Viscoelasticity of reversibly crosslinked networks of semiflexible polymers

Topological mechanism in the nonlinear power-law relaxation of cell cortex

Different types of cells exhibit a universal power-law rheology, but the mechanism underneath is still unclear. Based on the exponential distribution of actin filament length, we treat the cell cortex as a collection of chains of crosslinkers with exponentially distributed binding energy, and show that the power-law exponent of its stress relaxation should scale with the chain length. Through this model, we are able to explain how the exponent can be regulated by the crosslinker number and imposed strain during cortex relaxation. Network statistics show that the average length of filament-crosslinker chains decreases with the crosslinker number, which endows a denser network with lower exponent. Due to gradual molecular alignment with the stretch direction, the number of effectively stretched crosslinkers in the network is found to increase with the imposed strain. This effective growth in network density diminishes the exponent under large strain. By incorporating the inclined angle of crosslinkers into the model without in-series structure, we show that the exponent cannot be altered by crosslinker rotation directly, refining our previous conjectures. This work may help to understand cellular mechanics from the molecular perspective.

High Thermal Stability and Low Dielectric Constant of BCB Modified Silicone Resins

Based on the excellent physical properties and flexible molecular modifiability, modified silicone resins have received favorable attention in the field of microelectronics, and recently a number of modified silicone resins have appeared while few breakthroughs have been made in low dielectric constant (low-k) materials field due to the limitations of structure or the curing process. In this work, functional silicone resin with different BCB contents was prepared with two monomers. The resins showed low dielectric constant (k = 2.77 at 10 MHz) and thermal stability (T_5% = 495.0 °C) after curing. Significant performance changes were observed with the increase in BCB structural units, and the functional silicone obtained does not require melting and dissolution during processing because of good fluidity at room temperature. Moreover, the mechanical properties of silicone resins can be also controlled by adjusting the BCB content. The obtained silicone resins could be potentially used in the field of electronic packaging materials.

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.

Start-up shear of spherocylinder packings: Effect of friction

We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient μ. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus g_{∞}, which is orders of magnitude larger than the modulus g_{0} in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length ℓ of the spherocylinders. One consequence of this motion is that the shear modulus g_{∞} approaches a finite value in the limit ℓ→∞, even though the density of the packings vanishes, ρ∝ℓ^{-2}. By way of contrast, the frictionless modulus decreases to zero, g_{0}∼ℓ^{-2}, in accordance with the behavior of density. Increasing the strain beyond a value γ_{c}∼μ, the packing strain weakens from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a "yield stress" σ_{y}=g_{∞}γ_{c} and the stress behaves as σ=σ_{y}+g_{0}γ. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.

Packings of frictionless spherocylinders

We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of interparticle contacts until a force-equilibrated state is reached. For different particle aspect ratios α=10⋯40, we calculate contacts z, pressure as well as bulk and shear modulus. Most important is the fraction f_{0}(α) of spherocylinders with contacts at both ends, as it governs the jamming threshold z_{c}(α)=8+2f_{0}(α). These results highlight the important role of the axial "sliding" degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end contacts are present.

The role of stickiness in the rheology of semiflexible polymers

Semiflexible polymers form central structures in biological material. Modelling approaches usually neglect influences of polymer-specific molecular features aiming to describe semiflexible polymers universally. Here, we investigate the influence of molecular details on networks assembled from filamentous actin, intermediate filaments, and synthetic DNA nanotubes. In contrast to prevalent theoretical assumptions, we find that bulk properties are affected by various inter-filament interactions. We present evidence that these interactions can be merged into a single parameter in the frame of the glassy wormlike chain model. The interpretation of this parameter as a polymer specific stickiness is consistent with observations from macro-rheological measurements and reptation behaviour. Our findings demonstrate that stickiness should generally not be ignored in semiflexible polymer models.

Origin of Slow Stress Relaxation in the Cytoskeleton

Dynamically cross-linked semiflexible biopolymers such as the actin cytoskeleton govern the mechanical behavior of living cells. Semiflexible biopolymers nonlinearly stiffen in response to mechanical loads, whereas the cross-linker dynamics allow for stress relaxation over time. Here we show, through rheology and theoretical modeling, that the combined nonlinearity in time and stress leads to an unexpectedly slow stress relaxation, similar to the dynamics of disordered systems close to the glass transition. Our work suggests that transient cross-linking combined with internal stress can explain prior reports of soft glassy rheology of cells, in which the shear modulus increases weakly with frequency.

Linear rheology of reversibly cross-linked biopolymer networks

We suggest a simple model for reversible cross-links, binding, and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the time scale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest time scale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.

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.

Single microtubules and small networks become significantly stiffer on short time-scales upon mechanical stimulation

The transfer of mechanical signals through cells is a complex phenomenon. To uncover a new mechanotransduction pathway, we study the frequency-dependent transport of mechanical stimuli by single microtubules and small networks in a bottom-up approach using optically trapped beads as anchor points. We interconnected microtubules to linear and triangular geometries to perform micro-rheology by defined oscillations of the beads relative to each other. We found a substantial stiffening of single filaments above a characteristic transition frequency of 1–30 Hz depending on the filament’s molecular composition. Below this frequency, filament elasticity only depends on its contour and persistence length. Interestingly, this elastic behavior is transferable to small networks, where we found the surprising effect that linear two filament connections act as transistor-like, angle dependent momentum filters, whereas triangular networks act as stabilizing elements. These observations implicate that cells can tune mechanical signals by temporal and spatial filtering stronger and more flexibly than expected.

Exact solution for the force-extension relation of a semiflexible polymer under compression

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.