Experimental logical gates in a reaction-diffusion medium: the XOR gate and beyond

Impact of Membership Functions on the Performance of AI-Assisted Neuro-Fuzzy System for Analysis of Anion-Responsive Behaviours of Polypyridyl-Imidazole Based Ru(II) Receptors

This study explores the anion sensing properties of mono-, bi-, and trinuclear Ru(II) complexes based on polypyridyl-imidazole ligands with varying numbers of dissociable protons in their secondary coordination sphere. The imidazole protons, influenced by the Ru2+ centers, facilitate interactions with anions like F- and CN- in acetonitrile, and CN- in water, through hydrogen bonding or via proton abstraction. The spectral properties of the metalloreceptors change in the presence of these anions, and the initial state can be restored with acid, allowing recycling. The complexes exhibit Boolean logic functions (Implication logic gates) using spectral outputs in the presence of specific anions and acids. To address the time and cost constraints of executing comprehensive sensing experiments, an adaptive neuro-fuzzy inference system (ANFIS) with five membership functions (triangular, trapezoidal, generalized bell-shaped, Gaussian, and pi-shaped) was used to predict experimental data and appropriate modeling of the sensing characteristics. Comparison of ANFIS model outputs with experimental data showed a good correlation, with the Gaussian and generalized bell-shaped functions providing high accuracy and close resemblance to experimental data. This neuro-fuzzification approach promises accurate prediction and modeling of sensing data for Ru(II)-based metalloreceptors.

On Emergence of Spontaneous Oscillations in Kombucha and Proteinoids

An important part of studying living systems is figuring out the complicated steps that lead to order from chaos. Spontaneous oscillations are a key part of self-organisation in many biological and chemical networks, including kombucha and proteinoids. This study examines the spontaneous oscillations in kombucha and proteinoids, specifically exploring their potential connection to the origin of life. As a community of bacteria and yeast work together, kombucha shows remarkable spontaneous oscillations in its biochemical parts. This system can keep a dynamic balance and organise itself thanks to metabolic processes and complex chemical reactions. Similarly, proteinoids, which may have been primitive forms of proteins, undergo spontaneous fluctuations in their structure and function periodically. Because these oscillations happen on their own, they may play a very important part in the development of early life forms. This paper highlights the fundamental principles governing the transition from chaos to order in living systems by examining the key factors that influence the frequency and characteristics of spontaneous oscillations in kombucha and proteinoids. Looking into these rhythms not only helps us understand where life came from but also shows us ways to make self-organising networks in synthetic biology and biotechnology. There is significant discussion over the emergence of biological order from chemical disorder. This article contributes to the ongoing discussion by examining at the theoretical basis, experimental proof, and implications of spontaneous oscillations. The results make it clear that random oscillations are an important part of the change from nonliving to living matter. They also give us important information about what life is all about.

Advancing Molecular-Scale Logic Devices through Multistage Switching in a Luminescent Bimetallic Ru(II)-Terpyridine Complex

Stimuli-responsive multistep switching phenomena of a luminescent bimetallic Ru(II) complex are employed herein to fabricate multiple configurable logic devices. The complex exhibits "off-on" and "on-off" emission switching upon alternative treatment with visible and UV light. Additionally, remarkable augmentation of the rate as well as quantum yield of photoisomerization was achieved via the use of a chemical oxidant (Ce4+) as well as a reductant (metallic sodium). Upon exploiting the emission spectral response of the complex, several advanced Boolean logic functions, including IMPLICATION as well as 2-input 2-output and 3-input 2-output complex combinational logic gates, are successfully implemented. Additionally, by utilizing the vast efficacy of Python, a novel "logic_circuit" model is devised that is capable of making accurate decisions under the influence of various input combinations. This model transcends traditional Boolean logic gates, offering flexibility and intuition to design logical functions tailored to specific chemical contexts. By integrating principles of logic circuits with chemical processes, this innovative approach enables structure determination of the chemical states based on input conditions, thereby unlocking avenues for exploring intricate interactions and reactions beyond conventional Boolean logic paradigms.

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.

Optofluidic memory and self-induced nonlinear optical phase change for reservoir computing in silicon photonics

Nanophotonics allows to employ light-matter interaction to induce nonlinear optical effects and realize non-conventional memory and computation capabilities, however to date, light-liquid interaction was not considered as a potential mechanism to achieve computation on a nanoscale. Here, we experimentally demonstrate self-induced phase change effect which relies on the coupling between geometric changes of thin liquid film to optical properties of photonic waveguide modes, and then employ it for neuromorphic computing. In our optofluidic silicon photonics system we utilize thermocapillary-based deformation of thin liquid film capable to induce nonlinear effect which is more than one order of magnitude higher compared to the more traditional heat-based thermo-optical effect, and allowing operation as a nonlinear actuator and memory element, both residing at the same compact spatial region. The resulting dynamics allows to implement Reservoir Computing at spatial region which is approximately five orders of magnitude smaller compared to state-of-the-art experimental liquid-based systems.

Human brain-inspired chemical artificial intelligence tools for the analysis and prediction of the anion-sensing characteristics of an imidazole-based luminescent Os(II)-bipyridine complex

Neural network and decision tree-based soft computing techniques are implemented in this work for the thorough analysis of the multichannel anion-sensing characteristics of an Os(II)-bipyridine complex derived from imidazole-4,5-bis(benzimidazole) ligand. With the aid of three imidazole NH protons in its outer coordination sphere, a substantial change in the spectral response as well as Os^II/Os^III potential is made possible upon treating with anions of varying basicity. Initial hydrogen bonding between NH protons and anions and thereafter complete proton transfer from the complex backbone probably take place in the process. The deprotonation of the complex by specific anions and restoration to its original form by acid is also reversible. The responsiveness of the new compound is complex enough to imitate multiple sophisticated binary and ternary Boolean logic (BL) functions (NOT logic, combinational logic, traffic signal, set-reset flip-flop logic, and ternary NOR logic) by employing its spectral and redox outputs upon the action of suitable anions and acid in a proper sequence. Executing sensing investigations on altering the amount of the anions within a widespread range is often time-consuming and tedious. To overcome the lacuna, we implemented multiple soft computing techniques, viz., fuzzy logic (FL), artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS), and decision tree (DT) regression, for the thorough analysis and prediction of the experimentally observed results. The outcomes obtained from different techniques were compared among themselves as well as with the experimental data and utilized for the proper modeling of the anion-sensing behaviors of the complex.

Neural network and decision tree-based machine learning tools to analyse the anion-responsive behaviours of emissive Ru(ii)–terpyridine complexes

Artificial neural network, adaptive neuro-fuzzy inference and decision tree regression are implemented to analyse the anion-responsive behaviours of emissive Ru(ii)–terpyridine complexes.

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.

Neuro-Fuzzification Architecture for Modeling of Electrochemical Ion-Sensing Data of Imidazole-Dicarboxylate-Based Ru(II)-Bipyridine Complex

Anion- and pH-sensing behaviors of an imidazole-dicarboxylate-based Ru(II)-bipyridine complex possessing a number of dissociable protons in its secondary coordination sphere are employed here for the creation of multiple Boolean and fuzzy logic systems. The absorption, emission, and electrochemical behaviors of the metalloreceptor were significantly modulated upon the influence of basic anions (such as F^-, AcO^-, and H₂PO₄^-) as well as by altering the pH of the solution. Interestingly, the deprotonation of the metalloreceptor by selected anions or by alkaline pH, followed by its restoration to its original form by acid or acidic pH is reversible and could be repeated many times. The metalloreceptor is capable to demonstrate several advanced Boolean functions, namely, three-input OR gate, set-reset flip-flop logic, and traffic signal, by employing its electrochemical responses through proper use of different inputs. Administering exhaustive sensing experiments by changing the analyte concentration within a wide range is usually tedious as well as exorbitantly costly. To get rid of these difficulties, we employed here several soft computing approaches such as artificial neural networks (ANN), fuzzy logic systems (FLS), or adaptive neuro-fuzzy inference system (ANFIS) to foresee the experimental sensing data and to appropriately model the protonation-deprotonation behaviors of the metalloreceptor. Reasonably good correlation between the experimental and model output data is also reflected in their tested root-mean-square error values (0.115961 and 0.118894 for the ANFIS model).

Computation by Convective Logic Gates and Thermal Communication

We demonstrate a novel computational architecture based on fluid convection logic gates and heat flux-mediated information flows. Our previous work demonstrated that Boolean logic operations can be performed by thermally driven convection flows. In this work, we use numerical simulations to demonstrate a different , but universal Boolean logic operation (NOR), performed by simpler convective gates. The gates in the present work do not rely on obstacle flows or periodic boundary conditions, a significant improvement in terms of experimental realizability. Conductive heat transfer links can be used to connect the convective gates, and we demonstrate this with the example of binary half addition. These simulated circuits could be constructed in an experimental setting with modern, 2-dimensional fluidics equipment, such as a thin layer of fluid between acrylic plates. The presented approach thus introduces a new realm of unconventional, thermal fluid-based computation.

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.

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.

Native Chemical Computation. A Generic Application of Oscillating Chemistry Illustrated With the Belousov-Zhabotinsky Reaction. A Review

Computing with molecules is at the center of complex natural phenomena, where the information contained in ordered sequences of molecules is used to implement functionalities of synthesized materials or to interpret the environment, as in Biology. This uses large macromolecules and the hindsight of billions of years of natural evolution. But, can one implement computation with small molecules? If so, at what levels in the hierarchy of computing complexity? We review here recent work in this area establishing that all physically realizable computing automata, from Finite Automata (FA) (such as logic gates) to the Linearly Bound Automaton (LBA, a Turing Machine with a finite tape) can be represented/assembled/built in the laboratory using oscillatory chemical reactions. We examine and discuss in depth the fundamental issues involved in this form of computation exclusively done by molecules. We illustrate their implementation with the example of a programmable finite tape Turing machine which using the Belousov-Zhabotinsky oscillatory chemistry is capable of recognizing words in a Context Sensitive Language and rejecting words outside the language. We offer a new interpretation of the recognition of a sequence of chemicals representing words in the machine's language as an illustration of the “Maximum Entropy Production Principle” and concluding that word recognition by the Belousov-Zhabotinsky Turing machine is equivalent to extremal entropy production by the automaton. We end by offering some suggestions to apply the above to problems in computing, polymerization chemistry, and other fields of science.

Light-Activated Signaling in DNA-Encoded Sender-Receiver Architectures

Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver cells. A variety of nonliving artificial cell models have been developed in recent years that mimic various aspects of diffusion-based intercellular communication. However, localized secretion of diffusive signals from individual protocells, which is critical for mimicking biological sender-receiver systems, has remained challenging to control precisely. Here, we engineer light-responsive, DNA-encoded sender-receiver architectures, where protein-polymer microcapsules act as cell mimics and molecular communication occurs through diffusive DNA signals. We prepare spatial distributions of sender and receiver protocells using a microfluidic trapping array and set up a signaling gradient from a single sender cell using light, which activates surrounding receivers through DNA strand displacement. Our systematic analysis reveals how the effective signal range of a single sender is determined by various factors including the density and permeability of receivers, extracellular signal degradation, signal consumption, and catalytic regeneration. In addition, we construct a three-population configuration where two sender cells are embedded in a dense array of receivers that implement Boolean logic and investigate spatial integration of nonidentical input cues. The results offer a means for studying diffusion-based sender-receiver topologies and present a strategy to achieve the congruence of reaction-diffusion and positional information in chemical communication systems that have the potential to reconstitute collective cellular patterns.

How Does a Simple Network of Chemical Oscillators See the Japanese Flag?

Chemical computing is something we use every day (e.g., in the brain), but we can still not explore and master its potential in human-made experiments. It is expected that the maximum computational efficiency of a chemical medium can be achieved if information is processed in parallel by different parts of the medium. In this paper, we use computer simulations to explore the efficiency of chemical computing performed by a small network of three coupled chemical oscillators. We optimize the network to recognize the white and red regions of the Japanese flag. The input information is introduced as the inhibition times of individual oscillators, and the output information is coded in the number of activator maxima observed on a selected oscillator. We have used the Oregonator model to simulate the network time evolution and the evolutionary optimization to find the best network for the considered task. We have found that even a network of three interacting oscillators can recognize the color of a randomly selected point with 95% accuracy.

Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers

It is commonly believed that information processing in living organisms is based on chemical reactions. However, the human achievements in constructing chemical information processing devices demonstrate that it is difficult to design such devices using the bottom-up strategy. Here I discuss the alternative top-down design of a network of chemical oscillators that performs a selected computing task. As an example, I consider a simple network of interacting chemical oscillators that operates as a comparator of two real numbers. The information on which of the two numbers is larger is coded in the number of excitations observed on oscillators forming the network. The parameters of the network are optimized to perform this function with the maximum accuracy. I discuss how information theory methods can be applied to obtain the optimum computing structure.

Logical response induced by temperature asymmetry

It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths. It has been found that if a given state is kept at a sufficiently low temperature compared to the other, the system shows one kind of logic behavior (say, or). Interestingly, the system's response turns into the other kind (say, and) if the temperature of the initial low-temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value. However, the reliability of the second kind of logical response (and) is not as good as the first kind (or) and depends on the amplitude of the inputs. Still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low-temperature well.

How Chemistry Computes: Language Recognition by Non-Biochemical Chemical Automata. From Finite Automata to Turing Machines

Every problem in computing can be cast as decision problems of whether strings are in a language or not. Computations and language recognition are carried out by three classes of automata, the most complex of which is the Turing machine. Living systems compute using biochemistry; in the artificial, computation today is mostly electronic. Thinking of chemical reactions as molecular recognition machines, and without using biochemistry, we realize one automaton in each class by means of one-pot, table top chemical reactors: from the simplest, Finite automata, to the most complex, Turing machines. Language acceptance/rejection criteria by automata can be formulated using energy considerations. Our Turing machine uses the Belousov-Zhabotinsky chemical reaction and checks the same symbol in an Avogadro′s number of processors. Our findings have implications for chemical and general computing, artificial intelligence, bioengineering, the study of the origin and presence of life on other planets, and for artificial biology.

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Computations are language recognition events carried out by “computing automata”

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Chemical reactions are molecular recognition events equivalent to automata

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Words in a language can be represented by sequences of chemical reactants

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Inorganic reactions like automata, including Turing machines, recognize languages

Boolean logic by convective obstacle flows

We present a potential new mode of natural computing in which simple, heat-driven fluid flows perform Boolean logic operations. The system comprises a two-dimensional single-phase fluid that is heated from below and cooled from above, with two obstacles placed on the horizontal mid-plane. The obstacles remove all vertical momentum that flows into them. The horizontal momentum extraction of the obstacles is controlled in a binary fashion, and constitutes the 2-bit input. The output of the system is a thresholded measure of the energy extracted by the obstacles. Due to the existence of multiple attractors in the phase space of this system, the input–output relationships are equivalent to those of the OR, XOR or NAND gates, depending on the threshold and obstacle separation. The ability to reproduce these logical operations suggests that convective flows might have the potential to perform more general computations, despite the fact that they do not involve electronics, chemistry or multiple fluid phases.

Cancer classification with a network of chemical oscillators

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

Chemical computing with reaction-diffusion processes

Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed.

An organic jelly made fractal logic gate with an infinite truth table

Widely varying logic gates invented over a century are all finite. As data deluge problem looms large on the information processing and communication industry, the thrust to explore radical concepts is increasing rapidly. Here, we design and synthesis a molecule, wherein, the input energy transmits in a cycle inside the molecular system, just like an oscillator, then, we use the molecule to make a jelly that acts as chain of oscillators with a fractal like resonance band. Hence, with the increasing detection resolution, in the vacant space between two energy levels of a given resonance band, a new band appears, due to fractal nature, generation of newer energy levels never stops. This is natural property of a linear chain oscillator. As we correlate each energy level of the resonance band of organic jelly, as a function of pH and density of the jelly, we realize a logic gate, whose truth table is finite, but if we zoom any small part, a new truth table appears. In principle, zooming of truth table would continue forever. Thus, we invent a new class of infinite logic gate for the first time.

Maze solving using temperature-induced Marangoni flow

A temperature gradient can be utilized for maze solving using a temperature-induced Marangoni flow. Induced liquid flow drags passive tracers such as small dye particles, which dissolve in a water phase thus visualizing the shortest path.

Routing of Physarum polycephalum "signals" using simple chemicals

In previous work the chemotaxis toward simple organic chemicals was assessed. We utilize the knowledge gained from these chemotactic assays to route Physarum polycephalum “signals” at a series of junctions. By applying chemical inputs at a simple T-junction we were able to reproducibly control the path taken by the plasmodium of P. Polycephalum. Where the chemoattractant farnesene was used at one input a routed signal could be reproducibly generated i.e., P. Polycephalum moves toward the source of chemoattractant. Where the chemoattractant was applied at both inputs the signal was reproducibly split i.e., at the junction the plasmodium splits and moves toward both sources of chemoattractant. If a chemorepellent was used then the signal was reproducibly suppressed i.e., P. Polycephalum did not reach either output and was confined to the input channel. This was regardless of whether a chemoattractant was used in combination with the chemorepellent showing a hierarchy of inhibition over attraction. If no chemical input was used in the simple circuit then a random signal was generated, whereby P. Polycephalum would move toward one output at the junction, but the direction was randomly selected.

Information coding with frequency of oscillations in Belousov-Zhabotinsky encapsulated disks

Information processing with an excitable chemical medium, like the Belousov-Zhabotinsky (BZ) reaction, is typically based on information coding in the presence or absence of excitation pulses. Here we present a new concept of Boolean coding that can be applied to an oscillatory medium. A medium represents the logical TRUE state if a selected region oscillates with a high frequency. If the frequency fails below a specified value, it represents the logical FALSE state. We consider a medium composed of disks encapsulating an oscillatory mixture of reagents, as related to our recent experiments with lipid-coated BZ droplets. We demonstrate that by using specific geometrical arrangements of disks containing the oscillatory medium one can perform logical operations on variables coded in oscillation frequency. Realizations of a chemical signal diode and of a single-bit memory with oscillatory disks are also discussed.

Pattern transformation with DNA circuits

Readily programmable chemical networks are important tools as the scope of chemistry expands from individual molecules to larger molecular systems. Although many complex systems are constructed using conventional organic and inorganic chemistry, the programmability of biological molecules such as nucleic acids allows for precise, high-throughput and automated design, as well as simple, rapid and robust implementation. Here we show that systematic and quantitative control over the diffusivity and reactivity of DNA molecules yields highly programmable chemical reaction networks (CRNs) that execute at the macroscale. In particular, we designed and implemented non-enzymatic DNA circuits capable of performing pattern-transformation algorithms such as edge detection. We also showed that it is possible to fine-tune and multiplex such circuits. We believe these strategies will provide programmable platforms on which to prototype CRNs, discover bottom-up construction principles and generate patterns in materials.

Control of logic gates by dichotomous noise in energetic and entropic systems

We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.

Logic gates for entropic transport

We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.

Logical and arithmetic circuits in Belousov-Zhabotinsky encapsulated disks

Excitation waves on a subexcitable Belousov-Zhabotinsky (BZ) substrate can be manipulated by chemical variations in the substrate and by interactions with other waves. Symbolic assignment and interpretation of wave dynamics can be used to perform logical and arithmetic computations. We present chemical analogs of elementary logic and arithmetic circuits created entirely from interconnected arrangements of individual BZ encapsulated cell-like disk. Interdisk wave migration is confined in carefully positioned connecting pores. This connection limits wave expansion and unifies the input-output characteristic of the disks. Circuit designs derived from numeric simulations are optically encoded onto a homogeneous photosensitive BZ substrate.

Implementation of glider guns in the light-sensitive Belousov-Zhabotinsky medium

In cellular automata models a glider gun is an oscillating pattern of nonquiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical gates and thus realize universal computation. The glider gun is the only means of ensuring the negation operation without additional external input and therefore is an essential component of a collision-based computing circuit. We demonstrate the existence of glider-gun-like structures in both experimental and numerical studies of an excitable chemical system-the light-sensitive Belousov-Zhabotinsky reaction. These discoveries could provide the basis for future designs of collision-based reaction-diffusion computers.

Spatiotemporal chemical dynamics in living cells: from information trafficking to cell physiology

Biological thought in the 20th century was dominated by the study of structures at increasingly minute levels. For biology to advance beyond structural reductionism and contribute its full measure to clinical care, living biological structures must be understood in the context of their collective chemical processes at the relevant chemical time-scales. Using high-speed fluorescence microscopy, we have studied intra- and inter-cellular signaling using shutter speeds ( approximately 100 ns) that remove the effects of wave motion and diffusion from optical images. By collecting a series of such images, stop-action movies of signal trafficking in living cells are created; these have revealed a new level of spatiotemporal chemical organization within cells. Numerous types of chemical waves have been found in living cells expressing a great variety of physical properties. In this article I will review some of these basic findings, discuss these events in the context of information trafficking, and illustrate the potential implications of this work in medicine.

Voronoi diagrams generated by regressing edges of precipitation fronts

Reaction-diffusion systems where one of the reagents (outer electrolyte) penetrates into a gel by diffusion and forms a precipitate with the other reagent (inner electrolyte) homogenized in the gel, are able to produce various complex precipitation patterns. The previously studied NaOH + AgNO3 and recently discovered CuCl2 + K3[Fe(CN)6] processes, (where the first reagent is the outer electrolyte and the other is the inner electrolyte homogenized in the gel), when reacted using the above mentioned method, are able to generate tessellations of a plane by a mechanism dependant on the dynamics of so-called regressing edges of the reaction fronts. The spontaneous partitioning of the reacted phases results in the construction of a pattern analogous to a Voronoi diagram or one of their generalizations.