Effects of local incompressibility on the rheology of composite biopolymer networks.

Fibrous networks such as collagen are common in biological systems. Recent theoretical and experimental efforts have shed light on the mechanics of single component networks. Most real biopolymer networks, however, are composites made of elements with different rigidity. For instance, the extracellular matrix in mammalian tissues consists of stiff collagen fibers in a background matrix of flexible polymers such as hyaluronic acid (HA). The interplay between different biopolymer components in such composite networks remains unclear. In this work, we use 2D coarse-grained models to study the nonlinear strain-stiffening behavior of composites. We introduce a local volume constraint to model the incompressibility of HA. We also perform rheology experiments on composites of collagen with HA. Theoretically and experimentally, we demonstrate that the linear shear modulus of composite networks can be increased by approximately an order of magnitude above the corresponding moduli of the pure components. Our model shows that this synergistic effect can be understood in terms of the local incompressibility of HA, which acts to suppress density fluctuations of the collagen matrix with which it is entangled.

Motor crosslinking augments elasticity in active nematics.

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks.

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Motor crosslinking augments elasticity in active nematics.

In active materials, uncoordinated internal stresses lead to emergent long-range flows. An understanding of how the behavior of active materials depends on mesoscopic (hydrodynamic) parameters is developing, but there remains a gap in knowledge concerning how hydrodynamic parameters depend on the properties of microscopic elements. In this work, we combine experiments and multiscale modeling to relate the structure and dynamics of active nematics composed of biopolymer filaments and molecular motors to their microscopic properties, in particular motor processivity, speed, and valency. We show that crosslinking of filaments by both motors and passive crosslinkers not only augments the contributions to nematic elasticity from excluded volume effects but dominates them. By altering motor kinetics we show that a competition between motor speed and crosslinking results in a nonmonotonic dependence of nematic flow on motor speed. By modulating passive filament crosslinking we show that energy transfer into nematic flow is in large part dictated by crosslinking. Thus motor proteins both generate activity and contribute to nematic elasticity. Our results provide new insights for rationally engineering active materials.

Structural Features and Nonlinear Rheology of Self-Assembled Networks of Cross-Linked Semiflexible Polymers.

Disordered networks of semiflexible filaments are common support structures in biology. Familiar examples include fibrous matrices in blood clots, bacterial biofilms, and essential components of cells and tissues of plants, animals, and fungi. Despite the ubiquity of these networks in biomaterials, we have only a limited understanding of the relationship between their structural features and their highly strain-sensitive mechanical properties. In this work, we perform simulations of three-dimensional networks produced by the irreversible formation of cross-links between linker-decorated semiflexible filaments. We characterize the structure of networks formed by a simple diffusion-dependent assembly process and measure their associated steady-state rheological features at finite temperature over a range of applied prestrains that encompass the strain-stiffening transition. We quantify the dependence of network connectivity on cross-linker availability and detail the associated connectivity dependence of both linear elasticity and nonlinear strain-stiffening behavior, drawing comparisons with prior experimental measurements of the cross-linker concentration-dependent elasticity of actin gels.

Signatures of irreversibility in microscopic models of flocking.

Flocking in d=2 is a genuine nonequilibrium phenomenon for which irreversibility is an essential ingredient. We study a class of minimal flocking models whose only source of irreversibility is self-propulsion and use the entropy production rate (EPR) to quantify the departure from equilibrium across their phase diagrams. The EPR is maximal in the vicinity of the order-disorder transition, where reshuffling of the interaction network is fast. We show that signatures of irreversibility come in the form of asymmetries in the steady-state distribution of the flock's microstates. These asymmetries occur as consequences of the time-reversal symmetry breaking in the considered self-propelled systems, independently of the interaction details. In the case of metric pairwise forces, they reduce to local asymmetries in the distribution of pairs of particles. This study suggests a possible use of pair asymmetries both to quantify the departure from equilibrium and to learn relevant information about aligning interaction potentials from data.

Unique Role of Vimentin Networks in Compression Stiffening of Cells and Protection of Nuclei from Compressive Stress.

In this work, we investigate whether stiffening in compression is a feature of single cells and whether the intracellular polymer networks that comprise the cytoskeleton (all of which stiffen with increasing shear strain) stiffen or soften when subjected to compressive strains. We find that individual cells, such as fibroblasts, stiffen at physiologically relevant compressive strains, but genetic ablation of vimentin diminishes this effect. Further, we show that unlike networks of purified F-actin or microtubules, which soften in compression, vimentin intermediate filament networks stiffen in both compression and extension, and we present a theoretical model to explain this response based on the flexibility of vimentin filaments and their surface charge, which resists volume changes of the network under compression. These results provide a new framework by which to understand the mechanical responses of cells and point to a central role of intermediate filaments in response to compression.

Shear-induced phase transition and critical exponents in three-dimensional fiber networks.

When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiments have shown that this phenomenon is controlled by an underlying mechanical phase transition that is critical in nature. Growing simulation evidence points to non-mean-field behavior for this transition and a hyperscaling relation has been proposed to relate the corresponding critical exponents. Here, we report simulations on two distinct network structures in three dimensions. By performing a finite-size scaling analysis, we test hyperscaling and identify various critical exponents. From the apparent validity of hyperscaling, as well as the non-mean-field exponents we observe, our results suggest that the upper critical dimension for the strain-controlled phase transition is above three, in contrast to the jamming transition that represents another athermal, mechanical phase transition.

Compression stiffening of fibrous networks with stiff inclusions.

Tissues commonly consist of cells embedded within a fibrous biopolymer network. Whereas cell-free reconstituted biopolymer networks typically soften under applied uniaxial compression, various tissues, including liver, brain, and fat, have been observed to instead stiffen when compressed. The mechanism for this compression-stiffening effect is not yet clear. Here, we demonstrate that when a material composed of stiff inclusions embedded in a fibrous network is compressed, heterogeneous rearrangement of the inclusions can induce tension within the interstitial network, leading to a macroscopic crossover from an initial bending-dominated softening regime to a stretching-dominated stiffening regime, which occurs before and independently of jamming of the inclusions. Using a coarse-grained particle-network model, we first establish a phase diagram for compression-driven, stretching-dominated stress propagation and jamming in uniaxially compressed two- and three-dimensional systems. Then, we demonstrate that a more detailed computational model of stiff inclusions in a subisostatic semiflexible fiber network exhibits quantitative agreement with the predictions of our coarse-grained model as well as qualitative agreement with experiments.

Finite size effects in critical fiber networks.

Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.

Nonlinear Poisson Effect Governed by a Mechanical Critical Transition.

Under extensional strain, fiber networks can exhibit an anomalously large and nonlinear Poisson effect accompanied by a dramatic transverse contraction and volume reduction for applied strains as small as a few percent. We demonstrate that this phenomenon is controlled by a collective mechanical phase transition that occurs at a critical uniaxial strain that depends on network connectivity. This transition is punctuated by an anomalous peak in the apparent Poisson's ratio and other critical signatures such as diverging nonaffine strain fluctuations.

Stress-stabilized subisostatic fiber networks in a ropelike limit.

The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between 3 and 4. Such networks are sub-isostatic and linearly unstable to deformation with only central force interactions, but exhibit a mechanical phase transition between floppy and rigid states under strain. The introduction of weak bending interactions stabilizes these networks and suppresses the critical signatures of this transition. We show that applying external stress can also stabilize subisostatic networks with only tensile central force interactions, i.e., a ropelike potential. Moreover, we find that the linear shear modulus shows a power-law scaling with the external normal stress, with a non-mean-field exponent. For networks with finite bending rigidity, we find that the critical stain shifts to lower values under prestress.

Scaling Theory for Mechanical Critical Behavior in Fiber Networks.

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.

Normal stress anisotropy and marginal stability in athermal elastic networks.

Hydrogels of semiflexible biopolymers such as collagen have been shown to contract axially under shear strain, in contrast to the axial dilation observed for most elastic materials. Recent work has shown that this behavior can be understood in terms of the porous, two-component nature and consequent time-dependent compressibility of hydrogels. The apparent normal stress measured by a torsional rheometer reflects only the tensile contribution of the axial component σzz on long (compressible) timescales, crossing over to the first normal stress difference, N1 = σxx - σzz at short (incompressible) times. While the behavior of N1 is well understood for isotropic viscoelastic materials undergoing affine shear deformation, biopolymer networks are often anisotropic and deform nonaffinely. Here, we numerically study the normal stresses that arise under shear in subisostatic, athermal semiflexible polymer networks. We show that such systems exhibit strong deviations from affine behavior and that these anomalies are controlled by a rigidity transition as a function of strain.