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

Using non-adiabatic excitation transfer for signal transmission between molecular logic gates

Molecular logic gates (MLGs) are molecules which perform logic operations. They can potentially be used as building blocks for nano-sized computational devices. However, their physical and functional integration is a difficult task which remains to be solved. The problem lies in the field of signal exchange between the gates within the system. We propose using non-adiabatic excitation transfer between the gates to address this problem while absorption and fluorescence are left to communicate with external devices. Excitation transfer was studied using the modified Bixon-Jortner-Plotnikov theory with the example of the 3H-thioxanthene-TTF-dibenzo-BODIPY covalently linked triad. Several designs of the molecule were studied in a vacuum and cyclohexane. It was found that the molecular logic system has to be planar and rigid to isolate radiative interfaces from other gates. Functioning of these gates is based on dark πσ*-states in contrast to bright ππ*-states of radiative interfaces. There are no fundamental differences between ππ* → πσ* and ππ* → ππ* transitions for cases when an exciton hops from one gate to another. The rates of such transitions depend only on an energy gap between states and the distance between gates. The circuit is highly sensitive to the choice of solvent which could rearrange its state structure thereby altering its behavior. According to the obtained results, non-adiabatic transfer can be considered as one of the possible ways for transmitting a signal between MLGs.

Non-Biochemical Gradient Sequence-Controlled Polymers with Tuned Kinetics and Self-Assembled Morphologies

Two key challenges in the multidisciplinary field of sequence-controlled polymers are their efficient synthesis and the establishment of correlation with polymer properties. In this context, in this paper, gradient architecture in the hydrophobic tail of an amphiphile is implemented and synthesized for a fixed hydrophilic unit (polyethylene glycol, PEG), by means of two monomers (2-hydroxypropyl methacrylate, HPMA, and diacetone acrylamide, DAAM) of contrasting reactivities. The resulting non-biochemical gradient sequence-controlled polymers are generated from a one-pot, homogeneous mixture through a PET-RAFT-PISA (photoinduced electron/energy transfer-reversible addition-fragmentation chain transfer-polymerization-induced self-assembly) method. In addition, the initial concentration ratio of the monomers in the gradient is varied as an input for a set of fixed experimental parameters and conditions, and its correlation with kinetics, gradient and self-assembled morphologies is established, as the output of the process. These results are extensively corroborated via nuclear magnetic resonance (NMR) spectroscopy analysis, together with transmission electron microscopy (TEM) images, dynamic light scattering (DLS), and gel permeation chromatography (GPC) experiments. These results have implications for chemical computation carried out by PISA, programmable self-assembly, information storage, biomimetics, origins of life and synthetic protocell studies.

Chemical reservoir computation in a self-organizing reaction network

Chemical reaction networks, such as those found in metabolism and signalling pathways, enable cells to process information from their environment1,2. Current approaches to molecular information processing and computation typically pursue digital computation models and require extensive molecular-level engineering3. Despite considerable advances, these approaches have not reached the level of information processing capabilities seen in living systems. Here we report on the discovery and implementation of a chemical reservoir computer based on the formose reaction4. We demonstrate how this complex, self-organizing chemical reaction network can perform several nonlinear classification tasks in parallel, predict the dynamics of other complex systems and achieve time-series forecasting. This in chemico information processing system provides proof of principle for the emergent computational capabilities of complex chemical reaction networks, paving the way for a new class of biomimetic information processing systems.

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.

M-State and N-Color (M-N = 1-1, 2-1, and 1-2) Turing Algorithms Demonstrated via DNA Self-Assembly

The fast and extensive generation of patterns using specific algorithms is a major challenge in the field of DNA algorithmic self-assembly. Turing machines (TMs) are simple computable machines that execute certain algorithms using carefully designed logic gates. We investigate Turing algorithms for the generation of patterns on algorithmic lattices using specific logic gates. Logic gates can be implemented into Turing building blocks. We discuss comprehensive methods for designing Turing building blocks to demonstrate an M-state and N-color Turing machine (M-N TM). The M-state and N-color (M-N = 1-1, 2-1, and 1-2) TMs generate Turing patterns that can be fabricated via DNA algorithmic self-assembly. The M-N TMs require two-input and three-output logic gates. We designed the head, tape, and transition rule tiles to demonstrate TMs for the 1-1, 2-1, and 1-2 Turing algorithms. By analyzing the characteristics of the Turing patterns, we classified them into two classes (DL and DR for states grown diagonally to the left and right, respectively) for the 1-1 TM, three for the 2-1 TM, and nine for the 1-2 TM. Among these, six representative Turing patterns generated using rules R11-0 and R11-1 for 1-1 TM, R21-01 and R21-09 for 2-1 TM, and R12-02 and R12-08 for 1-2 TM were constructed with DNA building blocks. Turing patterns on the DNA lattices were visualized by atomic force microscopy. The Turing patterns on the DNA lattices were similar to those simulated patterns. Implementing the Turing algorithms into DNA building blocks, as demonstrated via DNA algorithmic self-assembly, can be extended to a higher order of state and color to generate more complicated patterns, compute arithmetic operations, and solve mathematical functions.

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.

Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process

A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.

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.

Quantitative estimation of chemical microheterogeneity through the determination of fuzzy entropy

Chemical micro-heterogeneity is an attribute of all living systems and most of the soft and crystalline materials. Its characterization requires a plethora of techniques. This work proposes a strategy for quantifying the degree of chemical micro-heterogeneity. First of all, our approach needs the collection of time-evolving signals that can be fitted through poly-exponential functions. The best fit is determined through the Maximum Entropy Method. The pre-exponential terms of the poly-exponential fitting function are used to estimate Fuzzy Entropy. Related to the possibility of implementing Fuzzy sets through the micro-heterogeneity of chemical systems. Fuzzy Entropy becomes a quantitative estimation of the Fuzzy Information that can be processed through micro-heterogeneous chemical systems. We conclude that our definition of Fuzzy Entropy can be extended to other kinds of data, such as morphological and structural distributions, spectroscopic bands and chromatographic peaks. The chemical implementation of Fuzzy sets and Fuzzy logic will promote the development of Chemical Artificial Intelligence.

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.

Thermodynamic State Machine Network

We describe a model system—a thermodynamic state machine network—comprising a network of probabilistic, stateful automata that equilibrate according to Boltzmann statistics, exchange codes over unweighted bi-directional edges, update a state transition memory to learn transitions between network ground states, and minimize an action associated with fluctuation trajectories. The model is grounded in four postulates concerning self-organizing, open thermodynamic systems—transport-driven self-organization, scale-integration, input-functionalization, and active equilibration. After sufficient exposure to periodically changing inputs, a diffusive-to-mechanistic phase transition emerges in the network dynamics. The evolved networks show spatial and temporal structures that look much like spiking neural networks, although no such structures were incorporated into the model. Our main contribution is the articulation of the postulates, the development of a thermodynamically motivated methodology addressing them, and the resulting phase transition. As with other machine learning methods, the model is limited by its scalability, generality, and temporality. We use limitations to motivate the development of thermodynamic computers—engineered, thermodynamically self-organizing systems—and comment on efforts to realize them in the context of this work. We offer a different philosophical perspective, thermodynamicalism, addressing the limitations of the model and machine learning in general.

pH Oscillating System for Molecular Computation as a Chemical Turing Machine

It has previously been demonstrated that native chemical Turing machines can be constructed by exploiting the nonlinear dynamics of the homogeneous oscillating Belousov-Zhabotinsky reaction. These Turing machines can perform word recognition of a Chomsky type 1 context sensitive language (CSL), demonstrating their high computing power. Here, we report on a chemical Turing machine that has been developed using the H2O2-H2SO4-SO3 2--CO3 2- pH oscillating system. pH oscillators are different to bromate oscillators in two key ways: the proton is the autocatalytic agent, and at least one of the reductants is always fully consumed in each turnover-meaning the system has to be operated as a flow reactor. Through careful design, we establish a system that can also perform Chomsky type 1 CSL word recognition and demonstrate its power through the testing of a series of in-language and out-of-language words.

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.

Exploring the symbol processing 'time interval' parametric constraint in a Belousov-Zhabotinsky operated chemical Turing machine

Chemical reactions are powerful molecular recognition machines. This power has been recently harnessed to build actual instances of each class of experimentally realizable computing automata, using exclusively small-molecule chemistry (i.e. without requiring biomolecules). The most powerful of them, a programmable Turing machine, uses the Belousov-Zhabotinsky oscillatory chemistry, and accepts/rejects input sequences through a dual oscillatory and thermodynamic output signature. The time interval between the aliquots representing each letter of the input is the parameter that determines the time it takes to run the computation. Here, we investigate this critical performance parameter, and its effect not only on the computation speed, but also on the robustness of the accept/reject oscillatory and thermodynamic criteria. Our work demonstrates that the time interval is a non-trivial design parameter, whose choice should be made with great care. The guidelines we provide can be used in the optimization of the speed, robustness, and energy efficiency of chemical automata computations.

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.

Concurrent self-regulated autonomous synthesis and functionalization of pH-responsive giant vesicles by a chemical pH oscillator

The semibatch BrO3--SO32- pH oscillator serves as the radical source for the in situ polymerization of the pH-responsive 2-(diisopropylamino)-ethyl methacrylate monomer on poly(ethylene-glycol)-macroCTA chain and generates an amphiphilic block copolymer. These building blocks concurrently self-assemble to micelles and then transforms to vesicles as the chain length of the hydrophobic block growths. Large amplitude oscillations in the concentration of H+ by the semibatch BrO3--SO32- are provoked when the conditions in the system are favorable. The oscillations control the protonation state of the tertiary amine group in the core segment of the block copolymer. Rhythmic assembly-disassembly of the polymer structures is observed. All processes, from the time- regulated autonomous formation of the building blocks, their self-assembly and the rhythmic disassembly-reassembly are governed by the same simple chemical system, in the same reaction vessel, without complicated multi step procedures and are fueled and kept out of equilibrium by the uniform inflow of SO32-.

PISA: construction of self-organized and self-assembled functional vesicular structures

PISA reaction networks alone, integrated with other networks, or designing properties into the amphiphiles confer functionalities to the supramolecular assemblies.

In-vitro reconfigurability of native chemical automata, the inclusiveness of their hierarchy and their thermodynamics

Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.

Flow chemistry controls self-assembly and cargo in Belousov-Zhabotinsky driven polymerization-induced self-assembly

Amphiphilic block-copolymer vesicles are increasingly used for medical and chemical applications, and a novel method for their transient self-assembly orchestrated by periodically generated radicals during the oscillatory Belousov-Zhabotinsky (BZ) reaction was recently developed. Here we report how combining this one pot polymerization-induced self-assembly (PISA) method with a continuously stirred tank reactor (CSTR) strategy allows for continuous and reproducible control of both the PISA process and the chemical features (e.g. the radical generation and oscillation) of the entrapped cargo. By appropriately tuning the residence time (τ), target degree of polymerization (DP) and the BZ reactants, intermediate self-assembly structures are also obtained (micelles, worms and nano-sized vesicles). Simultaneously, the chemical properties of the cargo at encapsulation are known and tunable, a key advantage over batch operation. Finally, we also show that BZ-driven polymerization in CSTR additionally supports more non-periodic dynamics such as bursting.