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Summary The non-muscle actomyosin cytoskeleton generates contractile force through the dynamic rearrangement of its constituent parts. Actomyosin rings are a specialization of the non-muscle actomyosin cytoskeleton that drive cell shape changes during division, wound healing, and other events. Contractile rings throughout phylogeny and in a range of cellular contexts are built from conserved components including non-muscle myosin II (NMMII), actin filaments (F-actin), and crosslinking proteins. However, it is unknown whether diverse actomyosin rings close via a single unifying mechanism. To explore how contractile forces are generated by actomyosin rings, we studied three instances of ring closure within the common cytoplasm of theC. elegansoogenic germline: mitotic cytokinesis of germline stem cells (GSCs), apoptosis of meiotic compartments, and cellularization of oocytes. We found that each ring type closed with unique kinetics, protein density and abundance dynamics. These measurements suggested that the mechanism of contractile force generation varied across the subcellular contexts. Next, we formulated a physical model that related the forces generated by filament-filament interactions to the material properties of these rings that dictate the kinetics of their closure. Using this framework, we related the density of conserved cytoskeletal proteins anillin and NMMII to the kinematics of ring closure. We fitted model rings to in situ measurements to estimate parameters that are currently experimentally inaccessible, such as the asymmetric distribution of protein along the length of F-actin, which occurs naturally due to differences in the dimensions of the crosslinker and NMMII filaments. Our work predicted that the role of NMMII varies across these ring types, due in part to its distribution along F-actin and motoring. Our model also predicted that the degree of contractility and the impact of ring material properties on contractility differs among ring types. 

Cytoskeletal networks are the main actuators of cellular mechanics, and a foundational example for active matter physics. In cytoskeletal networks, motion is generated on small scales by filaments that push and pull on each other via molecular-scale motors. These local actuations give rise to large-scale stresses and motion. To understand how microscopic processes can give rise to self-organized behavior on larger scales it is important to consider what mechanisms mediate long-ranged mechanical interactions in the systems. Two scenarios have been considered in the recent literature. The first scenario is systems that are relatively sparse, in which most of the large-scale momentum transfer is mediated by the solvent in which cytoskeletal filaments are suspended. The second scenario is systems in which filaments are coupled via cross-link molecules throughout. Here, we review the differences and commonalities between the physics of these two regimes. We also survey the literature for the numbers that allow us to place a material within either of these two classes. 

Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer-scale motor activity inside individual cilia. Our study of a one-dimensional lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that, in homogeneous beds of cilia, these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that, in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves. 

Abstract Living matter moves, deforms, and organizes itself. In cells this is made possible by networks of polymer filaments and crosslinking molecules that connect filaments to each other and that act as motors to do mechanical work on the network. For the case of highly cross-linked filament networks, we discuss how the material properties of assemblies emerge from the forces exerted by microscopic agents. First, we introduce a phenomenological model that characterizes the forces that crosslink populations exert between filaments. Second, we derive a theory that predicts the material properties of highly crosslinked filament networks, given the crosslinks present. Third, we discuss which properties of crosslinks set the material properties and behavior of highly crosslinked cytoskeletal networks. The work presented here, will enable the better understanding of cytoskeletal mechanics and its molecular underpinnings. This theory is also a first step toward a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab.