Combinatorial displacement of DNA strands: application to matrix multiplication and weighted sums

Fluorescence-Based Multimodal DNA Logic Gates

The use of DNA structures in creating multimodal logic gates bears high potential for building molecular devices and computation systems. However, due to the complex designs or complicated working principles, the implementation of DNA logic gates within molecular devices and circuits is still quite limited. Here, we designed simple four-way DNA logic gates that can serve as multimodal platforms for simple to complex operations. Using the proximity quenching of the fluorophore-quencher pair in combination with the toehold-mediated strand displacement (TMSD) strategy, we have successfully demonstrated that the fluorescence output, which is a result of gate opening, solely relies on the oligonucleotide(s) input. We further demonstrated that this strategy can be used to create multimodal (tunable displacement initiation sites on the four-way platform) logic gates including YES, AND, OR, and the combinations thereof. The four-way DNA logic gates developed here bear high promise for building biological computers and next-generation smart molecular circuits with biosensing capabilities.

DNA as a universal chemical substrate for computing and data storage

DNA computing and DNA data storage are emerging fields that are unlocking new possibilities in information technology and diagnostics. These approaches use DNA molecules as a computing substrate or a storage medium, offering nanoscale compactness and operation in unconventional media (including aqueous solutions, water-in-oil microemulsions and self-assembled membranized compartments) for applications beyond traditional silicon-based computing systems. To build a functional DNA computer that can process and store molecular information necessitates the continued development of strategies for computing and data storage, as well as bridging the gap between these fields. In this Review, we explore how DNA can be leveraged in the context of DNA computing with a focus on neural networks and compartmentalized DNA circuits. We also discuss emerging approaches to the storage of data in DNA and associated topics such as the writing, reading, retrieval and post-synthesis editing of DNA-encoded data. Finally, we provide insights into how DNA computing can be integrated with DNA data storage and explore the use of DNA for near-memory computing for future information technology and health analysis applications.

Integrating Ligands into Nucleic Acid Systems

Signal transduction from non-nucleic acid ligands (small molecules and proteins) to structural changes of nucleic acids plays a crucial role in both biomedical analysis and cellular regulations. However, how to bridge between these two types of molecules without compromising the expandable complexity and programmability of the nucleic acid nanomachines is a critical challenge. Compared with the previously most widely applied transduction strategies, we review the latest advances of a kinetically controlled approach for ligand-oligonucleotide transduction in this Concept article. This new design works through an intrinsic conformational alteration of the nucleic acid aptamer upon the ligand binding as a governing factor for nucleic acid strand displacement reactions. The functionalities and applications of this transduction system as a ligand converter on biosensing and DNA computation are described and discussed. Furthermore, we propose some potential scenarios for utilization of this ligand transduction design to regulate gene expression through synthetic RNA switches in the cellular contexts. Finally, future perspectives regarding this ligand-oligonucleotide transduction platform are also discussed.

DNA strand displacement based computational systems and their applications

DNA computing has become the focus of computing research due to its excellent parallel processing capability, data storage capacity, and low energy consumption characteristics. DNA computational units can be precisely programmed through the sequence specificity and base pair principle. Then, computational units can be cascaded and integrated to form large DNA computing systems. Among them, DNA strand displacement (DSD) is the simplest but most efficient method for constructing DNA computing systems. The inputs and outputs of DSD are signal strands that can be transferred to the next unit. DSD has been used to construct logic gates, integrated circuits, artificial neural networks, etc. This review introduced the recent development of DSD-based computational systems and their applications. Some DSD-related tools and issues are also discussed.

Tunable and Modular miRNA Classifier through Indirect Associative Toehold Strand Displacement

The programmability of nucleic acids allows detection devices with complex behaviors to be designed de novo. While highly specific, these high-order circuits are usually sequence constrained, making their adaptability toward biological targets challenging. Here, we devise a new strategy called indirect associative strand displacement to decouple sequence constraints between miRNA inputs and de novo strand displacement circuits. By splitting circuit inputs into their toehold and branch migration regions and controlling their association through a docking strand, we demonstrate how any miRNA sequence can be interfaced with synthetic DNA circuits, including catalytic hairpin assembly and a four-input classifier.

DNA Matrix Operation Based on the Mechanism of the DNAzyme Binding to Auxiliary Strands to Cleave the Substrate

Numerical computation is a focus of DNA computing, and matrix operations are among the most basic and frequently used operations in numerical computation. As an important computing tool, matrix operations are often used to deal with intensive computing tasks. During calculation, the speed and accuracy of matrix operations directly affect the performance of the entire computing system. Therefore, it is important to find a way to perform matrix calculations that can ensure the speed of calculations and improve the accuracy. This paper proposes a DNA matrix operation method based on the mechanism of the DNAzyme binding to auxiliary strands to cleave the substrate. In this mechanism, the DNAzyme binding substrate requires the connection of two auxiliary strands. Without any of the two auxiliary strands, the DNAzyme does not cleave the substrate. Based on this mechanism, the multiplication operation of two matrices is realized; the two types of auxiliary strands are used as elements of the two matrices, to participate in the operation, and then are combined with the DNAzyme to cut the substrate and output the result of the matrix operation. This research provides a new method of matrix operations and provides ideas for more complex computing systems.

Solution of Simultaneous Higher Order Equations Based on DNA Strand Displacement Circuit

Currently, DNA strand displacement is often used to build neural networks or solve logical problems. While there are few studies on the use of DNA strand displacement to solve the higher order equations. In this paper, the catalysis, degradation, annihilation and adjusted reaction modules are built through DNA strand displacement. The chemical reaction networks of the corresponding higher order equations and simultaneous equations are established through these modules, and these chemical reaction networks can be used to build analog circuits to solve binary primary simultaneous equations and binary quadratic simultaneous equations. Finally, through Visual DSD software verification, this design can realize the solution of binary primary simultaneous equations and binary quadratic simultaneous equations, which provides a reference for DNA computation in the future.

A kinetically controlled platform for ligand-oligonucleotide transduction

Ligand-oligonucleotide transduction provides the critical pathway to integrate non-nucleic acid molecules into nucleic acid circuits and nanomachines for a variety of strand-displacement related applications. Herein, a general platform is constructed to convert the signals of ligands into desired oligonucleotides through a precise kinetic control. In this design, the ligand-aptamer binding sequence with an engineered duplex stem is introduced between the toehold and displacement domains of the invading strand to regulate the strand-displacement reaction. Employing this platform, we achieve efficient transduction of both small molecules and proteins orthogonally, and more importantly, establish logical and cascading operations between different ligands for versatile transduction. Besides, this platform is capable of being directly coupled with the signal amplification systems to further enhance the transduction performance. This kinetically controlled platform presents unique features with designing simplicity and flexibility, expandable complexity and system compatibility, which may pave a broad road towards nucleic acid-based developments of sophisticated transduction networks.

Controllable DNA strand displacement by independent metal-ligand complexation

Introduction of artificial metal-ligand base pairs can enrich the structural diversity and functional controllability of nucleic acids. In this work, we revealed a novel approach by placing a ligand-type nucleoside as an independent toehold to control DNA strand-displacement reactions based on metal-ligand complexation. This metal-mediated artificial base pair could initiate strand invasion similar to the natural toehold DNA, but exhibited flexible controllability to manipulate the dynamics of strand displacement that was only governed by its intrinsic coordination properties. External factors that influence the intrinsic properties of metal-ligand complexation, including metal species, metal concentrations and pH conditions, could be utilized to regulate the strand dynamics. Reversible control of DNA strand-displacement reactions was also achieved through combination of the metal-mediated artificial base pair with the conventional toehold-mediated strand exchange by cyclical treatments of the metal ion and the chelating reagent. Unlike previous studies of embedded metal-mediated base pairs within natural base pairs, this metal-ligand complexation is not integrated into the nucleic acid structure, but functions as an independent toehold to regulate strand displacement, which would open a new door for the development of versatile dynamic DNA nanotechnologies.

Dynamically elongated associative toehold for tuning DNA circuit kinetics and thermodynamics

Associative toehold is a powerful concept enabling efficient combinatorial computation in DNA circuit. A longer association length boosts circuit kinetics and equilibrium signal but results in higher leak rate. We reconcile this trade-off by using a hairpin lock design to dynamically elongate the effective associative toehold length in response to the input target. Design guidelines were established to achieve robust elongation without incurring additional leakages. Three hairpin initiators with different combinations of elongated associative toehold (4 → 6 nt, 5 → 8 nt and 6 → 9 nt) were shortlisted from the design framework for further discussion. The circuit performance improved in terms of reaction kinetics, equilibrium signal generated and limit of detection. Overall, the elongated associative toehold served as a built-in function to stabilize and favour the forward, desired reaction when triggered.

Handhold-Mediated Strand Displacement: A Nucleic Acid Based Mechanism for Generating Far-from-Equilibrium Assemblies through Templated Reactions

The use of templates is a well-established method for the production of sequence-controlled assemblies, particularly long polymers. Templating is canonically envisioned as akin to a self-assembly process, wherein sequence-specific recognition interactions between a template and a pool of monomers favor the assembly of a particular polymer sequence at equilibrium. However, during the biogenesis of sequence-controlled polymers, template recognition interactions are transient; RNA and proteins detach spontaneously from their templates to perform their biological functions and allow template reuse. Breaking template recognition interactions puts the product sequence distribution far from equilibrium, since specific product formation can no longer rely on an equilibrium dominated by selective copy-template bonds. The rewards of engineering artificial polymer systems capable of spontaneously exhibiting nonequilibrium templating are large, but fields like DNA nanotechnology lack the requisite tools; the specificity and drive of conventional DNA reactions rely on product stability at equilibrium, sequestering any recognition interaction in products. The proposed alternative is handhold-mediated strand displacement (HMSD), a DNA-based reaction mechanism suited to producing out-of-equilibrium products. HMSD decouples the drive and specificity of the reaction by introducing a transient recognition interaction, the handhold. We measure the kinetics of 98 different HMSD systems to prove that handholds can accelerate displacement by 4 orders of magnitude without being sequestered in the final product. We then use HMSD to template the selective assembly of any one product DNA duplex from an ensemble of equally stable alternatives, generating a far-from-equilibrium output. HMSD thus brings DNA nanotechnology closer to the complexity of out-of-equilibrium biological systems.

Morphological Manipulation of DNA Gel Microbeads with Biomolecular Stimuli

Hydrogels are essential in many fields ranging from tissue engineering and drug delivery to food sciences or cosmetics. Hydrogels that respond to specific biomolecular stimuli such as DNA, mRNA, miRNA and small molecules are highly desirable from the perspective of medical applications, however interfacing classical hydrogels with nucleic acids is still challenging. Here were demonstrate the generation of microbeads of DNA hydrogels with droplet microfluidic, and their morphological actuation with DNA strands. Using strand displacement and the specificity of DNA base pairing, we selectively dissolved gel beads, and reversibly changed their size on-the-fly with controlled swelling and shrinking. Lastly, we performed a complex computing primitive-A Winner-Takes-All competition between two populations of gel beads. Overall, these results show that strand responsive DNA gels have tantalizing potentials to enhance and expand traditional hydrogels, in particular for applications in sequencing and drug delivery.

Cofactor-assisted three-way DNA junction-driven strand displacement

Toehold-mediated strand displacement is widely used to construct and operate DNA nanodevices. Cooperative regulation of strand displacement with diverse factors is pivotal in the design and construction of functional and dynamic devices. Herein, a cofactor-assisted three-way DNA junction-driven strand displacement strategy was reported, which could tune the reaction kinetics by the collaboration of DNA and other types of stimulus. This strategy is responsive to various inputs by incorporation of the specific sequence into the three-way junction structure. Specifically, the cooperation of multiple factors changes the conformation of the specific domain and promotes the reaction. To demonstrate the strategy, adenosine triphosphate (ATP), HG²⁺, and pH were used as cofactors to modulate the displacement reaction. The electrophoresis and fluorescence experiments showed that the cooperative regulation of the strand displacement reaction could be achieved by diverse factors using this strategy. The proposed strategy provides design flexibility for dynamic DNA devices and may have potential in biosensing and biocomputing.

Cooperative regulation of strand displacement with diverse factors was achieved by a cofactor-assisted three-way DNA junction-driven strategy. Using this strategy nanodevices reacted to various inputs by incorporating a specific sequence into the three-way junction structure.

Cross-Inhibitor: a time-sensitive molecular circuit based on DNA strand displacement

Designing biochemical systems that can be effectively used in diverse fields, including diagnostics, molecular computing and nanomachines, has long been recognized as an important goal of molecular programming and DNA nanotechnology. A key issue in the development of such practical devices on the nanoscale lies in the development of biochemical components with information-processing capacity. In this article, we propose a molecular device that utilizes DNA strand displacement networks and allows interactive inhibition between two input signals; thus, it is termed a cross-inhibitor. More specifically, the device supplies each input signal with a processor such that the processing of one input signal will interdict the signal of the other. Biochemical experiments are conducted to analyze the interdiction performance with regard to effectiveness, stability and controllability. To illustrate its feasibility, a biochemical framework grounded in this mechanism is presented to determine the winner of a tic-tac-toe game. Our results highlight the potential for DNA strand displacement cascades to act as signal controllers and event triggers to endow molecular systems with the capability of controlling and detecting events and signals.

Conditional guide RNA through two intermediate hairpins for programmable CRISPR/Cas9 function: building regulatory connections between endogenous RNA expressions

A variety of nanodevices developed for nucleic acid computation provide great opportunities to construct versatile synthetic circuits for manipulation of gene expressions. In our study, by employing a two-hairpin mediated nucleic acid strand displacement as a processing joint for conditional guide RNA, we aim to build artificial connections between naturally occurring RNA expressions through programmable CRISPR/Cas9 function. This two-hairpin joint possesses a sequence-switching machinery, in which a random trigger strand can be processed to release an unconstrained sequence-independent strand and consequently activate the self-inhibitory guide RNA for conditional gene regulation. This intermediate processor was characterized by the fluorescence reporter system and applied for regulation of the CRISPR/Cas9 binding activity. Using plasmids to generate this sequence-switching machinery in situ, we achieved the autonomous genetic regulation of endogenous RNA expressions controlled by other unrelated endogenous RNAs in both E. coli and human cells. Unlike previously reported strand-displacement genetic circuits, this advanced nucleic acid nanomachine provides a novel approach that can establish regulatory connections between naturally occurring endogenous RNAs. In addition to CRISPR systems, we anticipate this two-hairpin machine can serve as a general processing joint for wide applications in the development of other RNA-based genetic circuits.

Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

Molecular and DNA Artificial Neural Networks via Fractional Coding

This article considers implementation of artificial neural networks (ANNs) using molecular computing and DNA based on fractional coding. Prior work had addressed molecular two-layer ANNs with binary inputs and arbitrary weights. In prior work using fractional coding, a simple molecular perceptron that computes sigmoid of scaled weighted sum of the inputs was presented where the inputs and the weights lie between [-1,1]. Even for computing the perceptron, the prior approach suffers from two major limitations. First, it cannot compute the sigmoid of the weighted sum, but only the sigmoid of the scaled weighted sum. Second, many machine learning applications require the coefficients to be arbitrarily positive and negative numbers that are not bounded between [-1,1]; such numbers cannot be handled by the prior perceptron using fractional coding. This paper makes four contributions. First molecular perceptrons that can handle arbitrary weights and can compute sigmoid of the weighted sums are presented. Thus, these molecular perceptrons are ideal for regression applications and multi-layer ANNs. A new molecular divider is introduced and is used to compute sigmoid(ax) where . Second, based on fractional coding, a molecular artificial neural network (ANN) with one hidden layer is presented. Third, a trained ANN classifier with one hidden layer from seizure prediction application from electroencephalogram is mapped to molecular reactions and DNA and their performances are presented. Fourth, molecular activation functions for rectified linear unit (ReLU) and softmax are also presented.

DNA logic circuits based on FokI enzyme regulation

A series of DNA logic devices was constructed based on the allosteric strategy of the enzyme-assisted cleavage regulation system, which are simple in scale, modular, and work efficiently.

De novo-designed translation-repressing riboregulators for multi-input cellular logic

Efforts to construct synthetic biological circuits with more complex functions have often been hindered by the idiosyncratic behavior, limited dynamic range, and crosstalk of commonly utilized parts. Here, we employ de novo RNA design to develop two high-performance translational repressors with sensing and logic capabilities. These synthetic riboregulators, termed toehold repressors and three-way junction (3WJ) repressors, detect transcripts with nearly arbitrary sequences, repress gene expression by up to 300-fold, and yield orthogonal sets of up to 15 devices. Automated forward engineering is used to improve toehold repressor dynamic range and SHAPE-Seq is applied to confirm the designed switching mechanism of 3WJ repressors in living cells. We integrate the modular repressors into biological circuits that execute universal NAND and NOR logic and evaluate the four-input expression NOT ((A1 AND A2) OR (B1 AND B2)) in Escherichia coli. These capabilities make toehold and 3WJ repressors valuable new tools for biotechnological applications.

Thermodynamics and kinetics guided probe design for uniformly sensitive and specific DNA hybridization without optimization

Sensitive and specific DNA hybridization is essential for nucleic acid chemistry. Competitive composition of probe and blocker has been the most adopted probe design for its relatively high sensitivity and specificity. However, the sensitivity and specificity were inversely correlated over the length and concentration of the blocker strand, making the optimization process cumbersome. Herein, we construct a theoretical model for competitive DNA hybridization, which disclose that both the thermodynamics and kinetics contribute to the inverse correlation. Guided by this, we invent the 4-way Strand Exchange LEd Competitive DNA Testing (SELECT) system, which breaks up the inverse correlation. Using SELECT, we identified 16 hot-pot mutations in human genome under uniform conditions, without optimization at all. The specificities were all above 140. As a demonstration of the clinical practicability, we develop probe systems that detect mutations in human genomic DNA extracted from ovarian cancer patients with a detection limit of 0.1%.

Optimisation of nucleic acid probes and blocker strands can be laborious. Here the authors construct a theoretical model of competitive DNA hybridisation to design DNA probes for optimisation-free mutation detection.

Temporal Pattern Recognition through Analog Molecular Computation

Living cells communicate information about physiological conditions by producing signaling molecules in a specific timed manner. Different conditions can result in the same total amount of a signaling molecule, differing only in the pattern of the molecular concentration over time. Such temporally coded information can be completely invisible to even state-of-the-art molecular sensors with high chemical specificity that respond only to the total amount of the signaling molecule. Here, we demonstrate design principles for circuits with temporal specificity, that is, molecular circuits that respond to specific temporal patterns in a molecular concentration. We consider pulsatile patterns in a molecular concentration characterized by three fundamental temporal features: time period, duty fraction, and number of pulses. We develop circuits that respond to each one of these features while being insensitive to the others. We demonstrate our design principles using general chemical reaction networks and with explicit simulations of DNA strand displacement reactions. In this way, our work develops building blocks for temporal pattern recognition through molecular computation.

Automated sequence-level analysis of kinetics and thermodynamics for domain-level DNA strand-displacement systems

As an engineering material, DNA is well suited for the construction of biochemical circuits and systems, because it is simple enough that its interactions can be rationally designed using Watson-Crick base pairing rules, yet the design space is remarkably rich. When designing DNA systems, this simplicity permits using functional sections of each strand, called domains, without considering particular nucleotide sequences. However, the actual sequences used may have interactions not predicted at the domain-level abstraction, and new rigorous analysis techniques are needed to determine the extent to which the chosen sequences conform to the system's domain-level description. We have developed a computational method for verifying sequence-level systems by identifying discrepancies between the domain-level and sequence-level behaviour. This method takes a DNA system, as specified using the domain-level tool Peppercorn, and analyses data from the stochastic sequence-level simulator Multistrand and sequence-level thermodynamic analysis tool NUPACK to estimate important aspects of the system, such as reaction rate constants and secondary structure formation. These techniques, implemented as the Python package KinDA, will allow researchers to predict the kinetic and thermodynamic behaviour of domain-level systems after sequence assignment, as well as to detect violations of the intended behaviour.

Nicking enzyme-controlled toehold regulation for DNA logic circuits

DNA strand displacement is widely used in DNA-related nanoengineering for its remarkable specificity and predictability. We report a nicking enzyme-assisted mechanism to regulate strand displacement, where DNA toeholds are dynamically controlled. To demonstrate the strategy, a protein/DNA-based Boolean operation system is constructed and based on it a two-channel multiplexer controlled by three different nicking enzymes is realized. The proposed regulatory mechanism can be used for switch logic statement and bridges protein and DNA logic circuits.

Complex cellular logic computation using ribocomputing devices

Synthetic biology aims to develop engineering-driven approaches to the programming of cellular functions that could yield transformative technologies. Synthetic gene circuits that combine DNA, protein, and RNA components have demonstrated a range of functions such as bistability, oscillation, feedback, and logic capabilities. However, it remains challenging to scale up these circuits owing to the limited number of designable, orthogonal, high-performance parts, the empirical and often tedious composition rules, and the requirements for substantial resources for encoding and operation. Here, we report a strategy for constructing RNA-only nanodevices to evaluate complex logic in living cells. Our 'ribocomputing' systems are composed of de-novo-designed parts and operate through predictable and designable base-pairing rules, allowing the effective in silico design of computing devices with prescribed configurations and functions in complex cellular environments. These devices operate at the post-transcriptional level and use an extended RNA transcript to co-localize all circuit sensing, computation, signal transduction, and output elements in the same self-assembled molecular complex, which reduces diffusion-mediated signal losses, lowers metabolic cost, and improves circuit reliability. We demonstrate that ribocomputing devices in Escherichia coli can evaluate two-input logic with a dynamic range up to 900-fold and scale them to four-input AND, six-input OR, and a complex 12-input expression (A1 AND A2 AND NOT A1*) OR (B1 AND B2 AND NOT B2*) OR (C1 AND C2) OR (D1 AND D2) OR (E1 AND E2). Successful operation of ribocomputing devices based on programmable RNA interactions suggests that systems employing the same design principles could be implemented in other host organisms or in extracellular settings.

Integration of G-quadruplex and DNA-templated Ag NCs for nonarithmetic information processing

To create sophisticated molecular logic circuits from scratch, you may not believe how common the building blocks can be and how diverse and powerful such circuits can be when scaled up. Using the two simple building blocks of G-quadruplex and silver nanoclusters (Ag NCs), we experimentally construct a series of multifunctional, label-free, and multi-output logic circuits to perform nonarithmetic functions: a 1-to-2 decoder, a 4-to-2 encoder, an 8-to-3 encoder, dual transfer gates, a 2 : 1 multiplexer, and a 1 : 2 demultiplexer. Moreover, a parity checker which is capable of identifying odd and even numbers from natural numbers is constructed conceptually. Finally, a multi-valued logic gate (ternary inhibit gate) is readily achieved by taking this DNA/Ag NC system as a universal platform. All of the above logic circuits share the same building blocks, indicating the great prospects of the assembly of nanomaterials and DNA for biochemical logic devices. Considering its biocompatibility, the novel prototypes developed here may have potential applications in the fields of biological computers and medical diagnosis and serve as a promising proof of principle in the not-too-distant future.

Engineering chemical reaction modules via programming the assembly of DNA hairpins

The architect of enzyme-free chemical reaction modules, working as building blocks in implementing complex computing tasks, was achieved by modulating the assembly of DNA hairpins, including non-catalytic and catalytic systems. The performance of heterogeneous outputted sequences, which were programmed on different hairpins for triggering the downstream reaction, was asymmetric in the non-catalytic system, whereas symmetric in the catalytic system. Furthermore, complicated DNA-only chemical modules possessing controllable species of inputs or outputs were constructed based on our strategy. The kinetic studies revealed that the performance of the chemical modules was toehold length correlated; on the basis of which, a DNA concentration monitor was constructed.

Availability: A Metric for Nucleic Acid Strand Displacement Systems

DNA strand displacement systems have transformative potential in synthetic biology. While powerful examples have been reported in DNA nanotechnology, such systems are plagued by leakage, which limits network stability, sensitivity, and scalability. An approach to mitigate leakage in DNA nanotechnology, which is applicable to synthetic biology, is to introduce mismatches to complementary fuel sequences at key locations. However, this method overlooks nuances in the secondary structure of the fuel and substrate that impact the leakage reaction kinetics in strand displacement systems. In an effort to quantify the impact of secondary structure on leakage, we introduce the concepts of availability and mutual availability and demonstrate their utility for network analysis. Our approach exposes vulnerable locations on the substrate and quantifies the secondary structure of fuel strands. Using these concepts, a 4-fold reduction in leakage has been achieved. The result is a rational design process that efficiently suppresses leakage and provides new insight into dynamic nucleic acid networks.

Analog Computation by DNA Strand Displacement Circuits

DNA circuits have been widely used to develop biological computing devices because of their high programmability and versatility. Here, we propose an architecture for the systematic construction of DNA circuits for analog computation based on DNA strand displacement. The elementary gates in our architecture include addition, subtraction, and multiplication gates. The input and output of these gates are analog, which means that they are directly represented by the concentrations of the input and output DNA strands, respectively, without requiring a threshold for converting to Boolean signals. We provide detailed domain designs and kinetic simulations of the gates to demonstrate their expected performance. On the basis of these gates, we describe how DNA circuits to compute polynomial functions of inputs can be built. Using Taylor Series and Newton Iteration methods, functions beyond the scope of polynomials can also be computed by DNA circuits built upon our architecture.

High-resolution mapping of bifurcations in nonlinear biochemical circuits

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

A DNA-based system for selecting and displaying the combined result of two input variables

Oligonucleotide-based technologies for biosensing or bio-regulation produce huge amounts of rich high-dimensional information. There is a consequent need for flexible means to combine diverse pieces of such information to form useful derivative outputs, and to display those immediately. Here we demonstrate this capability in a DNA-based system that takes two input numbers, represented in DNA strands, and returns the result of their multiplication, writing this as a number in a display. Unlike a conventional calculator, this system operates by selecting the result from a library of solutions rather than through logic operations. The multiplicative example demonstrated here illustrates a much more general capability—to generate a unique output for any distinct pair of DNA inputs. The system thereby functions as a lookup table and could be a key component in future, more powerful data-processing systems for diagnostics and sensing.

DNA based sensors provide substantial amounts of information that requires integration and processing. Here the authors demonstrate a DNA-based calculator that takes two inputs, identifies the solution in a library of answers and displays the result.

Sequence Design for a Test Tube of Interacting Nucleic Acid Strands

We describe an algorithm for designing the equilibrium base-pairing properties of a test tube of interacting nucleic acid strands. A target test tube is specified as a set of desired "on-target" complexes, each with a target secondary structure and target concentration, and a set of undesired "off-target" complexes, each with vanishing target concentration. Sequence design is performed by optimizing the test tube ensemble defect, corresponding to the concentration of incorrectly paired nucleotides at equilibrium evaluated over the ensemble of the test tube. To reduce the computational cost of accepting or rejecting mutations to a random initial sequence, the structural ensemble of each on-target complex is hierarchically decomposed into a tree of conditional subensembles, yielding a forest of decomposition trees. Candidate sequences are evaluated efficiently at the leaf level of the decomposition forest by estimating the test tube ensemble defect from conditional physical properties calculated over the leaf subensembles. As optimized subsequences are merged toward the root level of the forest, any emergent defects are eliminated via ensemble redecomposition and sequence reoptimization. After successfully merging subsequences to the root level, the exact test tube ensemble defect is calculated for the first time, explicitly checking for the effect of the previously neglected off-target complexes. Any off-target complexes that form at appreciable concentration are hierarchically decomposed, added to the decomposition forest, and actively destabilized during subsequent forest reoptimization. For target test tubes representative of design challenges in the molecular programming and synthetic biology communities, our test tube design algorithm typically succeeds in achieving a normalized test tube ensemble defect ≤1% at a design cost within an order of magnitude of the cost of test tube analysis.

Design of a biochemical circuit motif for learning linear functions

Learning and adaptive behaviour are fundamental biological processes. A key goal in the field of bioengineering is to develop biochemical circuit architectures with the ability to adapt to dynamic chemical environments. Here, we present a novel design for a biomolecular circuit capable of supervised learning of linear functions, using a model based on chemical reactions catalysed by DNAzymes. To achieve this, we propose a novel mechanism of maintaining and modifying internal state in biochemical systems, thereby advancing the state of the art in biomolecular circuit architecture. We use simulations to demonstrate that the circuit is capable of learning behaviour and assess its asymptotic learning performance, scalability and robustness to noise. Such circuits show great potential for building autonomous in vivo nanomedical devices. While such a biochemical system can tell us a great deal about the fundamentals of learning in living systems and may have broad applications in biomedicine (e.g. autonomous and adaptive drugs), it also offers some intriguing challenges and surprising behaviours from a machine learning perspective.

Target-driven DNA association to initiate cyclic assembly of hairpins for biosensing and logic gate operation

Target-driven DNA association is designed for initiating the cyclic assembly of hairpins for target detection and logic gate operation.

A target-driven DNA association was designed to initiate cyclic assembly of hairpins, which led to an enzyme-free amplification strategy for detection of a nucleic acid or aptamer substrate and flexible construction of logic gates. The cyclic system contained two ssDNA (S1 and S2) and two hairpins (H1 and H2). These ssDNA could co-recognize the target to produce an S1–target–S2 structure, which brought their toehold and branch-migration domains into close proximity to initiate the cyclic assembly of hairpins. The assembly product further induced the dissociation of a double-stranded probe DNA (Q:F) via toehold-mediated strand displacement to switch the fluorescence signal. This method could detect DNA and ATP as model analytes down to 21.6 pM and 38 nM, respectively. By designing different DNA input strands, the “AND”, “INHIBIT” and “NAND” logic gates could be activated to achieve the output signal. The proposed biosensing and logic gate operation platform showed potential applications in disease diagnosis.

Ternary DNA computing using 3 × 3 multiplication matrices

Ternary computing, beyond Boolean logic, is anticipated to enhance computational complexity. DNA-based ternary computing is demonstrated by the assembly of a 3 × 3 multiplication table, and the parallel operation of three 3 × 3 multiplication matrices is highlighted.

Non-Boolean computations implementing operations on multi-valued variables beyond base 2 allow enhanced computational complexity. We introduce DNA as a functional material for ternary computing, and in particular demonstrate the use of three-valued oligonucleotide inputs to construct a 3 × 3 multiplication table. The system consists of two three-valued inputs of –1; 0; +1 and a fluorophore/quencher functional hairpin acting as computational and reporter module. The interaction of the computational hairpin module with the different values of the inputs yields a 3 × 3 multiplication matrix consisting of nine nanostructures that are read out by three distinct fluorescence intensities. By combining three different hairpin computational modules, each modified with a different fluorophore/quencher pair, and using different sets of inputs, the parallel operation of three multiplication tables is demonstrated.

Programmable energy landscapes for kinetic control of DNA strand displacement

DNA is used to construct synthetic systems that sense, actuate, move and compute. The operation of many dynamic DNA devices depends on toehold-mediated strand displacement, by which one DNA strand displaces another from a duplex. Kinetic control of strand displacement is particularly important in autonomous molecular machinery and molecular computation, in which non-equilibrium systems are controlled through rates of competing processes. Here, we introduce a new method based on the creation of mismatched base pairs as kinetic barriers to strand displacement. Reaction rate constants can be tuned across three orders of magnitude by altering the position of such a defect without significantly changing the stabilities of reactants or products. By modelling reaction free-energy landscapes, we explore the mechanistic basis of this control mechanism. We also demonstrate that oxDNA, a coarse-grained model of DNA, is capable of accurately predicting and explaining the impact of mismatches on displacement kinetics.

Reversion of DNA strand displacement using functional nucleic acids as toeholds

Herein we report the reversion of DNA strand displacement using functional nucleic acids as toeholds.

Aptamer-based sensing platform using three-way DNA junction-driven strand displacement and its application in DNA logic circuit

We proposed a new three-way DNA junction-driven strand displacement mode and fabricated an aptamer-based label-free fluorescent sensing platform on the basis of this mechanism. Assembling the aptamer sequence into the three-way DNA junction makes the platform sensitive to the target of the aptamer. A label-free signal readout method, split G-quadruplex enhanced fluorescence of protoporphyrin IX (PPIX), was used to report the final signal. Here, adenosine triphosphatase (ATP) was taken as a model and detected through this approach, and DNA strand could also be detected by it. The mechanism was investigated by native polyacrylamide gel electrophoresis. Furthermore, on the basis of this molecular platform, we built a logic circuit with ATP and DNA strands as input. Aptamer played an important role in mediating the small molecule ATP to tune the DNA logic gate. Through altering the aptamer sequence, this molecular platform will be sensitive to various stimuli and applied in a wide field.

Four-way junction-driven DNA strand displacement and its application in building majority logic circuit

We introduced a four-way DNA junction-driven toehold-mediated strand displacement method. Separation of the different functional domains on different strands in the four-way junction structure and usage of glue strand to recombine them for different logic gates make the design more flexible. On the basis of this mechanism, a majority logic circuit fabricated by DNA strands was designed and constructed by assembling three AND gates and one OR gate together. The output strand drew the G-rich segments together to form a split G-quadruplex, which could specifically bind PPIX and enhance its fluorescence. Just like a poll with three voters, the high fluorescence signal would be given off only when two or three voters vote in favor. Upon slight modification, the majority circuit was utilized to select the composite number from 0 to 9 represented by excess-three code. It is a successful attempt to integrate the logic gates into a circuit and to achieve desired functions.

Binding-induced formation of DNA three-way junctions and its application to protein detection and DNA strand displacement

DNA three-way junctions (DNA TWJs) are important building blocks to construct DNA architectures and dynamic assemblies. We describe here a binding-induced DNA TWJ strategy that is able to convert protein bindings to the formation of DNA TWJ. The binding-induced DNA TWJ makes use of two DNA motifs each conjugated to an affinity ligand. The binding of two affinity ligands to the target molecule triggers assembly of the DNA motifs and initiates the subsequent DNA strand displacement, resulting in a binding-induced TWJ. Real-time fluorescence monitoring of the binding-induced TWJ enables detection of the specific protein targets. A detection limit of 2.8 ng/mL was achieved for prostate-specific antigen. The binding-induced TWJ approach compares favorably with the toehold-mediated DNA strand-displacement, the associative (combinative) toehold-mediated DNA strand-displacement, and the binding-induced DNA strand-displacement. Importantly, the binding-induced TWJ broadens the scope of dynamic DNA assemblies and provides a new strategy to design protein-responsive DNA devices and assemblies.