Tunable dynamics of microtubule-based active isotropic gels

Heterogeneous distribution of kinesin-streptavidin complexes revealed by Mass Photometry

Kinesin-streptavidin complexes are widely used in microtubule-based active-matter studies. The stoichiometry of the complexes is empirically tuned but experimentally challenging to determine. Here, mass photometry measurements reveal heterogenous distributions of kinesin-streptavidin complexes. Our binding model indicates that heterogeneity arises from both the kinesin-streptavidin mixing ratio and the kinesin-biotinylation efficiency.

A machine learning approach to robustly determine director fields and analyze defects in active nematics

Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Maximally mixing active nematics

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) "topological entropy"-the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

Flow patterns and defect dynamics of active nematic liquid crystals under an electric field

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics with simultaneous creation of two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.

Dissipation and energy propagation across scales in an active cytoskeletal material

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Active Bending of Disordered Microtubule Bundles by Kinesin Motors

Active networks of biopolymers and motor proteins in vitro self-organize and exhibit dynamic structures on length scales much larger than the interacting individual components of which they consist. How the dynamics is related across the range of length scales is still an open question. Here, we experimentally characterize and quantify the dynamic behavior of isolated microtubule bundles that bend due to the activity of motor proteins. At the motor level, we track and describe the motion features of kinesin-1 clusters stepping within the bending bundles. We find that there is a separation of length scales by at least 1 order of magnitude. At a run length of <1 μm, kinesin-1 activity leads to a bundle curvature in the range of tens of micrometers. We propose that the distribution of microtubule polarity plays a crucial role in the bending dynamics that we observe at both the bundle and motor levels. Our results contribute to the understanding of fundamental principles of vital intracellular processes by disentangling the multiscale dynamics in out-of-equilibrium active networks composed of cytoskeletal elements.

Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity

Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.

Competing instabilities reveal how to rationally design and control active crosslinked gels

How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.

Dispersion of activity at an active-passive nematic interface

Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems known as active nematics. However, the dynamics of this mixing is non-trivial as there is a coupling between nutrients concentration and velocity field. To address this question, we solve the hydrodynamic equation for active nematics to model the bacterial swarms coupled to an advection-diffusion equation for the activity field, which is proportional to the concentration of nutrients. At the interface between active and passive nematics the activity field is transported by the interfacial flows and in turn it modifies them through the generation of active stresses. We find that the dispersion of this conserved activity field is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects.

Cross-linker design determines microtubule network organization by opposing motors

During cell division, cross-linking motors determine the architecture of the spindle, a dynamic microtubule network that segregates the chromosomes in eukaryotes. It is unclear how motors with opposite directionality coordinate to drive both contractile and extensile behaviors in the spindle. Particularly, the impact of different cross-linker designs on network self-organization is not understood, limiting our understanding of self-organizing structures in cells but also our ability to engineer new active materials. Here, we use experiment and theory to examine active microtubule networks driven by mixtures of motors with opposite directionality and different cross-linker design. We find that although the kinesin-14 HSET causes network contraction when dominant, it can also assist the opposing kinesin-5 KIF11 to generate extensile networks. This bifunctionality results from HSET's asymmetric design, distinct from symmetric KIF11. These findings expand the set of rules underlying patterning of active microtubule assemblies and allow a better understanding of motor cooperation in the spindle.

Active Microphase Separation in Mixtures of Microtubules and Tip-Accumulating Molecular Motors

Mixtures of filaments and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. To develop a multiscale of these materials, we map the nonequilibrium phase diagram of microtubules and tip-accumulating kinesin-4 molecular motors. We find that kinesin-4 can drive either global contractions or turbulentlike extensile dynamics, depending on the concentrations of both microtubules and a bundling agent. We also observe a range of spatially heterogeneous nonequilibrium phases, including finite-sized radial asters, 1D wormlike chains, extended 2D bilayers, and system-spanning 3D active foams. Finally, we describe intricate kinetic pathways that yield microphase separated structures and arise from the inherent frustration between the orientational order of filamentous microtubules and the positional order of tip-accumulating molecular motors. Our work reveals a range of novel active states. It also shows that the form of active stresses is not solely dictated by the properties of individual motors and filaments, but is also contingent on the constituent concentrations and spatial arrangement of motors on the filaments.

Assembling Microtubule-Based Active Matter

Studied for more than a century, equilibrium liquid crystals provided insight into the properties of ordered materials, and led to commonplace applications such as display technology. Active nematics are a new class of liquid crystal materials that are driven out of equilibrium by continuous motion of the constituent anisotropic units. A versatile experimental realization of active nematic liquid crystals is based on rod-like cytoskeletal filaments that are driven out of equilibrium by molecular motors. We describe protocols for assembling microtubule-kinesin based active nematic liquid crystals and associated isotropic fluids. We describe the purification of each protein and the assembly process of a two-dimensional active nematic on a water-oil interface. Finally, we show examples of nematic formation and describe methods for quantifying their non-equilibrium dynamics.

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.

Effects of confinement on the dynamics and correlation scales in kinesin-microtubule active fluids

We study the influence of solid boundaries on dynamics and structure of kinesin-driven microtubule active fluids as the height of the container, H, increases from hundreds of micrometers to several millimeters. By three-dimensional tracking of passive tracers dispersed in the active fluid, we observe that the activity level, characterized by velocity fluctuations, increases as system size increases and retains a small-scale isotropy. Concomitantly, as the confinement level decreases, the velocity-velocity temporal correlation develops a strong positive correlation at longer times, suggesting the establishment of a "memory". We estimate the characteristic size of the flow structures from the spatial correlation function and find that, as the confinement becomes weaker, the correlation length, l_{c}, saturates at approximately 400 microns. This saturation suggests an intrinsic length scale which, along with the small-scale isotropy, demonstrates the multiscale nature of this kinesin-driven bundled microtubule active system.

Multiscale Microtubule Dynamics in Active Nematics

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

Behavior of chiral active nematics confined to nanoscopic circular region

We performed molecular dynamic simulations of a model active nematic confined to a two-dimensional nanoscopic circular region under both tangential and radial anchoring boundary conditions. This active material is assumed to be composed of elongated chiral particles which interact with each other by means of isotropic Lennard-Jones and anisotropic Maier-Saupe-like potentials. These particles have the lateral appendage emitting a jet of some substance generated by a certain internal chemical reaction. As a result, such elongated particles are exposed to both the reactive self-propelled force and the torque that provide an additional translational movement of particles and a self-rotation with respect to their geometric centers. It has been found that the chiral active nematics under consideration form time-dependent vortex-like structures with two +1/2 topological defects which are similar to experimentally observed structures in active materials.

Active liquid crystals powered by force-sensing DNA-motor clusters

Cytoskeletal active nematics exhibit striking nonequilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold, the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale nonequilibrium dynamics of active nematics.

Flow coupling between active and passive fluids across water-oil interfaces

Active fluid droplets surrounded by oil can spontaneously develop circulatory flows. However, the dynamics of the surrounding oil and their influence on the active fluid remain poorly understood. To investigate interactions between the active fluid and the passive oil across their interface, kinesin-driven microtubule-based active fluid droplets were immersed in oil and compressed into a cylinder-like shape. The droplet geometry supported intradroplet circulatory flows, but the circulation was suppressed when the thickness of the oil layer surrounding the droplet decreased. Experiments with tracers and network structure analyses and continuum models based on the dynamics of self-elongating rods demonstrated that the flow transition resulted from flow coupling across the interface between active fluid and oil, with a millimeter-scale coupling length. In addition, two novel millifluidic devices were developed that could trigger and suppress intradroplet circulatory flows in real time: one by changing the thickness of the surrounding oil layer and the other by locally deforming the droplet. This work highlights the role of interfacial dynamics in the active fluid droplet system and shows that circulatory flows within droplets can be affected by millimeter-scale flow coupling across the interface between the active fluid and the oil.

Fractal generation in a two-dimensional active-nematic fluid

Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a quasi-two-dimensional (2D) nematic phase and driven by adenosine-triphosphate-fueled kinesin motor proteins. This system exhibits robust chaotic advection and gives rise to a pronounced fractal structure in the nematic contours. We characterize such experimentally derived fractals using the power spectrum and discover that the power spectrum decays as k^-β for large wavenumbers k. The parameter β is measured for several experimental realizations. Though β is effectively constant in time, it does vary with experimental parameters, indicating differences in the scale-free behavior of the microtubule-based active nematic. Though the fractal patterns generated in this active system are reminiscent of passively advected dye in 2D chaotic flows, the underlying mechanism for fractal generation is more subtle. We provide a simple, physically inspired mathematical model of fractal generation in this system that relies on the material being locally compressible, though the total area of the material is conserved globally. The model also requires that large-scale density variations are injected into the material periodically. The model reproduces the power-spectrum decay k^-β seen in experiments. Linearizing the model of fractal generation about the equilibrium density, we derive an analytic relationship between β and a single dimensionless quantity r, which characterizes the compressibility.

The many behaviors of deformable active droplets

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.

Confinement Controls the Bend Instability of Three-Dimensional Active Liquid Crystals

Spontaneous growth of long-wavelength deformations is a defining feature of active liquid crystals. We investigate the effect of confinement on the instability of 3D active liquid crystals in the isotropic phase composed of extensile microtubule bundles and kinesin molecular motors. When shear aligned, such fluids exhibit finite-wavelength self-amplifying bend deformations. By systematically changing the channel size we elucidate how the instability wavelength and its growth rate depend on the channel dimensions. Experimental findings are qualitatively consistent with a minimal hydrodynamic model, where the fastest growing deformation is set by a balance of active driving and elastic relaxation. Our results demonstrate that confinement determines the structure and dynamics of active fluids on all experimentally accessible length scales.

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.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

Active microfluidic transport in two-dimensional handlebodies

Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.

Pattern formation in active model C with anchoring: bands, aster networks, and foams

We study the dynamics of pattern formation in a minimal model for active mixtures made of microtubules and molecular motors. We monitor the evolution of the (conserved) microtubule density and of the (non-conserved) nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred microtubule direction and their density gradient. The key control parameter is the ratio between activity and elasticity. When elasticity dominates, the interplay between activity and anchoring leads to formation of banded structures that can undergo additional bending, rotational or splaying instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, disordered foams and spindle-like patterns. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analogue of the microtubule cytoskeleton.

Actin and microtubule crosslinkers tune mobility and control co-localization in a composite cytoskeletal network

Actin and microtubule filaments, with their auxiliary proteins, enable the cytoskeleton to carry out vital processes in the cell by tuning the organizational and mechanical properties of the network. Despite their critical importance and interactions in cells, we are only beginning to uncover information about the composite network. The challenge is due to the high complexity of combining actin, microtubules, and their hundreds of known associated proteins. Here, we use fluorescence microscopy, fluctuation, and cross-correlation analysis to examine the role of actin and microtubules in the presence of an antiparallel microtubule crosslinker, MAP65, and a generic, strong actin crosslinker, biotin-NeutrAvidin. For a fixed ratio of actin and microtubule filaments, we vary the amount of each crosslinker and measure the organization and fluctuations of the filaments. We find that the microtubule crosslinker plays the principle role in the organization of the system, while, actin crosslinking dictates the mobility of the filaments. We have previously demonstrated that the fluctuations of filaments are related to the mechanics, implying that actin crosslinking controls the mechanical properties of the network, independent of the microtubule-driven re-organization.

Novel Trends in Lyotropic Liquid Crystals

We introduce and shortly summarize a variety of more recent aspects of lyotropic liquid crystals (LLCs), which have drawn the attention of the liquid crystal and soft matter community and have recently led to an increasing number of groups studying this fascinating class of materials, alongside their normal activities in thermotopic LCs. The diversity of topics ranges from amphiphilic to inorganic liquid crystals, clays and biological liquid crystals, such as viruses, cellulose or DNA, to strongly anisotropic materials such as nanotubes, nanowires or graphene oxide dispersed in isotropic solvents. We conclude our admittedly somewhat subjective overview with materials exhibiting some fascinating properties, such as chromonics, ferroelectric lyotropics and active liquid crystals and living lyotropics, before we point out some possible and emerging applications of a class of materials that has long been standing in the shadow of the well-known applications of thermotropic liquid crystals, namely displays and electro-optic devices.

Filamentous active matter: Band formation, bending, buckling, and defects

Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

A theoretical phase diagram for an active nematic on a spherical surface

Systems combining rod-shaped objects with self-generated motion such as suspensions of microtubules or growing bacterial colonies are commonly modeled as active nematics - nematic liquid crystals with an additional active stress term. Confining a 2D active nematic to the surface of a sphere generates novel behaviour as the four +1/2 nematic defects which are produced by the spherical geometry move round each other in an intricate dance. Here, these defects are modeled as point particles experiencing elastic forces from defect position and orientation, and self-propulsion due to activity. This model exhibits four qualitatively distinct types of trajectory state: two which are consistent with previous experimental and simulated trajectories; and two others, which are apparently novel and in regions of parameter space that may not yet have been explored. This work also explains a discrepancy between some previous point-particle models and the trajectories seen in experiments and simulations: this was due to a failure to fully account for the spherical geometry in the point-particle models.

Time-reversal symmetry breaking in two-dimensional nonequilibrium viscous fluids

We study the rheological signatures of departure from equilibrium in two-dimensional viscous fluids with and without internal spin. Under the assumption of isotropy, we provide the most general linear constitutive relations for stress and couple stress in terms of the velocity and spin fields. Invoking Onsager's regression hypothesis for fluctuations about steady states, we derive the Green-Kubo formulas relating the transport coefficients to time-correlation functions of the fluctuating stress. In doing so, we show that one of the nonequilibrium transport coefficients, the odd viscosity, requires time-reversal symmetry breaking in the case of systems without internal spin. However, the Green-Kubo relations for systems with internal spin also show that there is a possibility for nonvanishing odd viscosity even when time-reversal symmetry is preserved. Furthermore, we find that breakdown of equipartition in nonequilibrium steady states results in the decoupling of the two rotational viscosities relating the vorticity and the internal spin.

Self-assembly of magnetically-functionalized molecular motors and microtubules into active gels

The diversity of functions achieved by living cells result from the collective behavior of biological components that interact through multiple scales in time and space. The cytoskeleton constitutes one canonical system forming dynamic organizations when interacting with molecular motors. These materials constitute a state of active matter that exhibit out-of-equilibrium behavior with oriented order in the presence of energy. However, such active materials are highly dependent on the intrinsic properties of their constituents (fibers, molecular motors, and energy), which makes it difficult to control their behavior. Being able to manipulate directly the constitutive elements of the active gel could provide additional control parameters. Here, we report a strategy to functionalize and manipulate active microtubule-based structures upon magnetic actuation. We engineered protein nanocage ferritins as magnetic labels targeting molecular motors (Eg5 kinesin motors). We first mixed these magnetic motors with individual microtubules, allowing for their manipulation. In order to generate a magnetic-responsive gel, we then mixed the magnetic motors with active microtubule-based structures and characterized their dynamic behavior. We found that the magnetic forces applied on magnetic motors slowed down the dynamics of the microtubule structures as well as constrained their rotation. Our results highlight how genetically encoded magnetic elements, behaving as magnetic actuators, could perturb active gels.

Tunable corrugated patterns in an active nematic sheet

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures

As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.

Collective dynamics of microtubule-based 3D active fluids from single microtubules

Self-organization of kinesin-driven, microtubule-based 3D active fluids relies on the collective dynamics of single microtubules. However, the connection between macroscopic fluid flows and microscopic motion of microtubules remains unclear. In this work, the motion of single microtubules was characterized by means of 2D gliding assays and compared with the flows of 3D active fluids. While the scales of the two systems differ by ∼1000×, both were driven by processive, non-processive or an equal mixture of both molecular motor proteins. To search for the dynamic correlation between both systems, the motor activities were tuned by varying temperature and ATP concentration, and the changes in both systems were compared. Motor processivity played an important role in active fluid flows but only when the fluids were nearly motionless; otherwise, flows were dominated by hydrodynamic resistance controlled by sample size. Furthermore, while the motors' thermal reaction led active fluids to flow faster with increasing temperature, such temperature dependence could be reversed by introducing temperature-varying depletants, emphasizing the potential role of the depletant in designing an active fluid's temperature response. The temperature response of active fluids was nearly immediate (⪅10 s). Such a characteristic enables active fluids to be controlled with a temperature switch. Overall, this work not only clarifies the role of temperature in active fluid activity, but also sheds light on the underlying principles of the relationship between the collective dynamics of active fluids and the dynamics of their constituent single microtubules.

Self-organization of spindle-like microtubule structures

Microtubule self-organization is an essential physical process underlying several essential cellular functions, including cell division. In cell division, the dominant arrangement is the mitotic spindle, a football-shaped microtubule-based machine responsible for separating the chromosomes. We are interested in the underlying fundamental principles behind the self-organization of the spindle shape. Prior biological works have hypothesized that motor proteins control the proper formation of the spindle. Many of these motor proteins are also microtubule-crosslinkers, so it is unclear if the critical aspect is the motor activity or the crosslinking. In this study, we seek to address this question by examining the self-organization of microtubules using crosslinkers alone. We use a minimal system composed of tubulin, an antiparallel microtubule-crosslinking protein, and a crowding agent to explore the phase space of organizations as a function of tubulin and crosslinker concentration. We find that the concentration of the antiparallel crosslinker, MAP65, has a significant effect on the organization and resulted in spindle-like arrangements at relatively low concentration without the need for motor activity. Surprisingly, the length of the microtubules only moderately affects the equilibrium phase. We characterize both the shape and dynamics of these spindle-like organizations. We find that they are birefringent homogeneous tactoids. The microtubules have slow mobility, but the crosslinkers have fast mobility within the tactoids. These structures represent a first step in the recapitulation of self-organized spindles of microtubules that can be used as initial structures for further biophysical and active matter studies relevant to the biological process of cell division.

Stress fluctuations in transient active networks

Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and birth at a randomly chosen node. The model captures features such as the build-up of self-stress, that are not easily incorporated into hydrodynamic theories. We study the model numerically and show that our observations can largely be understood through a stochastic effective-medium model. The resulting dynamically extending force-dipole network displays many features of yielded plastic solids, and offers a way to incorporate strongly non-affine effects into theories of active solids. A rather distinctive form for the stress distribution, and a Herschel-Bulkley dependence of stress on activity, are our major predictions.

Effects of spatial dimensionality and steric interactions on microtubule-motor self-organization

Active networks composed of filaments and motor proteins can self-organize into a variety of architectures. Computer simulations in two or three spatial dimensions and including or omitting steric interactions between filaments can be used to model active networks. Here we examine how these modelling choices affect the state space of network self-organization. We compare the networks generated by different models of a system of dynamic microtubules and microtubule-crosslinking motors. We find that a thin 3D model that includes steric interactions between filaments is the most versatile, capturing a variety of network states observed in recent experiments. In contrast, 2D models either with or without steric interactions which prohibit microtubule crossings can produce some, but not all, observed network states. Our results provide guidelines for the most appropriate choice of model for the study of different network types and elucidate mechanisms of active network organization.

Statistical properties of autonomous flows in 2D active nematics

We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil-water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis-Menten kinetics that governs the motion of individual kinesin motors.

Determinants of Polar versus Nematic Organization in Networks of Dynamic Microtubules and Mitotic Motors

During cell division, mitotic motors organize microtubules in the bipolar spindle into either polar arrays at the spindle poles or a "nematic" network of aligned microtubules at the spindle center. The reasons for the distinct self-organizing capacities of dynamic microtubules and different motors are not understood. Using in vitro reconstitution experiments and computer simulations, we show that the human mitotic motors kinesin-5 KIF11 and kinesin-14 HSET, despite opposite directionalities, can both organize dynamic microtubules into either polar or nematic networks. We show that in addition to the motor properties the natural asymmetry between microtubule plus- and minus-end growth critically contributes to the organizational potential of the motors. We identify two control parameters that capture system composition and kinetic properties and predict the outcome of microtubule network organization. These results elucidate a fundamental design principle of spindle bipolarity and establish general rules for active filament network organization.

Kinetic theory of pattern formation in mixtures of microtubules and molecular motors

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E 74, 031915 (2006)PLEEE81539-375510.1103/PhysRevE.74.031915] we model the motor-induced reorientation of microtubules as collision rules, and devise a semianalytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behavior by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behavior than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.

Microtubule Dynamics, Kinesin-1 Sliding, and Dynein Action Drive Growth of Cell Processes

Recent experimental studies of the role of microtubule sliding in neurite outgrowth suggested a qualitative model, according to which kinesin-1 motors push the minus-end-out microtubules against the cell membrane and generate the early cell processes. At the later stage, dynein takes over the sliding, expels the minus-end-out microtubules from the neurites, and pulls in the plus-end-out microtubules that continue to elongate the nascent axon. This model leaves unanswered a number of questions: why is dynein unable to generate the processes alone, whereas kinesin-1 can? What is the role of microtubule dynamics in process initiation and growth? Can the model correctly predict the rates of process growth in control and dynein-inhibited cases? What triggers the transition from kinesin-driven to dynein-driven sliding? To answer these questions, we combine computational modeling of a network of elastic dynamic microtubules and kinesin-1 and dynein motors with measurements of the process growth kinetics and pharmacological perturbations in Drosophila S2 cells. The results verify quantitatively the qualitative model of the microtubule polarity sorting and suggest that dynein-powered elongation is effective only when the processes are longer than a threshold length, which explains why kinesin-1 alone, but not dynein, is sufficient for the process growth. Furthermore, we show that the mechanism of process elongation depends critically on microtubule dynamic instability. Both modeling and experimental measurements show, surprisingly, that dynein inhibition accelerates the process extension. We discuss implications of the model for the general problems of cell polarization, cytoskeletal polarity emergence, and cell process protrusion.

Active nematics

Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.

Insensitivity of active nematic liquid crystal dynamics to topological constraints

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Cooperative Accumulation of Dynein-Dynactin at Microtubule Minus-Ends Drives Microtubule Network Reorganization

Cytoplasmic dynein-1 is a minus-end-directed motor protein that transports cargo over long distances and organizes the intracellular microtubule (MT) network. How dynein motor activity is harnessed for these diverse functions remains unknown. Here, we have uncovered a mechanism for how processive dynein-dynactin complexes drive MT-MT sliding, reorganization, and focusing, activities required for mitotic spindle assembly. We find that motors cooperatively accumulate, in limited numbers, at MT minus-ends. Minus-end accumulations drive MT-MT sliding, independent of MT orientation, resulting in the clustering of MT minus-ends. At a mesoscale level, activated dynein-dynactin drives the formation and coalescence of MT asters. Macroscopically, dynein-dynactin activity leads to bulk contraction of millimeter-scale MT networks, suggesting that minus-end accumulations of motors produce network-scale contractile stresses. Our data provide a model for how localized dynein activity is harnessed by cells to produce contractile stresses within the cytoskeleton, for example, during mitotic spindle assembly.