which the directed velocity takes its maximal value.

Diffusion of active chiral particles

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Statistics of actin-propelled trajectories in noisy environments

Actin polymerization is ubiquitously utilized to power the locomotion of eukaryotic cells and pathogenic bacteria in living systems. Inevitably, actin polymerization and depolymerization proceed in a fluctuating environment that renders the locomotion stochastic. Previously, we have introduced a deterministic model that manages to reproduce actin-propelled trajectories in experiments, but not to address fluctuations around them. To remedy this, here we supplement the deterministic model with noise terms. It enables us to compute the effects of fluctuating actin density and forces on the trajectories. Specifically, the mean-squared displacement (MSD) of the trajectories is computed and found to show a super-ballistic scaling with an exponent 3 in the early stage, followed by a crossover to a normal, diffusive scaling of exponent 1 in the late stage. For open-end trajectories such as straights and S-shaped curves, the time of crossover matches the decay time of orientational order of the velocities along trajectories, suggesting that it is the spreading of velocities that leads to the crossover. We show that the super-ballistic scaling of MSD arises from the initial, linearly increasing correlation of velocities, before time translational symmetry is established. When the spreading of velocities reaches a steady state in the long-time limit, short-range correlation then yields a diffusive scaling in MSD. In contrast, close-loop trajectories like circles exhibit localized periodic motion, which inhibits spreading. The initial super-ballistic scaling of MSD arises from velocity correlation that both linearly increases and oscillates in time. Finally, we find that the above statistical features of the trajectories transcend the nature of noises, be it additive or multiplicative, and generalize to other self-propelled systems that are not necessarily actin based.

WHAMM Directs the Arp2/3 Complex to the ER for Autophagosome Biogenesis through an Actin Comet Tail Mechanism

Nucleation-promoting factors (NPFs) control the spatio-temporal activity of Arp2/3 complex in cells]. Thus, WASP and the WAVE complex direct the formation of branched actin networks at the leading edge during cell motility and endo/exocytosis, whereas the WASH complex is involved in endosomal transport. Less understood are WHAMM and JMY, two NPFs with similar domain architecture. JMY is found in the nucleus and the cytosol and is involved in transcriptional regulation, cell motility, and trans-Golgi transport. WHAMM was reported to bind microtubules and to be involved in ER to cis-Golgi transport. Here, we show that WHAMM directs the activity of Arp2/3 complex for autophagosome biogenesis through an actin-comet tail motility mechanism. Macroautophagy--the process by which cytosolic material is engulfed into autophagosomes for degradation and/or recycling--was recently shown to involve actin, but the mechanism is unknown. We found that WHAMM forms puncta that colocalize and comigrate with the autophagy markers LC3, DFCP1, and p62 through a WHAMM-dependent actin-comet tail mechanism. Under starvation, WHAMM and actin are observed at the interface between neighboring autophagosomes, whose number and size increase with WHAMM expression. Interfering with actin polymerization, inhibiting Arp2/3 complex, knocking down WHAMM, or blocking its interaction with Arp2/3 complex through mutagenesis all inhibit comet tail formation and reduce the size and number of autophagosomes. Finally, JMY shows similar localization to WHAMM and could be involved in similar processes. These results reveal a link between Arp2/3-complex-dependent actin assembly and autophagy.

Rectification and diffusion of self-propelled particles in a two-dimensional corrugated channel

Rectification and diffusion of noninteracting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient. It is found that the self-propelled particles can be rectified by the self-propelled velocity. There exist optimal values of the parameters (the self-propelled velocity, the translational diffusion constant, and the height of the potential) at which the average velocity takes its maximal value. There exists an optimal translational diffusion at which the effective diffusion constant is maximal. The self-propelled velocity can strongly increase the effective diffusion, while the large rotational diffusion rate can strongly suppress the effective diffusion.

Control of actin-based motility through localized actin binding

A wide variety of cell biological and biomimetic systems use actin polymerization to drive motility. It has been suggested that an object such as a bacterium can propel itself by self-assembling a high concentration of actin behind it, if it is repelled by actin. However, it is also known that it is essential for the moving object to bind actin. Therefore, a key question is how the actin tail can propel an object when it both binds and repels the object. We present a physically consistent Brownian dynamics model for actin-based motility that includes the minimal components of the dendritic nucleation model and allows for both attractive and repulsive interactions between actin and a moveable disc. We find that the concentration gradient of filamentous actin generated by polymerization is sufficient to propel the object, even with moderately strong binding interactions. Additionally, actin binding can act as a biophysical cap, and may directly control motility through modulation of network growth. Overall, this mechanism is robust in that it can drive motility against a load up to a stall pressure that depends on the Young's modulus of the actin network and can explain several aspects of actin-based motility.

Capturing self-propelled particles in a moving microwedge

Catching fish with a fishing net is typically done either by dragging a fishing net through quiescent water or by placing a stationary basket trap into a stream. We transfer these general concepts to micron-sized self-motile particles moving in a solvent at low Reynolds number and study their collective trapping behavior by means of computer simulations of a two-dimensional system of self-propelled rods. A chevron-shaped obstacle is dragged through the active suspension with a constant speed v and acts as a trapping "net." Three trapping states can be identified corresponding to no trapping, partial trapping, and complete trapping and their relative stability is studied as a function of the apex angle of the wedge, the swimmer density, and the drag speed v. When the net is dragged along the inner wedge, complete trapping is facilitated and a partially trapped state changes into a complete trapping state if the drag speed exceeds a certain value. Reversing the drag direction leads to a reentrant transition from no trapping to complete trapping and then back to no trapping upon increasing the drag speed along the outer wedge contour. The transition to complete trapping is marked by a templated self-assembly of rods forming polar smectic structures anchored onto the inner contour of the wedge. Our predictions can be verified in experiments of artificial or microbial swimmers confined in microfluidic trapping devices.

Oscillatory motions of an active deformable particle

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of n- and 2n-mode deformations for n=1, and those for n=2. We show that an oscillatory bifurcation occurs for n=2, which corresponds mathematically to the bifurcation for n=1 where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

Trajectories of Listeria-type motility in two dimensions

Force generated by actin polymerization is essential in cell motility and the locomotion of organelles or bacteria such as Listeria monocytogenes. Both in vivo and in vitro experiments on actin-based motility have observed geometrical trajectories including straight lines, circles, S-shaped curves, and translating figure eights. This paper reports a phenomenological model of an actin-propelled disk in two dimensions that generates geometrical trajectories. Our model shows that when the evolutions of actin density and force per filament on the disk are strongly coupled to the disk self-rotation, it is possible for a straight trajectory to lose its stability. When the instability is due to a pitchfork bifurcation, the resulting trajectory is a circle; a straight trajectory can also lose stability through a Hopf bifurcation, and the resulting trajectory is an S-shaped curve. We also show that a half-coated disk, which mimics the distribution of functionalized proteins in Listeria, also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses stability. For both a fully coated disk and a half-coated disk, when the trajectory is an S-shaped curve, the angular frequency of the disk self-rotation is different from that of the disk trajectory. However, for circular trajectories, these angular frequencies are different for a fully coated disk but the same for a half-coated disk.

Spinning motion of a deformable self-propelled particle in two dimensions

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

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.

There are two major ideas about how actin networks generate force against an obstacle: one is that the force comes directly from the elongation and bending of individual actin filaments against the surface of the obstacle; the other is that a growing actin gel can build up stress around the obstacle to squeeze it forward. Neither of the two models can explain why actin-propelled ellipsoidal beads move with equal bias toward long- and short-axes. We propose a hybrid model by combining those two ideas so that individual actin filaments are embedded into the boundary of a deformable actin gel. Simulations of this model show that the combined effects of pushing from individual filaments and squeezing from the actin network explain the observed bi-orientation of ellipsoidal beads as well as the curvature of trajectories of spherical beads and the force-velocity relation of actin networks.

A circle swimmer at low Reynolds number

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.

Locomotion of C. elegans: a piecewise-harmonic curvature representation of nematode behavior

Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase.

Self-propelled Brownian spinning top: dynamics of a biaxial swimmer at low Reynolds numbers

Recently the Brownian dynamics of self-propelled (active) rodlike particles was explored to model the motion of colloidal microswimmers, catalytically driven nanorods, and bacteria. Here we generalize this description to biaxial particles with arbitrary shape and derive the corresponding Langevin equation for a self-propelled Brownian spinning top. The biaxial swimmer is exposed to a hydrodynamic Stokes friction force at low Reynolds numbers, to fluctuating random forces and torques as well as to an external and an internal (effective) force and torque. The latter quantities control its self-propulsion. Due to biaxiality and hydrodynamic translational-rotational coupling, the Langevin equation can only be solved numerically. In the special case of an orthotropic particle in the absence of external forces and torques, the noise-free (zero-temperature) trajectory is analytically found to be a circular helix. This trajectory is confirmed numerically to be more complex in the general case of an arbitrarily shaped particle under the influence of arbitrary forces and torques involving a transient irregular motion before ending up in a simple periodic motion. By contrast, if the external force vanishes, no transient regime is found, and the particle moves on a superhelical trajectory. For orthotropic particles, the noise-averaged trajectory is a generalized concho-spiral. We furthermore study the reduction of the model to two spatial dimensions and classify the noise-free trajectories completely finding circles, straight lines with and without transients, as well as cycloids and arbitrary periodic trajectories.

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.

Deformable self-propelled domain in an excitable reaction-diffusion system in three dimensions

We derive a set of equations of motion for an isolated domain in an excitable reaction-diffusion system in three dimensions. In the singular limit where the interface is infinitesimally thin, the motion of the center of mass coupled with deformation is investigated near the drift bifurcation where a motionless domain becomes unstable and undergoes migration. This is an extension of our previous theory in two dimensions. We show that there are three basic motions of a domain, straight motion, rotating motion, and helical motion. The last one is a characteristic of three dimensions. The phase diagram of these three solutions is given in the parameter space of the original reaction-diffusion equations.

Brownian motion of a self-propelled particle

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the 'active' particle is driven along its internal orientation axis. We calculate the first four moments of the probability distribution function for displacements as a function of time for a spherical particle with isotropic translational diffusion, as well as for an anisotropic ellipsoidal particle. In both cases the translational and rotational motion is either unconfined or confined to one or two dimensions. A significant non-Gaussian behaviour at finite times t is signalled by a non-vanishing kurtosis γ(t). To delimit the super-diffusive regime, which occurs at intermediate times, two timescales are identified. For certain model situations a characteristic t(3) behaviour of the mean-square displacement is observed. Comparing the dynamics of real and artificial microswimmers, like bacteria or catalytically driven Janus particles, to our analytical expressions reveals whether their motion is Brownian or not.

Observation and kinematic description of long actin tracks induced by spherical beads

We report an in vitro study comparing the growth of long actin tails induced by spherical beads coated with the verprolin central acidic domain of the polymerization enzyme N-WASP to that induced by Listeria monocytogenes in similar cellular extracts. The tracks behind the beads show characteristic differences in shape and curvature from those left by the bacteria, which have an elongated shape and a similar polymerization-inducing enzyme distributed only on the rear surface of the cell. The experimental tracks are simulated using a generalized kinematic model, which incorporates three modes of bead rotation with respect to the tail. The results show that the trajectories of spherical beads are mechanically deterministic rather than random, as suggested by stochastic models. Assessment of the bead rotation and its mechanistic basis offers insights into the biological function of actin-based motility.

A microscopic formulation for the actin-driven motion of listeria in curved paths

Using a generalized Brownian ratchet model that accounts for the interactions of actin filaments with the surface of Listeria mediated by proteins like ActA and Arp2/3, we have developed a microscopic model for the movement of Listeria. Specifically, we show that a net torque can be generated within the comet tail, causing the bacteria to spin about its long axis, which in conjunction with spatially varying polymerization at the surface leads to motions of bacteria in curved paths that include circles, sinusoidal-like curves, translating figure eights, and serpentine shapes, as observed in recent experiments. A key ingredient in our formulation is the coupling between the motion of Listeria and the force-dependent rate of filament growth. For this reason, a numerical scheme was developed to determine the kinematic parameters of motion and stress distribution among filaments in a self-consistent manner. We find that a 5-15% variation in polymerization rates can lead to radii of curvatures of the order of 4-20 microm, measured in experiments. In a similar way, our results also show that most of the observed trajectories can be produced by a very low degree of correlation, <10%, among filament orientations. Since small fluctuations in polymerization rate, as well as filament orientation, can easily be induced by various factors, our findings here provide a reasonable explanation for why Listeria can travel along totally different paths under seemingly identical experimental conditions. Besides trajectories, stress distributions corresponding to different polymerization profiles are also presented. We have found that although some actin filaments generate propelling forces that push the bacteria forward, others can exert forces opposing the movement of Listeria, consistent with recent experimental observations.

Mechanistic insights from a quantitative analysis of pollen tube guidance

BACKGROUND

Plant biologists have long speculated about the mechanisms that guide pollen tubes to ovules. Although there is now evidence that ovules emit a diffusible attractant, little is known about how this attractant mediates interactions between the pollen tube and the ovules.

RESULTS

We employ a semi-in vitro assay, in which ovules dissected from Arabidopsis thaliana are arranged around a cut style on artificial medium, to elucidate how ovules release the attractant and how pollen tubes respond to it. Analysis of microscopy images of the semi-in vitro system shows that pollen tubes are more attracted to ovules that are incubated on the medium for longer times before pollen tubes emerge from the cut style. The responses of tubes are consistent with their sensing a gradient of an attractant at 100-150 mum, farther than previously reported. Our microscopy images also show that pollen tubes slow their growth near the micropyles of functional ovules with a spatial range that depends on ovule incubation time.

CONCLUSIONS

We propose a stochastic model that captures these dynamics. In the model, a pollen tube senses a difference in the fraction of receptors bound to an attractant and changes its direction of growth in response; the attractant is continuously released from ovules and spreads isotropically on the medium. The model suggests that the observed slowing greatly enhances the ability of pollen tubes to successfully target ovules. The relation of the results to guidance in vivo is discussed.

A novel pseudopodial component of the dendritic cell anti-fungal response: the fungipod

Fungal pathologies are seen in immunocompromised and healthy humans. C-type lectins expressed on immature dendritic cells (DC) recognize fungi. We report a novel dorsal pseudopodial protrusion, the “fungipod”, formed by DC after contact with yeast cell walls. These structures have a convoluted cell-proximal end and a smooth distal end. They persist for hours, exhibit noticeable growth and total 13.7±5.6 µm long and 1.8±0.67 µm wide at the contact. Fungipods contain clathrin and an actin core surrounded by a sheath of cortactin. The actin cytoskeleton, but not microtubules, is required for fungipod integrity and growth. An apparent rearward flow (225±55 nm/second) exists from the zymosan contact site into the distal fungipod. The phagocytic receptor Dectin-1 is not required for fungipod formation, but CD206 (Mannose Receptor) is the generative receptor for these protrusions. The human pathogen Candida parapsilosis induces DC fungipod formation strongly, but the response is species specific since the related fungal pathogens Candida tropicalis and Candida albicans induce very few and no fungipods, respectively. Our findings show that fungipods are dynamic actin-driven cellular structures involved in fungal recognition by DC. They may promote yeast particle phagocytosis by DC and are a specific response to large (i.e., 5 µm) particulate ligands. Our work also highlights the importance of this novel protrusive structure to innate immune recognition of medically significant Candida yeasts in a species specific fashion.

Yeasts are normal microbial commensals of humans and a significant source of opportunistic infections, especially in immunocompromised individuals. We report a novel cellular protrusive structure, the fungipod, which participates in the host-microbe interaction between human immature dendritic cells (DC) and yeasts. The fungipod's structure is based on and propelled by a robust process of local actin cytoskeleton growth at the DC-yeast contact site, and this cytoskeletal remodeling results in a durable tubular structure over 10 µm long connecting the dorsal DC membrane and yeast. The fungal cell wall polysaccharides mannan and chitin trigger fungipod formation by stimulating the carbohydrate pattern recognition receptor CD206. Fungipods are part of a specific response to large particulate objects (i.e., yeast), and they may promote the human immature DC's relatively poor phagocytosis of yeast. The human fungal pathogen, Candida parapsilosis, induces a strong fungipod response from DC, and this response is highly species specific since the related pathogens Candida albicans and Candida tropicalis induce fungipods rarely. Our work highlights a novel cell biological element of fungal recognition by the innate immune system.

Catalytic microtubular jet engines self-propelled by accumulated gas bubbles

Strain-engineered microtubes with an inner catalytic surface serve as self-propelled microjet engines with speeds of up to approximately 2 mm s(-1) (approximately 50 body lengths per second). The motion of the microjets is caused by gas bubbles ejecting from one opening of the tube, and the velocity can be well approximated by the product of the bubble radius and the bubble ejection frequency. Trajectories of various different geometries are well visualized by long microbubble tails. If a magnetic layer is integrated into the wall of the microjet engine, we can control and localize the trajectories by applying external rotating magnetic fields. Fluid (i.e., fuel) pumping through the microtubes is revealed and directly clarifies the working principle of the catalytic microjet engines.

Mechanics model for actin-based motility

We present here a mechanics model for the force generation by actin polymerization. The possible adhesions between the actin filaments and the load surface, as well as the nucleation and capping of filament tips, are included in this model on top of the well-known elastic Brownian ratchet formulation. A closed form solution is provided from which the force-velocity relationship, summarizing the mechanics of polymerization, can be drawn. Model predictions on the velocity of moving beads driven by actin polymerization are consistent with experiment observations. This model also seems capable of explaining the enhanced actin-based motility of Listeria monocytogenes and beads by the presence of Vasodilator-stimulated phosphoprotein, as observed in recent experiments.

Dynamics of a Brownian circle swimmer

Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulates. Using a non-Hamiltonian rate theory and computer simulations, we study the motion of a Brownian "circle swimmer" in a confining channel. A sliding mode close to the wall leads to a huge acceleration as compared to the bulk motion, which can further be enhanced by an optimal effective torque-to-force ratio.

Helical twist controls the thickness of F-actin bundles

In the presence of condensing agents such as nonadsorbing polymer, multivalent counter ions, and specific bundling proteins, chiral biopolymers typically form bundles with a finite thickness, rather than phase-separating into a polymer-rich phase. Although short-range repulsive interactions or geometrical frustrations are thought to force the equilibrium bundle size to be limited, the precise mechanism is yet to be resolved. The importance of the tight control of biopolymer bundle size is illustrated by the ubiquitous cytoskeletal actin filament bundles that are crucial for the proper functioning of cells. Using an in vitro model system, we show that size control relies on a mismatch between the helical structure of individual actin filaments and the geometric packing constraints within bundles. Small rigid actin-binding proteins change the twist of filamentous actin (F-actin) in a concentration-dependent manner, resulting in small, well defined bundle thickness up to approximately 20 filaments, comparable to those found in filopodia. Other F-actin cross-linking proteins can subsequently link these small, well organized bundles into larger structures of several hundred filaments, comparable to those found in, for example, Drosophila bristles. The energetic tradeoff between filament twisting and cross-linker binding within a bundle is suggested as a fundamental mechanism by which cells can precisely adjust bundle size and strength.

Curvature and torsion in growing actin networks

Intracellular pathogens such as Listeria monocytogenes and Rickettsia rickettsii move within a host cell by polymerizing a comet-tail of actin fibers that ultimately pushes the cell forward. This dense network of cross-linked actin polymers typically exhibits a striking curvature that causes bacteria to move in gently looping paths. Theoretically, tail curvature has been linked to details of motility by considering force and torque balances from a finite number of polymerizing filaments. Here we track beads coated with a prokaryotic activator of actin polymerization in three dimensions to directly quantify the curvature and torsion of bead motility paths. We find that bead paths are more likely to have low rather than high curvature at any given time. Furthermore, path curvature changes very slowly in time, with an autocorrelation decay time of 200 s. Paths with a small radius of curvature, therefore, remain so for an extended period resulting in loops when confined to two dimensions. When allowed to explore a three-dimensional (3D) space, path loops are less evident. Finally, we quantify the torsion in the bead paths and show that beads do not exhibit a significant left- or right-handed bias to their motion in 3D. These results suggest that paths of actin-propelled objects may be attributed to slow changes in curvature, possibly associated with filament debranching, rather than a fixed torque.

Mathematics of cell motility: have we got its number?

Mathematical and computational modeling is rapidly becoming an essential research technique complementing traditional experimental biological methods. However, lack of standard modeling methods, difficulties of translating biological phenomena into mathematical language, and differences in biological and mathematical mentalities continue to hinder the scientific progress. Here we focus on one area-cell motility-characterized by an unusually high modeling activity, largely due to a vast amount of quantitative, biophysical data, 'modular' character of motility, and pioneering vision of the area's experimental leaders. In this review, after brief introduction to biology of cell movements, we discuss quantitative models of actin dynamics, protrusion, adhesion, contraction, and cell shape and movement that made an impact on the process of biological discovery. We also comment on modeling approaches and open questions.

Cytosolic extract induces Tir translocation and pedestals in EPEC-infected red blood cells

Enteropathogenic Escherichia coli (EPEC) are deadly contaminants in water and food, and induce protrusion of actin-filled membranous pedestals beneath themselves upon attachment to intestinal epithelia. Pedestal formation requires clustering of Tir and subsequent recruitment of cellular tyrosine kinases including Abl, Arg, and Etk as well as signaling molecules Nck, N-WASP, and Arp2/3 complex. We have developed a cytosolic extract-based cellular system that recapitulates actin pedestal formation in permeabilized red blood cells (RBC) infected with EPEC. RBC support attachment of EPEC and translocation of virulence factors, but not pedestal formation. We show here that extract induces a rapid Ca⁺⁺-dependent release of Tir from the EPEC Type III secretion system, and that cytoplasmic factor(s) present in the extract facilitate translocation of Tir into the RBC plasma membrane. We show that Abl and related kinases in the extract phosphorylate Tir and that actin polymerization can be reconstituted in infected RBC following addition of cytosolic extract. Reconstitution requires the bacterial virulence factors Tir and intimin, and phosphorylation of Tir on tyrosine residue 474 results in the recruitment of Nck, N-WASP, and Arp2/3 complex beneath attached bacteria at sites of actin polymerization. Together these data describe a biochemical system for dissection of host components that mediate Type III secretion and the mechanisms by which complexes of proteins are recruited to discrete sites within the plasma membrane to initiate localized actin polymerization and morphological changes.

Enteropathogenic Escherichia coli (EPEC) is a diarrheagenic enteric pathogen that attaches to host cells and forms actin-filled membranous protrusions called pedestals. Pedestal formation is initiated when the EPEC virulence factor, Tir, is translocated into the host cell via bacterial Type III secretion (T3S) and inserted into the plasma membrane, initiating a signaling cascade that results in actin polymerization beneath attached bacteria. We have developed a cytoplasmic extract-based system in permeabilized cells to study these early events in EPEC pathogenesis, many of which are not easily studied in intact cells. We have taken advantage of the observation that EPEC fail to form pedestals on red blood cells (RBC). We report that low calcium triggers T3S of Tir into RBC, indicating how the T3S apparatus may sense entry into the host cytoplasm. Additionally, insertion of Tir into the host membrane depends upon host cytoplasmic components, a requirement not previously recognized or accessible to experimental manipulation in intact cells. Finally, cytoplasmic extract reconstitutes actin polymerization beneath attached bacteria using signaling molecules required in intact cells. We are currently purifying the components that mediate these processes. Together, these experiments show how functional biochemistry approaches can reveal novel roles for cytoplasmic factors in host–pathogen interactions.