Search

We study how the rigidity transition in a triangular lattice changes as a function of anisotropy by preferentially filling bonds on the lattice in one direction. We discover that the onset of rigidity in anisotropic spring networks arises in at least two steps, reminiscent of the two-step melting transition in two dimensional crystals. In particular, our simulations demonstrate that the percolation of stress-supporting bonds happens at different critical volume fractions along different directions. By examining each independent component of the elasticity tensor, we determine universal exponents and develop universal scaling functions to analyze isotropic rigidity percolation as a multicritical point. We expect that these results will be important for elucidating the underlying mechanical phase transitions governing the properties of biological materials ranging from the cytoskeletons of cells to the extracellular networks of tissues such as tendon where the networks are often preferentially aligned., Comment: 13 pages, 17 figures

Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these filamentous tissues' mechanics to the concentrations of their constituents. Past studies have generally considered tuning of networks by spatially homogeneous variation in concentration, while ignoring structural correlation. We here introduce a model in which dilute fiber networks are built in a correlated manner that produces alternating sparse and dense regions. Our simulations indicate that structural correlation consistently allows tissues to attain rigidity with less material. We further find that the percolation threshold varies non-monotonically with the degree of correlation, such that it decreases with moderate correlation and once more increases for high correlation. We explain the eventual reentrance in the dependence of the rigidity percolation threshold on correlation as the consequence of large, stiff clusters that are too poorly coupled to transmit forces across the network. Our study offers deeper understanding of how spatial heterogeneity may enable tissues to robustly adapt to different mechanical contexts., Comment: This article contains 10 pages and 5 figures

The cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable non-equilibrium processes ranging from mitosis to chemotaxis. Its versatile reconfigurability, programmed by interactions between its constituents, make the cytoskeleton foundational active matter. Yet, current active matter endeavors are limited largely to single force-generating components acting on a single substrate, far from the composite cytoskeleton in cells. Here, we engineer actin-microtubule double-networks, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or microtubules has an opposite effect. Our minimal advection-diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and de-mixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the non-equilibrium dynamics across all networks and timescales can be organized into three classes: slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems, and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.

Healthy cartilage is a remarkable tissue, able to withstand tens of millions of loading cycles with minimal damage. While much is known about the structural origins of its compressive mechanics, how composition determines its mechanical behavior in shear, a major mode of failure, is poorly understood. Through a combination of microscale structure-function experiments and modeling, we develop a rigidity percolation framework to explain the structural origins of cartilage shear mechanics. This framework provides a new quantitative understanding for how the known degradative events in osteoarthritis determine the mechanical changes that are a hallmark of this disease. As such, this work provides a road map for understanding disease progression and in combination with non-invasive techniques such as MRI will enable more effective diagnosis and treatment., Comment: 9 pages, 3 pages of SI, 5 figures

The cytoskeleton is a model active matter system that controls diverse cellular processes from division to motility. While both active actomyosin dynamics and actin-microtubule interactions are key to the cytoskeleton's versatility and adaptability, an understanding of their interplay is lacking. Here, we couple microscale experiments with mechanistic modeling to elucidate how connectivity, rigidity, and force-generation affect emergent material properties in in vitro composites of actin, tubulin, and myosin. We use time-resolved differential dynamic microscopy and spatial image autocorrelation to show that ballistic contraction occurs in composites with sufficient flexibility and motor density, but that a critical fraction of microtubules is necessary to sustain controlled dynamics. Our active double-network models reveal that percolated actomyosin networks are essential for contraction, but that networks with comparable actin and microtubule densities can uniquely resist mechanical stresses while simultaneously supporting substantial restructuring. Our findings provide a much-needed blueprint for designing cytoskeleton-inspired materials that couple tunability with resilience and adaptability.

Hierarchically structured materials, which possess distinct features on different length scales, are ubiquitous in nature and engineering. In many cases, one structural level may be ordered while another structural level may be disordered. Here, we investigate the impact of structural disorder on the mechanical properties of hierarchical filamentous structures. Through simulations of networks with two hierarchical levels, we show that disorder does not change how stiffness scales with the mean coordination number - the average number of bonds per node - on large and small length scales. However, we find that network rigidity and stiffness depend strongly on the presence or absence of disorder on the small length scale, but not on the large length scale. In fact, the amount of material necessary for a fully connected, network ordered on the small scale is insufficient to create even a marginally rigid network with small-scale disorder. We trace these phenomena back to a difference in the maximum mean coordination number on the small scale. While single length scale ordered and disordered networks have similar mean coordination numbers in the interior and on surfaces, we find that disorder strongly impacts the structure of surfaces, resulting in a larger fraction of surface nodes on the small scale. While this effect increases in strength as large scale bonds become narrower, it persists even for bonds that are wider than they are long (i.e., aspect ratios < 1).

Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature; diverse biological materials, such as bone, cellulose, and muscle, have as many as ten hierarchical levels. Structural hierarchy confers many mechanical advantages, including improved toughness and economy of material. However, it also presents a problem: each hierarchical level adds a new source of assembly errors, and substantially increases the information required for proper assembly. This seems to conflict with the prevalence of naturally occurring hierarchical structures, suggesting that a common mechanical source of hierarchical robustness may exist. However, our ability to identify such a unifying phenomenon is limited by the lack of a general mechanical framework for structures exhibiting organization on disparate length scales. Here, we use simulations to substantiate a generalized model for the tensile stiffness of hierarchical, stretching-stabilized, filamentous networks with a nested, dilute triangular lattice structure. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics, and find a mathematically similar dependence of material stiffness upon each hierarchical level. Using this model, we find that the stiffness of such networks becomes less sensitive to errors in assembly with additional levels of hierarchy; though surprising, we show that this result is analytically predictable from first principles, and thus likely model-independent. More broadly, this work helps account for the success of hierarchical, filamentous materials in biology and materials design, and offers a heuristic for ensuring that desired material properties are achieved within the required tolerance.