Structure formation in active networks

Direct detection of deformation modes on varying length scales in active biopolymer networks

Correlated flows and forces that emerge from active matter orchestrate complex processes such as shape regulation and deformations in biological cells and tissues. The active materials central to cellular mechanics are cytoskeletal networks, where molecular motor activity drives deformations and remodeling. Here, we investigate deformation modes in contractile actin networks driven by the molecular motor myosin II through quantitative fluorescence microscopy. We examine the deformation anisotropy at different length scales in networks of sparsely cross-linked and bundled actin. In sparsely cross-linked networks, we find myosin-dependent biaxial buckling modes across length scales. Interestingly, both long and short-wavelength buckling may contribute to network contractility. In cross-linked bundled networks, uniaxial contraction predominates on long length scales, while the uniaxial or biaxial nature of the deformation depends on bundle microstructure at shorter length scales. The anisotropy of deformations may provide insight to the mechanical origins of contractility in actin networks and regulation of collective behavior in a variety of active materials.

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Cofilin-mediated actin filament network flexibility facilitates 2D to 3D actomyosin shape change

The organization of actin filaments (F-actin) into crosslinked networks determines the transmission of mechanical stresses within the cytoskeleton and subsequent changes in cell and tissue shape. Principally mediated by proteins such as α-actinin, F-actin crosslinking increases both network connectivity and rigidity, thereby facilitating stress transmission at low crosslinking yet attenuating transmission at high crosslinker concentration. Here, we engineer a two-dimensional model of the actomyosin cytoskeleton, in which myosin-induced mechanical stresses are controlled by light. We alter the extent of F-actin crosslinking by the introduction of oligomerized cofilin. At pH 6.5, F-actin severing by cofilin is weak, but cofilin bundles and crosslinks filaments. Given its effect of lowering the F-actin bending stiffness, cofilin- crosslinked networks are significantly more flexible and softer in bending than networks crosslinked by α-actinin. Thus, upon local activation of myosin-induced contractile stress, the network bends out-of-plane in contrast to the in-plane compression as observed with networks crosslinked by α-actinin. Here, we demonstrate that local effects on filament mechanics by cofilin introduces novel large-scale network material properties that enable the sculpting of complex shapes in the cell cytoskeleton.

Cytosolic actin isoforms form networks with different rheological properties that indicate specific biological function

The implications of the existence of different actins expressed in epithelial cells for network mechanics and dynamics is investigated by microrheology and confocal imaging. γ-actin predominately found in the apical cortex forms stiffer networks compared to β-actin, which is preferentially organized in stress fibers. We attribute this to selective interactions with Mg2+-ions interconnecting the filaments' N-termini. Bundling propensity of the isoforms is different in the presence of Mg2+-ions, while crosslinkers such as α-actinin, fascin, and heavy meromyosin alter the mechanical response independent of the isoform. In the presence of myosin, β-actin networks show a large number of small contraction foci, while γ-actin displays larger but fewer foci indicative of a stronger interaction with myosin motors. We infer that subtle changes in the amino acid sequence of actin isoforms lead to alterations of the mechanical properties on the network level with potential implications for specific biological functions.

Spontaneous motion of a passive fluid droplet in an active microchannel

We numerically study the dynamics of a passive fluid droplet confined within a microchannel whose walls are covered with a thin layer of active gel. The latter represents a fluid of extensile material modelling, for example, a suspension of cytoskeletal filaments and molecular motors. Our results show that the layer is capable of producing a spontaneous flow triggering a rectilinear motion of the passive droplet. For a hybrid design (a single wall covered by the active layer), at the steady state the droplet attains an elliptical shape, resulting from an asymmetric saw-toothed structure of the velocity field. In contrast, if the active gel covers both walls, the velocity field exhibits a fully symmetric pattern considerably mitigating morphological deformations. We further show that the structure of the spontaneous flow in the microchannel can be controlled by the anchoring conditions of the active gel at the wall. These findings are also confirmed by selected 3D simulations. Our results may stimulate further research addressed to design novel microfludic devices whose functioning relies on the collective properties of active gels.

A deep learning framework for quantitative analysis of actin microridges

Microridges are evolutionarily conserved actin-rich protrusions present on the apical surface of squamous epithelial cells. In zebrafish epidermal cells, microridges form self-evolving patterns due to the underlying actomyosin network dynamics. However, their morphological and dynamic characteristics have remained poorly understood owing to a lack of computational methods. We achieved ~95% pixel-level accuracy with a deep learning microridge segmentation strategy enabling quantitative insights into their bio-physical-mechanical characteristics. From the segmented images, we estimated an effective microridge persistence length of ~6.1 μm. We discovered the presence of mechanical fluctuations and found relatively greater stresses stored within patterns of yolk than flank, indicating distinct regulation of their actomyosin networks. Furthermore, spontaneous formations and positional fluctuations of actin clusters within microridges were associated with pattern rearrangements over short length/time-scales. Our framework allows large-scale spatiotemporal analysis of microridges during epithelial development and probing of their responses to chemical and genetic perturbations to unravel the underlying patterning mechanisms.

Self-emergent vortex flow of microtubule and kinesin in cell-sized droplets under water/water phase separation

By facilitating a water/water phase separation (w/wPS), crowded biopolymers in cells form droplets that contribute to the spatial localization of biological components and their biochemical reactions. However, their influence on mechanical processes driven by protein motors has not been well studied. Here, we show that the w/wPS droplet spontaneously entraps kinesins as well as microtubules (MTs) and generates a micrometre-scale vortex flow inside the droplet. Active droplets with a size of 10-100 µm are generated through w/wPS of dextran and polyethylene glycol mixed with MTs, molecular-engineered chimeric four-headed kinesins and ATP after mechanical mixing. MTs and kinesin rapidly created contractile network accumulated at the interface of the droplet and gradually generated vortical flow, which can drive translational motion of a droplet. Our work reveals that the interface of w/wPS contributes not only to chemical processes but also produces mechanical motion by assembling species of protein motors in a functioning manner.

Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles

The collective behavior of a binary mixture of polar self-propelled particles (SPPs) with different motile properties is studied. The binary mixture consists of slow-moving SPPs (sSPPs) of fixed velocity v_{s} and fast-moving SPPs (fSPPs) of fixed velocity v_{f}. These SPPs interact via a short-range interaction irrespective of their types. They move following certain position and velocity update rules similar to the Vicsek model (VM) under the influence of an external noise η. The system is studied at different values of v_{f} keeping v_{s}=0.01 constant for a fixed density ρ=0.5. Different phase-separated collective patterns that appear in the system over a wide range of noise η are characterized. The fSPPs and the sSPPs are found to be orientationally phase synchronized at the steady state. We studied an orientational order-disorder transition varying the angular noise η and identified the critical noise η_{c} for different v_{f}. Interestingly, both the species exhibit continuous transition for v_{f}<100v_{s} and discontinuous transition for v_{f}>100v_{s}. A new set of critical exponents is determined for the continuous transitions. However, the binary model is found to be nonuniversal as the values of the critical exponents depend on the velocity. The effect of interaction radius on the system behavior is also studied.

Engineering stability, longevity, and miscibility of microtubule-based active fluids

Microtubule-based active matter provides insight into the self-organization of motile interacting constituents. We describe several formulations of microtubule-based 3D active isotropic fluids. Dynamics of these fluids is powered by three types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. Another modification uses a specific microtubule crosslinker to induce bundle formation instead of a non-specific polymer depletant. In comparison to the already established system, each formulation exhibits distinct properties. These developments reveal the temporal stability of microtubule-based active fluids while extending their reach and the applicability.

Extensile to contractile transition in active microtubule-actin composites generates layered asters with programmable lifetimes

We study a reconstituted composite system consisting of an active microtubule network interdigitated with a passive network of entangled F-actin filaments. Increasing the concentration of filamentous actin controls the emergent dynamics, inducing a transition from turbulent-like flows to bulk contractions. At intermediate concentrations, where the active stresses change their symmetry from anisotropic extensile to isotropic contracting, the composite separates into layered asters that coexist with the background turbulent fluid. Contracted onion-like asters have a radially extending microtubule-rich cortex that envelops alternating layers of microtubules and F-actin. These self-regulating structures undergo internal reorganization, which appears to minimize the surface area and maintain the ordered layering, even when undergoing aster merging events. Finally, the layered asters are metastable structures. Their lifetime, which ranges from minutes to hours, is encoded in the material properties of the composite. These results challenge the current models of active matter. They demonstrate self-organized dynamical states and patterns evocative of those observed in the cytoskeleton do not require precise biochemical regulation, but can arise from purely mechanical interactions of actively driven filamentous materials.

A printable active network actuator built from an engineered biomolecular motor

Leveraging the motion and force of individual molecular motors in a controlled manner to perform macroscopic tasks can provide substantial benefits to many applications, including robotics. Nonetheless, although millimetre-scale movement has been demonstrated with synthetic and biological molecular motors, their efficient integration into engineered systems that perform macroscopic tasks remains challenging. Here, we describe an active network capable of macroscopic actuation that is hierarchically assembled from an engineered kinesin, a biomolecular motor, and microtubules, resembling the contractile units in muscles. These contracting materials can be formed in desired areas using patterned ultraviolet illumination, allowing their incorporation into mechanically engineered systems, being also compatible with printing technologies. Due to the designed filamentous assembly of kinesins, the generated forces reach the micronewton range, enabling actuation of millimetre-scale mechanical components. These properties may be useful for the fabrication of soft robotic systems with advanced functionalities.

Synthesis and characterization of chemically fueled supramolecular materials driven by carbodiimide-based fuels

Many supramolecular materials in biological systems are driven to a nonequilibrium state by the irreversible consumption of high-energy molecules such as ATP or GTP. As a result, they exhibit unique dynamic properties such as a tunable lifetime, adaptivity or the ability to self-heal. In contrast, synthetic counterparts that exist in or close to equilibrium are controlled by thermodynamic parameters and therefore lack these dynamic properties. To mimic biological materials more closely, synthetic self-assembling systems have been developed that are driven out of equilibrium by chemical reactions. This protocol describes the synthesis and characterization of such an assembly, which is driven by carbodiimide fuels. Depending on the amount of chemical fuel added to the material, its lifetime can be tuned. In the first step, the protocol details the synthesis and purification of the peptide-based precursors for the fuel-driven assemblies by solid-phase peptide synthesis. Then, we explain how to analyze the kinetic response of the precursors to a carbodiimide-based chemical fuel by HPLC and kinetic models. Finally, we detail how to study the emerging assembly's macro- and microscopic properties by time-lapse photography, UV-visible spectroscopy, shear rheology, confocal laser scanning microscopy and electron microscopy. The procedure is described using the example of a colloid-forming precursor Fmoc-E-OH and a fiber-forming precursor Fmoc-AAD-OH to emphasize the differences in characterization depending on the type of assembly. The characterization of a precursor's transient assembly can be done within 5 d. The synthesis and purification of a peptide precursor requires 2 d of work.

Intra-bundle contractions enable extensile properties of active actin networks

The cellular cortex is a dynamic and contractile actomyosin network modulated by actin-binding proteins. We reconstituted a minimal cortex adhered to a model cell membrane mimicking two processes mediated by the motor protein myosin: contractility and high turnover of actin monomers. Myosin reorganized these networks by extensile intra‑bundle contractions leading to an altered growth mechanism. Hereby, stress within tethered bundles induced nicking of filaments followed by repair via incorporation of free monomers. This mechanism was able to break the symmetry of the previously disordered network resulting in the generation of extensile clusters, reminiscent of structures found within cells.

Shear-Induced Gelation of Self-Yielding Active Networks

An enticing feature of active materials is the possibility of controlling macroscale rheological properties through the activity of the microscopic constituents. Using a unique combination of microscopy and rheology we study three dimensional microtubule-based active materials whose autonomous flows are powered by a continually rearranging connected network. We quantify the relationship between the microscopic dynamics and the bulk mechanical properties of these nonequilibrium networks. Experiments reveal a surprising nonmonotonic viscosity that strongly depends on the relative magnitude of the rate of internally generated activity and the externally applied shear. A simple two-state mechanical model that accounts for both the solidlike and yielded fluidlike elements of the network accurately describes the rheological measurements.

A comparative study between two models of active cluster crystals

We study a system of active particles with soft repulsive interactions that lead to an active cluster-crystal phase in two dimensions. We use two different modelizations of the active force - Active Brownian particles (ABP) and Ornstein-Uhlenbeck particles (AOUP) - and focus on analogies and differences between them. We study the different phases appearing in the system, in particular, the formation of ordered patterns drifting in space without being altered. We develop an effective description which captures some properties of the stable clusters for both ABP and AOUP. As an additional point, we confine such a system in a large channel, in order to study the interplay between the cluster crystal phase and the well-known accumulation near the walls, a phenomenology typical of active particles. For small activities, we find clusters attached to the walls and deformed, while for large values of the active force they collapse in stripes parallel to the walls.

Uncovering the dynamic precursors to motor-driven contraction of active gels

Cells and tissues have the remarkable ability to actively generate the forces required to change their shape. This active mechanical behavior is largely mediated by the actin cytoskeleton, a crosslinked network of actin filaments that is contracted by myosin motors. Experiments and active gel theories have established that the length scale over which gel contraction occurs is governed by a balance between molecular motor activity and crosslink density. By contrast, the dynamics that govern the contractile activity of the cytoskeleton remain poorly understood. Here we investigate the microscopic dynamics of reconstituted actin-myosin networks using simultaneous real-space video microscopy and Fourier-space dynamic light scattering. Light scattering reveals different regimes of microscopic dynamics as a function of sample age. We uncover two dynamical precursors that precede macroscopic gel contraction. One is characterized by a progressive acceleration of stress-induced rearrangements, while the other consists of sudden, heterogeneous rearrangements. Intriguingly, our findings suggest a qualitative analogy between self-driven rupture and collapse of active gels and the delayed rupture of passive gels observed in earlier studies of colloidal gels under external loads.

Clustering and anisotropic correlated percolation in polar flocks

We study clustering and percolation phenomena in the Vicsek model, taken here in its capacity of prototypical model for dry aligning active matter. Our results show that the order-disorder transition is not related in any way to a percolation transition, contrary to some earlier claims. We study geometric percolation in each of the phases at play, but we mostly focus on the ordered Toner-Tu phase, where we find that the long-range correlations of density fluctuations give rise to an anisotropic percolation transition.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

Chemical Nanomotors at the Gram Scale Form a Dense Active Optorheological Medium

The rheological properties of a colloidal suspension are a function of the concentration of the colloids and their interactions. While suspensions of passive colloids are well studied and have been shown to form crystals, gels, and glasses, examples of energy-consuming "active" colloidal suspensions are still largely unexplored. Active suspensions of biological matter, such as motile bacteria or dense mixtures of active actin-motor-protein mixtures have, respectively, reveals superfluid-like and gel-like states. Attractive inanimate systems for active matter are chemically self-propelled particles. It has so far been challenging to use these swimming particles at high enough densities to affect the bulk material properties of the suspension. Here, it is shown that light-triggered asymmetric titanium dioxide that self-propel, can be obtained in large quantities, and self-organize to make a gram-scale active medium. The suspension shows an activity-dependent tenfold reversible change in its bulk viscosity.

Activity induced delocalization and freezing in self-propelled systems

We study a system of interacting active particles, propelled by colored noises, characterized by an activity time τ, and confined by a single-well anharmonic potential. We assume pair-wise repulsive forces among particles, modelling the steric interactions among microswimmers. This system has been experimentally studied in the case of a dilute suspension of Janus particles confined through acoustic traps. We observe that already in the dilute regime - when inter-particle interactions are negligible - increasing the persistent time, τ, pushes the particles away from the potential minimum, until a saturation distance is reached. We compute the phase diagram (activity versus interaction length), showing that the interaction does not suppress this delocalization phenomenon but induces a liquid- or solid-like structure in the densest regions. Interestingly a reentrant behavior is observed: a first increase of τ from small values acts as an effective warming, favouring fluidization; at higher values, when the delocalization occurs, a further increase of τ induces freezing inside the densest regions. An approximate analytical scheme gives fair predictions for the density profiles in the weakly interacting case. The analysis of non-equilibrium heat fluxes reveals that in the region of largest particle concentration equilibrium is restored in several aspects.

Myosin-II activity generates a dynamic steady state with continuous actin turnover in a minimal actin cortex

Dynamic reorganization of the actomyosin cytoskeleton allows fast modulation of the cell surface, which is vital for many cellular functions. Myosin-II motors generate the forces required for this remodeling by imparting contractility to actin networks. However, myosin-II activity might also have a more indirect contribution to cytoskeletal dynamics; it has been proposed that myosin activity increases actin turnover in various cellular contexts, presumably by enhancing disassembly. In vitro reconstitution of actomyosin networks has confirmed the role of myosin in actin network disassembly, but the reassembly of actin in these assays was limited by factors such as diffusional constraints and the use of stabilized actin filaments. Here, we present the reconstitution of a minimal dynamic actin cortex, where actin polymerization is catalyzed on the membrane in the presence of myosin-II activity. We demonstrate that myosin activity leads to disassembly and redistribution in this simplified cortex. Consequently, a new dynamic steady state emerges in which the actin network undergoes constant turnover. Our findings suggest a multifaceted role of myosin-II in the dynamics of the eukaryotic actin cortex. This article has an associated First Person interview with the first author of the paper.

Entropy production rate is maximized in non-contractile actomyosin

The actin cytoskeleton is an active semi-flexible polymer network whose non-equilibrium properties coordinate both stable and contractile behaviors to maintain or change cell shape. While myosin motors drive the actin cytoskeleton out-of-equilibrium, the role of myosin-driven active stresses in the accumulation and dissipation of mechanical energy is unclear. To investigate this, we synthesize an actomyosin material in vitro whose active stress content can tune the network from stable to contractile. Each increment in activity determines a characteristic spectrum of actin filament fluctuations which is used to calculate the total mechanical work and the production of entropy in the material. We find that the balance of work and entropy does not increase monotonically and the entropy production rate is maximized in the non-contractile, stable state of actomyosin. Our study provides evidence that the origins of entropy production and activity-dependent dissipation relate to disorder in the molecular interactions between actin and myosin.

Biological Tissues as Active Nematic Liquid Crystals

Live tissues can self-organize and be described as active materials composed of cells that generate active stresses through continuous injection of energy. In vitro reconstituted molecular networks, as well as single-cell cytoskeletons show that their filamentous structures can portray nematic liquid crystalline properties and can promote nonequilibrium processes induced by active processes at the microscale. The appearance of collective patterns, the formation of topological singularities, and spontaneous phase transition within the cell cytoskeleton are emergent properties that drive cellular functions. More integrated systems such as tissues have cells that can be seen as coarse-grained active nematic particles and their interaction can dictate many important tissue processes such as epithelial cell extrusion and migration as observed in vitro and in vivo. Here, a brief introduction to the concept of active nematics is provided, and the main focus is on the use of this framework in the systematic study of predominantly 2D tissue architectures and dynamics in vitro. In addition how the nematic state is important in tissue behavior, such as epithelial expansion, tissue homeostasis, and the atherosclerosis disease state, is discussed. Finally, how the nematic organization of cells can be controlled in vitro for tissue engineering purposes is briefly discussed.

Self-propulsion of droplets driven by an active permeating gel

We discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the Brinkman equation, the porous medium is characterised by a single lengthscale [Formula: see text] --the square root of the permeability. We compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of [Formula: see text]. We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit [Formula: see text], corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, [Formula: see text], corresponding to a space filling gel, is singular and not equivalent to Darcy's equation, which cannot account for self-propulsion.

Nonequilibrium phase diagrams for actomyosin networks

Living cells dynamically modulate the local morphologies of their actin networks to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors, as well as filament lengths, we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between the modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials.

Dissipative assemblies that inhibit their deactivation

Dissipative self-assembly is a process in which energy-consuming chemical reaction networks drive the assembly of molecules. Prominent examples from biology include the GTP-fueled microtubule and ATP-driven actin assembly. Pattern formation and oscillatory behavior are some of the unique properties of the emerging assemblies. While artificial counterparts exist, researchers have not observed such complex responses. One reason for the missing complexity is the lack of feedback mechanisms of the assemblies on their chemical reaction network. In this work, we describe the dissipative self-assembly of colloids that protect the hydrolysis of their building blocks. The mechanism of inhibition is generalized and explored for other building blocks. We show that we can tune the level of inhibition by the assemblies. Finally, we show that the robustness of the assemblies towards starvation is affected by the degree of inhibition.

Self-organized stress patterns drive state transitions in actin cortices

Biological functions rely on ordered structures and intricately controlled collective dynamics. This order in living systems is typically established and sustained by continuous dissipation of energy. The emergence of collective patterns of motion is unique to nonequilibrium systems and is a manifestation of dynamic steady states. Mechanical resilience of animal cells is largely controlled by the actomyosin cortex. The cortex provides stability but is, at the same time, highly adaptable due to rapid turnover of its components. Dynamic functions involve regulated transitions between different steady states of the cortex. We find that model actomyosin cortices, constructed to maintain turnover, self-organize into distinct nonequilibrium steady states when we vary cross-link density. The feedback between actin network structure and organization of stress-generating myosin motors defines the symmetries of the dynamic steady states. A marginally cross-linked state displays divergence-free long-range flow patterns. Higher cross-link density causes structural symmetry breaking, resulting in a stationary converging flow pattern. We track the flow patterns in the model actomyosin cortices using fluorescent single-walled carbon nanotubes as novel probes. The self-organization of stress patterns we have observed in a model system can have direct implications for biological functions.

Large-scale chirality in an active layer of microtubules and kinesin motor proteins

During the early developmental process of organisms, the formation of left-right laterality requires a subtle mechanism, as it is associated with other principal body axes. Any inherent chiral feature in an egg cell can in principal trigger this spontaneous breaking of chiral symmetry. Individual microtubules, major cytoskeletal filaments, are known as chiral objects. However, to date there lacks convincing evidence of a hierarchical connection of the molecular nature of microtubules to large-scale chirality, particularly at the length scale of an entire cell. Here we assemble an in vitro active layer, consisting of microtubules and kinesin motor proteins, on a glass surface. Upon inclusion of methyl cellulose, the layered system exhibits a long-range active nematic phase, characterized by the global alignment of gliding MTs. This nematic order spans over the entire system size in the millimeter range and, remarkably, allows hidden collective chirality to emerge as counterclockwise global rotation of the active MT layer. The analysis based on our theoretical model suggests that the emerging global nematic order results from the local alignment of MTs, stabilized by methyl cellulose. It also suggests that the global rotation arises from the MTs' intrinsic curvature, leading to preferential handedness. Given its flexibility, this layered in vitro cytoskeletal system enables the study of membranous protein behavior responsible for important cellular developmental processes.

Collective motion of active Brownian particles with polar alignment

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles. We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. We analyze the onset of collective motion (flocking) in a low-density regime (10% surface area) and show that it is mainly controlled by the strength of velocity-alignment interactions: the competition between self-propulsion and crowding effects plays a minor role in the emergence of flocking. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions (active brownian particles) or excluded volume effects (Vicsek-like models). Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form (and usually a hybrid structure which is halfway in between both). We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.

Active nematic emulsions

The formation of emulsions from multiple immiscible fluids is governed by classical concepts such as surface tension, differential chemical affinity and viscosity, and the action of surface-active agents. Much less is known about emulsification when one of the components is active and thus inherently not constrained by the laws of thermodynamic equilibrium. We demonstrate one such realization consisting in the encapsulation of an active liquid crystal (LC)-like gel, based on microtubules and kinesin molecular motors, into a thermotropic LC. These active nematic emulsions exhibit a variety of dynamic behaviors that arise from the cross-talk between topological defects separately residing in the active and passive components. Using numerical simulations, we show a feedback mechanism by which active flows continuously drive the passive defects that, in response, resolve the otherwise degenerated trajectories of the active defects. Our experiments show that the choice of surfactant, which stabilizes the active/passive interface, allows tuning the regularity of the self-sustained dynamic events. The hybrid active-passive system demonstrated here provides new perspectives for dynamic self-assembly driven by an active material but regulated by the equilibrium properties of the passive component.

Active colloids with collective mobility status and research opportunities

The collective mobility of active matter (self-propelled objects that transduce energy into mechanical work to drive their motion, most commonly through fluids) constitutes a new frontier in science and achievable technology. This review surveys the current status of the research field, what kinds of new scientific problems can be tackled in the short term, and what long-term directions are envisioned. We focus on: (1) attempts to formulate design principles to tailor active particles; (2) attempts to design principles according to which active particles interact under circumstances where particle-particle interactions of traditional colloid science are augmented by a family of nonequilibrium effects discussed here; (3) attempts to design intended patterns of collective behavior and dynamic assembly; (4) speculative links to equilibrium thermodynamics. In each aspect, we assess achievements, limitations, and research opportunities.

Polarity sorting drives remodeling of actin-myosin networks

Cytoskeletal networks of actin filaments and myosin motors drive many dynamic cell processes. A key characteristic of these networks is their contractility. Despite intense experimental and theoretical efforts, it is not clear what mechanism favors network contraction over expansion. Recent work points to a dominant role for the nonlinear mechanical response of actin filaments, which can withstand stretching but buckle upon compression. Here we present an alternative mechanism. We study how interactions between actin and myosin-2 at the single filament level translate into contraction at the network scale by performing time-lapse imaging on reconstituted quasi-2D-networks mimicking the cell cortex. We observe myosin end-dwelling after it runs processively along actin filaments. This leads to transport and clustering of actin filament ends and the formation of transiently stable bipolar structures. Further we show that myosin-driven polarity sorting produces polar actin asters, which act as contractile nodes that drive contraction in crosslinked networks. Computer simulations comparing the roles of the end-dwelling mechanism and a buckling-dependent mechanism show that the relative contribution of end-dwelling contraction increases as the network mesh-size decreases.

Control of active turbulence through addressable soft interfaces

We present an experimental study of a kinesin/tubulin active nematic formed at different oil interfaces. By tuning the interfacial rheology of the contacting oil, we have been able to condition and control the seemingly chaotic motion that characterizes the self-sustained active flows in our preparations. The active nematic is inherently unstable and spontaneously develops defects from an initial homogeneous state. We show that the steady state and, in particular, the density and dynamics of the defects strongly depends on the rheology of the contacting oil. Using a smectic-A thermotropic liquid crystal as the oil phase, we pattern the interface thanks to the anisotropy of the shear viscosity in this material. The geometry of the active nematic adapts to the boundary conditions at the interface by changing from the so-called active turbulent regime to laminar flows along the easy flow directions. The latter can be either a lattice of self-assembled circular paths or reconfigurable homogeneous orientations that can be addressed by means of an external magnetic field. We show that, under all confinement conditions, the spatiotemporal modes exhibited by the active liquid are consistent with a single intrinsic length scale, which can be tuned by the material parameters, and obey basic topological requirements imposed on the defects that drive the active flows. Future control strategies, including a tunable depleting agent, are discussed.

Filament rigidity and connectivity tune the deformation modes of active biopolymer networks

Molecular motors embedded within collections of actin and microtubule filaments underlie the dynamics of cytoskeletal assemblies. Understanding the physics of such motor-filament materials is critical to developing a physical model of the cytoskeleton and designing biomimetic active materials. Here, we demonstrate through experiments and simulations that the rigidity and connectivity of filaments in active biopolymer networks regulates the anisotropy and the length scale of the underlying deformations, yielding materials with variable contractility. We find that semiflexible filaments can be compressed and bent by motor stresses, yielding materials that undergo predominantly biaxial deformations. By contrast, rigid filament bundles slide without bending under motor stress, yielding materials that undergo predominantly uniaxial deformations. Networks dominated by biaxial deformations are robustly contractile over a wide range of connectivities, while networks dominated by uniaxial deformations can be tuned from extensile to contractile through cross-linking. These results identify physical parameters that control the forces generated within motor-filament arrays and provide insight into the self-organization and mechanics of cytoskeletal assemblies.

Scale dependence of the mechanics of active gels with increasing motor concentration

Actin is a protein that plays an essential role in maintaining the mechanical integrity of cells. In response to strong external stresses, it can assemble into large bundles, but it grows into a fine branched network to induce cell motion. In some cases, the self-organization of actin fibers and networks involves the action of bipolar filaments of the molecular motor myosin. Such self-organization processes mediated by large myosin bipolar filaments have been studied extensively in vitro. Here we create active gels, composed of single actin filaments and small myosin bipolar filaments. The active steady state in these gels persists long enough to enable the characterization of their mechanical properties using one and two point microrheology. We study the effect of myosin concentration on the mechanical properties of this model system for active matter, for two different motor assembly sizes. In contrast to previous studies of networks with large motor assemblies, we find that the fluctuations of tracer particles embedded in the network decrease in amplitude as motor concentration increases. Nonetheless, we show that myosin motors stiffen the actin networks, in accordance with bulk rheology measurements of networks containing larger motor assemblies. This implies that such stiffening is of universal nature and may be relevant to a wider range of cytoskeleton-based structures.

Bidirectional motion of filaments: the role of motor proteins and passive cross linkers

In eukaryotic cells, motor proteins (MPs) bind to cytoskeletal filaments and move along them in a directed manner generating active stresses. During cell division a spindle structure of overlapping antiparallel microtubules forms whose stability and dynamics under the influence of MPs have been studied extensively. Although passive cross linkers (PCLs) are known to provide structural stability to a filamentous network, consequences of the interplay between ATP dependent active forces of MPs and passive entropic forces of PCLs on filamentous overlap remain largely unexplored. Here, we formulate and characterize a model to study this, using linear stability analysis and numerical integration. In the presence of PCLs, we find dynamic phase transitions with changing activity exhibiting regimes of stable partial overlap with or without oscillations, instability towards complete overlap, and stable limit cycle oscillations that emerge via a supercritical Hopf bifurcation characterized by an oscillation frequency determined by the MP and PCL parameters. We show that the overlap dynamics and stability depend crucially on whether both the filaments of an overlapping pair are movable or one is immobilized, having potential implications for in vivo and in vitro studies.

A theory that predicts behaviors of disordered cytoskeletal networks

Morphogenesis in animal tissues is largely driven by actomyosin networks, through tensions generated by an active contractile process. Although the network components and their properties are known, and networks can be reconstituted in vitro, the requirements for contractility are still poorly understood. Here, we describe a theory that predicts whether an isotropic network will contract, expand, or conserve its dimensions. This analytical theory correctly predicts the behavior of simulated networks, consisting of filaments with varying combinations of connectors, and reveals conditions under which networks of rigid filaments are either contractile or expansile. Our results suggest that pulsatility is an intrinsic behavior of contractile networks if the filaments are not stable but turn over. The theory offers a unifying framework to think about mechanisms of contractions or expansion. It provides the foundation for studying a broad range of processes involving cytoskeletal networks and a basis for designing synthetic networks.

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots

Biological systems have evolved to harness non-equilibrium processes from the molecular to the macro scale. It is currently a grand challenge of chemistry, materials science, and engineering to understand and mimic biological systems that have the ability to autonomously sense stimuli, process these inputs, and respond by performing mechanical work. New chemical systems are responding to the challenge and form the basis for future responsive, adaptive, and active materials. In this article, we describe a particular biochemical-biomechanical network based on the microtubule cytoskeletal filament - itself a non-equilibrium chemical system. We trace the non-equilibrium aspects of the system from molecules to networks and describe how the cell uses this system to perform active work in essential processes. Finally, we discuss how microtubule-based engineered systems can serve as testbeds for autonomous chemical robots composed of biological and synthetic components.

Taming active turbulence with patterned soft interfaces

Active matter embraces systems that self-organize at different length and time scales, often exhibiting turbulent flows apparently deprived of spatiotemporal coherence. Here, we use a layer of a tubulin-based active gel to demonstrate that the geometry of active flows is determined by a single length scale, which we reveal in the exponential distribution of vortex sizes of active turbulence. Our experiments demonstrate that the same length scale reemerges as a cutoff for a scale-free power law distribution of swirling laminar flows when the material evolves in contact with a lattice of circular domains. The observed prevalence of this active length scale can be understood by considering the role of the topological defects that form during the spontaneous folding of microtubule bundles. These results demonstrate an unexpected strategy for active systems to adapt to external stimuli, and provide with a handle to probe the existence of intrinsic length and time scales.

Active nematics consist of self-driven components that develop orientational order and turbulent flow. Here Guillamat et al. investigate an active nematic constrained in a quasi-2D geometrical setup and show that there exists an intrinsic length scale that determines the geometry in all forcing regimes.

Parallel Compression Is a Fast Low-Cost Assay for the High-Throughput Screening of Mechanosensory Cytoskeletal Proteins in Cells

Cellular mechanosensing is critical for many biological processes, including cell differentiation, proliferation, migration, and tissue morphogenesis. The actin cytoskeletal proteins play important roles in cellular mechanosensing. Many techniques have been used to investigate the mechanosensory behaviors of these proteins. However, a fast, low-cost assay for the quantitative characterization of these proteins is still lacking. Here, we demonstrate that compression assay using agarose overlay is suitable for the high throughput screening of mechanosensory proteins in live cells while requiring minimal experimental setup. We used several well-studied myosin II mutants to assess the compression assay. On the basis of elasticity theories, we simulated the mechanosensory accumulation of myosin II's and quantitatively reproduced the experimentally observed protein dynamics. Combining the compression assay with confocal microscopy, we monitored the polarization of myosin II oligomers at the subcellular level. The polarization was dependent on the ratio of the two principal strains of the cellular deformations. Finally, we demonstrated that this technique could be used on the investigation of other mechanosensory proteins.

Force percolation of contractile active gels

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

A Radial Actin Network in Apical Constriction

Contractile actomyosin networks are central to cell shape change, rearrangements, and migration during animal tissue morphogenesis. In this issue of Developmental Cell, Coravos and Martin (2016) report that the actin network is radially polarized in apically constricting cells, suggesting a constriction model similar to the contraction mechanism in muscle sarcomeres.

Spontaneous Formation of a Globally Connected Contractile Network in a Microtubule-Motor System

Microtubule (MT) networks play key roles in cell division, intracellular transport, and cell motility. These functions of MT networks occur through interactions between MTs and various associated proteins, notably motor proteins that bundle and slide MTs. Our objective in this study was to address the question of how motors determine the nature of MT networks. We conducted in vitro assays using homotetrameric kinesin Eg5, a motor protein involved in the formation and maintenance of the mitotic spindle. The mixing of Eg5 and MTs produced a range of spatiotemporal dynamics depending on the motor/filament ratio. Low motor/filament ratios produced globally connected static MT networks with sparsely distributed contractile active nodes (motor-accumulating points with radially extending MTs). Increasing the motor/filament ratio facilitated the linking of contractile active nodes and led to a global contraction of the network. When the motor/filament ratio was further increased, densely distributed active nodes formed local clusters and segmented the network into pieces with their strong contractile forces. Altering the properties of the motor through the use of chimeric Eg5, which has kinesin-1 heads, resulted in the generation of many isolated asters. These results suggest that the spatial distribution of contractile active nodes determines the dynamics of MT-motor networks. We then developed a coarse-grained model of MT-motor networks and identified two essential features for reproducing the experimentally observed patterns: an accumulation of motors that form the active nodes necessary to generate contractile forces, and a nonlinear dependency of contractile force on motor densities. Our model also enabled us to characterize the mechanical properties of the contractile network. Our study provides insight into how local motor-MT interactions generate the spatiotemporal dynamics of macroscopic network structures.

Dynamics in steady state in vitro acto-myosin networks

It is well known that many biochemical processes in the cell such as gene regulation, growth signals and activation of ion channels, rely on mechanical stimuli. However, the mechanism by which mechanical signals propagate through cells is not as well understood. In this review we focus on stress propagation in a minimal model for cell elasticity, actomyosin networks, which are comprised of a sub-family of cytoskeleton proteins. After giving an overview of th actomyosin network components, structure and evolution we review stress propagation in these materials as measured through the correlated motion of tracer beads. We also discuss the possibility to extract structural features of these networks from the same experiments. We show that stress transmission through these networks has two pathways, a quickly dissipative one through the bulk, and a long ranged weakly dissipative one through the pre-stressed actin network.

Sensitivity of small myosin II ensembles from different isoforms to mechanical load and ATP concentration

Based on a detailed crossbridge model for individual myosin II motors, we systematically study the influence of mechanical load and adenosine triphosphate (ATP) concentration on small myosin II ensembles made from different isoforms. For skeletal and smooth muscle myosin II, which are often used in actomyosin gels that reconstitute cell contractility, fast forward movement is restricted to a small region of phase space with low mechanical load and high ATP concentration, which is also characterized by frequent ensemble detachment. At high load, these ensembles are stalled or move backwards, but forward motion can be restored by decreasing ATP concentration. In contrast, small ensembles of nonmuscle myosin II isoforms, which are found in the cytoskeleton of nonmuscle cells, are hardly affected by ATP concentration due to the slow kinetics of the bound states. For all isoforms, the thermodynamic efficiency of ensemble movement increases with decreasing ATP concentration, but this effect is weaker for the nonmuscle myosin II isoforms.

Boundaries steer the contraction of active gels

Cells set up contractile actin arrays to drive various shape changes and to exert forces to their environment. To understand their assembly process, we present here a reconstituted contractile system, comprising F-actin and myosin II filaments, where we can control the local activation of myosin by light. By stimulating different symmetries, we show that the force balancing at the boundaries determine the shape changes as well as the dynamics of the global contraction. Spatially anisotropic attachment of initially isotropic networks leads to a self-organization of highly aligned contractile fibres, being reminiscent of the order formation in muscles or stress fibres. The observed shape changes and dynamics are fully recovered by a minimal physical model.

Disordered actomyosin networks are sufficient to produce cooperative and telescopic contractility

While the molecular interactions between individual myosin motors and F-actin are well established, the relationship between F-actin organization and actomyosin forces remains poorly understood. Here we explore the accumulation of myosin-induced stresses within a two-dimensional biomimetic model of the disordered actomyosin cytoskeleton, where myosin activity is controlled spatiotemporally using light. By controlling the geometry and the duration of myosin activation, we show that contraction of disordered actin networks is highly cooperative, telescopic with the activation size, and capable of generating non-uniform patterns of mechanical stress. We quantitatively reproduce these collective biomimetic properties using an isotropic active gel model of the actomyosin cytoskeleton, and explore the physical origins of telescopic contractility in disordered networks using agent-based simulations.

Role of Turnover in Active Stress Generation in a Filament Network

We study the effect of turnover of cross-linkers, motors, and filaments on the generation of a contractile stress in a network of filaments connected by passive cross-linkers and subjected to the forces exerted by molecular motors. We perform numerical simulations where filaments are treated as rigid rods and molecular motors move fast compared to the time scale of an exchange of cross-linkers. We show that molecular motors create a contractile stress above a critical number of cross-linkers. When passive cross-linkers are allowed to turn over, the stress exerted by the network vanishes due to the formation of clusters. When both filaments and passive cross-linkers turn over, clustering is prevented and the network reaches a dynamic contractile steady state. A maximum stress is reached for an optimum ratio of the filament and cross-linker turnover rates. Taken together, our work reveals conditions for stress generation by molecular motors in a fluid isotropic network of rearranging filaments.