Chemical Memory with Discrete Turing Patterns Appearing in the Glycolytic Reaction

Memory is an essential element in information processing devices. We investigated a network formed by just three interacting nodes representing continuously stirred tank reactors (CSTRs) in which the glycolytic reaction proceeds as a potential realization of a chemical memory unit. Our study is based on the 2-variable computational model of the reaction. The model parameters were selected such that the system has a stable limit cycle and several distinct, discrete Turing patterns characterized by stationary concentrations at the nodes. In our interpretation, oscillations represent a blank memory unit, and Turing patterns code information. The considered memory can preserve information on one of six different symbols. The time evolution of the nodes was individually controlled by the inflow of ATP. We demonstrate that information can be written with a simple and short perturbation of the inflow. The perturbation applies to only one or two nodes, and it is symbol specific. The memory can be erased with identical inflow perturbation applied to all nodes. The presented idea of pattern-coded memory applies to other reaction networks that allow for discrete Turing patterns. Moreover, it hints at the experimental realization of memory in a simple system with the glycolytic reaction.

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%.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br₂. The present studies suggest that the distribution of the inhibitor, Br^-, which is produced from Br₂, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Memory, switches, and an OR-port through bistability in chemically fueled crystals

The ability to store information in chemical reaction networks is essential for the complex behavior we associate with life. In biology, cellular memory is regulated through transcriptional states that are bistable, i.e., a state that can either be on or off and can be flipped from one to another through a transient signal. Such memory circuits have been realized synthetically through the rewiring of genetic systems in vivo or through the rational design of reaction networks based on DNA and highly evolved enzymes in vitro. Completely bottom-up analogs based on small molecules are rare and hard to design and thus represent a challenge for systems chemistry. In this work, we show that bistability can be designed from a simple non-equilibrium reaction cycle that is coupled to crystallization. The crystals exert the necessary feedback on the reaction cycle required for the bistability resulting in an on-state with assemblies and an off-state without. Each state represents volatile memory that can be stored in continuously stirred tank reactors indefinitely even though molecules are turned over on a minute-timescale. We showcase the system’s abilities by creating a matrix display that can store images and by creating an OR-gate by coupling several switches together.

In biology, information is stored and processed using highly evolved molecules in bistable states. Here, the authors demonstrate bistability in a synthetic system without the need for evolved biomolecules or autocatalytic networks.

Parallel transmission in a synthetic nerve

Bioelectronic devices that are tetherless and soft are promising developments in medicine, robotics and chemical computing. Here, we describe bioinspired synthetic neurons, composed entirely of soft, flexible biomaterials, capable of rapid electrochemical signal transmission over centimetre distances. Like natural cells, our synthetic neurons release neurotransmitters from their terminals, which initiate downstream reactions. The components of the neurons are nanolitre aqueous droplets and hydrogel fibres, connected through lipid bilayers. Transmission is powered at these interfaces by light-driven proton pumps and mediated by ion-conducting protein pores. By bundling multiple neurons into a synthetic nerve, we have shown that distinct signals can propagate simultaneously along parallel axons, thereby transmitting spatiotemporal information. Synthetic nerves might play roles in next-generation implants, soft machines and computing devices.

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.

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.

Infochemistry and the Future of Chemical Information Processing

Nowadays, information processing is based on semiconductor (e.g., silicon) devices. Unfortunately, the performance of such devices has natural limitations owing to the physics of semiconductors. Therefore, the problem of finding new strategies for storing and processing an ever-increasing amount of diverse data is very urgent. To solve this problem, scientists have found inspiration in nature, because living organisms have developed uniquely productive and efficient mechanisms for processing and storing information. We address several biological aspects of information and artificial models mimicking corresponding bioprocesses. For instance, we review the formation of synchronization patterns and the emergence of order out of chaos in model chemical systems. We also consider molecular logic and ion fluxes as information carriers. Finally, we consider recent progress in infochemistry, a new direction at the interface of chemistry, biology, and computer science, considering unconventional methods of information processing.

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.

Switching between Two Oscillatory States Depending on the Electrical Potential

Various spatiotemporal patterns were created on the surface or in the body of cation-exchange resin beads which were loaded with the catalyst of the Belousov-Zhabotinsky (BZ) reaction. Either global oscillations (GO) or traveling waves (TW) and the switching between them were observed in the previous papers, but it was not clear how chemicals contribute to the reaction inside/around the BZ bead. In this paper, we scanned the electrical potential, E, from +1 to -1 V (negative scan) and then turned from -1 to +1 V (positive scan) to control the switching between GO and TW. We found that the electrical switching potential from TW to GO, E_TG, and from GO to TW, E_GT, depended on the scanning direction of E and the diameter of the bead, d. The present study suggests that the electrode-induced increase of the inhibitor, Br^-, and the activator, HBrO₂, around the BZ bead plays an important role in determining E_TG and E_GT.

Distance dependent types of coupling of chemical micro-oscillators immersed in a water-in-oil microemulsion

A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally.

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%.

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.

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.

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.

Coupling pH-Regulated Multilayers with Inorganic Surfaces for Bionic Devices and Infochemistry

This article summarizes more than 10 years of cooperation with Prof. Helmuth Möhwald. Here we describe how the research moved from light-regulated feedback sustainable systems and control biodevices to the current focus on infochemistry in aqueous solution. An important advanced characteristic of such materials and devices is the pH concentration gradient in aqueous solution. A major part of the article focuses on the use of localized illumination for proton generation as a reliable, minimal-reagent-consuming, stable light-promoted proton pump. The in situ scanning vibration electrode technique (SVET) and scanning ion-selective electrode technique (SIET) are efficient for the spatiotemporal evolution of ions on the surface. pH-sensitive polyelectrolyte (PEs) multilayers with different PE architectures are composed with a feedback loop for bionic devices. We show here that pH-regulated PE multilayers can change their properties-film thickness and stiffness, permeability, hydrophilicity, and/or fluorescence-in response to light or electrochemical or biological processes instead of classical acid/base titration.

Thermal switch of oscillation frequency in Belousov-Zhabotinsky liquid marbles

External control of oscillation dynamics in the Belousov-Zhabotinsky (BZ) reaction is important for many applications including encoding computing schemes. When considering the BZ reaction, there are limited studies dealing with thermal cycling, particularly cooling, for external control. Recently, liquid marbles (LMs) have been demonstrated as a means of confining the BZ reaction in a system containing a solid-liquid interface. BZ LMs were prepared by rolling 50 μl droplets in polyethylene (PE) powder. Oscillations of electrical potential differences within the marble were recorded by inserting a pair of electrodes through the LM powder coating into the BZ solution core. Electrical potential differences of up to 100 mV were observed with an average period of oscillation ca 44 s. BZ LMs were subsequently frozen to -1°C to observe changes in the frequency of electrical potential oscillations. The frequency of oscillations reduced upon freezing to 11 mHz cf. 23 mHz at ambient temperature. The oscillation frequency of the frozen BZ LM returned to 23 mHz upon warming to ambient temperature. Several cycles of frequency fluctuations were able to be achieved.

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.

Cancer classification with a network of chemical oscillators

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