Chemical computing with reaction-diffusion processes

pH-Controlled enzymatic computing for digital circuits and neural networks

Unconventional computing paradigms explore new methods for processing information beyond the capabilities of traditional electronic architectures. In this work, we present our approach to digital computation through enzymatic reactions in chemically buffered environments. A key aspect of this approach is its reliance on pH-sensitive enzymatic reactions, with the direction of the reaction controlled by maintaining pH levels within a specific range. When the pH crosses a defined threshold, the reaction moves forward and vice versa, akin to the switching action of electronic switches in digital circuits. The binary signals (0 and 1) are encoded as different concentrations of strong acids or bases, offering a bio-inspired method for computation. The final readout is done using UV-vis spectroscopy after applying detection reactions to indicate whether the output is 1 (indicated by the presence of the enzymatic reaction's product) or 0 (indicated by the absence of the enzymatic reaction's product). We build and evaluate a set of digital circuits in the lab using our proposed methodology to model the circuits using chemical reactions. In addition, we demonstrate the implementation of a neural network classifier using our framework.

A programmable hybrid digital chemical information processor based on the Belousov-Zhabotinsky reaction

The exponential growth of the power of modern digital computers is based upon the miniaturization of vast nanoscale arrays of electronic switches, but this will be eventually constrained by fabrication limits and power dissipation. Chemical processes have the potential to scale beyond these limits by performing computations through chemical reactions, yet the lack of well-defined programmability limits their scalability and performance. Here, we present a hybrid digitally programmable chemical array as a probabilistic computational machine that uses chemical oscillators using Belousov-Zhabotinsky reaction partitioned in interconnected cells as a computational substrate. This hybrid architecture performs efficient computation by distributing information between chemical and digital domains together with inbuilt error correction logic. The efficiency is gained by combining digital logic with probabilistic chemical logic based on nearest neighbour interactions and hysteresis effects. We demonstrated the computational capabilities of our hybrid processor by implementing one- and two-dimensional Chemical Cellular Automata demonstrating emergent dynamics of life-like entities called Chemits. Additionally, we demonstrate hybrid probabilistic logic as a viable logic for solving combinatorial optimization problems.

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.

The Role of Experimental Noise in a Hybrid Classical-Molecular Computer to Solve Combinatorial Optimization Problems

Chemical and molecular-based computers may be promising alternatives to modern silicon-based computers. In particular, hybrid systems, where tasks are split between a chemical medium and traditional silicon components, may provide access and demonstration of chemical advantages such as scalability, low power dissipation, and genuine randomness. This work describes the development of a hybrid classical-molecular computer (HCMC) featuring an electrochemical reaction on top of an array of discrete electrodes with a fluorescent readout. The chemical medium, optical readout, and electrode interface combined with a classical computer generate a feedback loop to solve several canonical optimization problems in computer science such as number partitioning and prime factorization. Importantly, the HCMC makes constructive use of experimental noise in the optical readout, a milestone for molecular systems, to solve these optimization problems, as opposed to in silico random number generation. Specifically, we show calculations stranded in local minima can consistently converge on a global minimum in the presence of experimental noise. Scalability of the hybrid computer is demonstrated by expanding the number of variables from 4 to 7, increasing the number of possible solutions by 1 order of magnitude. This work provides a stepping stone to fully molecular approaches to solving complex computational problems using chemistry.

Digital circuits and neural networks based on acid-base chemistry implemented by robotic fluid handling

Acid-base reactions are ubiquitous, easy to prepare, and execute without sophisticated equipment. Acids and bases are also inherently complementary and naturally map to a universal representation of "0" and "1." Here, we propose how to leverage acids, bases, and their reactions to encode binary information and perform information processing based upon the majority and negation operations. These operations form a functionally complete set that we use to implement more complex computations such as digital circuits and neural networks. We present the building blocks needed to build complete digital circuits using acids and bases for dual-rail encoding data values as complementary pairs, including a set of primitive logic functions that are widely applicable to molecular computation. We demonstrate how to implement neural network classifiers and some classes of digital circuits with acid-base reactions orchestrated by a robotic fluid handling device. We validate the neural network experimentally on a number of images with different formats, resulting in a perfect match to the in-silico classifier. Additionally, the simulation of our acid-base classifier matches the results of the in-silico classifier with approximately 99% similarity.

Origin of the Second-Order Proton Catalysis of Ferriin Reduction in Belousov-Zhabotinsky Reactions: Density Functional Studies of Ferroin and Ferriin Aggregates with Outer Sphere Ligands Sulfate, Bisulfate, and Sulfuric Acid

The detailed mechanisms of Belousov-Zhabotinsky oscillating reactions continue to present grand challenges, even after half a century of study. The origin of the pH dependence of the oscillation pattern had never been rigorously identified. In our recent kinetic study of one of the key Belousov-Zhabotinsky reactions, the iron-catalyzed bromate oxidation of malonic acid, compelling agreement between experiments and kinetic simulations was achieved only with the inclusion of second-order proton catalysis of the reduction of the [Fe(phen)₃]³⁺ species. After exhausting all other avenues in search of an explanation of this proton catalysis, we considered the possibility that the parent iron-phenanthroline complexes could aggregate with neutral and anionic outer sphere ligands (OSLs) in the highly concentrated sulfuric acid solution, and we hypothesized that OSL protonation would increase the capacity of the aggregated complex to oxidize the organic fuel. We performed potential energy surface analyses at the SMD(APFD/6-311G*) level of complexes of the types [Fe(phen)₃(SO₄^2-)_m(HSO₄^-)_n(H₂SO₄)_o]^(c-2m-n)+ for ferriin (c = 3) and ferroin (c = 2) aggregated with m sulfate, n bisulfate, and o sulfuric acid OSLs. We present structures of the OSL aggregates, develop a nomenclature for their description, and characterize their electronic structure. The structural chemistry provides the foundation to discuss the ferroin/ferriin redox couple with emphasis on the relationship between the vertical electron affinities of ferriin aggregates and their OSL protonation states. For proton catalysis to manifest itself, double-protonation paths that are slightly endergonic should be present, and proton affinities of aggregated OSLs allow the identification of such double-protonation chains. As a first test of our mechanistic proposal for the second-order proton catalysis of the Belousov-Zhabotinsky reaction, the results presented here provide compelling evidence in support of the importance of outer sphere ligation of the iron catalyst.

Provenance of life: Chemical autonomous agents surviving through associative learning

We present a benchmark study of autonomous, chemical agents exhibiting associative learning of an environmental feature. Associative learning systems have been widely studied in cognitive science and artificial intelligence but are most commonly implemented in highly complex or carefully engineered systems, such as animal brains, artificial neural networks, DNA computing systems, and gene regulatory networks, among others. The ability to encode environmental information and use it to make simple predictions is a benchmark of biological resilience and underpins a plethora of adaptive responses in the living hierarchy, spanning prey animal species anticipating the arrival of predators to epigenetic systems in microorganisms learning environmental correlations. Given the ubiquitous and essential presence of learning behaviors in the biosphere, we aimed to explore whether simple, nonliving dissipative structures could also exhibit associative learning. Inspired by previous modeling of associative learning in chemical networks, we simulated simple systems composed of long- and short-term memory chemical species that could encode the presence or absence of temporal correlations between two external species. The ability to learn this association was implemented in Gray-Scott reaction-diffusion spots, emergent chemical patterns that exhibit self-replication and homeostasis. With the novel ability of associative learning, we demonstrate that simple chemical patterns can exhibit a broad repertoire of lifelike behavior, paving the way for in vitro studies of autonomous chemical learning systems, with potential relevance to artificial life, origins of life, and systems chemistry. The experimental realization of these learning behaviors in protocell or coacervate systems could advance a new research direction in astrobiology, since our system significantly reduces the lower bound on the required complexity for autonomous chemical learning.

Information Processing Using Networks of Chemical Oscillators

I believe the computing potential of systems with chemical reactions has not yet been fully explored. The most common approach to chemical computing is based on implementation of logic gates. However, it does not seem practical because the lifetime of such gates is short, and communication between gates requires precise adjustment. The maximum computational efficiency of a chemical medium is achieved if the information is processed in parallel by different parts of it. In this paper, I review the idea of computing with coupled chemical oscillators and give arguments for the efficiency of such an approach. I discuss how to input information and how to read out the result of network computation. I describe the idea of top-down optimization of computing networks. As an example, I consider a small network of three coupled chemical oscillators designed to differentiate the white from the red points of the Japanese flag. My results are based on computer simulations with the standard two-variable Oregonator model of the oscillatory Belousov−Zhabotinsky reaction. An optimized network of three interacting oscillators can recognize the color of a randomly selected point with >98% accuracy. The presented ideas can be helpful for the experimental realization of fully functional chemical computing networks.

The Concilium of Information Processing Networks of Chemical Oscillators for Determining Drug Response in Patients With Multiple Myeloma

It can be expected that medical treatments in the future will be individually tailored for each patient. Here we present a step towards personally addressed drug therapy. We consider multiple myeloma treatment with drugs: bortezomib and dexamethasone. It has been observed that these drugs are effective for some patients and do not help others. We describe a network of chemical oscillators that can help to differentiate between non-responsive and responsive patients. In our numerical simulations, we consider a network of 3 interacting oscillators described with the Oregonator model. The input information is the gene expression value for one of 15 genes measured for patients with multiple myeloma. The single-gene networks optimized on a training set containing outcomes of 239 therapies, 169 using bortezomib and 70 using dexamethasone, show up to 71% accuracy in differentiating between non-responsive and responsive patients. If the results of single-gene networks are combined into the concilium with the majority voting strategy, then the accuracy of predicting the patient’s response to the therapy increases to ∼ 85%.

Chemical Wave Computing from Labware to Electrical Systems

Unconventional and, specifically, wave computing has been repeatedly studied in laboratory based experiments by utilizing chemical systems like a thin film of Belousov–Zhabotinsky (BZ) reactions. Nonetheless, the principles demonstrated by this chemical computer were mimicked by mathematical models to enhance the understanding of these systems and enable a more detailed investigation of their capacity. As expected, the computerized counterparts of the laboratory based experiments are faster and less expensive. A further step of acceleration in wave-based computing is the development of electrical circuits that imitate the dynamics of chemical computers. A key component of the electrical circuits is the memristor which facilitates the non-linear behavior of the chemical systems. As part of this concept, the road-map of the inspiration from wave-based computing on chemical media towards the implementation of equivalent systems on oscillating memristive circuits was studied here. For illustration reasons, the most straightforward example was demonstrated, namely the approximation of Boolean gates.

Collective Behavior of Urease pH Clocks in Nano- and Microvesicles Controlled by Fast Ammonia Transport

The transmission of chemical signals via an extracellular solution plays a vital role in collective behavior in cellular biological systems and may be exploited in applications of lipid vesicles such as drug delivery. Here, we investigated chemical communication in synthetic micro- and nanovesicles containing urease in a solution of urea and acid. We combined experiments with simulations to demonstrate that the fast transport of ammonia to the external solution governs the pH-time profile and synchronizes the timing of the pH clock reaction in a heterogeneous population of vesicles. This study shows how the rate of production and emission of a small basic product controls pH changes in active vesicles with a distribution of sizes and enzyme amounts, which may be useful in bioreactor or healthcare applications.

Computing With Networks of Chemical Oscillators and its Application for Schizophrenia Diagnosis

Chemical reactions are responsible for information processing in living organisms, yet biomimetic computers are still at the early stage of development. The bottom-up design strategy commonly used to construct semiconductor information processing devices is not efficient for chemical computers because the lifetime of chemical logic gates is usually limited to hours. It has been demonstrated that chemical media can efficiently perform a specific function like labyrinth search or image processing if the medium operates in parallel. However, the number of parallel algorithms for chemical computers is very limited. Here we discuss top-down design of such algorithms for a network of chemical oscillators that are coupled by the exchange of reaction activators. The output information is extracted from the number of excitations observed on a selected oscillator. In our model of a computing network, we assume that there is an external factor that can suppress oscillations. This factor can be applied to control the nodes and introduce input information for processing by a network. We consider the relationship between the number of oscillation nodes and the network accuracy. Our analysis is based on computer simulations for a network of oscillators described by the Oregonator model of a chemical oscillator. As the example problem that can be solved with an oscillator network, we consider schizophrenia diagnosis on the basis of EEG signals recorded using electrodes located at the patient’s scalp. We demonstrated that a network formed of interacting chemical oscillators can process recorded signals and help to diagnose a patient. The parameters of considered networks were optimized using an evolutionary algorithm to achieve the best results on a small training dataset of EEG signals recorded from 45 ill and 39 healthy patients. For the optimized networks, we obtained over 82% accuracy of schizophrenia detection on the training dataset. The diagnostic accuracy can be increased to almost 87% if the majority rule is applied to answers of three networks with different number of nodes.

Identification of the best medium for experiments on chemical computation with Belousov–Zhabotinsky reaction and ferroin-loaded Dowex beads

Our study is focused on identification of the best medium for future experiments on information processing with Belousov–Zhabotinsky reaction proceeding in Dowex beads with immobilized catalyst inside. The optimum medium should be characterized by long and stable nonlinear behavior, mechanical stability and should allow for control with electric potential. We considered different types of Dowex ion-exchange resins, bead distributions and various initial concentrations of substrates: malonic acid and 1,4-cyclohexanedione. The electric potential on platinum electrodes, stabilized by a potentiostat is used to control medium evolution. A negative electric potential generates activator species HBrO2 on the working electrode according to the reaction: BrO3−  + 2e−  + 3H+  → HBrO2 + H2O, while positive electric potential attracts inhibitor species Br− to the proximity of it. We study oscillation amplitude and period stability in systems with ferroin loaded Dowex 50W-X2 and Dowex 50W-X8 beads during experiments exceeding 16 h. It has been observed, that the above mentioned resins generate a smaller number of CO2 bubbles close to the beads than Dowex 50W-X4, which makes Dowex 50W-X2 and Dowex 50W-X8 more suitable for applications in chemical computing. We report amplitude stability, oscillation frequency, merging and annihilation of travelling waves in a lattice of Dowex 50W-X8 beads (mesh size 50–100) in over 19 h long experiments with equimolar solution of malonic acid and 1,4-cyclohexanedione. This system looks as a promising candidate for chemical computing devices that can operate for a day.

Origin of jumping oscillons in an excitable reaction-diffusion system

Oscillons, i.e., immobile spatially localized but temporally oscillating structures, are the subject of intense study since their discovery in Faraday wave experiments. However, oscillons can also disappear and reappear at a shifted spatial location, becoming jumping oscillons (JOs). We explain here the origin of this behavior in a three-variable reaction-diffusion system via numerical continuation and bifurcation theory, and show that JOs are created via a modulational instability of excitable traveling pulses (TPs). We also reveal the presence of bound states of JOs and TPs and patches of such states (including jumping periodic patterns) and determine their stability. This rich multiplicity of spatiotemporal states lends itself to information and storage handling.

Light sensitive Belousov-Zhabotinsky medium accommodates multiple logic gates

Computational functionality has been implemented successfully on chemical reactions in living systems. In the case of Belousov-Zhabotinsky (BZ) reaction, this was achieved by using collision-based techniques and by exploiting the light sensitivity of BZ. In order to unveil the computational capacity of the light sensitive BZ medium and the possibility to implement re-configurable logic, the design of multiple logic gates in a fixed BZ reservoir was investigated. The three basic logic gates (namely NOT, OR and AND) were studied to prove the Turing completeness of the architecture. Namely, all possible Boolean functions can be implemented as a combination of these logic gates. Nonetheless, a more complicated logic function was investigated, aiming to illustrate further capabilities of a fixed size BZ reservoir. The experiments executed within this study were implemented with a Cellular Automata (CA)-based model of the Oregonator equations that simulate excitation and wave propagation on a light sensitive BZ thin film. Given that conventional or von Neumann architecture computations is proved possible on the proposed configuration, the next step would be the realization of unconventional types of computation, such as neuromorphic and fuzzy computations, where the chemical substrate may prove more efficient than silicon.

Implementing parallel arithmetic via acetylation and its application to chemical image processing

Chemical mixtures can be leveraged to store large amounts of data in a highly compact form and have the potential for massive scalability owing to the use of large-scale molecular libraries. With the parallelism that comes from having many species available, chemical-based memory can also provide the physical substrate for computation with increased throughput. Here, we represent non-binary matrices in chemical solutions and perform multiple matrix multiplications and additions, in parallel, using chemical reactions. As a case study, we demonstrate image processing, in which small greyscale images are encoded in chemical mixtures and kernel-based convolutions are performed using phenol acetylation reactions. In these experiments, we use the measured concentrations of reaction products (phenyl acetates) to reconstruct the output image. In addition, we establish the chemical criteria required to realize chemical image processing and validate reaction-based multiplication. Most importantly, this work shows that fundamental arithmetic operations can be reliably carried out with chemical reactions. Our approach could serve as a basis for developing more advanced chemical computing architectures.

Leveraging autocatalytic reactions for chemical domain image classification

Autocatalysis is fundamental to many biological processes, and kinetic models of autocatalytic reactions have mathematical forms similar to activation functions used in artificial neural networks. Inspired by these similarities, we use an autocatalytic reaction, the copper-catalyzed azide-alkyne cycloaddition, to perform digital image recognition tasks. Images are encoded in the concentration of a catalyst across an array of liquid samples, and the classification is performed with a sequence of automated fluid transfers. The outputs of the operations are monitored using UV-vis spectroscopy. The growing interest in molecular information storage suggests that methods for computing in chemistry will become increasingly important for querying and manipulating molecular memory.

Experimental verification of an opto-chemical "neurocomputer"

A theoretically predicted hierarchical network of pulse coupled chemical micro-oscillators and excitable micro-cells that we call a chemical "neurocomputer" (CN) or even a chemical "brain" is tested experimentally using the Belousov-Zhabotinsky reaction. The CN consists of five functional units: (1) a central pattern generator (CPG), (2) an antenna, (3) a reader for the CPG, (4) a reader for the antenna unit, and (5) a decision making (DM) unit. A hybrid CN, in which such chemical units as readers and DM units are replaced by electronic units, is tested as well. All these variations of the CN respond intelligently to external signals, since they perform an automatic transition from a current to a new dynamic mode of the CPG, which is similar to the antenna dynamic mode that in turn is induced by external signals. In other words, we show for the first time that a network of pulse coupled chemical micro-oscillators is capable of intelligent adaptive behavior.

A programmable chemical computer with memory and pattern recognition

Current computers are limited by the von Neumann bottleneck, which constrains the throughput between the processing unit and the memory. Chemical processes have the potential to scale beyond current computing architectures as the processing unit and memory reside in the same space, performing computations through chemical reactions, yet their lack of programmability limits them. Herein, we present a programmable chemical processor comprising of a 5 by 5 array of cells filled with a switchable oscillating chemical (Belousov-Zhabotinsky) reaction. Each cell can be individually addressed in the 'on' or 'off' state, yielding more than 2.9 × 10¹⁷ chemical states which arise from the ability to detect distinct amplitudes of oscillations via image processing. By programming the array of interconnected BZ reactions we demonstrate chemically encoded and addressable memory, and we create a chemical Autoencoder for pattern recognition able to perform the equivalent of one million operations per second.

Directed adaptation of synchronization levels in oscillator communities

We present an adaptive control scheme that realizes desired dynamics of an oscillator network with a given number of communities by adjusting the coupling weights between oscillators accordingly. The scheme allows, for example, to simultaneously establish different pregiven synchronization levels in the particular communities as well as phase relationships between them. We apply the method in numerical simulations with all-to-all and randomly coupled networks. Moreover, we provide an experimental proof of concept validating our numerical findings in a network of optically coupled photosensitive chemical micro-oscillators.

Towards fungal computer

We propose that fungi Basidiomycetes can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In a series of scoping experiments, we demonstrate that electrical activity recorded on fruits might act as a reliable indicator of the fungi's response to thermal and chemical stimulation. A stimulation of a fruit is reflected in changes of electrical activity of other fruits of a cluster, i.e. there is distant information transfer between fungal fruit bodies. In an automaton model of a fungal computer, we show how to implement computation with fungi and demonstrate that a structure of logical functions computed is determined by mycelium geometry.

Moving Droplets in 3D Using Light

The emulation of the complex cellular and bacterial vesicles used to transport materials through fluids has the potential to add revolutionary capabilities to fluidic platforms. Although a number of artificial motile vesicles or microdroplets have been demonstrated previously, control over their movement in liquid in 3D has not been achieved. Here it is shown that by adding a chemical "fuel," a photoactive material, to the droplet, it can be moved in any direction (3D) in water using simple light sources without the need for additives in the water. The droplets can be made up of a range of solvents and move with speeds as high as 10.4 mm s^-1 toward or away from the irradiation source as a result of a light-induced isothermal change in interfacial tension (Marangoni flow). It is further demonstrated that more complex functions can be accomplished by merging a photoactive droplet with a droplet carrying a "cargo" and moving the new larger droplet to a "reactor" droplet where the cargo undergoes a chemical reaction. The control and versatility of this light-activated, motile droplet system will open up new possibilities for fluidic chemical transport and applications.

Functional aqueous droplet networks

Droplet interface bilayers (DIBs), comprising individual lipid bilayers between pairs of aqueous droplets in an oil, are proving to be a useful tool for studying membrane proteins. Recently, attention has turned to the elaboration of networks of aqueous droplets, connected through functionalized interface bilayers, with collective properties unachievable in droplet pairs. Small 2D collections of droplets have been formed into soft biodevices, which can act as electronic components, light-sensors and batteries. A substantial breakthrough has been the development of a droplet printer, which can create patterned 3D droplet networks of hundreds to thousands of connected droplets. The 3D networks can change shape, or carry electrical signals through defined pathways, or express proteins in response to patterned illumination. We envisage using functional 3D droplet networks as autonomous synthetic tissues or coupling them with cells to repair or enhance the properties of living tissues.

Chemical memory with states coded in light controlled oscillations of interacting Belousov–Zhabotinsky droplets

The information storing potential of droplets, in which an oscillatory, photosensitive Belousov–Zhabotinsky (BZ) reaction proceeds, is investigated experimentally.

On Emulation of Flueric Devices in Excitable Chemical Medium

Flueric devices are fluidic devices without moving parts. Fluidic devices use fluid as a medium for information transfer and computation. A Belousov-Zhabotinsky (BZ) medium is a thin-layer spatially extended excitable chemical medium which exhibits travelling excitation wave-fronts. The excitation wave-fronts transfer information. Flueric devices compute via jets interaction. BZ devices compute via excitation wave-fronts interaction. In numerical model of BZ medium we show that functions of key flueric devices are implemented in the excitable chemical system: signal generator, and, xor, not and nor Boolean gates, delay elements, diodes and sensors. Flueric devices have been widely used in industry since late 1960s and are still employed in automotive and aircraft technologies. Implementation of analog of the flueric devices in the excitable chemical systems opens doors to further applications of excitation wave-based unconventional computing in soft robotics, embedded organic electronics and living technologies.

Microfluidic platform for reproducible self-assembly of chemically communicating droplet networks with predesigned number and type of the communicating compartments

We report a microfluidic system for individually tailored generation and incubation of core-shell liquid structures with multiple cores that chemically communicate with each other via lipid membranes. We encapsulate an oscillating reaction-diffusion Belousov-Zhabotinsky (BZ) medium inside the aqueous droplets and study the propagation of chemical wave-fronts through the membranes. We further encapsulate the sets of interconnected BZ-droplets inside oil-lipid shells in order to i) chemically isolate the structures and ii) confine them via tunable capillary forces which leads to self-assembly of predesigned topologies. We observe that doublets (pairs) of droplets encapsulated in the shell exhibit oscillation patterns that evolve in time. We collect statistical data from tens of doublets all created under precisely controlled, almost identical conditions from which we conclude that the different types of transitions between the patterns depend on the relative volumes of the droplets within a chemically coupled pair. With this we show that the volume of the compartment is an important control parameter in designing chemical networks, a feature previously appreciated only by theory. Our system not only allows for new insights into the dynamics of geometrically complex and interacting chemical systems but is also suitable for generating autonomous chemically interconnected microstructures with possible future use, e.g., as smart biosensors or drug-release capsules.

Minimum size for a nanoscale temperature discriminator based on a thermochemical system

What are the limits of size reduction for information processing devices based on chemical reactions? In this paper, we partially answer this question. We show that a thermochemical system can be used to design a discriminator of the parameters associated with oscillations of the ambient temperature. Depending on the amplitude and frequency of the oscillations, the system exhibits sharp transitions between different types of its time evolutions. This phenomenon can be used to discriminate between different parameter values describing the oscillating environment. We investigate the reliability of the thermochemical discriminator as a function of the number of molecules involved in the reactions. A stochastic model of chemical reactions and heat exchange with the neighborhood, in which the number of molecules explicitly appears, is introduced. For the selected values of the parameters, thermochemical discriminators operating with less than 10(5) molecules appear to be unreliable.

Binary full adder, made of fusion gates, in a subexcitable Belousov-Zhabotinsky system

In an excitable thin-layer Belousov-Zhabotinsky (BZ) medium a localized perturbation leads to the formation of omnidirectional target or spiral waves of excitation. A subexcitable BZ medium responds to asymmetric local perturbation by producing traveling localized excitation wave-fragments, distant relatives of dissipative solitons. The size and life span of an excitation wave-fragment depend on the illumination level of the medium. Under the right conditions the wave-fragments conserve their shape and velocity vectors for extended time periods. I interpret the wave-fragments as values of Boolean variables. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. States of the logic variables, represented by the wave-fragments, are changed in the result of the collision between the wave-fragments. Thus, a logical gate is implemented. Several theoretical designs and experimental laboratory implementations of Boolean logic gates have been proposed in the past but little has been done cascading the gates into binary arithmetical circuits. I propose a unique design of a binary one-bit full adder based on a fusion gate. A fusion gate is a two-input three-output logical device which calculates the conjunction of the input variables and the conjunction of one input variable with the negation of another input variable. The gate is made of three channels: two channels cross each other at an angle, a third channel starts at the junction. The channels contain a BZ medium. When two excitation wave-fragments, traveling towards each other along input channels, collide at the junction they merge into a single wave-front traveling along the third channel. If there is just one wave-front in the input channel, the front continues its propagation undisturbed. I make a one-bit full adder by cascading two fusion gates. I show how to cascade the adder blocks into a many-bit full adder. I evaluate the feasibility of my designs by simulating the evolution of excitation in the gates and adders using the numerical integration of Oregonator equations.

Heterotic computing: exploiting hybrid computational devices

Current computational theory deals almost exclusively with single models: classical, neural, analogue, quantum, etc. In practice, researchers use ad hoc combinations, realizing only recently that they can be fundamentally more powerful than the individual parts. A Theo Murphy meeting brought together theorists and practitioners of various types of computing, to engage in combining the individual strengths to produce powerful new heterotic devices. 'Heterotic computing' is defined as a combination of two or more computational systems such that they provide an advantage over either substrate used separately. This post-meeting collection of articles provides a wide-ranging survey of the state of the art in diverse computational paradigms, together with reflections on their future combination into powerful and practical applications.