Non-exponential kinetics of unfolding under a constant force

We examine the population dynamics of naturally folded globular polymers, with a super-hydrophobic "core" inserted at a prescribed point in the polymer chain, unfolding under an application of external force, as in AFM force-clamp spectroscopy. This acts as a crude model for a large class of folded biomolecules with hydrophobic or hydrogen-bonded cores. We find that the introduction of super-hydrophobic units leads to a stochastic variation in the unfolding rate, even when the positions of the added monomers are fixed. This leads to the average non-exponential population dynamics, which is consistent with a variety of experimental data and does not require any intrinsic quenched disorder that was traditionally thought to be at the origin of non-exponential relaxation laws.This work is supported by the EPSRC through a studentship award and the Critical Mass Grant for Cambridge Theoretical Condensed Matter EP/J017639

Kinetics of Tethered Ligands Binding to a Surface Receptor

The rate of binding of a grafted polymer to the surface is controlled by entropic barriers. Using a mean field approximation of ideal polymer dynamics, we fi rst calculate the characteristic binding time for a tethered ligand reaching for a binding site located on the tethering surface. This time is determined by two separate entropic effects: a barrier for the chain to be stretched sufficiently to reach the distant target, and a restriction on chain conformations near the surface, versus the increase in available phase space for longer chains. The competition between these two constraints determines the optimal (shortest) binding time. The theory is then extended to model bridging between two surfaces, in particular relevant for cell adhesion. Here the tethered ligand reaches for a receptor on a parallel surface, and the binding time depends on the gap between the two constraining surfaces. Again, an optimal binding time is determined for the given tether geometry. The results look similar to those for free particles in the `narrow escape problem', but modi fied by an entropic activation factor introduced by the tether

Shape instability on swelling of a stretched nematic elastomer filament.

Liquid crystalline elastomers combine the ordering properties of liquid crystals with elasticity of crosslinked polymer networks. In monodomain (permanently aligned) elastomers, altering the orientational (nematic) order causes changes in the equilibrium sample length, which is the basis of the famous effect of large-amplitude reversible mechanical actuation. The stimulus for this effect could be a change in temperature, or illumination by light in photosensitized elastomers, but equally the nematic order changes by mixing with a solvent. This work theoretically investigates a competition between the spontaneous contraction on swelling of a monodomain nematic elastomer and the externally imposed stretching. We find that this competition leads to bistability in the system and allows a two-phase separation between a nematic state with lower swelling and an isotropic state with higher solvent concentration. We calculated the conditions in which the instability occurs as well as the mechanical and geometric parameters of equilibrium states. Being able to predict how this instability arises will provide opportunities for exploiting nematic elastomer filaments.This work has been carried out as part of the Cavendish Masters programme in Physics, and supported by the EPSRC Critical Mass grant for Theoretical Condensed Matter.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevE.92.04250

Rheology of hard glassy materials.

Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural (α) relaxation rate and the shear-induced relaxation rate. A different model is formulated here which, instead, assumes that the slowest (global) relaxation process controls the overall relaxation. We show that the first model is not compatible with the existence of finite elastic shear modulus for quasistatic (low-frequency) deformation, while the second model is able to describe all key features of deformation of 'hard' glassy solids, including the yielding transition, the nonaffine-to-affine plateau crossover, and the rate-stiffening of the modulus. The proposed framework provides an operational way to distinguish between 'soft' glasses and 'hard' glasses based on the shear-rate dependence of the structural relaxation time.US Army ARO Cooperative Agreement W911NF-19-2-0055 EPSRC Theory of Condensed Matter Critical Mass Grant EP/J01763

Microtubule buckling in an elastic matrix with quenched disorder

The intracellular elastic matrix has been recognized as an important factor to stabilize microtubules and increase their critical buckling force in vivo. This phenomenon was qualitatively explained by the Winkler model, which investigated buckling of a filament embedded in a homogeneous elastic medium. However, the assumption of homogeneity of the matrix in Winkler's, and other advanced models, is unrealistic inside cells, where the local environment is highly variable along the filament. Considering this to be a quenched-disorder system, we use a Poisson distribution for confinements, and apply the replica technique combined with the Gaussian variational method to address the buckling of a long filament. The results show two types of filament buckling: one corresponding to the first-order, and the other to a continuous second-order phase transition. The critical point, i.e. the switch from first- to second-order buckling transition, is induced by the increase in disorder strength. We also discover that this random disorder of the elastic environment destabilizes the filament by decreasing $P_c$ from the Winkler result, and the matrix with stronger mean elasticity has a stronger role of disorder (inhomogeneity). For microtubules in vivo, buckling follows the discontinuous first-order transition, with the threshold reduced to the fraction between 0.9 and 0.75 of the Winkler prediction for the homogeneous elastic matrix. We also show that disorder can affect the force-displacement relationship at non-zero temperature, while at zero temperature this effect vanishes.This work has been supported by the Theory of Condensed Matter Critical Mass Grant from EPSRC (EP/J017639)

Mechanisms and rates of nucleation of amyloid fibrils

The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the `critical nucleaus size', n$_{c}$. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle), and then undergo conversion into the conformation rich in β-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nucleation kinetics, using a specific case of Aβ$_{1-42}$ amyloidogenic peptide for illustration, to find theoretical expressions for the effective rate of amyloid nucleation. We find that at low monomer concentration in solution, and also at low interaction energy between two peptide conformations in the micelle, the nucleation occurs via the classical route. At higher monomer concentration, and a range of other interaction parameters between peptides, the two-step `aggregation-conversion' mechanism of nucleation takes over. In this regime, the effective rate of the process can be interpreted as a power of monomer concentration in a certain range of parameters, however, the exponent is determined by a complicated interplay of interaction parameters and is not related to the minimum size of the growing nucleus (which we find to be $\sim$ 7-8 for Aβ$_{1-42}$).This work has been supported by the Theory of Condensed Matter Critical Mass Grant from EPSRC (EP/J017639)

F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft.

F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which compete for control of their shared γ -shaft. We present a self-consistent physical model of F1 motor as a simplified two-state Brownian ratchet using the asymmetry of torsional elastic energy of the coiled-coil γ -shaft. This stochastic model unifies the physical concepts of linear and rotary motors, and explains the stepped unidirectional rotary motion. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the 'no-load' angular velocity is ca. 400 rad/s anticlockwise at 4 mM ATP. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of 'stall torque'. We discuss the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the 'useful outcome' is measured in the number of H(+) pushed against the chemical gradient.The authors have benefited from extensive discussions with J. R. Blundell, C. Prior, and G. Fraser, as well as the conceptual input from J. E. Walker (who has originally suggested that the torsional energy of the γ–shaft might be asymmetric). This work has been funded by the {100 + 100 + 100} program by the Ukrainian Government, and the EPSRC Critical Mass Grant for Cambridge Theoretical Condensed Matter EP/J017639

Heliotracking Device using Liquid Crystalline Elastomer Actuators

Many living organisms in nature respond to light stimulus and track the light source. Inspired by this, and to maximize the light-harvesting ability of solar cells, here, a spontaneous helio-tracking device based on the differential light-induced actuation of liquid crystalline elastomers (LCEs) is demonstrated. The synthesis of the actuator material involves a robust thiol “click” polymerization, while the addition of indocyanine green (ICG) dye imparts the sensitivity to broad-spectrum and near-infrared light. Highly reproducible thermal and photo-induced linear actuation is demonstrated. The device is based on a freely pivoting payload platform held in place by several linear LCE actuators around the 360° circumference. The side of the device, which is exposed to light, has the actuators contracting and tilting the platform toward the light source. As the light source (e.g., the Sun) is moving around the device, the platform tilt followed, always exposing the payload face to the light; in the dark, the device recovers its neutral position

Elasticity and Relaxation in Full and Partial Vitrimer Networks

We develop a continuum model of dynamic-mechanical response of vitrimers, where the elastic energy of the material accounts for the conserved number of the crosslinks in the network. We also prepare partial vitrimer networks, which consist of variable fractions of transient network based on boronic ester bond-exchange, and of a permanent polymer network. By fitting the theory to our experimental data on stress relaxation, the bond-exchange rate and the fraction of the permanent elastic network are obtained with a linear relationship between the fraction of the transient polymer network and the ratio between the boronic ester and the flexible spacer among the chain-extending thiols. For a 100% vitrimer undergoing a ramp deformation, the stress of the material fi rst increases and then decreases, where the yield time decreases with the increasing strain rate. A partial vitrimer can behave as a pure elastic material without yielding at low strain rates or show a non-monotonic `S-shaped' stress-strain relationship at high strain rates.This work was supported by the European Research Council grant No: 786659. F. M. acknowledges Humboldt Foundation for the support

Transesterification in Epoxy-Thiol Exchangeable Liquid Crystalline Elastomers

The incorporation of vitrimer bond-exchange chemistry into liquid crystalline elastomer networks produces ‘exchangeable liquid crystal elastomers’ (xLCE). These materials offer a facile method of material re-shaping and alignment post-polymerisation via the application of a mechanical stress above the temperature of activation of bond exchange. We use di-epoxy mesogenic monomers with thiol-terminated spacers and crosslinker to investigate a range of resulting xLCE. The “click” chemistry of thiols results in good control over the network topology, and low glass transition in this family of materi-als. By combining different spacers, we were able to obtain smectic and nematic phases, and adjust the liquid crystal to iso-tropic phase transition between 42 and 140 °C, while the elastic-plastic transition temperature was maintained close to 200 °C. The broad gap between these temperatures ensures that thermally actuating uniformly aligned elastomers are stable and show no residual plastic creep, making epoxy-thiol xLCE promising for a range of engineering applications.ERC H202