Transient shape morphing of active gel plates: geometry and physics.

The control of shape in active structures is a key problem for the realization of smart sensors and actuators, which often draw inspiration from natural systems. In this context, slender structures, such as thin plates, have been studied as a relevant example of shape morphing systems where curvature is generated by in-plane incompatibilities. In particular, in hydrogel plates these incompatibilities can be programmed at fabrication time, such that a target configuration is attained at equilibrium upon swelling or shrinking. While these aspects have been examined in detail, understanding the transient morphing of such active structures deserves further investigation. In this study, we develop a geometrical model for the transient shaping of thin hydrogel plates by extending the theory of non-Euclidean plates. We validate the proposed model using experiments on gel samples that are programmed to reach axisymmetric equilibrium shapes. Interestingly, our experiments show the emergence of non-axisymmetric shapes for early times, as a consequence of boundary layer effects induced by solvent transport. We rationalize these observations using numerical simulations based on a detailed poroelastic model. Overall, this work highlights the limitations of purely geometrical models and the importance of transient, reduced theories for morphing plates that account for the coupled physics driving the evolution of shape. Computational approaches employing these theories will allow to achieve accurate control on the morphing dynamics and ultimately advance 4D printing technologies.

Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes.

The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.

Entropic Forces Drive Cellular Contact Guidance.

Contact guidance-the widely known phenomenon of cell alignment induced by anisotropic environmental features-is an essential step in the organization of adherent cells, but the mechanisms by which cells achieve this orientational ordering remain unclear. Here, we seeded myofibroblasts on substrates micropatterned with stripes of fibronectin and observed that contact guidance emerges at stripe widths much greater than the cell size. To understand the origins of this surprising observation, we combined morphometric analysis of cells and their subcellular components with a, to our knowledge, novel statistical framework for modeling nonthermal fluctuations of living cells. This modeling framework is shown to predict not only the trends but also the statistical variability of a wide range of biological observables, including cell (and nucleus) shapes, sizes, and orientations, as well as stress-fiber arrangements within the cells with remarkable fidelity with a single set of cell parameters. By comparing observations and theory, we identified two regimes of contact guidance: 1) guidance on stripe widths smaller than the cell size (w ≤ 160 µm), which is accompanied by biochemical changes within the cells, including increasing stress-fiber polarization and cell elongation; and 2) entropic guidance on larger stripe widths, which is governed by fluctuations in the cell morphology. Overall, our findings suggest an entropy-mediated mechanism for contact guidance associated with the tendency of cells to maximize their morphological entropy through shape fluctuations.

Nanoscale Topography and Poroelastic Properties of Model Tissue Breast Gland Basement Membranes.

Basement membranes (BMs) are thin layers of condensed extracellular matrix proteins serving as permeability filters, cellular anchoring sites, and barriers against cancer cell invasion. It is believed that their biomechanical properties play a crucial role in determining cellular behavior and response, especially in mechanically active tissues like breast glands. Despite this, so far, relatively little attention has been dedicated to their analysis because of the difficulty of isolating and handling such thin layers of material. Here, we isolated BMs derived from MCF10A spheroids-three-dimensional breast gland model systems mimicking in vitro the most relevant phenotypic characteristics of human breast lobules-and characterized them by atomic force microscopy, enhanced resolution confocal microscopy, and scanning electron microscopy. By performing atomic force microscopy height-clamp experiments, we obtained force-relaxation curves that offered the first biomechanical data on isolated breast gland BMs to our knowledge. Based on enhanced resolution confocal microscopy and scanning electron microscopy imaging data, we modeled the system as a polymer network immersed in liquid and described it as a poroelastic material. Finite-element simulations matching the experimental force-relaxation curves allowed for the first quantification, to our knowledge, of the bulk and shear moduli of the membrane as well as its water permeability. These results represent a first step toward a deeper understanding of the mechanism of tensional homeostasis regulating mammary gland activity as well as its disruption during processes of membrane breaching and metastatic invasion.

Coupled swelling and nematic reordering in liquid crystal gels.

We derive a multiphysics model that accounts for network elasticity with spontaneous strains, swelling and nematic interactions in liquid crystal gels (LCGs). We discuss the coupling among the various physical mechanisms, with particular reference to the effects of nematic interactions on chemical equilibrium and that of swelling on the nematic-isotropic transition. Building upon this discussion and using numerical simulations, we explore the transient phenomena involving concurrent swelling and phase transition in LCGs subject to a temperature change. Specifically, we demonstrate separation in time scales between solvent uptake and phase change, in agreement with experiments, which determines a kinetic decoupling between shape and volume changes. Finally, we discuss possible applications in the context of microswimmers, where such a kinetic decoupling is exploited to achieve non-reciprocal actuation and net motion in Stokes flow.

Motion planning and motility maps for flagellar microswimmers.

We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

Hydraulic Fracture and Toughening of a Brittle Layer Bonded to a Hydrogel.

Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.

Three-sphere low-Reynolds-number swimmer with a passive elastic arm.

One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.

Reverse engineering the euglenoid movement.

Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.

Spontaneous division and motility in active nematic droplets.

We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.

Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions.

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We put forward the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle reproduces the stochastic nature of lamellipodia protrusion (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is a well-known signature of self-organized criticality and is confirmed by unique optical tweezer measurements performed in vivo on neuronal growth cones.

Photochemically Induced Propulsion of a 4D Printed Liquid Crystal Elastomer Biomimetic Swimmer.

Underwater organisms exhibit sophisticated propulsion mechanisms, enabling them to navigate fluid environments with exceptional dexterity. Recently, substantial efforts have focused on integrating these movements into soft robots using smart shape-changing materials, particularly by using light for their propulsion and control. Nonetheless, challenges persist, including slow response times and the need of powerful light beams to actuate the robot. This last can result in unintended sample heating and potentially necessitate tracking specific actuation spots on the swimmer. To tackle these challenges, new azobenzene-containing photopolymerizable inks are introduced, which can be processed by extrusion printing into liquid crystalline elastomer (LCE) elements of precise shape and morphology. These LCEs exhibit rapid and significant photomechanical response underwater, driven by moderate-intensity ultraviolet (UV) and green light, being the actuation mechanism predominantly photochemical. Inspired by nature, a biomimetic four-lapped ephyra-like LCE swimmer is printed. The periodically illumination of the entire swimmer with moderate-intensity UV and green light, induces synchronous lappet bending toward the light source and swimmer propulsion away from the light. The platform eliminates the need of localized laser beams and tracking systems to monitor the swimmer's motion through the fluid, making it a versatile tool for creating light-fueled robotic LCE free-swimmers.

Contact guidance as a consequence of coupled morphological evolution and motility of adherent cells.

Adherent cells seeded on substrates spread and evolve their morphology while simultaneously displaying motility. Phenomena such as contact guidance, viz. the alignment of cells on patterned substrates, are strongly linked to the coupling of morphological evolution with motility. Here, we employ a recently developed statistical thermodynamics framework for modelling the non-thermal fluctuating response of cells to probe this coupling. This thermodynamic framework is first extended via a Langevin style model to predict temporal responses of cells to unpatterned and patterned substrates. The Langevin model is then shown to not only predict the different experimentally observed temporal scales for morphological observables such as cell area and elongation but also the interplay of morphology with motility that ultimately leads to contact guidance.

A finite element model of the mechanical interactions between peripheral nerves and intrafascicular implants.

Objective.Intrafascicular peripheral nerve implants are key components in the development of bidirectional neuroprostheses such as touch-enabled bionic limbs for amputees. However, the durability of such interfaces is hindered by the immune response following the implantation. Among the causes linked to such reaction, the mechanical mismatch between host nerve and implant is thought to play a decisive role, especially in chronic settings.Approach.Here we focus on modeling mechanical stresses induced on the peripheral nerve by the implant's micromotion using finite element analysis. Through multiple parametric sweeps, we analyze the role of the implant's material, geometry (aspect-ratio and shape), and surface coating, deriving a set of parameters for the design of better-integrated implants.Main results.Our results indicate that peripheral nerve implants should be designed and manufactured with smooth edges, using materials at most three orders of magnitude stiffer than the nerve, and with innovative geometries to redistribute micromotion-associated loads to less delicate parts of the nerve such as the epineurium.Significance.Overall, our model is a useful tool for the peripheral nerve implant designer that is mindful of the importance of implant mechanics for long term applications.

Euglena International Network (EIN): Driving euglenoid biotechnology for the benefit of a challenged world.

Euglenoids (Euglenida) are unicellular flagellates possessing exceptionally wide geographical and ecological distribution. Euglenoids combine a biotechnological potential with a unique position in the eukaryotic tree of life. In large part these microbes owe this success to diverse genetics including secondary endosymbiosis and likely additional sources of genes. Multiple euglenoid species have translational applications and show great promise in production of biofuels, nutraceuticals, bioremediation, cancer treatments and more exotically as robotics design simulators. An absence of reference genomes currently limits these applications, including development of efficient tools for identification of critical factors in regulation, growth or optimization of metabolic pathways. The Euglena International Network (EIN) seeks to provide a forum to overcome these challenges. EIN has agreed specific goals, mobilized scientists, established a clear roadmap (Grand Challenges), connected academic and industry stakeholders and is currently formulating policy and partnership principles to propel these efforts in a coordinated and efficient manner.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis.

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

How Euglena gracilis swims: Flow field reconstruction and analysis.

Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.

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.

Shape Programming by Modulating Actuation over Hierarchical Length Scales.

Many active materials used in shape-morphing respond to an external stimulus by stretching or contracting along a director field. The programming of such actuators remains complex because of the single degree of freedom (the orientation) in local actuation. Here, texturing this field in zigzag patterns is shown to provide an extended family of biaxial active stretches out of an otherwise single uniaxial active deformation, opening a larger parameter space. By further modulating the zigzag patterns at the larger scale of the structure, its deployed shape can be controlled. This notion of texturing over hierarchical length scales follows geometrical principles, and is robust against changes in size and materials. The robustness of the approach is demonstrated by considering three different responsive materials: inextensible flat fabrics, channel-bearing elastomer (respectively, contracting and expanding perpendicularly to the director field when actuated pneumatically), and 3D-printed thermoplastic (composed of extruded filaments that contract when heated). It is shown that large-scale shape-morphing structures can be generated and that their geometry can be controlled with high accuracy.

Blueprinting Photothermal Shape-Morphing of Liquid Crystal Elastomers.

Liquid crystal elastomers (LCEs) are an attractive platform for dynamic shape-morphing due to their ability to rapidly undergo large deformations. While recent work has focused on patterning the director orientation field to achieve desired target shapes, this strategy cannot be generalized to material systems where high-resolution surface alignment is impractical. Instead of programming the local orientation of anisotropic deformation, an alternative strategy for prescribed shape-morphing by programming the magnitude of stretch ratio in a thin LCE sheet with constant director orientation is developed here. By spatially patterning the concentration of gold nanoparticles, uniform illumination leads to gradients in photothermal heat generation and therefore spatially nonuniform deformation profiles that drive out-of-plane buckling of planar films into predictable 3D shapes. Experimentally realized shapes are shown to agree closely with both finite element simulations and geometric predictions for systems with unidirectional variation in deformation magnitude. Finally, the possibility to achieve complex oscillatory motion driven by uniform illumination of a free-standing patterned sheet is demonstrated.