The inflammasome is a multiprotein complex necessary for the onset of inflammation. The adapter protein ASC assembles inflammasome components by acting as a molecular glue between danger-signal sensors and procaspase-1. The assembly is mediated by ASC self-association and protein interactions via its two Death Domains, PYD and CARD. Truncated versions of ASC have been shown to form filaments, but information on the filaments formed by full-length ASC is needed to construct a meaningful model of inflammasome assembly. To gain insights into this system, we used a combination of transmission EM, NMR, and computational analysis to investigate intact ASC structures. We show that ASC forms ϳ6 -7-nm-wide filaments that stack laterally to form bundles. The structural characteristics and dimensions of the bundles indicate that both PYD and CARD are integral parts of the filament. A truncated version of ASC with only the CARD domain (ASC CARD ) forms different filaments (ϳ3-4-nm width), providing further evidence that both domains work in concert in filament assembly. Ring-shaped protein particles bound to pre-existing filaments match the size of ASC dimer structures generated by NMR-based protein docking, suggesting that the ASC dimer could be a basic building block for filament formation. Solution NMR binding studies identified the protein surfaces involved in the ASC CARD -ASC CARD interaction. These data provide new insights into the structural underpinnings of the inflammasome and should inform future efforts to interrogate this important biological system. Figure 13. Model for ASC-dependent inflammasome assembly based on TEM data. ASC dimer is shown as the minimal building block. The ASC filament shows two interacting sides, one for recruiting procaspase-1 CARD and the other for interaction with the PYD of NLR sensor proteins. ASC domains, PYD and CARD, form ASC filament core

The cytoskeleton of living cells contains many types of crosslinkers. Some crosslinkers allow energy-free rotations between filaments and others do not. The mechanical interplay between these different crosslinkers is an open issue in cytoskeletal mechanics. Therefore, we develop a theoretical framework based on rigidity percolation to study a generic filamentous system containing both stretching and bond-bending forces to address this issue. The framework involves both analytical calculations via effective medium theory and numerical simulations on a percolating triangular lattice with very good agreement between both. We find that the introduction of angle-constraining crosslinkers to a semiflexible filamentous network with freely rotating crosslinks can cooperatively lower the onset of rigidity to the connectivity percolation threshold—a result argued for years but never before obtained via effective medium theory. This allows the system to ultimately attain rigidity at the lowest concentration of material possible. We further demonstrate that introducing angle-constraining crosslinks results in mechanical behaviour similar to just freely rotating crosslinked semflexible filaments, indicating redundancy and universality. Our results also impact upon collagen and fibrin networks in biological and bio-engineered tissues.

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.The interplay of constraints, forces, and driving gives rise to the jamming transition in granular media. It is now wellestablished that the frictionless jamming transition has characteristics of both second-and first-order transitions. Both the average coordination number and the largest rigid cluster size jump at the transition, yet there exists a diverging lengthscale [1][2][3][4]. Frictional jamming is more puzzling: The hysteresis observed in the stress-strain rate curves of stresscontrolled flow simulations [5][6][7][8] and experiments [9] has lead to an interpretation as a first-order transition. Yet, signs of second-order criticality appear when treating the fraction of contacts at the Coulomb threshold as an additional parameter [10][11][12].To elucidate the frictional jamming transition from a microscopic viewpoint, we extend concepts and tools from rigidity percolation, i.e., the onset of mechanical rigidity in disordered spring networks [13][14][15][16], to frictional packings. The former is driven by the emergence of a system-spanning rigid cluster that can be mapped out (in 2d) using the pebble game [17], an improved constraint counting method that goes beyond meanfield by identifying redundant constraints. We, for the first time, implement a generalized pebble game for 2d frictional systems and use it to identify rigid clusters in very slowly sheared packings. As we show below, this allows us to identify a second-order rigidity transition and to link stresses and nonaffine motions to the microscopic structure of frictionally jammed packings.Generalized isostaticity: To establish context, we first review the application of Maxwell constraint counting to jamming [18]. For N particles in d dimensions and a mean number of contacts per particle z, interparticle forces yield dzN/2 constraints. Since each particle has 1 2 d(d + 1) translational and rotational degrees of freedom, there are 1 2 (N − 1)d(d + 1) total degrees of freedom (subtracting out global degrees of freedom). When these match the force constraints, we arrive at the isostatic criterion, or dzN/2 = 1 2 (N − 1)d(d + 1). In the limit N → ∞, z iso = d + 1 for frictional granular materials. For frictionless packings, we ignore rotations and obtain the familiar z iso = 2d.Despite being mean field, i.e. neglecting spatial correla- tions, isostaticity works seemingly well to locate the jamming transition in static frictionless systems [1]. For frictional syste...

Swarming is a phenomenon where collective motion arises from simple local interactions between typically identical individuals. Here, we investigate the effects of variability in behavior among the agents in finite swarms with both alignment and cohesive interactions. We show that swarming is abolished above a critical fraction of non-aligners who do not participate in alignment. In certain regimes, however, swarms above the critical threshold can dynamically reorganize and sort out excess non-aligners to maintain the average fraction close to the critical value. This persists even in swarms with a distribution of alignment interactions, suggesting a simple, robust and efficient mechanism that allows heterogeneously mixed populations to naturally regulate their composition and remain in a collective swarming state or even differentiate among behavioral phenotypes. We show that, for evolving swarms, this self-organized sorting behavior can couple to the evolutionary dynamics leading to new evolutionarily stable equilibrium populations set by the physical swarm parameters.

The emergence of collective motion, or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that occurs at multiple spatio-temporal scales. Swarms that occur in natural environments typically have to contend with spatial disorder such as obstacles that can hinder an individual's motion or can disrupt communication with neighbors. We study swarming agents, possessing both aligning and mutually avoiding repulsive interactions, in a 2D percolated network representing a topologically disordered environment. We numerically find a phase transition from a collectively moving swarm to a disordered gas-like state above a critical value of the topological or environmental disorder. For agents that utilize only alignment interactions, we find that the swarming transition does not exist in the large system size limit, while the addition of a mutually repulsive interaction can restore the existence of the transition at a finite critical value of disorder. We find there is a finite range of topological disorder where swarming can occur and that this range can be maximized by an optimal amount of mutual repulsion.