Passive viscoelastic response of striated muscles.

Muscle cells with sarcomeric structure exhibit highly non trivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material', we use a stochastic micromodel, and derive a linear response theory for a half-sarcomere, which can be extended to the whole fibre. Instead of the first order rheological equation, anticipated by Hill on the phenomenological grounds, we obtain a novel second order equation which shows that tension depends not only on its current length and the velocity of stretching, but also on its acceleration. Expressing the model in terms of elementary rheological elements, we show that one contribution to the visco-elastic properties of the fibre originates in cross-bridges, while the other can be linked to inert elements which move in the sarcoplasm. We apply this model to explain the striking qualitative difference between the relaxation in experiments involving perturbation of length vs. those involving perturbation of force, and we use the values of the microscopic parameters for frog muscles to show that the model is in excellent quantitative agreement with physiological experiments.

Rigidity-Controlled Crossover: From Spinodal to Critical Failure.

Failure in disordered solids is accompanied by intermittent fluctuations extending over a broad range of scales. The implied scaling has been previously associated with either spinodal or critical points. We use an analytically transparent mean-field model to show that both analogies are relevant near the brittle-to-ductile transition. Our study indicates that in addition to the strength of quenched disorder, an appropriately chosen global measure of rigidity (connectivity) can be also used to tune the system to criticality. By interpreting rigidity as a timelike variable we reveal an intriguing parallel between earthquake-type critical failure and Burgers turbulence.

Guided active particles.

To account for the possibility of an externally driven taxis in active systems, we develop a model of a guided active drift which relies on the presence of an external guiding field and a vectorial coupling between the mechanical degrees of freedom and a chemical reaction. To characterize the ability of guided active particles to carry cargo, we generalize the notion of Stokes efficiency extending it to the case of stall conditions. To show the generality of the proposed mechanism, we discuss guided electric circuits capable of turning fluctuations into a directed current without a source of voltage.

Nonlinear elasticity of incompatible surface growth.

Surface growth is a crucial component of many natural and artificial processes, from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility, leading to residual stresses and triggering various instabilities. In a recent paper [G. Zurlo and L. Truskinovsky, Phys. Rev. Lett. 119, 048001 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.048001] we presented a linearized elasticity theory of incompatible surface growth, which provides a quantitative link between deposition protocols and postgrowth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. This development reveals the shortcomings of the linearized theory, in particular its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.

Functionality of Disorder in Muscle Mechanics.

A salient feature of skeletal muscles is their ability to take up an applied slack in a microsecond timescale. Behind this fast adaptation is a collective folding in a bundle of elastically interacting bistable elements. Since this interaction has a long-range character, the behavior of the system in force and length controlled ensembles is different; in particular, it can have two distinct order-disorder-type critical points. We show that the account of the disregistry between myosin and actin filaments places the elementary force-producing units of skeletal muscles close to both such critical points. The ensuing "double criticality" contributes to the system's ability to perform robustly and suggests that the disregistry is functional.

SNARE machinery is optimized for ultrafast fusion.

SNARE proteins zipper to form complexes (SNAREpins) that power vesicle fusion with target membranes in a variety of biological processes. A single SNAREpin takes about 1 s to fuse two bilayers, yet a handful can ensure release of neurotransmitters from synaptic vesicles much faster: in a 10th of a millisecond. We propose that, similar to the case of muscle myosins, the ultrafast fusion results from cooperative action of many SNAREpins. The coupling originates from mechanical interactions induced by confining scaffolds. Each SNAREpin is known to have enough energy to overcome the fusion barrier of 25-[Formula: see text]; however, the fusion barrier only becomes relevant when the SNAREpins are nearly completely zippered, and from this state, each SNAREpin can deliver only a small fraction of this energy as mechanical work. Therefore, they have to act cooperatively, and we show that at least three of them are needed to ensure fusion in less than a millisecond. However, to reach the prefusion state collectively, starting from the experimentally observed half-zippered metastable state, the SNAREpins have to mechanically synchronize, which takes more time as the number of SNAREpins increases. Incorporating this somewhat counterintuitive idea in a simple coarse-grained model results in the prediction that there should be an optimum number of SNAREpins for submillisecond fusion: three to six over a wide range of parameters. Interestingly, in situ cryoelectron microscope tomography has very recently shown that exactly six SNAREpins participate in the fusion of each synaptic vesicle. This number is in the range predicted by our theory.

Printing Non-Euclidean Solids.

Geometrically frustrated solids with a non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted configuration of incompatibility through the surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration developing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.

Volume Changes During Active Shape Fluctuations in Cells.

Cells modify their volume in response to changes in osmotic pressure but it is usually assumed that other active shape variations do not involve significant volume fluctuations. Here we report experiments demonstrating that water transport in and out of the cell is needed for the formation of blebs, commonly observed protrusions in the plasma membrane driven by cortex contraction. We develop and simulate a model of fluid-mediated membrane-cortex deformations and show that a permeable membrane is necessary for bleb formation which is otherwise impaired. Taken together, our experimental and theoretical results emphasize the subtle balance between hydrodynamics and elasticity in actively driven cell morphological changes.

Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain.

We present a family of exact solutions describing discrete solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. The family is sufficiently rich to cover the whole spectrum of known behaviors from delocalized quasicontinuum waves moving with near-sonic velocities to highly localized anticontinuum excitations with only one particle moving at a time.

Asymmetry between pushing and pulling for crawling cells.

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.

Minimal integer automaton behind crystal plasticity.

Power law fluctuations and scale-free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova-type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study, and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer-valued automaton revealing inherent discreteness of the plastic flow.

Driving-induced crossover: from classical criticality to self-organized criticality.

We propose a spin model with quenched disorder which exhibits in slow driving two drastically different types of critical nonequilibrium steady states. One of them corresponds to classical criticality requiring fine-tuning of the disorder. The other is a self-organized criticality which is insensitive to disorder. The crossover between the two types of criticality is determined by the mode of driving. As one moves from "soft" to "hard" driving the universality class of the critical point changes from a classical order-disorder to a quenched Edwards-Wilkinson universality class. The model is viewed as prototypical for a broad class of physical phenomena ranging from magnetism to earthquakes.

Training-induced criticality in martensites.

We propose an explanation for the self-organization towards criticality observed in martensites during the cyclic process known as "training." The scale-free behavior originates from the interplay between the reversible phase transformation and the concurrent activity of lattice defects. The basis of the model is a continuous dynamical system on a rugged energy landscape, which in the quasistatic limit reduces to a sandpile automaton. We reproduce all the principal observations in thermally driven martensites, including power-law statistics, hysteresis shakedown, asymmetric signal shapes, and correlated disorder.