Energetics of cytoskeletal gel contraction.

Cytoskeletal gels are prototyped to reproduce the mechanical contraction of the cytoskeleton in vitro. They are composed of a polymer network (backbone), swollen by the presence of a liquid solvent, and active molecules (molecular motors, MMs) that transduce chemical energy into the mechanical work of contraction. These motors attach to the polymer chains to shorten them and/or act as dynamic crosslinks, thereby constraining the thermal fluctuations of the chains. We describe both mechanisms thermodynamically as a microstructural reconfiguration, where the backbone stiffens to motivate solvent (out)flow and accommodate contraction. Via simple steady-state energetic analysis, under the simplest case of isotropic deformation, we quantify the mechanical energy required to achieve contraction as a function of polymer chain density and molecular motor density. We identify two limit regimes, namely, fast MM activation (FM), and slow MM activation (SM). FM assumes that MMs provide all the available mechanical energy 'instantaneously' and leave the polymer in a stiffened state, i.e. the MM activity occurs at a time scale that is much smaller than that of solvent diffusion. SM assumes that the timescale for MM activation is much longer than that of solvent diffusion. To achieve the same final contracted state, FM requires the largest amount of work per unit reference volume, while SM requires the least. For all intermediate cases where the timescale of MM activation is comparable with that of solvent diffusion, the required work ranges between these two limits. We provide all these quantities as a function of chain density and MM density. Finally, we compare our results on contraction energetics with experiments and observe good agreement.

The morphological role of ligand inhibitors in blocking receptor- and clathrin-mediated endocytosis.

Cells often internalize particles through endocytic pathways that involve the binding between cell receptors and particle ligands, which drives the cell membrane to wrap the particle into a delivery vesicle. Previous findings showed that receptor-mediated endocytosis is impossible for spherical particles smaller than a minimum size because of the energy barrier created by membrane bending. In this study, we investigate the morphological role of ligand inhibitors in blocking endocytosis, inspired by antibodies that inhibit virus ligands to prevent infection. While ligand inhibitors have the obvious effect of reducing the driving force due to adhesion, they also have a nontrivial (morphological) impact on the entropic and elastic energy of the system. We determine the necessary conditions for endocytosis by considering the additional energy barrier due to the membrane bending to wrap the inhibiting protrusions. We find that inhibitors increase the minimum radius previously reported, depending on their density and size. In addition, we extend this result to the case of clathrin-mediated endocytosis, which is the most common pathway for virus entry. The assembly of a clathrin coat with a spontaneous curvature increases the energy barrier and sets a maximum particle size (in agreement with experimental observations on spherical particles). Our investigation suggests that morphological considerations can inform the optimal design of neutralizing viral antibodies and new strategies for targeted nanomedicine.

Nutations in Plant Shoots: Endogenous and Exogenous Factors in the Presence of Mechanical Deformations.

We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots.

Peristalsis, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a "phase coordination" principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.