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 towards a theory of how molecular perturbations impact cytoskeletal organization, and provides a framework for designing cytoskeletal networks with desirable properties in the lab.
Cytoskeletal networks are foundational examples of active matter and central to self-organized structures in the cell. In vivo, these networks are active and heavily crosslinked. Relating their large-scale dynamics to properties of their constituents remains an unsolved problem. Here we study an in vitro system made from microtubules and XCTK2 kinesin motors, which forms an aligned and active gel. Using photobleaching we demonstrate that the gel's aligned microtubules, driven by motors, continually slide past each other at a speed independent of the local polarity. This phenomenon is also obse…
Inspired by the complex influence of the globular crosslinking proteins on the formation of biofilament bundles in living organisms, we study and analyze a theoretical model for the structure and thermodynamics of bundles of helical filaments assembled in the presence of crosslinking molecules. The helical structure of filaments, a universal feature of biopolymers such as filamentous actin, is shown to generically frustrate the geometry of crosslinking between the "grooves" of two neighboring filaments. We develop a coarse-grained model to investigate the interplay between the geometry of bind…
The actin cytoskeleton in living cells has many types of crosslinkers. The mechanical interplay between these different crosslinker types is an open issue in cytoskeletal mechanics. We develop a framework to study the cooperativity and redundancy in the mechanics of filamentous networks with two types of crosslinkers: crosslinkers that allow free rotations of filaments and crosslinkers that do not. The framework consists of numerical simulations and an effective medium theory on a percolating triangular lattice. We find that the introduction of angle-constraining crosslinkers significantly low…
Single-filament tracing has been a valuable tool to directly determine geometrical and mechanical properties of entangled polymer networks. However, systematically verifying how the stiffness of the tracer filament or its molecular interactions with the surrounding network impacts the measurement of these parameters has not been possible with the established experimental systems. Here, we use mechanically programmable DNA nanotubes embedded in crosslinked and entangled F-actin networks, as well as in synthetic DNA networks, in order to measure fundamental, structural network properties like tu…
We consider a biopolymer bundle consisting of filaments that are crosslinked together. The crosslinks are reversible: they can dynamically bind and unbind adjacent filament pairs as controlled by a binding enthalpy. The bundle is subjected to a bending deformation and the corresponding distribution of crosslinks is measured. For a bundle consisting of two filaments, upon increasing the bending amplitude, a first-order transition is observed. The transition is from a state where the filaments are tightly coupled by many bound crosslinks, to a state of nearly independent filaments with only a fe…
Motivated by recent experiments showing that stiff biopolymer gels exhibit highly unusual negative normal elastic stresses, we develop a computational model for stiff polymer networks subject to large strains. In all cases, we find that such networks develop normal stresses that are both negative and of magnitude comparable to the corresponding shear stress. We find that these normal stresses coincide with other nonlinearities in our networks, and specifically with compressive bucking of the individual filaments. Our results suggest that negative normal stresses are a characteristic feature of…
We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which…
We construct a coarse-grained model of parallel actin bundles crosslinked by compact, globular bundling proteins, such as fascin and espin, necessary components of filapodial and mechanosensory bundles. Consistent with structural observations of bundles, we find that the optimal geometry for crosslinking is overtwisted, requiring a coherent structural change of the helical geometry of the filaments. We study the linker-dependent thermodynamic transition of bundled actin filaments from their native state to the overtwisted state and map out the "twist-state'' phase diagram in terms of the avail…
We study the response of F-actin bundles to driving forces through a simple analytical model. We consider two filaments connected by reversibly bound crosslinks and driven by an external force. Two failure modes under load can be defined. \textit{Brittle failure} is observed when crosslinks suddenly and collectively unbind, leading to catastrophic loss of bundle integrity. During \textit{ductile failure}, on the other hand, bundle integrity is maintained, however at the cost of crosslink reorganization and defect formation. We present phase diagrams for the onset of failure, highlighting the i…
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of wich are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding/unbinding processes. We also deve…
We use optical tweezers microrheology and fluorescence microscopy to apply nonlinear microscale strains to entangled and crosslinked actin networks, and measure the resulting stress and actin filament deformations. We couple nonlinear stress response and subsequent relaxation to the velocity profiles of individual fluorescent-labeled actin segments at varying times throughout the strain and varying distances from the strain path to determine the underlying molecular dynamics that give rise to the debated nonlinear response and stress propagation of crosslinked and entangled actin networks at t…
The rheology of F-actin networks has attracted a great attention during the last years. In order to gain a complete understanding of the rheological properties of these novel materials, it is necessary the study in a large deformations regime to alter their internal structure. In this sense, Schmoller et al. 2010 showed that the reconstituted networks of F-actin crosslinked with $α$-actinin unexpectedly harden when they are subjected to a cyclical shear. This observation contradicts the expected Mullins effect observed in most soft materials, such as rubber and living tissues, where a pronounc…
Langevin dynamics is used to study equilibrium properties of the suspension of magnetic filaments (chains of nanoparticles permanently crosslinked with polymers). It is shown that the filament suspension generally has a larger magnetic susceptibility than the system of unlinked nanoparticles with the same average particle concentration. However, actual susceptibility gain strongly depends on length and flexibility of filaments. It is also shown that in a strong gravitational (centrifugal) field sedimentation profiles of filaments are less homogeneous than that of unlinked particles. The spatia…
We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics in the unstable regime and the tensile stress generated in the bundle are discussed. We find that the interaction of parallel filaments can induce unstable behavior and is responsible for active contraction and tension in the bundle. Interaction between antiparallel filaments leads to filament sorting. Our model could apply to simple contractile structures in cells such as stress fibers.
We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model over several plausible candidates, and derive analytical expressions for the elastic energy at arbitrary strain, with the corresponding stress-strain relationship. The theory fits well to a wide range of experimental data on simple shear in different filament networks, quantitatively matching the differential shear modulus variation with stress, with only two a…
The synthetic actin network demands great interest as bio-material due to its soft and wet nature that mimic many biological scaffolding structures. The study of these structures can contribute to a better understanding of this new micro/nano technology and the cytoskeleton like structural building blocks. Inside the cell the actin network is regulated by tens of actin-binding proteins (ABP's), which makes for a highly complex system with several emergent behavior. In particular Calponin is an ABP that was identified as an actin stabiliser, but its mechanism is poorly understood. Recent experi…
We present a generic theory for the dynamics of a stiff filament under tension, in an active medium with orientational correlations, such as a microtubule in contractile actin. In sharp contrast to the case of a passive medium, we find the filament can stiffen, and possibly oscillate, \textit{or} buckle, depending on the contractile or tensile nature of the activity \textit{and} the filament-medium anchoring interaction. We present experiments on the behaviour of microtubules in the growth cone of a neuron, which provide evidence for these apparently opposing behaviours. We also demonstrate a …
Actin is a key component of the cytoskeleton, which plays central roles in cell motility, division, growth, and tensile strength. To enable this wide range of transient mechanical processes and properties, networks of actin filaments continuously disassemble and reassemble via active de/re-polymerization. However, the question remains as to how de/re-polymerization kinetics of individual actin filaments translate to time-varying mechanics of dis/re-assembling networks. To address this question, to ultimately elucidate the molecular mechanisms that enable cells to exhibit a myriad of transitory…
We review the physical properties of macromolecular networks, consisting of semiflexible polymers such as actin. We start by giving a theoretical analysis of the conformational statistics and mechanical response of single filaments. Experimentally relevant quantities such as the end-to-end distribution function and the force-extension relation are discussed. The results are used to analyze the elastic modulus of an entangled solution of such objects. We also discuss the short time and long time (terminal regime) dynamics and compare our results with recent dynamic light scattering and viscoela…
