Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations

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 especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G'=0.11 +/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G(omega) as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G(omega) as \omega^(1/2), consistent with the predictions of the Rouse model for flexible polymers.Comment: 16 pages, with 15 PostScript figures (to be published in Macromolecules

Non-equilibrium mechanics and dynamics of motor activated gels

The mechanics of cells is strongly affected by molecular motors that generate forces in the cellular cytoskeleton. We develop a model for cytoskeletal networks driven out of equilibrium by molecular motors exerting transient contractile stresses. Using this model we show how motor activity can dramatically increase the network's bulk elastic moduli. We also show how motor binding kinetics naturally leads to enhanced low-frequency stress fluctuations that result in non-equilibrium diffusive motion within an elastic network, as seen in recent \emph{in vitro} and \emph{in vivo} experiments.Comment: 21 pages, 8 figure

Poisson's ratio in composite elastic media with rigid rods

We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poisson's ratio with respect to the addition of rods in 3D composites: there is an unstable fixed point for Poisson's ratio=1/2 (an incompressible system) and a stable fixed point for Poisson's ratio=1/4 (a compressible system). We also derive an approximate expression for the elastic constants for arbitrary rod density that yields exact results for both low and high density. These results may help to explain recent experiments [Physical Review Letters 102, 188303 (2009)] that reported compressibility for composites of microtubules in F-actin networks.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Mechanics and force transmission in soft composites of rods in elastic gels

We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rod-like inclusions. We show that the Poisson's ratio $\nu$ of such a composite evolves with increasing rod density towards a particular value, or {\em fixed point}, independent of the material properties of the matrix, so long as it has a finite initial compressibility. This fixed point is $\nu=1/4$ in three dimensions and $\nu=1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics.Comment: 10 pages, 8 figure

On-site residence time in a driven diffusive system: violation and recovery of mean-field

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using Domain wall theory (DWT), we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually interactive LK (TASEP + MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations

Spin 1 inversion: a Majorana tensor force for deuteron alpha scattering

We demonstrate, for the first time, successful S-matrix to potential inversion for spin one projectiles with non-diagonal $S^j_{ll'}$ yielding a $T_{\rm R}$ interaction. The method is a generalization of the iterative-perturbative, IP, method. We present a test case indicating the degree of uniqueness of the potential. The method is adapted, using established procedures, into direct observable to potential inversion, fitting $\sigma$, ${\rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ for d + alpha scattering over a range of energies near 10 MeV. The $T_{\rm R}$ interaction which we find is very different from that proposed elsewhere, both real and imaginary parts being very different for odd and even parity channels.Comment: 7 pages Revtex, 4 ps figure

Two Session Cognitive Bias Modification Training; Exercise Interpretation Bias

Cognitive bias modification is the direct manipulation of a target bias by extensive exposure to task contingencies that encourage predetermined patterns of processing selectivity1,2. Forty-eight participants from a general population sample recruited for a two-part study investigating the effect of two sessions of exercise orientated Positive CBM-I Training, in comparison to a Neutral Pseudo Training condition. Baseline, post session one and post session two self-report measures of Anxiety, Depression and Stress were collected. Measures of interpretation bias were collected at baseline and post session two, both with and without cognitive load. Results suggest that for individuals undergoing two sessions of Positive CBM-I Training over a fortnight had significantly decreased Trait Anxiety scores, relative to the Pseudo Neutral Training condition. The findings hold promise for the Cognitive Bias Modification paradigm for decreasing symptoms of Anxiety

Cognitive Interpretation Bias: The Effect of a Single Session Moderate Exercise Protocol on Anxiety and Depression

Research conducted within the Cognitive Bias Modification (CBM) paradigm has revealed that cognitive biases such as negative cognitive interpretation biases contribute to mental health disorders such as anxiety (Beard, 2011). It has been shown that exercise reduces anxiety (Ensari, Greenlee, Motl, & Petruzzello, 2015). Exercise has also been found to reduce negative cognitive attention biases (Tian & Smith, 2011), however no research to date has investigated the effect of exercise on cognitive interpretation bias. The key aims of the current project is to investigate whether moderate exercise reduces self-reported symptoms of depression and stress. Additionally, to establish which intensity of exercise is required to achieve anxiety reduction and reduce an individual’s negative cognitive interpretation biases. Study one recruited a healthy sample of adult participants who were randomly assigned to one of two conditions: a walking exercise protocol or a control condition (n=2x12). Participants completed anxiety and cognitive interpretation bias measures before and after the walking exercise or control condition. Those in the walking exercise condition presented less symptoms of trait anxiety on a measure of state and trait anxiety inventory (STAI), compared to controls relative to baseline measures following the intervention. Study two recruited frequent exercisers who were assigned to an exercise or control group (n=2x24). Participants completed anxiety, depression, psychological stress and cognitive interpretation bias measures before and after the exercise or control condition. Following the intervention, negative interpretation biases decreased in the exercise group and stayed stable in the control group. The exercise group also had significantly decreased anxiety, depression and stress measures after the exercise condition, whilst controls did not. The research concludes that CBM holds promise for the management of mood disorders and exercise is an effective accompaniment to psychotherapy