Self-Oscillating Membranes: Chemomechanical Sheets Show Autonomous Periodic Shape Transformation

Cycling and spiral-wave modes in an active cyclic Potts model

We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant state cycles via nucleation and growth, while spiral waves are formed at high energy. For large systems, a discontinuous transition occurs from these cyclic homogeneous phases to spiral waves, while the opposite transition is absent. Conversely, these two modes can coexist for small systems. The waves can be reproduced by a continuum theory, and the transition can be understood from the competition between nucleation and growth.

Active Pulsatile Gels: From a Chemical Microreactor to a Polymeric Actuator

We report on a synthesis protocol, experimental characterization, and theoretical modeling of active pulsatile Belousov-Zhabotinsky (BZ) hydrogels. Our two-step synthesis technique allows independent optimization of the geometry, the chemical, and the mechanical properties of BZ gels. We identify the role of the surrounding medium chemistry and gel radius for the occurrence of BZ gel oscillations, quantified by the Damköhler number, which is the ratio of chemical reaction to diffusion rates. Tuning the BZ gel size to maximize its chemomechanical oscillation amplitude, we find that its oscillatory strain amplitude is limited by the time scale of gel swelling relative to the chemical oscillation period. Our experimental findings are in good agreement with a Vanag-Epstein model of BZ chemistry and a Tanaka Fillmore theory of gel swelling dynamics.

Self-assembled active actomyosin gels spontaneously curve and wrinkle similar to biological cells and tissues

Living systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length scales, from cells to tissues and organismal scales. The common driving force for these dynamic shape changes are contractile stresses generated by myosin motors in the cell cytoskeleton, that converts chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different three-dimensional (3D) shapes and what are the shape selection rules that determine their final configurations is still lacking. To obtain insight into the relevant physical mechanisms, we recreate the actomyosin cytoskeleton in vitro, with precisely controlled composition and initial geometry. A set of actomyosin gel discs, intrinsically identical but of variable initial geometry, dynamically self-organize into a family of 3D shapes, such as domes and wrinkled shapes, without the need for specific preprogramming or additional regulation. Shape deformation is driven by the spontaneous emergence of stress gradients driven by myosin and is encoded in the initial disc radius to thickness aspect ratio, which may indicate shaping scalability. Our results suggest that while the dynamical pathways may depend on the detailed interactions between the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, our results emphasize the importance for the emergence of active stress gradients for buckling-driven shape deformations and provide insights on the mechanically induced spontaneous shape transitions in contractile active matter, revealing potential shared mechanisms with living systems across scales.

Shape transitions in a network model of active elastic shells

Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.

Capsule self-oscillating gels showing cell-like nonthermal membrane/shape fluctuations

A primary interest in cell membrane and shape fluctuations is establishing experimental models reflecting only nonthermal active contributions. Here we report a millimeter-scaled capsule self-oscillating gel model mirroring the active contribution effect on cell fluctuations. In the capsule self-oscillating gels, the propagating chemical signals during a Belousov-Zhabotinsky (BZ) reaction induce simultaneous local deformations in the various regions, showing cell-like shape fluctuations. The capsule self-oscillating gels do not fluctuate without the BZ reaction, implying that only the active chemical parameter induces the gel fluctuations. The period and amplitude depend on the gel layer thickness and the concentration of the chemical substrate for the BZ reaction. Our results allow for a solid experimental platform showing actively driven cell-like fluctuations, which can potentially contribute to investigating the active parameter effect on cell fluctuations.

Untangling the mechanics of entanglements in slide-ring gels towards both super-deformability and toughness

Entanglement plays a critical role in determining the dynamic properties of polymer systems, e.g., resulting in slip links and pulley effects for achieving large deformation and high strength. Although it has been studied for decades, the mechanics of entanglements for stiffness-toughness conflict is not well understood. In this study, topological knot theory incorporating an extended tube model is proposed to understand the entanglements in a slide-ring (SR) gel, which slips over a long distance to achieve large deformation and high toughness via the pulley effect. Based on topological knot theory, the sliding behavior and pulley effect of entanglements among molecular chains and cross-linked rings are thoroughly investigated. Based on rubber elasticity theory, a free-energy function is formulated to describe mechanical toughening and slipping of topological knots, while the SR gel retains the same binding energy. Finally, the effectiveness of the proposed model is verified using both finite element analysis and experimental results reported in the literature.

Self-Generated Convective Flows Enhance the Rates of Chemical Reactions

In chemical solutions, the products of catalytic reactions can occupy different volumes compared to the reactants and thus give rise to local density variations in the fluid. These density variations generate solutal buoyancy forces, which are exerted on the fluid and thus "pump" the fluid to flow. Herein, we examine if the reaction-induced pumping accelerates the chemical reaction by transporting the reactants to the catalyst at a rate faster than passive diffusion. Using both simulations and experiments, we show a significant increase in reaction rate when reaction-generated convective flow is present. In effect, through a feedback loop, catalysts speed up reactions not only by lowering the energy barrier but also by increasing the collision frequency between the reactants and the catalyst.

Multivalued Inverse Design: Multiple Surface Geometries from One Flat Sheet

Designing flat sheets that can be made to deform into three-dimensional shapes is an area of intense research with applications in micromachines, soft robotics, and medical implants. Thus far, such sheets were designed to adopt a single target shape. Here, we show that through anisotropic deformation applied inhomogeneously throughout a sheet, it is possible to design a single sheet that can deform into multiple surface geometries upon different actuations. The key to our approach is development of an analytical method for solving this multivalued inverse problem. Such sheets open the door to fabricating machines that can perform complex tasks through cyclic transitions between multiple shapes. As a proof of concept, we design a simple swimmer capable of moving through a fluid at low Reynolds numbers.

Chemically controlled pattern formation in self-oscillating elastic shells

Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.

Microgel that swims to the beat of light

Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.

Mechanochemical induction of wrinkling morphogenesis on elastic shells

Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that cell shape changes are induced by diffusible biomolecules that influence tissue contractility in a concentration-dependent manner - and whose concentration is in turn affected by the macroscopic tissue shape. We perform computational simulations of thin shell elastic dynamics to reveal propagating chemical and three-dimensional deformation patterns arising due to a sequence of buckling instabilities. Depending on the concentration threshold that actuates cell shape change, we find qualitatively different patterns. The mechanochemically coupled patterning dynamics are distinct from those driven by purely mechanical or purely chemical factors, and emerge even without diffusion. Using numerical simulations and theoretical arguments, we analyze the elastic instabilities that result from our model and provide simple scaling laws to identify wrinkling morphologies.

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to "pump" the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid-structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets' initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.