Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics

Rearrangement of GUV-confined actin networks in response to micropipette aspiration

Although diverse actin network architectures found inside the cell have been individually reconstituted outside of the cell, how different types of actin architectures reorganize under applied forces is not entirely understood. Recently, bottom-up reconstitution has enabled studies where dynamic and phenotypic characteristics of various actin networks can be recreated in an isolated cell-like environment. Here, by creating a giant unilamellar vesicle (GUV)-based cell model encapsulating actin networks, we investigate how actin networks rearrange in response to localized stresses applied by micropipette aspiration. We reconstitute actin bundles and branched bundles in GUVs separately and mechanically perturb them. Interestingly, we find that, when aspirated, protrusive actin bundles that are otherwise randomly oriented in the GUV lumen collapse and align along the axis of the micropipette. However, when branched bundles are aspirated, the network remains intact and outside of the pipette while the GUV membrane is aspirated into the micropipette. These results reveal distinct responses in the rearrangement of actin networks in a network architecture-dependent manner when subjected to physical forces.

Switchable microscale stress response of actin-vimentin composites emerges from scale-dependent interactions

The mechanical properties of the mammalian cell regulate many cellular functions and are largely dictated by the cytoskeleton, a composite network of protein filaments, including actin, microtubules, and intermediate filaments. Interactions between these distinct filaments give rise to emergent mechanical properties that are difficult to generate synthetically, and recent studies have made great strides in advancing our understanding of the mechanical interplay between actin and microtubule filaments. While intermediate filaments play critical roles in the stress response of cells, their effect on the rheological properties of the composite cytoskeleton remains poorly understood. Here, we use optical tweezers microrheology to measure the linear viscoelastic properties and nonlinear stress response of composites of actin and vimentin with varying molar ratios of actin to vimentin. We reveal a surprising, nearly opposite effect of actin-vimentin network mechanics compared to single-component networks in the linear versus nonlinear regimes. Namely, the linear elastic plateau modulus and zero-shear viscosity are markedly reduced in composites compared to single-component networks of actin or vimentin, whereas the initial response force and stiffness are maximized in composites versus single-component networks in the nonlinear regime. While these emergent trends are indicative of distinct interactions between actin and vimentin, nonlinear stiffening and longtime stress response appear to both be dictated primarily by actin, at odds with previous bulk rheology studies. We demonstrate that these complex, scale-dependent effects arise from the varied contributions of network density, filament stiffness, non-specific interactions, and poroelasticity to the mechanical response at different spatiotemporal scales. Cells may harness this complex behavior to facilitate distinct stress responses at different scales and in response to different stimuli to allow for their hallmark multifunctionality.

Nonlinear Microscale Mechanics of Actin Networks Governed by Coupling of Filament Crosslinking and Stabilization

Actin plays a vital role in maintaining the stability and rigidity of biological cells while allowing for cell motility and shape change. The semiflexible nature of actin filaments-along with the myriad actin-binding proteins (ABPs) that serve to crosslink, bundle, and stabilize filaments-are central to this multifunctionality. The effect of ABPs on the structural and mechanical properties of actin networks has been the topic of fervent investigation over the past few decades. Yet, the combined impact of filament stabilization, stiffening and crosslinking via ABPs on the mechanical response of actin networks has yet to be explored. Here, we perform optical tweezers microrheology measurements to characterize the nonlinear force response and relaxation dynamics of actin networks in the presence of varying concentrations of α-actinin, which transiently crosslinks actin filaments, and phalloidin, which stabilizes filamentous actin and increases its persistence length. We show that crosslinking and stabilization can act both synergistically and antagonistically to tune the network resistance to nonlinear straining. For example, phalloidin stabilization leads to enhanced elastic response and reduced dissipation at large strains and timescales, while the initial microscale force response is reduced compared to networks without phalloidin. Moreover, we find that stabilization switches this initial response from that of stress stiffening to softening despite the increased filament stiffness that phalloidin confers. Finally, we show that both crosslinking and stabilization are necessary to elicit these emergent features, while the effect of stabilization on networks without crosslinkers is much more subdued. We suggest that these intriguing mechanical properties arise from the competition and cooperation between filament connectivity, bundling, and rigidification, shedding light on how ABPs with distinct roles can act in concert to mediate diverse mechanical properties of the cytoskeleton and bio-inspired polymeric materials.

Biopolymer Filament Entanglement Softens Then Hardens with Shear

It is unsatisfactory that regarding the problem of entangled macromolecules driven out of equilibrium, experimentally based understanding is usually inferred from the ensemble average of polydisperse samples. Here, confronting with single-molecule imaging this common but poorly understood situation, over a wide range of shear rate we use single-molecule fluorescence imaging to track alignment and stretching of entangled aqueous filamentous actin filaments in a homebuilt rheo-microscope. With increasing shear rate, tube "softening" is followed by "hardening." Physically, this means that dynamical localization first weakens from molecular alignment, then strengthens from filament stretching, even for semiflexible biopolymers shorter than their persistence length.

Optical-Tweezers-integrating-Differential-Dynamic-Microscopy maps the spatiotemporal propagation of nonlinear strains in polymer blends and composites

How local stresses propagate through polymeric fluids, and, more generally, how macromolecular dynamics give rise to viscoelasticity are open questions vital to wide-ranging scientific and industrial fields. Here, to unambiguously connect polymer dynamics to force response, and map the deformation fields that arise in macromolecular materials, we present Optical-Tweezers-integrating-Differential -Dynamic-Microscopy (OpTiDMM) that simultaneously imposes local strains, measures resistive forces, and analyzes the motion of the surrounding polymers. Our measurements with blends of ring and linear polymers (DNA) and their composites with stiff polymers (microtubules) uncover an unexpected resonant response, in which strain alignment, superdiffusivity, and elasticity are maximized when the strain rate is comparable to the entanglement rate. Microtubules suppress this resonance, while substantially increasing elastic storage, due to varying degrees to which the polymers buildup, stretch and flow along the strain path, and configurationally relax induced stress. More broadly, the rich multi-scale coupling of mechanics and dynamics afforded by OpTiDDM, empowers its interdisciplinary use to elucidate non-trivial phenomena that sculpt stress propagation dynamics-critical to commercial applications and cell mechanics alike.

Understanding cytoskeletal avalanches using mechanical stability analysis

Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally happens through anomalously large displacements, reminiscent of earthquakes or avalanches. These cytoskeletal avalanches might indicate that the cytoskeleton's structural response to a changing cellular environment is highly sensitive, and they are therefore of significant biological interest. However, the physics underlying "cytoquakes" is poorly understood. Here, we use agent-based simulations of cytoskeletal self-organization to study fluctuations in the network's mechanical energy. We robustly observe non-Gaussian statistics and asymmetrically large rates of energy release compared to accumulation in a minimal cytoskeletal model. The large events of energy release are found to correlate with large, collective displacements of the cytoskeletal filaments. We also find that the changes in the localization of tension and the projections of the network motion onto the vibrational normal modes are asymmetrically distributed for energy release and accumulation. These results imply an avalanche-like process of slow energy storage punctuated by fast, large events of energy release involving a collective network rearrangement. We further show that mechanical instability precedes cytoquake occurrence through a machine-learning model that dynamically forecasts cytoquakes using the vibrational spectrum as input. Our results provide a connection between the cytoquake phenomenon and the network's mechanical energy and can help guide future investigations of the cytoskeleton's structural susceptibility.

Motor-Driven Restructuring of Cytoskeleton Composites Leads to Tunable Time-Varying Elasticity

The composite cytoskeleton, comprising interacting networks of semiflexible actin and rigid microtubules, generates forces and restructures by using motor proteins such as myosins to enable key processes including cell motility and mitosis. Yet, how motor-driven activity alters the mechanics of cytoskeleton composites remains an open challenge. Here, we perform optical tweezers microrheology and confocal imaging of composites with varying actin-tubulin molar percentages (25-75, 50-50, and 75-25), driven by light-activated myosin II motors, to show that motor activity increases the elastic plateau modulus by over 2 orders of magnitude by active restructuring of both actin and microtubules that persists for hours after motor activation has ceased. Nonlinear microrheology measurements show that motor-driven restructuring increases the force response and stiffness and suppresses actin bending. The 50-50 composite exhibits the most dramatic mechanical response to motor activity due to the synergistic effects of added stiffness from the microtubules and sufficient motor substrate for pronounced activity.

Unexpected entanglement dynamics in semidilute blends of supercoiled and ring DNA

Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of producing polymers of different topologies, the dynamics of topological polymer blends remains poorly understood. We address this void by using both passive and active microrheology to characterize the linear and nonlinear rheological properties of blends of relaxed circular and supercoiled DNA. We characterize the dynamics as we vary the concentration from below the overlap concentration c* to above (0.5c* to 2c*). Surprisingly, despite working at the dilute-semidilute crossover, entanglement dynamics, such as elastic plateaus and multiple relaxation modes, emerge. Finally, blends exhibit an unexpected sustained elastic response to nonlinear strains not previously observed even in well-entangled linear polymer solutions.

Non-monotonic dependence of stiffness on actin crosslinking in cytoskeleton composites

The cytoskeleton is able to precisely tune its structure and mechanics through interactions between semiflexible actin filaments, rigid microtubules and a suite of crosslinker proteins. However, the role that each of these components, as well as the interactions between them, plays in the dynamics of the composite cytoskeleton remains an open question. Here, we use optical tweezers microrheology and fluorescence confocal microscopy to reveal the surprising ways in which actin crosslinking tunes the viscoelasticity and mobility of actin-microtubule composites from steady-state to the highly nonlinear regime. While previous studies have shown that increasing crosslinking in actin networks increases elasticity and stiffness, we instead find that composite stiffness displays a striking non-monotonic dependence on actin crosslinking - first increasing then decreasing to a response similar to or even lower than un-linked composites. We further show that actin crosslinking has an unexpectedly strong impact on the mobility of microtubules; and it is in fact the microtubule mobility - dictated by crosslinker-driven rearrangements of actin filaments - that controls composite stiffness. This result is at odds with conventional thought that actin mobility drives cytoskeleton mechanics. More generally, our results demonstrate that - when crosslinking composite materials to confer strength and resilience - more is not always better.

Turnover versus treadmilling in actin network assembly and remodeling

Actin networks are highly dynamic cytoskeletal structures that continuously undergo structural remodeling. One prominent way to probe these processes is via Fluorescence Recovery After Photobleaching (FRAP), which can be used to estimate the rate of turnover for filamentous actin monomers. It is thought that head-to-tail treadmilling and de novo filament nucleation constitute two primary mechanisms underlying turnover kinetics. More generally, these self-assembly activities are responsible for many important cellular functions such as force generation, cellular shape dynamics, and cellular motility. In what relative proportions filament treadmilling and de novo filament nucleation contribute to actin network turnover is still not fully understood. We used an advanced stochastic reaction-diffusion model in three dimensions, MEDYAN, to study turnover dynamics of actin networks containing Arp2/3, formin and capping protein at experimentally meaningful length- and time-scales. Our results reveal that, most commonly, treadmilling of older filaments is the main contributor to actin network turnover. On the other hand, although turnover and treadmilling are often used interchangeably, we show clear instances where this assumption would not be justified, for example, finding that rapid turnover is accompanied by slow treadmilling in highly dendritic Arp2/3 networks.

Varying crosslinking motifs drive the mesoscale mechanics of actin-microtubule composites

The cytoskeleton precisely tunes its mechanics by altering interactions between semiflexible actin filaments, rigid microtubules, and crosslinking proteins. We use optical tweezers microrheology and confocal microscopy to characterize how varying crosslinking motifs impact the mesoscale mechanics and mobility of actin-microtubule composites. We show that, upon subtle changes in crosslinking patterns, composites can exhibit two distinct classes of force response - primarily elastic versus more viscous. For example, a composite in which actin and microtubules are crosslinked to each other but not to themselves is markedly more elastic than one in which both filaments are independently crosslinked. Notably, this distinction only emerges at mesoscopic scales in response to nonlinear forcing, whereas varying crosslinking motifs have little impact on the microscale mechanics and mobility. Our unexpected scale-dependent results not only inform the physics underlying key cytoskeleton processes and structures, but, more generally, provide valuable perspective to materials engineering endeavors focused on polymer composites.

Maximally stiffening composites require maximally coupled rather than maximally entangled polymer species

Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive characterisation of material properties over a highly-dimensional parameter space, as well as a quantitative understanding of the physical principles underlying desirable features. Here we couple large-scale Molecular Dynamics simulations with optical tweezers microrheology to characterise the viscoelastic response of DNA-actin composites. We discover that the previously observed non-monotonic stress-stiffening of these composites is robust, yet tunable, in a broad range of the parameter space that spans two orders of magnitude in DNA length. Importantly, we discover that the most pronounced stiffening is achieved when the species are maximally coupled, i.e., have similar number of entanglements, and not when the number of entanglements per DNA chain is largest. We further report novel dynamical oscillations of the microstructure of the composites, alternating between mixed and bundled phases, opening the door to future investigations. The generic nature of our system renders our results applicable to the behaviour of a broad class of polymer composites.

Remarkable structural transformations of actin bundles are driven by their initial polarity, motor activity, crosslinking, and filament treadmilling

Bundled actin structures play a key role in maintaining cellular shape, in aiding force transmission to and from extracellular substrates, and in affecting cellular motility. Recent studies have also brought to light new details on stress generation, force transmission and contractility of actin bundles. In this work, we are primarily interested in the question of what determines the stability of actin bundles and what network geometries do unstable bundles eventually transition to. To address this problem, we used the MEDYAN mechano-chemical force field, modeling several micron-long actin bundles in 3D, while accounting for a comprehensive set of chemical, mechanical and transport processes. We developed a hierarchical clustering algorithm for classification of the different long time scale morphologies in our study. Our main finding is that initially unipolar bundles are significantly more stable compared with an apolar initial configuration. Filaments within the latter bundles slide easily with respect to each other due to myosin activity, producing a loose network that can be subsequently severely distorted. At high myosin concentrations, a morphological transition to aster-like geometries was observed. We also investigated how actin treadmilling rates influence bundle dynamics, and found that enhanced treadmilling leads to network fragmentation and disintegration, while this process is opposed by myosin and crosslinking activities. Interestingly, treadmilling bundles with an initial apolar geometry eventually evolve to a whole gamut of network morphologies based on relative positions of filament ends, such as sarcomere-like organization. We found that apolar bundles show a remarkable sensitivity to environmental conditions, which may be important in enabling rapid cytoskeletal structural reorganization and adaptation in response to intracellular and extracellular cues.

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.

Triggered disassembly and reassembly of actin networks induces rigidity phase transitions

Non-equilibrium soft materials, such as networks of actin proteins, have been intensely investigated over the past decade due to their promise for designing smart materials and understanding cell mechanics. However, current methods are unable to measure the time-dependent mechanics of such systems or map mechanics to the corresponding dynamic macromolecular properties. Here, we present an experimental approach that combines time-resolved optical tweezers microrheology with diffusion-controlled microfluidics to measure the time-evolution of microscale mechanical properties of dynamic systems during triggered activity. We use these methods to measure the viscoelastic moduli of entangled and crosslinked actin networks during chemically-triggered depolymerization and repolymerization of actin filaments. During disassembly, we find that the moduli exhibit two distinct exponential decays, with experimental time constants of ∼169 min and ∼47 min. Conversely, during reassembly, measured moduli initially exhibit power-law increase with time, after which steady-state values are achieved. We develop toy mathematical models that couple the time-evolution of filament lengths with rigidity percolation theory to shed light onto the molecular mechanisms underlying the observed mechanical transitions. The models suggest that these two distinct behaviors both arise from phase transitions between a rigidly percolated network and a non-rigid regime. Our approach and collective results can inform the general principles underlying the mechanics of a large class of dynamic, non-equilibrium systems and materials of current interest.

Synergistic Interactions Between DNA and Actin Trigger Emergent Viscoelastic Behavior

Composites of flexible and rigid polymers are ubiquitous in biology and industry alike, yet the physical principles determining their mechanical properties are far from understood. Here, we couple force spectroscopy with large-scale Brownian dynamics simulations to elucidate the unique viscoelastic properties of custom-engineered blends of entangled flexible DNA molecules and semiflexible actin filaments. We show that composites exhibit enhanced stress stiffening and prolonged mechanomemory compared to systems of actin or DNA alone, and that these nonlinear features display a surprising nonmonotonic dependence on the fraction of actin in the composite. Simulations reveal that these counterintuitive results arise from synergistic microscale interactions between the two biopolymers. Namely, DNA entropically drives actin filaments to form bundles that stiffen the network but reduce the entanglement density, while a uniform well-connected actin network is required to reinforce the DNA network against yielding and flow. The competition between bundling and connectivity triggers an unexpected stress response that leads equal mass DNA-actin composites to exhibit the most pronounced stress stiffening and the most long-lived entanglements.

Co-Entangled Actin-Microtubule Composites Exhibit Tunable Stiffness and Power-Law Stress Relaxation

We use optical tweezers microrheology and fluorescence microscopy to characterize the nonlinear mesoscale mechanics and mobility of in vitro co-entangled actin-microtubule composites. We create a suite of randomly oriented, well-mixed networks of actin and microtubules by co-polymerizing varying ratios of actin and tubulin in situ. To perturb each composite far from equilibrium, we use optical tweezers to displace an embedded microsphere a distance greater than the lengths of the filaments at a speed much faster than their intrinsic relaxation rates. We simultaneously measure the force the filaments exert on the bead and the subsequent force relaxation. We find that the presence of a large fraction of microtubules (>0.7) is needed to substantially increase the measured force, which is accompanied by large heterogeneities in force response. Actin minimizes these heterogeneities by reducing the mesh size of the composites and supporting microtubules against buckling. Composites also undergo a sharp transition from strain softening to stiffening when the fraction of microtubules (ϕT) exceeds 0.5, which we show arises from faster poroelastic relaxation and suppressed actin bending fluctuations. The force after bead displacement relaxes via power-law decay after an initial period of minimal relaxation. The short-time relaxation profiles (t < 0.06 s) arise from poroelastic and bending contributions, whereas the long-time power-law relaxation is indicative of filaments reptating out of deformed entanglement constraints. The scaling exponents for the long-time relaxation exhibit a nonmonotonic dependence on ϕT, reaching a maximum for equimolar composites (ϕT = 0.5), suggesting that reptation is fastest in ϕT = 0.5 composites. Corresponding mobility measurements of steady-state actin and microtubules show that both filaments are indeed the most mobile in ϕT = 0.5 composites. This nonmonotonic dependence of mobility on ϕT demonstrates the important interplay between mesh size and filament rigidity in polymer networks and highlights the surprising emergent properties that can arise in composites.

Entangled chain polymer liquids under continuous shear deformation: consequences of a microscopically anharmonic confining tube

We generalize our non-classical theory for the shear rheology of entangled flexible polymer liquids to address the consequences of a deformation-modified anharmonic tube confinement field. Numerical results for stress-strain curves, orientational relaxation time, primitive path (PP) step orientational order parameter, dynamic tube diameter and transverse entropic barrier under nonequilibrium conditions are presented as a function of dimensionless shear rate, strain and degree of entanglement. Deformation-induced changes of the tube field have essentially no effect on rheology under fast deformations conditions corresponding to Rouse Weissenberg numbers WiR > 1 because of the dominance of PP chain stretch. However, the scaling behavior of the effective orientational relaxation time and rheological response at low deformation rates WiR < 1 are significantly modified, with the stress overshoot coordinates predicted to become shear rate and degree of entanglement dependent. Stress-assisted transverse activated barrier hopping as a new channel of orientational relaxation is found to be potentially important when WiR < 1. The dynamic tube diameter and transverse entropic barrier that confines chains in a tube are rich functions of strain, shear rate and degree of entanglement. Deformation can increase or decrease the tube diameter, and non-monotonic changes with strain are possible due to competing consequences of PP orientation, chain stretch and stress. The transverse barrier is relatively high for all strains below the stress overshoot, for weaker entanglement, and for WiR > 1, corresponding to a dynamically stable tube. But for high enough degrees of entanglement and WiR < 1, although the barrier still exists it can become very low.

Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Single Actin Bundle Rheology

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory.

Nonlinear Actin Deformations Lead to Network Stiffening, Yielding, and Nonuniform Stress Propagation

We use optical tweezers microrheology and fluorescence microscopy to apply nonlinear microscale strains to entangled and cross-linked actin networks, and measure the resulting stress and actin filament deformations. We couple nonlinear stress response and relaxation to the velocities and displacements of individual fluorescent-labeled actin segments, at varying times throughout the strain and varying distances from the strain path, to determine the underlying molecular dynamics that give rise to the debated nonlinear response and stress propagation of cross-linked and entangled actin networks at the microscale. We show that initial stress stiffening arises from acceleration of strained filaments due to molecular extension along the strain, while softening and yielding is coupled to filament deceleration, halting, and recoil. We also demonstrate a surprising nonmonotonic dependence of filament deformation on cross-linker concentration. Namely, networks with no cross-links or substantial cross-links both exhibit fast initial filament velocities and reduced molecular recoil while intermediate cross-linker concentrations display reduced velocities and increased recoil. We show that these collective results are due to a balance of network elasticity and force-induced cross-linker unbinding and rebinding. We further show that cross-links dominate entanglement dynamics when the length between cross-linkers becomes smaller than the length between entanglements. In accord with recent simulations, we demonstrate that post-strain stress can be long-lived in cross-linked networks by distributing stress to a small fraction of highly strained connected filaments that span the network and sustain the load, thereby allowing the rest of the network to recoil and relax.

Active microrheology determines scale-dependent material properties of Chaetopterus mucus

We characterize the lengthscale-dependent rheological properties of mucus from the ubiquitous Chaetopterus marine worm. We use optically trapped probes (2-10 μm) to induce microscopic strains and measure the stress response as a function of oscillation amplitude. Our results show that viscoelastic properties are highly dependent on strain scale (l), indicating three distinct lengthscale-dependent regimes at l1 ≤4 μm, l2≈4-10 μm, and l3≥10 μm. While mucus response is similar to water for l1, suggesting that probes rarely contact the mucus mesh, the response for l2 is distinctly more viscous and independent of probe size, indicative of continuum mechanics. Only for l3 does the response match the macroscopic elasticity, likely due to additional stiffer constraints that strongly resist probe displacement. Our results suggest that, rather than a single lengthscale governing crossover from viscous to elastic, mucus responds as a hierarchical network with a loose biopolymer mesh coupled to a larger scaffold responsible for macroscopic gel-like mechanics.

Microstructure of Sheared Entangled Solutions of Semiflexible Polymers

We study the influence of finite shear deformations on the microstructure and rheology of solutions of entangled semiflexible polymers theoretically and by numerical simulations and experiments with filamentous actin. Based on the tube model of semiflexible polymers, we predict that large finite shear deformations strongly affect the average tube width and curvature, thereby exciting considerable restoring stresses. In contrast, the associated shear alignment is moderate, with little impact on the average tube parameters, and thus expected to be long-lived and detectable after cessation of shear. Similarly, topologically preserved hairpin configurations are predicted to leave a long-lived fingerprint in the shape of the distributions of tube widths and curvatures. Our numerical and experimental data support the theory.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

Active Entanglement-Tracking Microrheology Directly Couples Macromolecular Deformations to Nonlinear Microscale Force Response of Entangled Actin

We track the deformation of discrete entangled actin segments while simultaneously measuring the resistive force the deformed filaments exert in response to an optically driven microsphere. We precisely map the network deformation field to show that local microscale stresses can induce filament deformations that propagate beyond mesoscopic length scales (60 μm, >3 persistence lengths l_p). We show that the filament persistence length controls the critical length scale at which distinct entanglement deformations become driven by collective network mechanics. Mesoscale propagation beyond l_p is coupled with nonlinear local stresses arising from steric entanglements mimicking cross-links.