Programmable chemical controllers made from DNA

Proto-neural networks from thermal proteins

Proteinoids are synthetic polymers that have structural similarities to natural proteins, and their formation is achieved through the application of heat to amino acid combinations in a dehydrated environment. The thermal proteins, initially synthesised by Sidney Fox during the 1960s, has the ability to undergo self-assembly, resulting in the formation of microspheres that resemble cells. These microspheres have fascinating biomimetic characteristics. In recent studies, substantial advancements have been made in elucidating the electrical signalling phenomena shown by proteinoids, hence showcasing their promising prospects in the field of neuro-inspired computing. This study demonstrates the advancement of experimental prototypes that employ proteinoids in the construction of fundamental neural network structures. The article provides an overview of significant achievements in proteinoid systems, such as the demonstration of electrical excitability, emulation of synaptic functions, capabilities in pattern recognition, and adaptability of network structures. This study examines the similarities and differences between proteinoid networks and spontaneous neural computation. We examine the persistent challenges associated with deciphering the underlying mechanisms of emergent proteinoid-based intelligence. Additionally, we explore the potential for developing bio-inspired computing systems using synthetic thermal proteins in forthcoming times. The results of this study offer a theoretical foundation for the advancement of adaptive, self-assembling electronic systems that operate using artificial bio-neural principles.

Chemical Logic Gates on Active Colloids

Recent studies have shown that active colloidal motors using enzymatic reactions for propulsion hold special promise for applications in fields ranging from biology to material science. It will be desirable to have active colloids with capability of computation so that they can act autonomously to sense their surroundings and alter their own dynamics. It is shown how small chemical networks that make use of enzymatic chemical reactions on the colloid surface can be used to construct motor-based chemical logic gates. The basic features of coupled enzymatic reactions that are responsible for propulsion and underlie the construction and function of chemical gates are described using continuum theory and molecular simulation. Examples are given that show how colloids with specific chemical logic gates, can perform simple sensing tasks. Due to the diverse functions of different enzyme gates, operating alone or in circuits, the work presented here supports the suggestion that synthetic motors using such gates could be designed to operate in an autonomous way in order to complete complicated tasks.

Time-encoded electrical detection of trace RNA biomarker by integrating programmable molecular amplifier on chip

One of the serious challenges facing modern point-of-care (PoC) molecular diagnostic platforms relate to reliable detection of low concentration biomarkers such as nucleic acids or proteins in biological samples. Non-specific analyte-receptor interactions due to competitive binding in the presence of abundant molecules, inefficient mass transport and very low number of analyte molecules in sample volume, in general pose critical hurdles for successful implementation of such PoC platforms for clinical use. Focusing on these specific challenges, this work reports a unique PoC biosensor that combines the advantages of nanoscale biologically-sensitive field-effect transistor arrays (BioFET-arrays) realized in a wafer-scale top-down nanofabrication as high sensitivity electrical transducers with that of sophisticated molecular programs (MPs) customized for selective recognition of analyte miRNAs and amplification resulting in an overall augmentation of signal transduction strategy. The MPs realize a programmable universal molecular amplifier (PUMA) in fluidic matrix on chip and provide a biomarker-triggered exponential release of small nucleic acid sequences easily detected by receptor-modified BioFETs. A common miRNA biomarker LET7a was selected for successful demonstration of this novel biosensor, achieving limit of detection (LoD) down to 10 fM and wide dynamic ranges (10 pM-10 nM) in complex physiological solutions. As the determination of biomarker concentration is implemented by following the electrical signal related to analyte-triggered PUMA in time-domain instead of measuring the threshold shifts of BioFETs, and circumvents direct hybridization of biomarkers at transducer surface, this new strategy also allows for multiple usage (>3 times) of the biosensor platform suggesting exceptional cost-effectiveness for practical use.

A DNA circuit that records molecular events

Characterizing the relative onset time, strength, and duration of molecular signals is critical for understanding the operation of signal transduction and genetic regulatory networks. However, detecting multiple such molecules as they are produced and then quickly consumed is challenging. A MER can encode information about transient molecular events as stable DNA sequences and are amenable to downstream sequencing or other analysis. Here, we report the development of a de novo molecular event recorder that processes information using a strand displacement reaction network and encodes the information using the primer exchange reaction, which can be decoded and quantified by DNA sequencing. The event recorder was able to classify the order at which different molecular signals appeared in time with 88% accuracy, the concentrations with 100% accuracy, and the duration with 75% accuracy. This simultaneous and highly programmable multiparameter recording could enable the large-scale deciphering of molecular events such as within dynamic reaction environments, living cells, or tissues.

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

A nicking enzyme-assisted allosteric strategy for self-resetting DNA switching circuits

The self-regulation of biochemical reaction networks is crucial for maintaining balance, stability, and adaptability within biological systems. DNA switching circuits, serving as basic units, play essential roles in regulating pathways, facilitating signal transduction, and processing biochemical reaction networks. However, the non-reusability of DNA switching circuits hinders its application in current complex information processing. Herein, we proposed a nicking enzyme-assisted allosteric strategy for constructing self-resetting DNA switching circuits to realize complex information processing. This strategy utilizes the unique cleavage ability of the nicking enzyme to achieve the automatic restoration of states. Based on this strategy, we implemented a self-resetting DNA switch. By leveraging the reusability of the DNA switch, we constructed a DNA switching circuit with selective activation characteristics and further extended its functionality to include fan-out and fan-in processes by expanding the number of functional modules and connection modes. Furthermore, we demonstrated the complex information processing capabilities of these switching circuits by integrating recognition, translation, and decision functional modules, which could analyze and transmit multiple input signals and realize parallel logic operations. This strategy simplifies the design of switching circuits and promotes the future development of biosensing, molecular computing, and nanomachines.

Real-time signal processing via chemical reactions for a microfluidic molecular communication system

Signal processing over the molecular domain is critical for analysing, modifying, and synthesising chemical signals in molecular communication systems. However, the lack of chemical signal processing blocks and the wide use of electronic devices to process electrical signals in existing molecular communication platforms can hardly meet the biocompatible, non-invasive, and size-miniaturised requirements of applications in various fields, e.g., medicine, biology, and environment sciences. To tackle this, here we design and construct a liquid-based microfluidic molecular communication platform for performing chemical concentration signal processing and digital signal transmission over distances. By specifically designing chemical reactions and microfluidic geometry, the transmitter of our platform is capable of shaping the emitted signals, and the receiver is able to threshold, amplify, and detect the chemical signals after propagation. By encoding bit information into the concentration of sodium hydroxide, we demonstrate that our platform can achieve molecular signal modulation and demodulation functionalities, and reliably transmit text messages over long distances. This platform is further optimised to maximise data rate while minimising communication error. The presented methodology for real-time chemical signal processing can enable the implementation of signal processing units in biological settings and then unleash its potential for interdisciplinary applications.

Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.

A geometric framework for reaction enumeration in computational nucleic acid devices

Cascades of DNA strand displacement reactions enable the design of potentially large circuits with complex behaviour. Computational modelling of such systems is desirable to enable rapid design and analysis. In previous work, the expressive power of graph theory was used to enumerate reactions implementing strand displacement across a wide range of complex structures. However, coping with the rich variety of possible graph-based structures required enumeration rules with complicated side-conditions. This paper presents an alternative approach to tackle the problem of enumerating reactions at domain level involving complex structures by integrating with a geometric constraint solving algorithm. The rule sets from previous work are simplified by replacing side-conditions with a general check on the geometric plausibility of structures generated by the enumeration algorithm. This produces a highly general geometric framework for reaction enumeration. Here, we instantiate this framework to solve geometric constraints by a structure sampling approach in which we randomly generate sets of coordinates and check whether they satisfy all the constraints. We demonstrate this system by applying it to examples from the literature where molecular geometry plays an important role, including DNA hairpin and remote toehold reactions. This work therefore enables integration of reaction enumeration and structural modelling.

Generation of DNA oligomers with similar chemical kinetics via in-silico optimization

Networks of interacting DNA oligomers are useful for applications such as biomarker detection, targeted drug delivery, information storage, and photonic information processing. However, differences in the chemical kinetics of hybridization reactions, referred to as kinetic dispersion, can be problematic for some applications. Here, it is found that limiting unnecessary stretches of Watson-Crick base pairing, referred to as unnecessary duplexes, can yield exceptionally low kinetic dispersions. Hybridization kinetics can be affected by unnecessary intra-oligomer duplexes containing only 2 base-pairs, and such duplexes explain up to 94% of previously reported kinetic dispersion. As a general design rule, it is recommended that unnecessary intra-oligomer duplexes larger than 2 base-pairs and unnecessary inter-oligomer duplexes larger than 7 base-pairs be avoided. Unnecessary duplexes typically scale exponentially with network size, and nearly all networks contain unnecessary duplexes substantial enough to affect hybridization kinetics. A new method for generating networks which utilizes in-silico optimization to mitigate unnecessary duplexes is proposed and demonstrated to reduce in-vitro kinetic dispersions as much as 96%. The limitations of the new design rule and generation method are evaluated in-silico by creating new oligomers for several designs, including three previously programmed reactions and one previously engineered structure.

Supervised Learning in a Multilayer, Nonlinear Chemical Neural Network

The development of programmable or trainable molecular circuits is an important goal in the field of molecular programming. Multilayer, nonlinear, artificial neural networks are a powerful framework for implementing such functionality in a molecular system, as they are provably universal function approximators. Here, we present a design for multilayer chemical neural networks with a nonlinear hyperbolic tangent transfer function. We use a weight perturbation algorithm to train the neural network which uses a simple construction to directly approximate the loss derivatives required for training. We demonstrate the training of this system to learn all 16 two-input binary functions from a common starting point. This work thus introduces new capabilities in the field of adaptive and trainable chemical reaction network (CRN) design. It also opens the door to potential future experimental implementations, including DNA strand displacement reactions.

Implementation of an Ultrasensitive Biomolecular Controller for Enzymatic Reaction Processes With Delay Using DNA Strand Displacement

In this article, a set of abstract chemical reactions has been employed to construct a novel nonlinear biomolecular controller, i.e, the Brink controller (BC) with direct positive autoregulation (DPAR) (namely BC-DPAR controller). In comparison to dual rail representation-based controllers such as the quasi sliding mode (QSM) controller, the BC-DPAR controller directly reduces the number of CRNs required for realizing an ultrasensitive input-output response because it does not involve the subtraction module, reducing the complexity of DNA implementations. Then, the action mechanism and steady-state condition constraints of two nonlinear controllers, BC-DPAR controller and QSM controller, are investigated further. Considering the mapping relationship between CRNs and DNA implementation, a CRNs-based enzymatic reaction process with delay is constructed, and a DNA strand displacement (DSD) scheme representing time delay is proposed. The BC-DPAR controller, when compared to the QSM controller, can reduce the number of abstract chemical reactions and DSD reactions required by 33.3% and 31.8%, respectively. Finally, an enzymatic reaction scheme with BC-DPAR controller is designed using DSD reactions. According to the findings, the enzymatic reaction process's output substance can approach the target level at a quasi-steady state in both delay-free and non-zero delay conditions, but the target level can only be achieved during a finite-time period, mainly due to the fuel stand depletion.

Parallel molecular computation on digital data stored in DNA

DNA is an incredibly dense storage medium for digital data. However, computing on the stored information is expensive and slow, requiring rounds of sequencing, in silico computation, and DNA synthesis. Prior work on accessing and modifying data using DNA hybridization or enzymatic reactions had limited computation capabilities. Inspired by the computational power of "DNA strand displacement," we augment DNA storage with "in-memory" molecular computation using strand displacement reactions to algorithmically modify data in a parallel manner. We show programs for binary counting and Turing universal cellular automaton Rule 110, the latter of which is, in principle, capable of implementing any computer algorithm. Information is stored in the nicks of DNA, and a secondary sequence-level encoding allows high-throughput sequencing-based readout. We conducted multiple rounds of computation on 4-bit data registers, as well as random access of data (selective access and erasure). We demonstrate that large strand displacement cascades with 244 distinct strand exchanges (sequential and in parallel) can use naturally occurring DNA sequence from M13 bacteriophage without stringent sequence design, which has the potential to improve the scale of computation and decrease cost. Our work merges DNA storage and DNA computing, setting the foundation of entirely molecular algorithms for parallel manipulation of digital information preserved in DNA.

Accelerating DNA computing via freeze-thaw cycling

DNA computing harnesses the immense potential of DNA molecules to enable sophisticated and transformative computational processes but is hindered by low computing speed. Here, we propose freeze-thaw cycling as a simple yet powerful method for high-speed DNA computing without complex procedures. Through iterative cycles, we achieve a substantial 20-fold speed enhancement in basic strand displacement reactions. This acceleration arises from the utilization of eutectic ice phase as a medium, temporarily increasing the effective local concentration of molecules during each cycle. In addition, the acceleration effect follows the Hofmeister series, where kosmotropic anions such as sulfate (SO42-) reduce eutectic phase volume, leading to a more notable enhancement in strand displacement reaction rates. Leveraging this phenomenon, freeze-thaw cycling demonstrates its generalizability for high-speed DNA computing across various circuit sizes, achieving up to a remarkable 120-fold enhancement in reaction rates. We envision its potential to revolutionize molecular computing and expand computational applications in diverse fields.

Conversion to Trimolecular G-Quadruplex by Spontaneous Hoogsteen Pairing-Based Strand Displacement Reaction between Bimolecular G-Quadruplex and Double G-Rich Probes

Bimolecular or tetramolecular G-quadruplexes (GQs) are predominantly self-assembled by the same sequence-identical G-rich oligonucleotides and usually remain inert to the strand displacement reaction (SDR) with other short G-rich invading fragments of DNA or RNA. Appealingly, in this study, we demonstrate that a parallel homomeric bimolecular GQ target of Tub10 d(CAGGGAGGGT) as the starting reactant, although completely folded in K+ solution and sufficiently stable (melting temperature of 57.7 °C), can still spontaneously accept strand invasion by a pair of short G-rich invading probes of P1 d(TGGGA) near room temperature. The final SDR product is a novel parallel heteromeric trimolecular GQ (tri-GQ) of Tub10/2P1 reassembled between one Tub10 strand and two P1 strands. Here we present, to the best of our knowledge, the first NMR solution structure of such a discrete heteromeric tri-GQ and unveil a unique mode of two probes vs one target in mutual recognition among G-rich canonical DNA oligomers. As a model system, the short invading probe P1 can spontaneously trap G-rich target Tub10 from a Watson-Crick duplex completely hybridized between Tub10 and its fully complementary strand d(ACCCTCCCTG). The Tub10 sequence of d(CAGGGAGGGT) is a fragment from the G-rich promoter region of the human β2-tubulin gene. Our findings provide new insights into the Hoogsteen pairing-based SDR between a GQ target and double invading probes of short G-rich DNA fragments and are expected to grant access to increasingly complex architectures in GQ-based DNA nanotechnology.

Design and Simulation of a Multilayer Chemical Neural Network That Learns via Backpropagation

The design and implementation of adaptive chemical reaction networks, capable of adjusting their behavior over time in response to experience, is a key goal for the fields of molecular computing and DNA nanotechnology. Mainstream machine learning research offers powerful tools for implementing learning behavior that could one day be realized in a wet chemistry system. Here we develop an abstract chemical reaction network model that implements the backpropagation learning algorithm for a feedforward neural network whose nodes employ the nonlinear "leaky rectified linear unit" transfer function. Our network directly implements the mathematics behind this well-studied learning algorithm, and we demonstrate its capabilities by training the system to learn a linearly inseparable decision surface, specifically, the XOR logic function. We show that this simulation quantitatively follows the definition of the underlying algorithm. To implement this system, we also report ProBioSim, a simulator that enables arbitrary training protocols for simulated chemical reaction networks to be straightforwardly defined using constructs from the host programming language. This work thus provides new insight into the capabilities of learning chemical reaction networks and also develops new computational tools to simulate their behavior, which could be applied in the design and implementations of adaptive artificial life.

Leveraging Steric Moieties for Kinetic Control of DNA Strand Displacement Reactions

DNA strand displacement networks are a critical part of dynamic DNA nanotechnology and are proven primitives for implementing chemical reaction networks. Precise kinetic control of these networks is important for their use in a range of applications. Among the better understood and widely leveraged kinetic properties of these networks are toehold sequence, length, composition, and location. While steric hindrance has been recognized as an important factor in such systems, a clear understanding of its impact and role is lacking. Here, a systematic investigation of steric hindrance within a DNA toehold-mediated strand displacement network was performed through tracking kinetic reactions of reporter complexes with incremental concatenation of steric moieties near the toehold. Two subsets of steric moieties were tested with systematic variation of structures and reaction conditions to isolate sterics from electrostatics. Thermodynamic and coarse-grained computational modeling was performed to gain further insight into the impacts of steric hindrance. Steric factors yielded up to 3 orders of magnitude decrease in the reaction rate constant. This pronounced effect demonstrates that steric moieties can be a powerful tool for kinetic control in strand displacement networks while also being more broadly informative of DNA structural assembly in both DNA-based therapeutic and diagnostic applications that possess elements of steric hindrance through DNA functionalization with an assortment of chemistries.

Pneumatic computers for embedded control of microfluidics

Alternative computing approaches that interface readily with physical systems are well suited for embedded control of those systems. We demonstrate finite state machines implemented as pneumatic circuits of microfluidic valves and use these controllers to direct microfluidic liquid handling procedures on the same chip. These monolithic integrated systems require only power to be supplied externally, in the form of a vacuum source. User input can be provided directly to the chip by covering pneumatic ports with a finger. State machines with up to four bits of state memory are demonstrated, and next-state combinational logic can be fully reprogrammed by changing the hole-punch pattern on a membrane in the chip. These pneumatic computers demonstrate a framework for the embedded control of physical systems and open a path to stand-alone lab-on-a-chip devices capable of highly complex functionality.

A Theoretical Framework for Implementable Nucleic Acids Feedback Systems

Chemical reaction networks can be utilised as basic components for nucleic acid feedback control systems' design for Synthetic Biology application. DNA hybridisation and programmed strand-displacement reactions are effective primitives for implementation. However, the experimental validation and scale-up of nucleic acid control systems are still considerably falling behind their theoretical designs. To aid with the progress heading into experimental implementations, we provide here chemical reaction networks that represent two fundamental classes of linear controllers: integral and static negative state feedback. We reduced the complexity of the networks by finding designs with fewer reactions and chemical species, to take account of the limits of current experimental capabilities and mitigate issues pertaining to crosstalk and leakage, along with toehold sequence design. The supplied control circuits are quintessential candidates for the first experimental validations of nucleic acid controllers, since they have a number of parameters, species, and reactions small enough for viable experimentation with current technical capabilities, but still represent challenging feedback control systems. They are also well suited to further theoretical analysis to verify results on the stability, performance, and robustness of this important new class of control systems.

Rapid Signal Amplification Based on Planetary Cross-Catalytic Hairpin Assembly Reactions

Non-enzymatic nucleic acid catalytic systems based on branch migration have been developed, with applications ranging from biological sensing to molecular computation. A scalable planetary cross-catalytic (PCC) system is built up in this work by cross-cascading three planetary catalytic hairpin assembly (CHA) reactions with a central three-arm-branched CHA reaction. With the bottom-up hierarchy strategy, we designed four levels of catalytic reactions, simple CHA reactions, two-layered linear cascades, conventional one-planetary PCC reactions, and two- and three-planetary PCC reactions, and examined the reaction products and intermediates in each level via native polyacrylamide gel electrophoresis. The gel shift assay optimized the designs of hairpin strands to keep the leaking reactions at a manageable level and protect against signal attenuation during serial signal transduction in nucleic acid circuits. The reaction kinetics, measured via fluorescence, are strongly dependent on the number of planetary reactions. As a result, the three-planetary PCC system achieved an exponential amplification factor of about 3^k, while the conventional one-planetary cross-catalytic system has an amplification factor of 2^k (k represents the cycling number). Finally, we demonstrated the rapid detection of a cancer biomarker, microRNA141, used as the catalyst in a two-planetary PCC system. We envision that the PCC systems could be applied in biological signal transduction, biocomputing, rapid detection of single- and multi-target nucleic acid probes, etc.

DNA Droplets: Intelligent, Dynamic Fluid

Breathtaking advances in DNA nanotechnology have established DNA as a promising biomaterial for the fabrication of programmable higher-order nano/microstructures. In the context of developing artificial cells and tissues, DNA droplets have emerged as a powerful platform for creating intelligent, dynamic cell-like machinery. DNA droplets are a microscale membrane-free coacervate of DNA formed through phase separation. This new type of DNA system couples dynamic fluid-like property with long-established DNA programmability. This hybrid nature offers an advantageous route to facile and robust control over the structures, functions, and behaviors of DNA droplets. This review begins by describing programmable DNA condensation, commenting on the physical properties and fabrication strategies of DNA hydrogels and droplets. By presenting an overview of the development pathways leading to DNA droplets, it is shown that DNA technology has evolved from static, rigid systems to soft, dynamic systems. Next, the basic characteristics of DNA droplets are described as intelligent, dynamic fluid by showcasing the latest examples highlighting their distinctive features related to sequence-specific interactions and programmable mechanical properties. Finally, this review discusses the potential and challenges of numerical modeling able to connect a robust link between individual sequences and macroscopic mechanical properties of DNA droplets.

Mapping Temporally Ordered Inputs to Binary Message Outputs with a DNA Temporal Logic Circuit

Molecular circuits and devices with temporal signal processing capability are of great significance for the analysis of complex biological processes. Mapping temporal inputs to binary messages is a process of history-dependent signal responses, which can help understand the signal-processing behavior of organisms. Here, we propose a DNA temporal logic circuit based on DNA strand displacement reactions, which can map temporally ordered inputs to corresponding binary message outputs. The presence or absence of the output signal is determined by the type of substrate reaction with the input so that different orders of inputs correspond to different binary outputs. We demonstrate that a circuit can be generalized to more complex temporal logic circuits by increasing or decreasing the number of substrates or inputs. We also show that our circuit had excellent responsiveness to temporally ordered inputs, flexibility, and expansibility in the case of symmetrically encrypted communications. We envision that our scheme can provide some new ideas for future molecular encryption, information processing, and neural networks.

Toehold-Mediated Strand Displacement in Random Sequence Pools

Toehold-mediated strand displacement (TMSD) has been used extensively for molecular sensing and computing in DNA-based molecular circuits. As these circuits grow in complexity, sequence similarity between components can lead to cross-talk, causing leak, altered kinetics, or even circuit failure. For small non-biological circuits, such unwanted interactions can be designed against. In environments containing a huge number of sequences, taking all possible interactions into account becomes infeasible. Therefore, a general understanding of the impact of sequence backgrounds on TMSD reactions is of great interest. Here, we investigate the impact of random DNA sequences on TMSD circuits. We begin by studying individual interfering strands and use the obtained data to build machine learning models that estimate kinetics. We then investigate the influence of pools of random strands and find that the kinetics are determined by only a small subpopulation of strongly interacting strands. Consequently, their behavior can be mimicked by a small collection of such strands. The equilibration of the circuit with the background sequences strongly influences this behavior, leading to up to 1 order of magnitude difference in reaction speed. Finally, we compare two established and one novel technique that speed up TMSD reactions in random sequence pools: a three-letter alphabet, protection of toeholds by intramolecular secondary structure, or by an additional blocking strand. While all of these techniques were useful, only the latter can be used without sequence constraints. We expect that our insights will be useful for the construction of TMSD circuits that are robust to molecular noise.

Operant conditioning of stochastic chemical reaction networks

Adapting one’s behavior to environmental conditions and past experience is a key trait of living systems. In the biological world, there is evidence for adaptive behaviors such as learning even in naturally occurring, non-neural, single-celled organisms. In the bioengineered world, advances in synthetic cell engineering and biorobotics have created the possibility of implementing lifelike systems engineered from the bottom up. This will require the development of programmable control circuitry for such biomimetic systems that is capable of realizing such non-trivial and adaptive behavior, including modification of subsequent behavior in response to environmental feedback. To this end, we report the design of novel stochastic chemical reaction networks capable of probabilistic decision-making in response to stimuli. We show that a simple chemical reaction network motif can be tuned to produce arbitrary decision probabilities when choosing between two or more responses to a stimulus signal. We further show that simple feedback mechanisms from the environment can modify these probabilities over time, enabling the system to adapt its behavior dynamically in response to positive or negative reinforcement based on its decisions. This system thus acts as a form of operant conditioning of the chemical circuit, in the sense that feedback provided based on decisions taken by the circuit form the basis of the learning process. Our work thus demonstrates that simple chemical systems can be used to implement lifelike behavior in engineered biomimetic systems.

A nanopore interface for higher bandwidth DNA computing

DNA has emerged as a powerful substrate for programming information processing machines at the nanoscale. Among the DNA computing primitives used today, DNA strand displacement (DSD) is arguably the most popular, with DSD-based circuit applications ranging from disease diagnostics to molecular artificial neural networks. The outputs of DSD circuits are generally read using fluorescence spectroscopy. However, due to the spectral overlap of typical small-molecule fluorescent reporters, the number of unique outputs that can be detected in parallel is limited, requiring complex optical setups or spatial isolation of reactions to make output bandwidths scalable. Here, we present a multiplexable sequencing-free readout method that enables real-time, kinetic measurement of DSD circuit activity through highly parallel, direct detection of barcoded output strands using nanopore sensor array technology (Oxford Nanopore Technologies’ MinION device). These results increase DSD output bandwidth by an order of magnitude over what is currently feasible with fluorescence spectroscopy.

Network topology-directed design of molecular CPU for cell-like dynamic information processing

Natural cells (NCs) can automatically and continuously respond to fluctuant external information and distinguish meaningful stimuli from weak noise depending on their powerful genetic and protein networks. We herein report a network topology-directed design of dynamic molecular processing system (DMPS) as a molecular central processing unit that powers an artificial cell (AC) able to process fluctuant information in its immediate environment similar to NCs. By constructing a mixed cell community, ACs and NCs have synchronous response to fluctuant extracellular stimuli under physiological condition and in a blood vessel-mimic circulation system. We also show that fluctuant bioinformation released by NCs can be received and processed by ACs. The molecular design of DMPS-powered AC is expected to allow a profound understanding of biological systems, advance the construction of intelligent molecular systems, and promote more elegant bioengineering applications.

DNA Strand-Displacement Temporal Logic Circuits

Molecular circuits capable of processing temporal information are essential for complex decision making in response to both the presence and history of a molecular environment. A particular type of temporal information that has been recognized to be important is the relative timing of signals. Here we demonstrate the strategy of temporal memory combined with logic computation in DNA strand-displacement circuits capable of making decisions based on specific combinations of inputs as well as their relative timing. The circuit encodes the timing information on inputs in a set of memory strands, which allows for the construction of logic gates that act on current and historical signals. We show that mismatches can be employed to reduce the complexity of circuit design and that shortening specific toeholds can be useful for improving the robustness of circuit behavior. We also show that a detailed model can provide critical insights for guiding certain aspects of experimental investigations that an abstract model cannot. We envision that the design principles explored in this study can be generalized to more complex temporal logic circuits and incorporated into other types of circuit architectures, including DNA-based neural networks, enabling the implementation of timing-dependent learning rules and opening up new opportunities for embedding intelligent behaviors into artificial molecular machines.

Massively Parallel DNA Computing Based on Domino DNA Strand Displacement Logic Gates

DNA computing has gained considerable attention due to the characteristics of high-density information storage and high parallel computing for solving computational problems. Building addressable logic gates with biomolecules is the basis for establishing biological computers. In the current calculation model, the multiinput AND operation often needs to be realized through a multilevel cascade between logic gates. Through experiments, it was found that the multilevel cascade causes signal leakage and affects the stability of the system. Using DNA strand displacement technology, we constructed a domino-like multiinput AND gate computing system instead of a cascade of operations, realizing multiinput AND computing on one logic gate and abandoning the traditional multilevel cascade of operations. Fluorescence experiments demonstrated that our methods significantly reduce system construction costs and improve the stability and robustness of the system. Finally, we proved stability and robustness of the domino AND gate by simulating the tic-tac-toe process with a massively parallel computing strategy.

Protecting Heterochiral DNA Nanostructures against Exonuclease-Mediated Degradation

Heterochiral DNA nanotechnology employs nucleic acids of both chiralities to construct nanoscale devices for applications in the intracellular environment. Interacting directly with cellular nucleic acids can be done most easily using D-DNA of the naturally occurring right-handed chirality; however, D-DNA is more vulnerable to degradation than enantiometric left-handed L-DNA. Here we report a novel combination of D-DNA and L-DNA nucleotides in triblock heterochiral copolymers, where the L-DNA domains act as protective caps on D-DNA domains. We demonstrate that the D-DNA components of strand displacement-based molecular circuits constructed using this technique resist exonuclease-mediated degradation during extended incubations in serum-supplemented media more readily than similar devices without the L-DNA caps. We show that this protection can be applied to both double-stranded and single-stranded circuit components. Our work enhances the state of the art for robust heterochiral circuit design and could lead to practical applications such as in vivo biomedical diagnostics.

Programming and training rate-independent chemical reaction networks

To program complex behavior in environments incompatible with electronic controllers such as within bioreactors or engineered cells, we turn to chemical information processors. While chemical reactions can perform computation in the stoichiometric exchange of reactants for products (how many molecules of which reactants result in how many molecules of which products), the control of reaction rates is usually thought to allow more complex computation. Motivated by the fact that correct stoichiometry is easier to ensure than reaction rates, we provide a method for programming and training chemical computation by stoichiometry. We show that such computation can be straightforwardly programmed in a manner analogous to sequential programming, and demonstrate the execution of neural networks capable of complex machine learning tasks.

Embedding computation in biochemical environments incompatible with traditional electronics is expected to have a wide-ranging impact in synthetic biology, medicine, nanofabrication, and other fields. Natural biochemical systems are typically modeled by chemical reaction networks (CRNs) which can also be used as a specification language for synthetic chemical computation. In this paper, we identify a syntactically checkable class of CRNs called noncompetitive (NC) whose equilibria are absolutely robust to reaction rates and kinetic rate law, because their behavior is captured solely by their stoichiometric structure. In spite of the inherently parallel nature of chemistry, the robustness property allows for programming as if each reaction applies sequentially. We also present a technique to program NC-CRNs using well-founded deep learning methods, showing a translation procedure from rectified linear unit (ReLU) neural networks to NC-CRNs. In the case of binary weight ReLU networks, our translation procedure is surprisingly tight in the sense that a single bimolecular reaction corresponds to a single ReLU node and vice versa. This compactness argues that neural networks may be a fitting paradigm for programming rate-independent chemical computation. As proof of principle, we demonstrate our scheme with numerical simulations of CRNs translated from neural networks trained on traditional machine learning datasets, as well as tasks better aligned with potential biological applications including virus detection and spatial pattern formation.

Programming Molecular Systems To Emulate a Learning Spiking Neuron

Hebbian theory seeks to explain how the neurons in the brain adapt to stimuli to enable learning. An interesting feature of Hebbian learning is that it is an unsupervised method and, as such, does not require feedback, making it suitable in contexts where systems have to learn autonomously. This paper explores how molecular systems can be designed to show such protointelligent behaviors and proposes the first chemical reaction network (CRN) that can exhibit autonomous Hebbian learning across arbitrarily many input channels. The system emulates a spiking neuron, and we demonstrate that it can learn statistical biases of incoming inputs. The basic CRN is a minimal, thermodynamically plausible set of microreversible chemical equations that can be analyzed with respect to their energy requirements. However, to explore how such chemical systems might be engineered de novo, we also propose an extended version based on enzyme-driven compartmentalized reactions. Finally, we show how a purely DNA system, built upon the paradigm of DNA strand displacement, can realize neuronal dynamics. Our analysis provides a compelling blueprint for exploring autonomous learning in biological settings, bringing us closer to realizing real synthetic biological intelligence.

Automated Leak Analysis of Nucleic Acid Circuits

Nucleic acids are a powerful engineering material that can be used to implement a broad range of computational circuits at the nanoscale, with potential applications in high-precision biosensing, diagnostics, and therapeutics. However, nucleic acid circuits are prone to leaks, which result from unintended displacement interactions between nucleic acid strands. Such leaks can grow combinatorially with circuit size, are challenging to mitigate, and can significantly compromise circuit behavior. While several techniques have been proposed to partially mitigate leaks, computational methods for designing new leak mitigation strategies and comparing their effectiveness on circuit behavior are limited. Here we present a general method for the automated leak analysis of nucleic acid circuits, referred to as DSD Leaks. Our method extends the logic programming functionality of the Visual DSD language, developed for the design and analysis of nucleic acid circuits, with predicates for leak generation, a leak reaction enumeration algorithm, and predicates to exclude low probability leak reactions. We use our method to identify the critical leak reactions affecting the performance of control circuits, and to analyze leak mitigation strategies by automatically generating leak reactions. Finally, we design new control circuits with substantially reduced leakage including a sophisticated proportional-integral controller circuit, which can in turn serve as building blocks for future circuits. By integrating our method within an open-source nucleic acid circuit design tool, we enable the leak analysis of a broad range of circuits, as an important step toward facilitating robust and scalable nucleic acid circuit design.

DNA Memristors and Their Application to Reservoir Computing

This paper introduces memristors realized by molecular and DNA reactions. Molecular memristors process one input molecule, generate two output molecules, and are realized using two molecular reactions with two different rate constants. The DNA memristors are realized using five DNA strand displacement (DSD) reactions with two effective rate constants. The hysteresis behavior is preserved in the proposed memristors, and this behavior can be altered by changing the ratios of the rate constants. The state of the memristor can be computed from the concentrations of the two output molecules using bipolar fractional coding. We describe how the proposed memristors can be used to learn the spatial and temporal properties of data via the reservoir computing (RC) model. An RC system can be divided into two parts: reservoir and readout layer. The first part transfers the information from the input space to a high-dimensional spatiotemporal feature space represented by the state of reservoirs. The connectivity structure of the reservoir will remain fixed through the dynamical evaluations. The readout layer effectively maps the projected features to the target output. A dynamical memristor array is used to implement an RC system that exploits the internal dynamical processes of the memristors. The readout layer implements a matrix-vector multiplication using molecular reactions, also based on bipolar fractional coding. All molecular reactions are mapped to DSD reactions. The RC system based on the DNA reservoir and the DNA readout layer is used to solve a handwritten digit recognition task and a second-order time series prediction task. The performance of the DNA RC system is comparable to that of an electronic memristor RC system for both tasks.

How fluorescent labels affect the kinetics of the toehold-mediated DNA strand displacement reaction

End modification of the toehold domain or near to it using fluorophore dyes or quenchers can significantly modulate the kinetics of the toehold-mediated strand displacement reaction (TMSDR) by almost two orders of magnitude. The labels at the end of the signal strand impede the TMSDR, while those at the end of the toehold domain of the substrate strand accelerate the TMSDR kinetics.

Chemical Reaction Networks’ Programming for Solving Equations

The computational ability of the chemical reaction networks (CRNs) using DNA as the substrate has been verified previously. To solve more complex computational problems and perform the computational steps as expected, the practical design of the basic modules of calculation and the steps in the reactions have become the basic requirements for biomolecular computing. This paper presents a method for solving nonlinear equations in the CRNs with DNA as the substrate. We used the basic calculation module of the CRNs with a gateless structure to design discrete and analog algorithms and realized the nonlinear equations that could not be solved in the previous work, such as exponential, logarithmic, and simple triangle equations. The solution of the equation uses the transformation method, Taylor expansion, and Newton iteration method, and the simulation verified this through examples. We used and improved the basic calculation module of the CRN++ programming language, optimized the error in the basic module, and analyzed the error’s variation over time.

Logical Analysis of Multiple Single-Nucleotide-Polymorphisms with Programmable DNA Molecular Computation for Clinical Diagnostics

Analyzing complex single-nucleotide-polymorphism (SNP) combinations in the genome is important for research and clinical applications, given that different SNP combinations can generate different phenotypic consequences. Recent works have shown that DNA-based molecular computing is powerful for simultaneously sensing and analyzing complex molecular information. Here, we designed a switching circuit-based DNA computational scheme that can integrate the sensing of multiple SNPs and simultaneously perform logical analysis of the detected SNP information to directly report clinical outcomes. As a demonstration, we successfully achieved automatic and accurate identification of 21 different blood group genotypes from 83 clinical blood samples with 100 % accuracy compared to sequencing data in a more rapid manner (3 hours). Our method enables a new mode of automatic and logical sensing and analyzing subtle molecular information for clinical diagnosis, as well as guiding personalized medication.

Cotranscriptionally encoded RNA strand displacement circuits

Engineered molecular circuits that process information in biological systems could address emerging human health and biomanufacturing needs. However, such circuits can be difficult to rationally design and scale. DNA-based strand displacement reactions have demonstrated the largest and most computationally powerful molecular circuits to date but are limited in biological systems due to the difficulty in genetically encoding components. Here, we develop scalable cotranscriptionally encoded RNA strand displacement (ctRSD) circuits that are rationally programmed via base pairing interactions. ctRSD circuits address the limitations of DNA-based strand displacement circuits by isothermally producing circuit components via transcription. We demonstrate circuit programmability in vitro by implementing logic and amplification elements, as well as multilayer cascades. Furthermore, we show that circuit kinetics are accurately predicted by a simple model of coupled transcription and strand displacement, enabling model-driven design. We envision ctRSD circuits will enable the rational design of powerful molecular circuits that operate in biological systems, including living cells.

Design and Realization of Triple dsDNA Nanocomputing Circuits in Microfluidic Chips

DNA logic gates, nanocomputing circuits, have already implemented basic computations and shown great signal potential for nano logic material application. However, the reaction temperature and computing speed still limit its development. Performing complicated computations requires a more stable component and a better computing platform. We proposed a more stable design of logic gates based on a triple, double-stranded, DNA (T-dsDNA) structure. We demonstrated a half adder and a full adder using these DNA nanocircuits and performed the computations in a microfluidic chip device at room temperature. When the solutions were mixed in the device, we obtained the expected results in real time, which suggested that the T-dsDNA combined microfluidic chip provides a concise strategy for large DNA nanocircuits.

Reservoir Computing Using DNA Oscillators

This paper presents novel implementations for reservoir computing (RC) using DNA oscillators. An RC system consists of two parts: reservoir and readout layer. The reservoir projects input signals into a high-dimensional feature space which is formed by the state of the reservoir. The internal connectivity structure of the reservoir remains unchanged throughout computation. After training, the readout layer maps the projected features into the desired output. It has been shown in prior work that coupled deoxyribozyme oscillators can be used as the reservoir. In this paper, we utilize the n-phase molecular oscillator (n ≥ 3) presented in our prior work. The readout layer implements a matrix-vector multiplication using molecular reactions based on molecular analog multiplication. All molecular reactions are mapped to DNA strand displacement (DSD) reactions. We also introduce a novel encoding method that can significantly reduce the reaction time. The feasibility of the proposed RC systems based on the DNA oscillator is demonstrated for the handwritten digit recognition task and a second-order nonlinear prediction task.

A facile biosynthesis strategy of plasmid DNA-derived nanowires for readable microRNA logic operations

Multiple microRNAs (miRNAs) logical assays have attracted wide attention recently, which can be applied to mimic and reveal cellular events at the molecular level. However, it remains challenging to develop...

Robust finite automata in stochastic chemical reaction networks

Finite-state automata (FSA) are simple computational devices that can nevertheless illustrate interesting behaviours. We propose that FSA can be employed as control circuits for engineered stochastic biological and biomolecular systems. We present an implementation of FSA using counts of chemical species in the range of hundreds to thousands, which is relevant for the counts of many key molecules such as mRNAs in prokaryotic cells. The challenge here is to ensure a robust representation of the current state in the face of stochastic noise. We achieve this by using a multistable approximate majority algorithm to stabilize and store the current state of the system. Arbitrary finite state machines can thus be compiled into robust stochastic chemical automata. We present two variants: one that consumes its input signals to initiate state transitions and one that does not. We characterize the state change dynamics of these systems and demonstrate their application to solve the four-bit binary square root problem. Our work lays the foundation for the use of chemical automata as control circuits in bioengineered systems and biorobotics.

A Cooperative DNA Catalyst

DNA catalysts are fundamental building blocks for diverse molecular information-processing circuits. Allosteric control of DNA catalysts has been developed to activate desired catalytic pathways at desired times. Here we introduce a new type of DNA catalyst that we call a cooperative catalyst: a pair of reversible reactions are employed to drive a catalytic cycle in which two signal species, which can be interpreted as an activator and an input, both exhibit catalytic behavior for output production. We demonstrate the role of a dissociation toehold in controlling the kinetics of the reaction pathway and the significance of a wobble base pair in promoting the robustness of the activator. We show near-complete output production with input and activator concentrations that are 0.1 times the gate concentration. The system involves just a double-stranded gate species and a single-stranded fuel species, as simple as the seesaw DNA catalyst, which has no allosteric control. The simplicity and modularity of the design make the cooperative DNA catalyst an exciting addition to strand-displacement motifs for general-purpose computation and dynamics.

A last-in first-out stack data structure implemented in DNA

DNA-based memory systems are being reported with increasing frequency. However, dynamic DNA data structures able to store and recall information in an ordered way, and able to be interfaced with external nucleic acid computing circuits, have so far received little attention. Here we present an in vitro implementation of a stack data structure using DNA polymers. The stack is able to record combinations of two different DNA signals, release the signals into solution in reverse order, and then re-record. We explore the accuracy limits of the stack data structure through a stochastic rule-based model of the underlying polymerisation chemistry. We derive how the performance of the stack increases with the efficiency of washing steps between successive reaction stages, and report how stack performance depends on the history of stack operations under inefficient washing. Finally, we discuss refinements to improve molecular synchronisation and future open problems in implementing an autonomous chemical data structure.

DNA is becoming increasingly used as a medium to store non-genetic information. Here the authors present a dynamic stack data structure implemented as a DNA polymer chemistry able to record and retrieve signals in a last-in first-out order.

Acceleration of DNA Hybridization Chain Reactions on 3D Nanointerfaces of Magnetic Particles and Their Direct Application in the Enzyme-Free Amplified Detection of microRNA

Accelerated DNA hybridization chain reactions (HCRs) using DNA origami as a scaffold have received considerable attention in dynamic DNA nanotechnology. However, tailor-made designs are essential for DNA origami scaffolds, hampering the practical application of accelerated HCRs. Here, we constructed the semilocalized HCR and localized HCR systems using magnetic beads (MBs) as a simple scaffold to explore them for the enzyme-free miR-21 detection. The semilocalized HCR system relied on free diffusing one hairpin DNA and MBs immobilized with another hairpin DNA, and the localized HCR system relied on MBs coimmobilized with two hairpin DNAs. We demonstrated that the DNA density on MBs plays a critical role in HCR kinetics and limit of detection (LOD). Among semilocalized HCR systems, MBs with a medium DNA density showed a faster HCR and lower LOD (10 pM) than the diffusive (conventional) HCR system (LOD: 86 pM). In contrast, the HCR further accelerated for the localized HCR systems as the DNA density increased. The localized HCR system with the highest DNA density showed the fastest HCR and the lowest LOD (533 fM). These findings are of great importance for the rational design of accelerated HCRs using simple scaffolds for practical applications.

DNA strand displacement reactions to accomplish a two-degree-of-freedom PID controller and its application in subtraction gate

Synthesis control circuits can be used to effectively control biochemical molecule processes. In the controller design based on chemical reaction networks (CRNs), generally only the tracking set-point is considered. However, the influence of disturbances, which are frequently encountered in biochemical systems, is often neglected, thus weakening the control effect of the system. In this article, tracking set-point input and suppressing disturbance input are considered in the control effect. Firstly, CRNs are adopted to construct a two-degree-of-freedom PID controller by combining a one-degree-of-freedom PID controller with a feedforward controller for the first time. Then, CRN expressions of the two input functions (step function and ramp function) used as input signals are defined. Furthermore, the two-degree-of-freedom PID controller is founded by DNA strand displacement (DSD) reaction networks, because DNA is an ideal engineering material to constitute molecular devices based on CRNs. The overshoot of the two-degree-of-freedom PID control system is significantly reduced compared to the one-degree-of-freedom PID control system. Finally, a leak reaction is treated as an extraneous disturbance input to a subtraction gate. The influence of external disturbance is solved by the two-degree-of-freedom PID controller. It is worth noting that the two-degree-of-freedom subtraction gate control system better restrains the impact of a disturbance input (leak reaction).

Structure sampling for computational estimation of localized DNA interaction rates

Molecular circuits implemented using molecular components tethered to a DNA tile nanostructure have certain advantages over solution-phase circuits. Tethering components in close proximity increases the speed of reactions by reducing diffusion and improves scalability by enabling reuse of identical DNA sequences at different locations in the circuit. These systems show great potential for practical applications including delivery of diagnostic and therapeutic molecular circuits to cells. When modeling such systems, molecular geometry plays an important role in determining whether the two species interact and at what rate. In this paper, we present an automated method for estimating reaction rates in tethered molecular circuits that takes the geometry of the tethered species into account. We probabilistically generate samples of structure distributions based on simple biophysical models and use these to estimate important parameters for kinetic models. This work provides a basis for subsequent enhanced modeling and design tools for localized molecular circuits.

The art of molecular computing: Whence and whither

An astonishingly diverse biomolecular circuitry orchestrates the functioning machinery underlying every living cell. These biomolecules and their circuits have been engineered not only for various industrial applications but also to perform other atypical functions that they were not evolved for-including computation. Various kinds of computational challenges, such as solving NP-complete problems with many variables, logical computation, neural network operations, and cryptography, have all been attempted through this unconventional computing paradigm. In this review, we highlight key experiments across three different ''eras'' of molecular computation, beginning with molecular solutions, transitioning to logic circuits and ultimately, more complex molecular networks. We also discuss a variety of applications of molecular computation, from solving NP-hard problems to self-assembled nanostructures for delivering molecules, and provide a glimpse into the exciting potential that molecular computing holds for the future. Also see the video abstract here: https://youtu.be/9Mw0K0vCSQw.