Living systems often exhibit internal driving: active, molecular processes drive nonequilibrium phenomena such as metabolism or migration. Active gels constitute a fascinating class of internally driven matter, where molecular motors exert localized stresses inside polymer networks. There is evidence that network crosslinking is required to allow motors to induce macroscopic contraction. Yet a quantitative understanding of how network connectivity enables contraction is lacking. Here we show experimentally that myosin motors contract crosslinked actin polymer networks to clusters with a scale-free size distribution. This critical behavior occurs over an unexpectedly broad range of crosslink concentrations. To understand this robustness, we develop a quantitative model of contractile networks that takes into account network restructuring: motors reduce connectivity by forcing crosslinks to unbind.Paradoxically, to coordinate global contractions, motor activity should be low. Otherwise, motors drive initially well-connected networks to a critical state where ruptures form across the entire network. Alvarado et al.Molecular motors robustly drive active gels to a critically connected state Page 2 of 21 behaviors has been proposed, since macroscopic contractions are known to occur above certain minimum values of crosslink or actin concentration 14,17,19,20 . We should expect remarkable critical behavior at the threshold of contraction. Recent theoretical models predict diverging correlation length-scales and a strong response to external fields 21-24 at the threshold of rigidity.In suspensions of self-propelled patches, critical slowing was predicted at the threshold of alignment 25 . Yet the threshold of contraction still remains poorly understood, and experimental evidence of criticality in active gels remains lacking. Alvarado et al. Molecular motors robustly drive active gels to a critically connected state Page 3 of 21Here, we experimentally study model cytoskeletal systems composed of actin filaments and myosin motors. We vary network connectivity over a broad range by adding controlled amounts of crosslink protein. We show that the motors can actively contract the networks into disjoint clusters that exhibit a power-law size distribution. This behavior is reminiscent of classical conductivity percolation 26 , for which a power-law size distribution of clusters occurs close to a critical point. However, in sharp contrast to this equilibrium phenomenon, we observe critical behavior over a wide range of initial network connectivities. To understand this robustness, we develop a general theoretical model of contractile gels that can quantitatively account for our observations. In this model, motors not only contract the network, but also reduce the connectivity of initially stable networks down to a marginal structure by promoting crosslink unbinding. Below this marginal connectivity, the network no longer supports stress and the system rapidly devolves to disjoint clusters which reflect the critical behavior of th...

Animal cell cytokinesis requires a contractile ring of crosslinked actin filaments and myosin motors. How contractile rings form and are stabilized in dividing cells remains unclear. We address this problem by focusing on septins, highly conserved proteins in eukaryotes whose precise contribution to cytokinesis remains elusive. We use the cleavage of the Drosophila melanogaster embryo as a model system, where contractile actin rings drive constriction of invaginating membranes to produce an epithelium in a manner akin to cell division. In vivo functional studies show that septins are required for generating curved and tightly packed actin filament networks. In vitro reconstitution assays show that septins alone bundle actin filaments into rings, accounting for the defects in actin ring formation in septin mutants. The bundling and bending activities are conserved for human septins, and highlight unique functions of septins in the organization of contractile actomyosin rings.

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

Living systems provide a paradigmatic example of active soft matter. Cells and tissues comprise viscoelastic materials that exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, an active gel of semiflexible filaments, crosslinks, and molecular motors inside cells. Although individual motors are only a few nm in size and exert minute forces of a few pN, cells spatially integrate the activity of an ensemble of motors to produce larger contractile forces (∼nN and greater) on cellular, tissue, and organismal length scales. Here we review experimental and theoretical studies on contractile active gels composed of actin filaments and myosin motors. Unlike other active soft matter systems, which tend to form ordered patterns, actin-myosin systems exhibit a generic tendency to contract. Experimental studies of reconstituted actin-myosin model systems have long suggested that a mechanical interplay between motor activity and the network's connectivity governs this contractile behavior. Recent theoretical models indicate that this interplay can be understood in terms of percolation models, extended to include effects of motor activity on the network connectivity. Based on concepts from percolation theory, we propose a state diagram that unites a large body of experimental observations. This framework provides valuable insights into the mechanisms that drive cellular shape changes and also provides design principles for synthetic active materials.

F-actin bundles are prominent cytoskeletal structures in eukaryotes. They provide mechanical stability in stereocilia, microvilli, filopodia, stress fibers and the sperm acrosome. Bundles are typically stabilized by a wide range of specific crosslinking proteins, most of which exhibit off-rates on the order of 1s(-1). Yet F-actin bundles exhibit structural and mechanical integrity on time scales that are orders of magnitude longer. By applying large deformations to reconstituted F-actin bundles using optical tweezers, we provide direct evidence of their differential mechanical response in vitro: bundles exhibit fully reversible, elastic response on short time scales and irreversible, elasto-plastic response on time scales that are long compared to the characteristic crosslink dissociation time. Our measurements show a broad range of characteristic relaxation times for reconstituted F-actin bundles. This can be reconciled by considering that bundle relaxation behavior is also modulated by the number of filaments, crosslinking type and occupation number as well as the consideration of defects due to filament ends.

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.

We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a cluster distribution inconsistent with RP. Our model not only can account for these experiments, but also exhibits an unusual type of mixed phase transition: We find that the transition is characterized by signatures of criticality, but with a discontinuity in the order parameter. DOI: 10.1103/PhysRevLett.114.098104 PACS numbers: 87.16.Ka, 64.60.ah, 64.60.Bd, 64.60.De Percolation theory has become pervasive in a number of fields ranging from physics to mathematics and even computer science [1]. In particular, it successfully describes connectivity and elastic properties of polymer networks [2,3]. The simplest percolation model is the random percolation (RP) model, consisting of a collection of nodes with controlled connectivity, p, representing the fraction of occupied bonds between the nodes. As a function of p, the order parameter-the mass fraction of the largest clusterbecomes finite above the percolation threshold p c . The nature of the transition is of special interest because the system properties are highly tunable at this point, especially if the transition is discontinuous; in that case, just a few bonds can have a significant impact, even for very large systems [4]. Usually, however, percolation transitions are second order, with a continuous variation of the order parameter and various critical signatures. More specialized percolation models can exhibit different phase behavior, including discontinuous transitions between the two phases (see discussion below).Here, we present a simple model based on random percolation that develops a discontinuous jump in the order parameter in the thermodynamic limit, while exhibiting other features of criticality in such quantities as the correlation length and susceptibility. Interestingly, the transition we observe occurs for the same p c < 1 as for random percolation. Moreover, our model can account for recent experimental results on active biopolymer gels that have been shown to self-organize towards a critical connectivity point [5]. The experimentally observed cluster properties at this point were found to be inconsistent with the ordinary random percolation model.In these experiments, we studied a model cytoskeletal system, composed of actin filaments, fascin cross-links and myosin motors in a quasi-2D chamber of dimensions 3 mm × 2 mm × 80 μm [5] (see Supplemental Material [6]). We observed a motor-driven collapse of the network into disjointed clusters (see Fig. 1(a) and movie of the collapse in the Supplemental Material [6]). The configuration of the clusters prior to the collapse is obtained by analyzing the timereversed movie [see Fig. 1(b)] and their masses were estimated from their initial areas. We found that, over a wide range of the experimental parameters, the number n s of clusters of mass s exhibits a power-l...

No abstract