Tube Models for Rubber-Elastic Systems

In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model for the confinement of long paths in polymer networks which is partially due to crosslinking and partially due to entanglements. Our model describes a non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube models. We present results for the macroscopic elastic properties as well as for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres

An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The model equations for the poroelastic medium are obtained from continuum force-balance equations that include the relevant mechanical fields and an incompressibility relation for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stresses. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a chemomechanical feedback. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.Comment: Additional supplemental material is supplie

Shear induced rigidity in athermal materials: a unified statistical framework

Recent studies of athermal systems such as dry grains and dense, non-Brownian suspensions have shown that shear can lead to solidification through the process of shear jamming in grains and discontinuous shear thickening in suspensions. The similarities observed between these two distinct phenomena suggest that the physical processes leading to shear-induced rigidity in athermal materials are universal. We present a non-equilibrium statistical mechanics model, which exhibits the phenomenology of these shear-driven transitions: shear jamming and discontinuous shear thickening in different regions of the predicted phase diagram. Our analysis identifies the crucial physical processes underlying shear-driven rigidity transitions, and clarifies the distinct roles played by shearing forces and the density of grains.Comment: Comments welcom

Collagen microarchitecture mechanically controls myofibroblast differentiation.

Altered microarchitecture of collagen type I is a hallmark of wound healing and cancer that is commonly attributed to myofibroblasts. However, it remains unknown which effect collagen microarchitecture has on myofibroblast differentiation. Here, we combined experimental and computational approaches to investigate the hypothesis that the microarchitecture of fibrillar collagen networks mechanically regulates myofibroblast differentiation of adipose stromal cells (ASCs) independent of bulk stiffness. Collagen gels with controlled fiber thickness and pore size were microfabricated by adjusting the gelation temperature while keeping their concentration constant. Rheological characterization and simulation data indicated that networks with thicker fibers and larger pores exhibited increased strain-stiffening relative to networks with thinner fibers and smaller pores. Accordingly, ASCs cultured in scaffolds with thicker fibers were more contractile, expressed myofibroblast markers, and deposited more extended fibronectin fibers. Consistent with elevated myofibroblast differentiation, ASCs in scaffolds with thicker fibers exhibited a more proangiogenic phenotype that promoted endothelial sprouting in a contractility-dependent manner. Our findings suggest that changes of collagen microarchitecture regulate myofibroblast differentiation and fibrosis independent of collagen quantity and bulk stiffness by locally modulating cellular mechanosignaling. These findings have implications for regenerative medicine and anticancer treatments