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 develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant-strainrate ramps.
We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their persistent directionality through the crosslinks. A Monte Carlo scheme is employed to obtain isotropic, homogeneous networks that minimize the free energy, and for which all of the relevant parameters can be varied: the persistence length, the contour length as well as the crosslinking length may be chosen at will. We also provide an initial survey of the mechanical…
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 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…
Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecu…
We demonstrate that a semiflexible bundle of wormlike chains exhibits a state-dependent bending stiffness that alters fundamentally its scaling behavior with respect to the standard wormlike chain. We explore the equilibrium conformational and mechanical behavior of wormlike bundles in isolation, in crosslinked networks, and in solution.
While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly crosslinked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of non-affine bending undulations.
Recent experimental investigations have revealed a non-Maxwellian absorption pattern in the rheological spectra of actin gels, which was interpreted in terms of transient bonds. Here we examine the consequences of reversible crosslinking on the apparent linear spectra of biopolymer solutions theoretically. For a schematic model consisting of a reversibly crosslinked power-law fluid we obtain a simple analytical prediction for the position of the absorption peak, which is backed up by a numerical evaluation of the inelastic glassy wormlike chain model. This establishes bond breaking as a nonlin…
We report temperature-responsive soft composites of semiflexible biopolymer networks (fibrin) containing dispersed microgel colloidal particles of poly(N-isopropylacrylamide) (pNIPAM) that undergo a thermodynamically driven de-swelling transition above a Lower Critical Solution Temperature (LCST). Unlike standard polymer-particle composites, decreasing the inclusion volume of the particles (by increasing temperature)is concomitant with a striking increase of the overall elastic stiffness of the composite. We observe such a behavior over a wide composition space. The composite elastic shear mod…
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…
Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, crosslinked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable materi…
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…
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…
Motivated by the organization of crosslinked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent crosslinks which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the crosslink density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization…
We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is …
A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-2D geometries adopt a characteristic order: the fibers wrap around the central axis at an angle which varies with radius and, in several cases, is strongly bimodally distributed. In this Letter, we investigate the general problem of a 2D crosslinked network of semiflexible fibers confined to a cylindrical substrate, and demonstrate that in such systems the trade-off between bending and stretching energi…
We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau v…
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…
We investigate theoretically the effect of polymer tension on the collective behavior of reversibly binding cross-links. For this purpose, we employ a model of two weakly bending wormlike chains aligned in parallel by a tensile force, with a sequence of inter-chain binding sites regularly spaced along the contours. Reversible cross-links attach and detach at the sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy of the system and find the emergence of a free-energy barrier which controls the reversible (un)binding. The tension affe…
The synthetic actin network arouses great interest as bio-material due to its soft and wet nature that mimics many biological scaffolding structures. Inside the cell, the actin network is regulated by tens of actin-binding proteins (ABP's), which make for a highly complex system with several emergent behaviours. In particular, calponin is an ABP that was identified as an actin stabiliser, but whose mechanism is still poorly understood. Recent experiments using an in vitro model system of cross-linked actin with calponin and large deformation bulk rheology, found that networks with basic calpon…
