Effective medium approach for stiff polymer networks with flexible cross-links

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.Comment: 12 pages, 8 figure

The bend stiffness of S-DNA

We formulate and solve a two-state model for the elasticity of nicked, double-stranded DNA that borrows features from both the Worm Like Chain and the Bragg--Zimm model. Our model is computationally simple, and gives an excellent fit to recent experimental data through the entire overstretching transition. The fit gives the first value for the bending stiffness of the overstretched state as about 10 nm*kbt, a value quite different from either B-form or single-stranded DNA.Comment: 7 pages, 1 figur

Fluctuation-stabilized marginal networks and anomalous entropic elasticity

We study the elastic properties of thermal networks of Hookean springs. In the purely mechanical limit, such systems are known to have vanishing rigidity when their connectivity falls below a critical, isostatic value. In this work we show that thermal networks exhibit a non-zero shear modulus $G$ well below the isostatic point, and that this modulus exhibits an anomalous, sublinear dependence on temperature $T$. At the isostatic point, $G$ increases as the square-root of $T$, while we find $G \propto T^{\alpha}$ below the isostatic point, where ${\alpha} \simeq 0.8$. We show that this anomalous $T$ dependence is entropic in origin.Comment: 9 pages, 7 figure

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.Comment: 4 pages, 3 figure

Off-lattice Monte Carlo Simulation of Supramolecular Polymer Architectures

We introduce an efficient, scalable Monte Carlo algorithm to simulate cross-linked architectures of freely-jointed and discrete worm-like chains. Bond movement is based on the discrete tractrix construction, which effects conformational changes that exactly preserve fixed-length constraints of all bonds. The algorithm reproduces known end-to-end distance distributions for simple, analytically tractable systems of cross-linked stiff and freely jointed polymers flawlessly, and is used to determine the effective persistence length of short bundles of semi-flexible worm-like chains, cross-linked to each other. It reveals a possible regulatory mechanism in bundled networks: the effective persistence of bundles is controlled by the linker density.Comment: 4 pages, 4 figure

Reply to "Comment on 'Theory of high-force DNA stretching and overstretching'"

In his Comment to an earlier paper [Phys. Rev. E 67, 051906 (2003)] Lam points out an error in Eq. (20) of the original paper. Here we show that use of the corrected expression produces results very similar to those presented in our original paper, so our qualitative conclusions are unchanged

Gait event detection in laboratory and real life settings: Accuracy of ankle and waist sensor based methods

Wearable sensors technology based on inertial measurement units (IMUs) is leading the transition from laboratory-based gait analysis, to daily life gait monitoring. However, the validity of IMU-based methods for the detection of gait events has only been tested in laboratory settings, which may not reproduce real life walking patterns. The aim of this study was to evaluate the accuracy of two algorithms for the detection of gait events and temporal parameters during free-living walking, one based on two shank-worn inertial sensors, and the other based on one waist-worn sensor. The algorithms were applied to gait data of ten healthy subjects walking both indoor and outdoor, and completing protocols that entailed both straight supervised and free walking in an urban environment. The values obtained from the inertial sensors were compared to pressure insoles data. The shank-based method showed very accurate initial contact, stride time and step time estimation (<14 ms error). Accuracy of final contact timings and stance time was lower (28–51 ms error range). The error of temporal parameter variability estimates was in the range 0.09–0.89%. The waist method failed to detect about 1% of the total steps and performed worse than the shank method, but the temporal parameter estimation was still satisfactory. Both methods showed negligible differences in their accuracy when the different experimental conditions were compared, which suggests their applicability in the analysis of free-living gait

Critical behaviour in the nonlinear elastic response of hydrogels

In this paper we study the elastic response of synthetic hydrogels to an applied shear stress. The hydrogels studied here have previously been shown to mimic the behaviour of biopolymer networks when they are sufficiently far above the gel point. We show that near the gel point they exhibit an elastic response that is consistent with the predicted critical behaviour of networks near or below the isostatic point of marginal stability. This point separates rigid and floppy states, distinguished by the presence or absence of finite linear elastic moduli. Recent theoretical work has also focused on the response of such networks to finite or large deformations, both near and below the isostatic point. Despite this interest, experimental evidence for the existence of criticality in such networks has been lacking. Using computer simulations, we identify critical signatures in the mechanical response of sub-isostatic networks as a function of applied shear stress. We also present experimental evidence consistent with these predictions. Furthermore, our results show the existence of two distinct critical regimes, one of which arises from the nonlinear stretch response of semi-flexible polymers.