Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics

Multiscale Approach for Tuning Communication among Chemical Oscillators Confined in Biomimetic Microcompartments

ConspectusInspired by the biological world, new cross-border disciplines and technologies have emerged. Relevant examples include systems chemistry, which offers a bottom-up approach toward chemical complexity, and bio/chemical information and communication technology (bio/chemical ICT), which explores the conditions for propagating signals among individual microreactors separated by selectively permeable membranes. To fabricate specific arrays of microreactors, microfluidics has been demonstrated as an excellent method. In particular, droplet-based microfluidics is a powerful tool for encapsulating biological entities and chemical reagents in artificial microenvironments, mostly water-in-oil microdroplets. In these systems, the interfaces are liquid-liquid, and their physicochemical properties are key factors for tuning the coupling between molecular diffusion. Simple and double emulsions, where aqueous domains are in equilibrium with oil domains through boundary layers of amphiphilic molecules, are organized assemblies with high interfacial-area-to-volume ratios. These membranes can be engineered to obtain different surface charges, single- or multilayer stacking, and a variable degree of defects in molecular packing. Emulsions find application in many fields, including the food industry, pharmaceutics, and cosmetics. Furthermore, micro- and nanoemulsions can be used to model the propagation of chemical species through long distances, which is not only vital for cell signaling but also significant in molecular computing. Here we present in-depth research on the faceted world of solutions confined in restricted environments. In particular, we focused on the multiscale aspects of structure and dynamics from molecular to micro and macro levels. The Belousov-Zhabotinsky chemical reaction, known for its robustness and well-documented oscillatory behavior, was selected to represent a generic signal emitter/receiver confined within microenvironments separated by liquid-liquid interfaces. In this pulse generator, the temporal and spatial progressions are governed by periodic fluctuations in the concentration of chemical species, which act as activatory or inhibitory messengers over long distances. When organized into "colonies" or arrays, these micro-oscillators exhibit emergent dynamical behaviors at the population level. These behaviors can be finely tuned by manipulating the geometrical distribution of the oscillators and the properties of the interfaces at the nanoscale. By carefully selecting the membrane composition, it is possible to drive the system toward either in-phase, antiphase, or mixed synchronization regimes among individual oscillators, depending on messenger molecules. This relatively simple lab-scale model replicates some of the communication strategies commonly found in biological systems, particularly those based on the passive diffusion of chemical and electrical signals. It can help shed light on fundamental life processes and inspire new implementations in molecular computing and smart materials.

The excitable nature of polymerizing actin and the Belousov-Zhabotinsky reaction

The intricate regulatory processes behind actin polymerization play a crucial role in cellular biology, including essential mechanisms such as cell migration or cell division. However, the self-organizing principles governing actin polymerization are still poorly understood. In this perspective article, we compare the Belousov-Zhabotinsky (BZ) reaction, a classic and well understood chemical oscillator known for its self-organizing spatiotemporal dynamics, with the excitable dynamics of polymerizing actin. While the BZ reaction originates from the domain of inorganic chemistry, it shares remarkable similarities with actin polymerization, including the characteristic propagating waves, which are influenced by geometry and external fields, and the emergent collective behavior. Starting with a general description of emerging patterns, we elaborate on single droplets or cell-level dynamics, the influence of geometric confinements and conclude with collective interactions. Comparing these two systems sheds light on the universal nature of self-organization principles in both living and inanimate systems.

A microfluidic double emulsion platform for spatiotemporal control of pH and particle synthesis

The temporal control of pH in microreactors such as emulsion droplets plays a vital role in applications including biomineralisation and microparticle synthesis. Typically, pH changes are achieved either by passive diffusion of species into a droplet or by acid/base producing reactions. Here, we exploit an enzyme reaction combined with the properties of a water-oil-water (W/O/W) double emulsion to control the pH-time profile in the droplets. A microfluidic platform was used for production of ∼100-200 μm urease-encapsulated double emulsions with a tuneable mineral oil shell thickness of 10-40 μm. The reaction was initiated on-demand by addition of urea and a pulse in base (ammonia) up to pH 8 was observed in the droplets after a time lag of the order of minutes. The pH-time profile can be manipulated by the diffusion timescale of urea and ammonia through the oil layer, resulting in a steady state pH not observed in bulk reactive solutions. This approach may be used to regulate the formation of pH sensitive materials under mild conditions and, as a proof of concept, the reaction was coupled to calcium phosphate precipitation in the droplets. The oil shell thickness was varied to select for either brushite microplatelets or hydroxyapatite particles, compared to the mixture of different precipitates obtained in bulk.

Hydrodynamics of a confined active Belousov-Zhabotinsky droplet

Self-sustained locomotion of synthetic droplet swimmers has been of great interest due to their ability to mimic the behavior of biological swimmers. Here we harness the Belousov-Zhabotinsky (BZ) reaction to induce Marangoni stresses on the fluid-droplet interface and elucidate the spontaneous locomotion of active BZ droplets in a confined two-dimensional channel. Our approach employs the lattice Boltzmann method to simulate a coupled system of multiphase hydrodynamics and BZ-reaction kinetics. Our investigation reveals the mechanism underlying the propulsion of active BZ droplets, in terms of convective and diffusive fluxes and deformation of the droplets. Furthermore, we demonstrate that by manipulating the degree of confinement, strength, and nature of coupling between surface tension and active species' concentration, the motion of the BZ droplet can be directed. In addition, we are able to capture two different kinds of droplet behaviors, namely, sustained and stationary, and establish conditions for the sustained long-time motion. We envisage that our findings can be used not only to understand the mechanics of biological swimmers but also to design reaction-driven self-propelled systems for a variety of biomimetic applications.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Pattern formation in a four-ring reaction-diffusion network with heterogeneity

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.

Research progress in self-oscillating polymer brushes

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications. Self-oscillating polymers are anchored on surfaces of certain materials and are coupled with some self-oscillating reactions (with the Belousov–Zhabotinsky (BZ) reaction as an example) to form self-oscillating polymer brushes. As an independent field of stimulus response functional surface research, the development of new intelligent bionic materials has good potential. This article reviews the oscillation mechanisms of self-oscillating polymer brushes and their classifications. First, the oscillation mechanisms of self-oscillating polymer brushes are introduced. Second, the research progress in self-oscillating polymers is discussed in terms of the type of self-oscillation reactions. Finally, possible future developments of self-oscillating polymer brushes are prospected.

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications.

Shape-Changing Particles: From Materials Design and Mechanisms to Implementation

Demands for next-generation soft and responsive materials have sparked recent interest in the development of shape-changing particles and particle assemblies. Over the last two decades, a variety of mechanisms that drive shape change have been explored and integrated into particulate systems. Through a combination of top-down fabrication and bottom-up synthesis techniques, shape-morphing capabilities extend from the microscale to the nanoscale. Consequently, shape-morphing particles are rapidly emerging in a variety of contexts, including photonics, microfluidics, microrobotics, and biomedicine. Herein, the key mechanisms and materials that facilitate shape changes of microscale and nanoscale particles are discussed. Recent progress in the applications made possible by these particles is summarized, and perspectives on their promise and key open challenges in the field are discussed.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

Entropic regression with neurologically motivated applications

The ultimate goal of cognitive neuroscience is to understand the mechanistic neural processes underlying the functional organization of the brain. The key to this study is understanding the structure of both the structural and functional connectivity between anatomical regions. In this paper, we use an information theoretic approach, which defines direct information flow in terms of causation entropy, to improve upon the accuracy of the recovery of the true network structure over popularly used methods for this task such as correlation and least absolute shrinkage and selection operator regression. The method outlined above is tested on synthetic data, which is produced by following previous work in which a simple dynamical model of the brain is used, simulated on top of a real network of anatomical brain regions reconstructed from diffusion tensor imaging. We demonstrate the effectiveness of the method of AlMomani et al. [Chaos 30, 013107 (2020)] when applied to data simulated on the realistic diffusion tensor imaging network, as well as on randomly generated small-world and Erdös-Rényi networks.

Synchronization scenarios induced by delayed communication in arrays of diffusively coupled autonomous chemical oscillators

We study the impact of delayed feedbacks in the collective synchronization of ensembles of identical and autonomous micro-oscillators. To this aim, we consider linear arrays of Belousov-Zhabotinsky (BZ) oscillators confined in micro-compartmentalised systems, where the delayed feedback mimics natural lags that can arise due to the confinement properties and mechanisms driving the inter-oscillator communication. The micro-oscillator array is modeled as a set of Oregonator-like kinetics coupled via mass exchange of the chemical messengers. Changes in the synchronization patterns are explored by varying the delayed feedback introduced in the messenger species Br2. A direct transition from anti-phase to in-phase synchronization and back to the initial anti-phase scheme is observed by progressively increasing the time delay from zero to the value T₀, which is the oscillation period characterising the system without any delayed coupling. The route from anti- to in-phase oscillations (and back) consists of regimes where windows of in-phase oscillations are periodically broken by anti-phase beats. Similarities between these phase transition dynamics and synchronization scenarios characterising the coordination of oscillatory limb movements are finally discussed.

Emergent Bioanalogous Properties of Blockchain-based Distributed Systems

We apply a novel definition of biological systems to a series of reproducible observations on a blockchain-based distributed virtual machine (dVM). We find that such blockchain-based systems display a number of bioanalogous properties, such as response to the environment, growth and change, replication, and homeostasis, that fit some definitions of life. We further present a conceptual model for a simple self-sustaining, self-organizing, self-regulating distributed 'organism' as an operationally closed system that would fulfill all basic definitions and criteria for life, and describe developing technologies, particularly artificial neural network (ANN) based artificial intelligence (AI), that would enable it in the near future. Notably, such systems would have a number of specific advantages over biological life, such as the ability to pass acquired traits to offspring, significantly improved speed, accuracy, and redundancy of their genetic carrier, and potentially unlimited lifespans. Public blockchain-based dVMs provide an uncontained environment for the development of artificial general intelligence (AGI) with the capability to evolve by self-direction.

Modulation of the Belousov-Zhabotinsky Reaction with Lipid Bilayers: Effects of Lipid Head Groups and Membrane Properties

The Belousov-Zhabotinsky (BZ) reaction is an oscillating reaction due to periodic oscillations that happen in the concentration of some intermediates. Such systems can be applied together with hydrophobic membranes to create an autonomous behavior in artificial systems. However, because of a complex set of reactions happening in such systems, the interferences caused by hydrophobic membranes are not easily understood. In this study, we tested lipid membranes composed of trimethylammonium-propane (TAP) and phosphate (PA) lipids in an attempt to break down how the polar region of phosphatidylcholine (PC) lipid membranes affect the BZ reaction. According to our findings, the trimethylammonium group and membrane fluidity are crucial to change the frequency of oscillations in the reaction. In addition, the results also indicate a possible complexation of cerium ions with membranes with a phosphate head group.

Modeling of Astrocyte Networks: Toward Realistic Topology and Dynamics

Neuronal firing and neuron-to-neuron synaptic wiring are currently widely described as orchestrated by astrocytes—elaborately ramified glial cells tiling the cortical and hippocampal space into non-overlapping domains, each covering hundreds of individual dendrites and hundreds thousands synapses. A key component to astrocytic signaling is the dynamics of cytosolic Ca²⁺ which displays multiscale spatiotemporal patterns from short confined elemental Ca²⁺ events (puffs) to Ca²⁺ waves expanding through many cells. Here, we synthesize the current understanding of astrocyte morphology, coupling local synaptic activity to astrocytic Ca²⁺ in perisynaptic astrocytic processes and morphology-defined mechanisms of Ca²⁺ regulation in a distributed model. To this end, we build simplified realistic data-driven spatial network templates and compile model equations as defined by local cell morphology. The input to the model is spatially uncorrelated stochastic synaptic activity. The proposed modeling approach is validated by statistics of simulated Ca²⁺ transients at a single cell level. In multicellular templates we observe regular sequences of cell entrainment in Ca²⁺ waves, as a result of interplay between stochastic input and morphology variability between individual astrocytes. Our approach adds spatial dimension to the existing astrocyte models by employment of realistic morphology while retaining enough flexibility and scalability to be embedded in multiscale heterocellular models of neural tissue. We conclude that the proposed approach provides a useful description of neuron-driven Ca²⁺-activity in the astrocyte syncytium.

Impact of PDMS-Based Microfluidics on Belousov-Zhabotinsky Chemical Oscillators

Sub-nanoliter volumes of the Belousov-Zhabotinsky (BZ) reaction are sealed in microfluidic devices made from polydimethylsiloxane (PDMS). Bromine, which is a BZ reaction intermediate that participates in the inhibitory pathway of the reaction, is known to permeate into PDMS, and it has been suggested that PDMS and bromine can react ( J. Phys. Chem. A. 108, 2004, 1325-1332). We characterize the extent to which PDMS affects BZ oscillations by varying the volume of the PDMS surrounding the BZ reactors. We measure how the oscillation period varies with PDMS volume and compare with a theoretical reaction-diffusion model, concluding that bromine reacts with PDMS. We demonstrate that minimizing the amount of PDMS by making the samples as thin as possible maximizes the number of oscillations before the BZ reaction reaches equilibrium and ceases to oscillate. We also demonstrate that the deleterious effects of the PDMS-BZ interactions are somewhat mitigated by imposing constant chemical boundary conditions through using a light-sensitive catalyst, ruthenium, in combination with patterned illumination. Furthermore, we show that light can modulate the frequency and phase of the BZ oscillators contained in a PDMS matrix by 20-30%.

Changes Caused by Liposomes to the Belousov-Zhabotinsky Reaction

The Belousov-Zhabotinsky (BZ) reaction has been applied to give autonomous dynamic behaviors to artificial systems. This reaction is conducted in an aqueous system, but it produces some hydrophobic intermediates, such as bromine. On the basis of previous works about reactions in the lipid bilayer, we investigated how liposome membranes (water-oil interface) affect the BZ reaction. Herein diacylglycerophosphocholine (PC) molecules with a variety of hydrocarbon tails were selected as components of liposomes, and the BZ reaction in the presence of the liposomes was characterized. As a result, membrane fluidity was the main characteristic leading to changes in the reaction behavior. The decrease of the frequency of oscillations was relevant to membrane fluidity, suggesting the interaction of bromine species in the hydrophobic site of the liposomes. In addition, the heterogeneous membrane (s_o+l_d) of DMPC showed a fast decrease in the amplitude of oscillations. Conclusively, characteristics of the hydrophobic environment play a role in the reaction.

Magnetic Field-Driven Deformation, Attraction, and Coalescence of Nonmagnetic Aqueous Droplets in an Oil-Based Ferrofluid

Stimuli-responsive compartments are attracting more and more attention through the years motivated by their wide applications in different fields including encapsulation, manipulation, and triggering of chemical reactions on demand. Among others, magnetic responsive compartments are particularly attractive due to the numerous advantages of magnetic fields compared to other external stimuli. In this article, we used an oil-based ferrofluid where the magnetic nanoparticles have been coated with different polymers to increase their amphiphilic character and surface activity, consequently rendering the interface magnetically responsive. Microliter aqueous nonmagnetic droplets dispersed in the oil-based ferrofluid were used as a model of microreactors. A comprehensive experimental and theoretical study of the deformation, attraction, and coalescence processes of the nonmagnetic water droplets coated with the magnetic nanoparticles under an applied magnetic field in the continuous oil-based ferrofluid phase is provided. To manipulate the packing of the nanoparticles at the water/oil interface, the ionic strength of the aqueous droplets was varied using different NaCl concentrations, and its effect on modulating the coalescence of the droplets was probed. Our results show that the water droplets deform along the magnetic field depending on the magnetic properties of the ferrofluid itself and on the surface properties of the interface, attract in pairs under the action of the magnetic dipole force, and coalesce by the action of the same force with a stochastic behavior. We have studied all of these phenomena as a function of the magnetic field applied, evaluating in each case the forces and/or pressures acting on the droplets with particular attention to roles of magnetic attraction, interface properties, and viscosity in the system. This work offers an overall set of tools to understand and predict the behavior of multiple water droplets in an oil-based ferrofluid for lab-on-a-chip applications.

Synchronization in reaction-diffusion systems with multiple pacemakers

Spatially extended oscillatory systems can be entrained by pacemakers, regions that oscillate with a higher frequency than the rest of the medium. Entrainment happens through waves originating at a pacemaker. Typically, biological and chemical media can contain multiple pacemaker regions, which compete with each other. In this paper, we perform a detailed numerical analysis of how wave propagation and synchronization of the medium depend on the properties of these pacemakers. We discuss the influence of the size and intrinsic frequency of pacemakers on the synchronization properties. We also study a system in which the pacemakers are embedded in a medium without any local dynamics. In this case, synchronization occurs if the coupling determined by the distance and diffusion is strong enough. The transition to synchronization is reminiscent of systems of discrete coupled oscillators.

Membrane Structure Drives Synchronization Patterns in Arrays of Diffusively Coupled Self-Oscillating Droplets

Networks of diffusively coupled inorganic oscillators, confined in nano- and microcompartments, are effective for predicting and understanding the global dynamics of those systems where the diffusion of activatory or inhibitory signals regulates the communication among different individuals. By taking advantage of a microfluidic device, we study the dynamics of arrays of diffusively coupled Belousov-Zhabotinsky (BZ) oscillators encapsulated in water-in-oil single emulsions. New synchronization patterns are induced and controlled by modulating the structural and chemical properties of the phospholipid-based biomimetic membranes via the introduction of specific dopants. Doping molecules do not alter the membrane basic backbone, but modify the lamellarity (and, in turn, the permeability) or interact chemically with the reaction intermediates. A transition from two-period clusters showing 1:2 period-locking to one-period antiphase synchronization is observed by decreasing the membrane lamellarity. An unsynchronized scenario is found when the dopant is able to interfere with chemical communication by reacting with the chemical messengers.

Size- and position-dependent bifurcations of chemical microoscillators in confined geometries

The present theoretical study deals with microparticles (beads) that contain an immobilized Belousov-Zhabotinsky (BZ) reaction catalyst. In the theoretical experiment, a BZ bead is immersed in a small water droplet that contains all of the BZ reaction reagents but no catalyst. Such heterogeneous reaction-diffusion BZ systems with the same BZ reactant concentrations demonstrate various dynamic modes, including steady state and low-amplitude, high-amplitude, and mixed-mode oscillations (MMOs). The emergence of such dynamics depends on the sizes of the bead and water droplet, as well as on the location of the bead inside the droplet. MMO emergence is explained by time-delayed positive feedback in combination with a canard phenomenon. If two identical BZ beads are immersed in the same droplet, many different dynamic modes including chaos are observed.

Microfluidic compartmentalization of diffusively coupled oscillators in multisomes induces a novel synchronization scenario

Multisome compartments encapsulating the Belousov–Zhabotinsky reaction produced by microfluidics arranged in 1D arrays showed a novel type of global synchronization.

Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100  μm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength: (i) unlocked, uncorrelated phase shifts between all oscillators; (ii) locked, arm hubs synchronized in phase with a k-dependent phase shift between the arm and central hub; and (iii) center silent, a central hub stopped oscillating and the arm hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

A brief history of liquid computers

A substrate does not have to be solid to compute. It is possible to make a computer purely from a liquid. I demonstrate this using a variety of experimental prototypes where a liquid carries signals, actuates mechanical computing devices and hosts chemical reactions. We show hydraulic mathematical machines that compute functions based on mass transfer analogies. I discuss several prototypes of computing devices that employ fluid flows and jets. They are fluid mappers, where the fluid flow explores a geometrically constrained space to find an optimal way around, e.g. the shortest path in a maze, and fluid logic devices where fluid jet streams interact at the junctions of inlets and results of the computation are represented by fluid jets at selected outlets. Fluid mappers and fluidic logic devices compute continuously valued functions albeit discretized. There is also an opportunity to do discrete operation directly by representing information by droplets and liquid marbles (droplets coated by hydrophobic powder). There, computation is implemented at the sites, in time and space, where droplets collide one with another. The liquid computers mentioned above use liquid as signal carrier or actuator: the exact nature of the liquid is not that important. What is inside the liquid becomes crucial when reaction-diffusion liquid-phase computing devices come into play: there, the liquid hosts families of chemical species that interact with each other in a massive-parallel fashion. I shall illustrate a range of computational tasks, including computational geometry, implementable by excitation wave fronts in nonlinear active chemical medium. The overview will enable scientists and engineers to understand how vast is the variety of liquid computers and will inspire them to design their own experimental laboratory prototypes. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Multivariate statistical analysis of chemical and electrochemical oscillators for an accurate frequency selection

The effect of experimental parameters on the frequency of chemical oscillators has been systematically studied since the first observations of clock reactions. The approach is mainly based on univariate changes in one specific parameter while others are kept constant. The frequency is then monitored and the effect of each parameter is discussed separately. This type of analysis, however, does not take into account the multiple interactions among the controllable parameters and the synergic responses on the oscillation frequency. We have carried out a multivariate statistical analysis of chemical (BZ-ferroin catalyzed reaction) and electrochemical (Cu/Cu₂O cathodic deposition) oscillators and identified the contributions of the experimental parameters on frequency variations. The BZ reaction presented a strong dependence on the initial concentration of sodium bromate and temperature, resulting in a frequency increase. The concentration of malonic acid, the organic substrate, affects the system but with lower intensity compared with the combination of sodium bromate and temperature. On the other hand, the Cu/Cu₂O electrochemical oscillator was shown to be less sensitive to changes in the temperature. The applied current density and pH were the two parameters which most perturbed the system. Interestingly, the frequency behaved nonmonotonically with a quadratic dependence. The multivariate analysis of both oscillators exhibited significant differences - while the homogenous oscillator displayed a linear dependence with the factors, the heterogeneous one revealed a more complex dependence with quadratic terms. Our results may contribute, for instance, in the synthesis of self-organized materials in which an accurate frequency selection is required and, depending on its value, different physicochemical properties are obtained.

Photochemically Excited, Pulsating Janus Colloidal Motors of Tunable Dynamics

Spontaneous periodicity is widely found in many biological and synthetic systems, and designing colloidal motors that mimic this feature may not only facilitate our understanding of how complexity emerges but also enable applications that benefit from a time-varying activity. However, there is so far no report on a colloidal motor system that shows controllable and spontaneous oscillation in speeds. Inspired by previous studies of oscillating silver microparticles, we report silver-poly(methyl methacrylate) microsphere Janus colloidal motors that moved, interacted with tracers, and exhibited negative gravitaxis all in an oscillatory fashion. Its dynamics, including pulsating speeds and magnitude, as well as whether moving forward in a pulsating or continuous mode, can be systematically modulated by varying chemical concentrations, light intensity, and the way light was applied. A qualitative mechanism is proposed to link the oscillation of Janus colloidal motors to ionic diffusiophoresis, while nonlinearity is suspected to arise from a sequence of autocatalytic decomposition of AgCl and its slow buildup in the presence of H₂O₂ and light. The generation of light-absorbing Ag nanoparticles is suspected to be the key. This study therefore establishes a robust model system of chemically driven, oscillatory colloidal motors with clear directionality, good tunability, and an improved mechanism, with which complex, emergent phenomena can be explored.

Exploring the water/oil/water interface of phospholipid stabilized double emulsions by micro-focusing synchrotron SAXS

Surfactant stabilized water/oil/water (w/o/w) double emulsions have received much attention in the last years motivated by their wide applications.

Towards Functional Droplet Architectures: a Belousov-Zhabotinsky Medium for Networks

The confluence of droplet-compartmentalised chemical systems and architectures composed of interacting droplets points towards a novel technology mimicking core features of the cellular architecture that dominates biology. A key challenge to achieve such a droplet technology is long-term stability in conjunction with interdroplet communication. Here, we probed the parameter space of the Belousov-Zhabotinsky (BZ) medium, an extensively studied model for non-equilibrium chemical reactions, pipetted as 2.5 mm droplets in hexadecane oil. The presence of asolectin lipids enabled the formation of arrays of contacted BZ droplets, of which the wave patterns were characterised over time. We utilised laser-cut acrylic templates with over 40 linear oil-filled slots in which arrays are formed by pipetting droplets of the desired BZ composition, enabling parallel experiments and automated image analysis. Using variations of conventional malonic acid BZ medium, wave propagation over droplet-droplet interfaces was not observed. However, a BZ medium containing both malonic acid and 1,4-cyclohexanedione was found to enable inter-droplet wave propagation. We anticipate that the chemical excitation properties of this mixed-substrate BZ medium, in combination with the droplet stability of the networks demonstrated here for nearly 400 droplets in a template-defined topology, will facilitate the development of scalable functional droplet networks.

Engineering reaction-diffusion networks with properties of neural tissue

We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale reactors containing the Belousov-Zhabotinsky (BZ) reaction. Microfluidic fabrication techniques are developed that provide the ability to vary the network topology and the reactor coupling strength and offer the freedom to choose whether an arbitrary reactor is inhibitory or excitatory coupled to its neighbor. This versatile experimental and theoretical framework can be used to create a wide variety of chemical networks. Here we design, construct and characterize chemical networks that achieve the complexity of central pattern generators (CPGs), which are found in the autonomic nervous system of a variety of organisms.

Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov–Zhabotinsky (BZ) reaction.

Dynamical modes of two almost identical chemical oscillators connected via both pulsatile and diffusive coupling

The dynamics of two almost identical chemical oscillators with mixed diffusive and pulsatile coupling are systematically studied.

Lipid-Stabilized Water-Oil Interfaces Studied by Microfocusing Small-Angle X-ray Scattering

Water-in-oil (w/o) simple emulsions are dispersed microconfined systems that find applications in many areas of advanced materials and biotechnology, such as the food industry, drug delivery, and cosmetics, to name but a few. In these systems, the structural and chemical properties of the boundary layer at the w/o interface are of paramount importance in determining functionality and stability. Recently, microfluidic methods have emerged as a valuable tool for fabricating monodisperse emulsion droplets. Because of the intrinsic flexibility of microfluidics, different interfaces can be obtained, and general principles governing their stability are needed to guide the experimental approach. Herein, we investigate the structural characteristics of the region encompassing the liquid/liquid (L/L) interface of w/o emulsions generated by a microfluidic device in the presence of phospholipid 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and other intercalating amphiphiles (dopants) using microfocused small-angle X-rays scattering (μ-SAXS). We show that phospholipids provide a stable and versatile boundary film of ∼100 μm whose basic units are swollen and uncorrelated DMPC bilayers. The internal arrangement of this interfacial film can be tuned by adding molecules with a different packing parameter, such as cholesterol, which is able to increase the stiffness of the lipid membranes and trigger interbilayer correlation.

A new droplet-forming fluidic junction for the generation of highly compartmentalised capsules

A new oscillatory microfluidic junction is described, which enables the consistent formation of highly uniform and complex double emulsions, and is demonstrated for the encapsulation of four different reagents within the inner droplets (called cores) of the double emulsion droplets. Once the double emulsion droplets had attained a spherical form, the cores assumed specific 3D arrangements, the orchestration of which appeared to depend upon the specific emulsion morphology. Such double emulsion droplets were used as templates to produce highly compartmentalised microcapsules and multisomes. Based on these construct models, we numerically demonstrated a model chemical reaction sequence between and within the liquid cores. This work could provide a platform to perform space/time-dependent applications, such as programmed experiments, synthesis, and delivery systems.

Cancer classification with a network of chemical oscillators

We discuss chemical information processing considering dataset classifiers formed with a network of interacting droplets.