Nonlinear study of symmetry breaking in actin gels: implications for cellular motility

Myosin-I synergizes with Arp2/3 complex to enhance the pushing forces of branched actin networks

Class I myosins (myosin-Is) colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by the Arp2/3 complex on the surface of beads coated with myosin-I and nucleation-promoting factor. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Myosin-I triggered symmetry breaking and comet tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations, suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

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.

The role of the nucleus for cell mechanics: an elastic phase field approach

The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.

Myosin-I Synergizes with Arp2/3 Complex to Enhance Pushing Forces of Branched Actin Networks

Myosin-Is colocalize with Arp2/3 complex-nucleated actin networks at sites of membrane protrusion and invagination, but the mechanisms by which myosin-I motor activity coordinates with branched actin assembly to generate force are unknown. We mimicked the interplay of these proteins using the "comet tail" bead motility assay, where branched actin networks are nucleated by Arp2/3 complex on the surface of beads coated with myosin-I and the WCA domain of N-WASP. We observed that myosin-I increased bead movement efficiency by thinning actin networks without affecting growth rates. Remarkably, myosin-I triggered symmetry breaking and comet-tail formation in dense networks resistant to spontaneous fracturing. Even with arrested actin assembly, myosin-I alone could break the network. Computational modeling recapitulated these observations suggesting myosin-I acts as a repulsive force shaping the network's architecture and boosting its force-generating capacity. We propose that myosin-I leverages its power stroke to amplify the forces generated by Arp2/3 complex-nucleated actin networks.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Hydration in aqueous NaCl

Atomistic details about the hydration of ions in aqueous solutions are still debated due to the disordered and statistical nature of the hydration process. However, many processes from biology, physical chemistry to materials sciences rely on the complex interplay between solute and solvent. Oxygen K-edge X-ray excitation spectra provide a sensitive probe of the local atomic and electronic surrounding of the excited sites. We used ab initio molecular dynamics simulations together with extensive spectrum calculations to relate the features found in experimental oxygen K-edge spectra of a concentration series of aqueous NaCl with the induced structural changes upon solvation of the salt and distill the spectral fingerprints of the first hydration shells around the Na⁺- and Cl^--ions. By this combined experimental and theoretical approach, we find the strongest spectral changes to indeed result from the first hydration shells of both ions and relate the observed shift of spectral weight from the post- to the main-edge to the origin of the post-edge as a shape resonance.

Active motion of passive asymmetric dumbbells in a non-equilibrium bath

Persistent motion of passive asymmetric bodies in non-equilibrium media has been experimentally observed in a variety of settings. However, fundamental constraints on the efficiency of such motion are not fully explored. Understanding such limits, and ways to circumvent them, is important for efficient utilization of energy stored in agitated surroundings for purposes of taxis and transport. Here, we examine such issues in the context of erratic movements of a passive asymmetric dumbbell driven by non-equilibrium noise. For uncorrelated (white) noise, we find a (non-Boltzmann) joint probability distribution for the velocity and orientation, which indicates that the dumbbell preferentially moves along its symmetry axis. The dumbbell thus behaves as an Ornstein-Uhlenbeck walker, a prototype of active matter. Exploring the efficiency of this active motion, we show that in the over-damped limit, the persistence length l of the dumbbell is bound from above by half its mean size, while the propulsion speed v_∥ is proportional to its inverse size. The persistence length can be increased by exploiting inertial effects beyond the over-damped regime, but this improvement always comes at the price of smaller propulsion speeds. This limitation is explained by noting that the diffusivity of a dumbbell, related to the product v_∥l, is always less than that of its components, thus severely constraining the usefulness of passive dumbbells as active particles.

Reversible elastic phase field approach and application to cell monolayers

Motion and generation of forces by single cells and cell collectives are essential elements of many biological processes, including development, wound healing and cancer cell migration. Quantitative wound healing assays have demonstrated that cell monolayers can be both dynamic and elastic at the same time. However, it is very challenging to model this combination with conventional approaches. Here we introduce an elastic phase field approach that allows us to predict the dynamics of elastic sheets under the action of active stresses and localized forces, e.g. from leader cells. Our method ensures elastic reversibility after release of forces. We demonstrate its potential by studying several paradigmatic situations and geometries relevant for single cells and cell monolayers, including elastic bars, contractile discs and expanding monolayers with leader cells.

Hydration in aqueous osmolyte solutions: the case of TMAO and urea

X-ray Raman scattering spectroscopy and first principles simulations reveal details of the hydration and hydrogen-bond topology of trimethylamine N-oxide (TMAO) and urea in aqueous solutions.

The effect of crystallite size on pressure amplification in switchable porous solids

Negative gas adsorption (NGA) in ordered mesoporous solids is associated with giant contractive structural transitions traversing through metastable states. Here, by systematically downsizing the crystal dimensions of a mesoporous MOF (DUT-49) from several micrometers to less than 200 nm, counterintuitive NGA phenomena are demonstrated to critically depend on the primary crystallite size. Adsorbing probe molecules, such as n-butane or nitrogen, gives insights into size-dependent activation barriers and thermodynamics associated with guest-induced network contraction. Below a critical crystal size, the nitrogen adsorption-induced breathing is completely suppressed as detected using parallelized synchrotron X-ray diffraction–adsorption instrumentation. In contrast, even the smallest particles show NGA in the presence of n-butane, however, associated with a significantly reduced pressure amplification. Consequently, the magnitude of NGA in terms of amount of gas expulsed and pressure amplification can be tuned, potentially paving the way towards innovative concepts for pressure amplification in micro- and macro-system engineering.

Pressure amplification phenomena have recently been observed in ordered mesoporous solids, but little is understood about this counter-intuitive behaviour. Here, Kaskel and colleagues demonstrate that crystal size can play an important role in modulating pressure amplification in metal-organic frameworks.

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.

Spontaneous polarization in an interfacial growth model for actin filament networks with a rigorous mechanochemical coupling

Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechanochemical coupling mechanisms that guide the growth process are poorly understood, and a general continuum description combining growth and mechanics is lacking. We develop a theory that bridges the gap between mesoscale and continuum limit and propose a general framework providing the evolution law of actin networks growing under stress. This formulation opens an area for the systematic study of actin dynamics in arbitrary geometries. Our framework predicts a morphological instability of actin growth on a rigid sphere, leading to a spontaneous polarization of the network with a mode selection corresponding to a comet, as reported experimentally. We show that the mechanics of the contact between the network and the surface plays a crucial role, in that it determines directly the existence of the instability. We extract scaling laws relating growth dynamics and network properties offering basic perspectives for new experiments on growing actin networks.

Modeling crawling cell movement on soft engineered substrates

Self-propelled motion, emerging spontaneously or in response to external cues, is a hallmark of living organisms. Systems of self-propelled synthetic particles are also relevant for multiple applications, from targeted drug delivery to the design of self-healing materials. Self-propulsion relies on the force transfer to the surrounding. While self-propelled swimming in the bulk of liquids is fairly well characterized, many open questions remain in our understanding of self-propelled motion along substrates, such as in the case of crawling cells or related biomimetic objects. How is the force transfer organized and how does it interplay with the deformability of the moving object and the substrate? How do the spatially dependent traction distribution and adhesion dynamics give rise to complex cell behavior? How can we engineer a specific cell response on synthetic compliant substrates? Here we generalize our recently developed model for a crawling cell by incorporating locally resolved traction forces and substrate deformations. The model captures the generic structure of the traction force distribution and faithfully reproduces experimental observations, like the response of a cell on a gradient in substrate elasticity (durotaxis). It also exhibits complex modes of cell movement such as "bipedal" motion. Our work may guide experiments on cell traction force microscopy and substrate-based cell sorting and can be helpful for the design of biomimetic "crawlers" and active and reconfigurable self-healing materials.

Asymmetry between pushing and pulling for crawling cells

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.

Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

Formation of a multiscale aggregate structure through spontaneous blebbing of an interface

The motion of an oil-water interface that mimics biological motility was investigated in a Hele-Shaw-like cell where elastic surfactant aggregates were formed at the oil-water interface. With the interfacial motion, millimeter-scale pillar structures composed of the aggregates were formed. The pillars grew downward in the aqueous phase, and the separations between pillars were roughly equal. Small-angle X-ray scattering using a microbeam X-ray revealed that these aggregates had nanometer-scale lamellar structures whose orientation correlated well with their location in the pillar structure. It is suggested that these hierarchical spatial structures are tailored by the spontaneous interfacial motion.

Modeling morphodynamic phenotypes and dynamic regimes of cell motion

Many cellular processes and signaling pathways converge onto cell morphology and cell motion, which share important components. The mechanisms used for propulsion could also be responsible for shape changes, if they are capable of generating the rich observed variety of dynamic regimes. Additionally, the analysis of cell shape changes in space and time promises insight into the state of the cytoskeleton and signaling pathways controlling it. While this has been obvious for some time by now, little effort has been made to systematically and quantitatively explore this source of information. First pioneering experimental work revealed morphodynamic phenotypes which can be associated with dynamic regimes like oscillations and excitability. Here, we review the current state of modeling of morphodynamic phenotypes, the experimental results and discuss the ideas on the mechanisms driving shape changes which are suggested by modeling.

Model for self-polarization and motility of keratocyte fragments

Computational modelling of cell motility on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion are not fully quantified. Additional challenges arise from the need to describe a moving deformable cell boundary. Here, we present a simple mathematical model coupling cell shape dynamics, treated by the phase-field approach, to a vector field describing the mean orientation (polarization) of the actin filament network. The model successfully reproduces the primary phenomenology of cell motility: discontinuous onset of motion, diversity of cell shapes and shape oscillations. The results are in qualitative agreement with recent experiments on motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of experiments.

Reconstruction of aperture functions during full fusion in vesicular exocytosis of neurotransmitters

Individual vesicular exocytosis of adrenaline by dense core vesicles in chromaffin cells is considered here as a paradigm of many situations encountered in biology, nanosciences and drug delivery in which a spherical container releases in the external environment through gradual uncovering of its surface. A procedure for extracting the aperture (opening) function of a biological vesicle fusing with a cell membrane from the released molecular flux of neurotransmitter as monitored by amperometry has been devised based on semi-analytical expressions derived in a former work [C. Amatore, A. I. Oleinick, I. Svir, ChemPhysChem 2009, 10, DOI: 10.1002/cphc.200900646]. This precise analysis shows that in the absence of direct information about the radius of the vesicle or about the concentration of the adrenaline cation stored by the vesicle matrix, current spikes do not contain enough information to determine the maximum aperture angle. Yet, a statistical analysis establishes that this maximum aperture angle is most probably less than a few tens of degrees, which suggests that full fusion is a very improbable event.

In silico reconstitution of actin-based symmetry breaking and motility

Computational modeling and experimentation in a model system for actin-based force generation explain how actin networks initiate and maintain directional movement.

Eukaryotic cells assemble viscoelastic networks of crosslinked actin filaments to control their shape, mechanical properties, and motility. One important class of actin network is nucleated by the Arp2/3 complex and drives both membrane protrusion at the leading edge of motile cells and intracellular motility of pathogens such as Listeria monocytogenes. These networks can be reconstituted in vitro from purified components to drive the motility of spherical micron-sized beads. An Elastic Gel model has been successful in explaining how these networks break symmetry, but how they produce directed motile force has been less clear. We have combined numerical simulations with in vitro experiments to reconstitute the behavior of these motile actin networks in silico using an Accumulative Particle-Spring (APS) model that builds on the Elastic Gel model, and demonstrates simple intuitive mechanisms for both symmetry breaking and sustained motility. The APS model explains observed transitions between smooth and pulsatile motion as well as subtle variations in network architecture caused by differences in geometry and conditions. Our findings also explain sideways symmetry breaking and motility of elongated beads, and show that elastic recoil, though important for symmetry breaking and pulsatile motion, is not necessary for smooth directional motility. The APS model demonstrates how a small number of viscoelastic network parameters and construction rules suffice to recapture the complex behavior of motile actin networks. The fact that the model not only mirrors our in vitro observations, but also makes novel predictions that we confirm by experiment, suggests that the model captures much of the essence of actin-based motility in this system.

Networks of actin filaments provide the force that drives eukaryotic cell movement. In a model system for this kind of force generation, a spherical bead coated with an actin nucleating protein builds and rockets around on an actin “comet tail,” much like the tails observed in some cellular systems. How does a spherically symmetric bead break the symmetry of the actin coat and begin to polymerize actin in a directional manner? A previous theoretical model successfully explained how symmetry breaks, but suggested that the subsequent motion was driven by actin squeezing the bead forwards—a prediction refuted by experiment. To understand how motility occurs, we created a parsimonious computer model that predicted novel experimental behaviors, then performed new experiments inspired by the model and confirmed these predictions. Our model demonstrates how the elastic properties of the actin network explain not only symmetry breaking, but also the details of subsequent motion and how the bead maintains direction.