Neuromorphic Engineering in Wetware: Discriminating Acoustic Frequencies through Their Effects on Chemical Waves.

Some features of the human nervous system can be mimicked not only through software or hardware but also through liquid solutions of chemical systems maintained under out-of-equilibrium conditions. We describe the possibility of exploiting a thin layer of the Belousov-Zhabotinsky (BZ) reaction as a surrogate for the cochlea for sensing acoustic frequencies. Experiments and simulations demonstrate that, as in the human ear where the cochlea transduces the mechanical energy of the acoustic frequencies into the electrochemical energy of neural action potentials and the basilar membrane originates topographic representations of sounds, our bioinspired chemoacoustic system, based on the BZ reaction, gives rise to spatiotemporal patterns as the representation of distinct acoustic bands through transduction of mechanical energy into chemical energy. Acoustic frequencies in the range 10-2000 Hz are partitioned into seven distinct bands based on three attributes of the emerging spatiotemporal patterns: (1) the types and frequencies of the chemical waves, (2) their velocities, and (3) the Faraday waves' wavelengths.

Role of Fast and Slow Inhibitors in Oscillatory Rhythm Design.

In biological or abiotic systems, rhythms occur, owing to the coupling between positive and negative feedback loops in a reaction network. Using the Semenov-Whitesides oscillatory network for thioester hydrolysis as a prototype, we experimentally and theoretically analyzed the role of fast and slow inhibitors in oscillatory reaction networks. In the presence of positive feedback, a single fast inhibitor generates a time delay, resulting in two saddle-node bifurcations and bistability in a continuously stirred tank reactor. A slow inhibitor produces a node-focus bifurcation, resulting in damped oscillations. With both fast and slow inhibitors present, the node-focus bifurcation repeatedly modulates the saddle-node bifurcations, producing stable periodic oscillations. These fast and slow inhibitions result in a pair of time delays between steeply ascending and descending dynamics, which originate from the positive and negative feedbacks, respectively. This pattern can be identified in many chemical relaxation oscillators and oscillatory models, e.g., the bromate-sulfite pH oscillatory system, the Belousov-Zhabotinsky reaction, the trypsin oscillatory system, and the Boissonade-De Kepper model. This study provides a novel understanding of chemical and biochemical rhythms and suggests an approach to designing such behavior.

Transitions of Collective Motions Driven by Phase Resetting.

The front cover artwork is provided by Prof. Gao's group. The image shows the motion patterns transition of the active gel group under the step light intensity, which describes the mechanism of a new collective emergence structure. Read the full text of the Research Article at 10.1002/cphc.202300054.

Transitions of Collective Motions Driven by Phase Resetting.

Abrupt (i. e. step) environmental changes, such as natural disasters or the intervention of predators, can alter the internal dynamics of groups with active units, leading to the rapid destruction and/or restructuring of the group, with the emergence of new collective structures that endow the system with adaptability. Few studies, to date, have considered the influence of abrupt environmental changes on emergent behavior. Here, we use a model of active matter, the Belousov-Zhabotinsky (BZ) self-oscillating gel, to study the mechanism of formation and transition between modes of collective locomotion caused by changes of illumination intensity in arrays of interacting photosensitive active units. New forms of collective motion can be generated by step changes of illumination intensity. These transformations arise from the phase resetting and wave-signal regeneration induced by the abrupt parameter variation, while gradual change results in different evolution of collective motion. Our results not only suggest a novel mechanism for emergence, but also imply that new collective behaviors could be accessible via discontinuous parameter changes.

Symmetry-breaking rhythms in coupled, identical fast-slow oscillators.

Symmetry-breaking in coupled, identical, fast-slow systems produces a rich, dramatic variety of dynamical behavior-such as amplitudes and frequencies differing by an order of magnitude or more and qualitatively different rhythms between oscillators, corresponding to different functional states. We present a novel method for analyzing these systems. It identifies the key geometric structures responsible for this new symmetry-breaking, and it shows that many different types of symmetry-breaking rhythms arise robustly. We find symmetry-breaking rhythms in which one oscillator exhibits small-amplitude oscillations, while the other exhibits phase-shifted small-amplitude oscillations, large-amplitude oscillations, mixed-mode oscillations, or even undergoes an explosion of limit cycle canards. Two prototypical fast-slow systems illustrate the method: the van der Pol equation that describes electrical circuits and the Lengyel-Epstein model of chemical oscillators.

Effect of obstructions on growing Turing patterns.

We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel-Epstein reaction-diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain, such as walls and slits, and local obstructions, such as small blocks. The pattern formation is significantly affected by the obstructions, leading to novel pattern morphologies. We show that obstructions can induce growth mode switching and disrupt local pattern formation and that these effects depend on the shape and placement of the objects as well as the domain growth rate. This work provides a customizable framework to perform numerical simulations on different types of obstructions and other heterogeneous domains, which may guide future numerical and experimental studies. These results may also provide new insights into biological pattern growth and formation, especially in non-idealized domains containing noise or discontinuities.

Peptide-Modulated pH Rhythms.

Many drugs adjust and/or control the spatiotemporal dynamics of periodic processes such as heartbeat, neuronal signaling and metabolism, often by interacting with proteins or oligopeptides. Here we use a quasi-biocompatible, non-equilibrium pH oscillatory system as a biomimetic biological clock to study the effect of pH-responsive peptides on rhythm dynamics. The added peptides generate feedback that can lengthen or shorten the oscillatory period during which the peptides alternate between random coil and coiled-coil conformations. This modulation of a chemical clock supports the notion that short peptide reagents may have utility as drugs to regulate human body clocks.

Nanogel Crosslinking-Based Belousov-Zhabotinsky Self-Oscillating Polyacrylamide Gel with Improved Mechanical Properties and Fast Oscillatory Response.

The Belousov-Zhabotinsky (BZ) self-oscillating gel is a unique actuator suited for studying the behavior of intelligent soft robots. However, the traditional BZ self-oscillating polyacrylamide (PAAm) gel is easily broken and is slow to response to stimuli, which limits its practical application. Therefore, the preparation of BZ gels with sensitive responses to external stimuli and desirable, robust mechanical properties remains a challenge. In this work, PAAm-activated nanogels with unpolymerized double bonds are used as nanocrosslinkers to synthesize a nanogel crosslinking-based BZ (NCBZ) self-oscillating PAAm gel, whose mechanical properties, for example, antipuncture, cutting, and tensile properties, are superior to those of traditional PAAm BZ-self-oscillating gels. The oscillatory period of the traditional gel is much longer than that of the corresponding homogeneous BZ system, resulting from the slow response of the gel to changes in redox potential, whereas large, interconnected pores inside the NCBZ gel provide efficient channels for rapid species transport, supporting fast response of the gel, which results in almost the same period of chemomechanical oscillations as the homogeneous system under the same conditions. Scanning electron microscopy results show that the NCBZ gel is more stable than the traditional BZ PAAm gel after 7 h of oscillation. Our results make it possible to prepare robust gel motors and provide promising application prospects for smart soft robots, actuators, sensors, tissue engineering, and other applications.

Mesoscopic Pitting Oscillation-Induced Periodic Anodic Layer Electrodissolution of Au(111).

The electrodissolution of Au(111) in anaerobic cupric/ammonia/thiosulfate solutions, typical of a non-equilibrium dissipative system, was investigated via in situ electrochemical atomic force microscopy. At a specific initial concentration ratio of aqueous ammonia to cupric ions, the pit number and average pit area increase autocatalytically, while the pit depth increases monotonically during dissolution. A further increase in this initial concentration ratio leads to oscillatory dynamics in the pit number and average pit area while the pit depth fluctuates between one and two atoms. Mechanistic analysis indicates that alternation between formation and dissolution of a sulfur film results in periodic pitting, which produces gold dissolution layer by layer. This work presents a new dissolution mode, i.e., periodic layer dissolution generated by oscillatory pitting processes in addition to a pitting mode with a continually increasing depth, and the use of high initial concentration ratios of ammonia to cupric ion to accelerate the elimination of passivating sulfur film for Au dissolution.

Rotational Locomotion of an Active Gel Driven by Internal Chemical Signals.

Chemical waves arising from coupled reaction and transport can serve as biomimetic "nerve signals" to study the underlying origin and regulation of active locomotion. During wave propagation in more than one spatial dimension, the propagation direction of spiral and pulse waves in a nanogel-based PAAm self-oscillating gel, i.e., the orientation of the driving force, may deviate from the normal direction to the wave fronts. Alternating forward and backward retrograde wave locomotion along the normal and tangential kinematic vectors with a phase difference leads to a curved path, i.e., rotational locomotion. This work indicates that appendages in an organism are not required for this type of locomotion. This locomotion mechanism reveals a general principle underlying the dynamical origin of biological helical locomotion and also suggests design approaches for complex locomotion of soft robots and smart materials.

Period-doubling route to mixed-mode chaos.

Mixed-mode oscillations (MMOs) are a complex dynamical behavior in which each cycle of oscillation consists of one or more large amplitude spikes followed by one or more small amplitude peaks. MMOs typically undergo period-adding bifurcations under parameter variation. We demonstrate here, in a set of three identical, linearly coupled van der Pol oscillators, a scenario in which MMOs exhibit a period-doubling sequence to chaos that preserves the MMO structure, as well as period-adding bifurcations. We characterize the chaotic nature of the MMOs and attribute their existence to a master-slave-like forcing of the inner oscillator by the outer two with a sufficient phase difference between them. Simulations of a single nonautonomous oscillator forced by two sine functions support this interpretation and suggest that the MMO period-doubling scenario may be more general.

Influence of survival, promotion, and growth on pattern formation in zebrafish skin.

The coloring of zebrafish skin is often used as a model system to study biological pattern formation. However, the small number and lack of movement of chromatophores defies traditional Turing-type pattern generating mechanisms. Recent models invoke discrete short-range competition and long-range promotion between different pigment cells as an alternative to a reaction-diffusion scheme. In this work, we propose a lattice-based "Survival model," which is inspired by recent experimental findings on the nature of long-range chromatophore interactions. The Survival model produces stationary patterns with diffuse stripes and undergoes a Turing instability. We also examine the effect that domain growth, ubiquitous in biological systems, has on the patterns in both the Survival model and an earlier "Promotion" model. In both cases, domain growth alone is capable of orienting Turing patterns above a threshold wavelength and can reorient the stripes in ablated cells, though the wavelength for which the patterns orient is much larger for the Survival model. While the Survival model is a simplified representation of the multifaceted interactions between pigment cells, it reveals complex organizational behavior and may help to guide future studies.

Chemomechanical origin of directed locomotion driven by internal chemical signals.

Asymmetry in the interaction between an individual and its environment is generally considered essential for the directional properties of active matter, but can directional locomotions and their transitions be generated only from intrinsic chemical dynamics and its modulation? Here, we examine this question by simulating the locomotion of a bioinspired active gel in a homogeneous environment. We find that autonomous directional locomotion emerges in the absence of asymmetric interaction with the environment and that a transition between modes of gel locomotion can be induced by adjusting the spatially uniform intensity of illumination or certain kinetic and mechanical system parameters. The internal wave dynamics and its structural modulation act as the impetus for signal-driven active locomotion in a manner similar to the way in which an animal's locomotion is generated via driving by nerve pulses. Our results may have implications for the development of soft robots and biomimetic materials.

Post-canard symmetry breaking and other exotic dynamic behaviors in identical coupled chemical oscillators.

We analyze a model of two identical chemical oscillators coupled through diffusion of the slow variable. As a parameter is varied, a single oscillator undergoes a canard explosion-a transition from small amplitude, nearly harmonic oscillations to large-amplitude, relaxation oscillations over a very small parameter interval. In the coupled system, if the two oscillators have the same initial conditions, then the oscillators remain synchronized and exhibit the same canard behavior observed for the single oscillator. If the oscillators are separated initially, then in the region of the canard they display a variety of complex behaviors, including intermittent spiking, mixed-mode oscillation, and quasiperiodicity. Further variation of the parameter leads to a return to synchronized large-amplitude oscillation followed by a post-canard symmetry-breaking, in which one oscillator shows small-amplitude, complex behavior (mixed-mode oscillation, quasiperiodicity, chaos,...) while the other undergoes essentially periodic large amplitude behavior, resembling a master-slave scenario. We analyze the origins of this behavior by looking at several modified coupling schemes.

Capillarity-Induced Propagation Reversal of Chemical Waves in a Self-oscillating Gel.

In a self-oscillating gel, unidirectional chemical waves generated by the Belousov-Zhabotinsky reaction can drive locomotion, which results from the difference between the push and pull forces in the wavefront and waveback, respectively. In a narrow tube, such a gel is subject not only to the asymmetric force engendered by the propagation of the chemical waves but also to additional forces originating from the capillary effect in the polymer skeleton. The ends of a self-oscillating gel in a tube are squeezed unequally during unidirectional motion, causing new waves of higher frequency and ultimately giving rise to reversal of the direction of chemical wave propagation. This peculiar phenomenon of a self-oscillating gel in a narrow glass tube results in a nonmonotonic evolution of the gel locomotion velocity.

Programmed Locomotion of an Active Gel Driven by Spiral Waves.

Active media that host spiral waves can display complex modes of locomotion driven by the dynamics of those waves. We use a model of a photosensitive stimulus-responsive gel that supports the propagation of spiral chemical waves to study locomotive transition and programmed locomotion. The mode transition between circular and toroidal locomotion results from the onset of spiral tip meandering that arises via a secondary Hopf bifurcation as the level of illumination is increased. This dynamic instability of the system introduces a second circular locomotion with a small diameter caused by tip meandering. The original circular locomotion with large diameter is driven by the push-pull asymmetry of the wavefront and waveback of the simple spiral waves initiated at one corner of gel. By harnessing this mode transition of the gel locomotion via coded illumination, we design programmable pathways of nature-inspired angular locomotion of the gel.

Effect of Reaction Parameters on the Wavelength of Pulse Waves in the Belousov-Zhabotinsky Reaction-Diffusion System.

The wavelength of Belousov-Zhabotinsky (BZ) traveling waves is the key factor that limits the scale of BZ self-oscillating gel motors. To achieve control of the wavelength, it is necessary to evaluate the wavelength dependence on species concentrations and temperature. In this work, the effect of reaction parameters on the wavelength of BZ pulse waves was studied. The most effective way to reduce the wavelength of pulse waves is to increase the concentration of organic species and/or the temperature. Decreasing the concentration of bromate, hydrogen ion, or metal catalyst also reduces the wavelength of pulse waves. This work provides a convenient and direct method to produce sub-millimeter BZ waves, which could be applied to designing BZ wave-driven small-scale gel motors as well as providing insight into other emergent behaviors of self-oscillating gels.

Phase-frequency model of strongly pulse-coupled Belousov-Zhabotinsky oscillators.

We demonstrate that the dynamical behavior of strongly pulse-coupled Belousov-Zhabotinsky oscillators can be reproduced and predicted using a model that treats both the phase and the instantaneous frequency of the oscillators. Model parameters are extracted from the experimental data obtained using a single pulse-perturbed oscillator and are used to simulate the temporal dynamics of a system of two coupled oscillators. Our model exhibits the out-of-phase and anti-phase synchronization and the 1:N and N:M temporal patterns as well as the oscillator suppression that are observed in experiments when the inhibitory coupling is asymmetric. This approach may be adapted to other systems, such as coupled neurons, where the oscillatory dynamics is affected by strong pulses.

Turing patterns on radially growing domains: experiments and simulations.

We study Turing pattern formation in a system undergoing radial growth in two dimensions. The photosensitive chlorine dioxide-iodine-malonic acid reaction is illuminated to inhibit patterning, with a growing non-illuminated circular domain in which the pattern develops. We examine the relationship between the linear radial growth rate and the resulting pattern morphology. Faster growth causes the pattern to form parallel to the growing boundary as concentric rings, while slower growth leads to pattern formation perpendicular to the growing boundary. We observe three distinct growth modes for the Turing patterns, which also depend on the radial growth rate. The experimental results are qualitatively reproduced in numerical simulations using the Lengyel-Epstein model with an additional term to account for the photosensitivity of the reaction. These results may provide new insight into how patterns form in growing biological systems.