Abstractions for DNA circuit design

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 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.

Aptamer-based DNA-catalyzed amplification strategy for sensitive fluorescence resonance energy transfer detection of Acinetobacter baumannii

Acinetobacter baumannii (A. baumannii) is a common pathogen that causes hospital-acquired infections and is resistant to a wide variety of antibiotics. Consequently, the rapid and highly sensitive detection of A. baumannii is required during the early stages of infection. Therefore, we developed a DNA-catalyzed amplification mechanism based on aptamers, combined with a novel fluorescence resonance energy transfer (FRET) method based on graphene oxide (GO), for the detection of A. baumannii. In the presence of A. baumannii, an aptamer bound to A. baumannii, releasing the template strand, which triggered an entropy-driven catalysis (EDC) reaction. One EDC product was then used as the catalyst for catalytic hairpin assembly (CHA) on a GO nanosheet. Finally, the GO released a huge amount of FAM-labeled DNA duplices, which could be detected with FRET. This strategy circumvented the extraction of nucleic acids and was easy to execute, with a detection time of ≤1.5 h. The detection of A. baumannii with this method ranges from 5 cfu/mL to 1 × 10⁵ cfu/mL, with a detection limit of 1.1 cfu/mL. The method was sufficiently sensitive and specific to detect A. baumannii rapidly in cerebrospinal fluid. In summary, our strategy provides a new option for the early detection and point-of-care testing (POCT) of A. baumannii infections, allowing their earlier and more precise treatment.

Design and Simulation of an Autonomous Molecular Mechanism Using Spatially Localized DNA Computation

As a well-established technique, DNA synthesis offers interesting possibilities for designing multifunctional nanodevices. The micro-processing system of modern semiconductor circuits is dependent on strategies organized on silicon chips to achieve the speedy transmission of substances or information. Similarly, spatially localized structures allow for fixed DNA molecules in close proximity to each other during the synthesis of molecular circuits, thus providing a different strategy that of opening up a remarkable new area of inquiry for researchers. Herein, the Visual DSD (DNA strand displacement) modeling language was used to design and analyze the spatially organized DNA reaction network. The execution rules depend on the hybridization reaction caused by directional complementary nucleotide sequences. A series of DNA strand displacement calculations were organized on the locally coded travel track, and autonomous movement and addressing operations are gradually realized. The DNA nanodevice operates in this manner follows the embedded "molecular program", which improves the reusability and scalability of the same sequence domain in different contexts. Through the communication between various building blocks, the DNA device-carrying the target molecule moves in a controlled manner along the programmed track. In this way, a variety of molecular functional group transport and specific partition storage can be realized. The simulation results of the visual DSD tool provide qualitative and quantitative proof for the operation of the system.

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.

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.

Synchronization of Hyper-Lorenz System Based on DNA Strand Displacement

Lorenz system is depicted by chemical reaction equations of an ideal formal chemical reaction network, and a series of reversible reactions are added into chemical reaction network in order to construct a cluster of hyper-Lorenz system. DNA as a universal substrate for chemical dynamics can approximate arbitrary dynamical characteristics of ideal formal chemical reaction network through auxiliary DNA strands and displacement reactions. Based on Lyapunov's stableness theory, a novel synchronization strategy is proposed. A 6-dimensional hyper-Lorenz system is taken as examples for simulation and shows that DNA strands displacement reactions can implement the synchronization of ideal formal chemical reaction networks. Numerical simulations indicate that synchronization based on DNA strand displacement is robust to the detection of DNA strand concentration, control of reaction rate, and noise.

Renewable DNA Proportional-Integral Controller with Photoresponsive Molecules

A molecular robot is an intelligent molecular system. A typical control problem of molecular robots is to maintain the concentration of a specific DNA strand at the desired level, which is typically attained by a molecular feedback control mechanism. A molecular feedback system can be constructed in a bottom-up method by transforming a nonlinear chemical reaction system into a pseudo-linear system. This method enables the implementation of a molecular proportional-integral (PI) controller on a DNA reaction system. However, a DNA reaction system is driven by fuel DNA strand consumption, and without a sufficient amount of fuel strands, the molecular PI controller cannot perform normal operations as a concentration regulator. In this study, we developed a design method for a molecular PI control system to regenerate fuel strands by introducing photoresponsive reaction control. To this end, we employed a photoresponsive molecule, azobenzene, to guide the reaction direction forward or backward using light irradiation. We validated our renewable design of the PI controller by numerical simulations based on the reaction kinetics. We also confirmed the proof-of-principle of our renewable design by conducting experiments using a basic DNA circuit.

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.

Molecular communication relays for dynamic cross-regulation of self-sorting fibrillar self-assemblies

Structures in living systems cross-regulate via exchange of molecular information to assemble or disassemble on demand and in a coordinated, signal-triggered fashion. DNA strand displacement (DSD) reaction networks allow rational design of signaling and feedback loops, but combining DSD with structural nanotechnology to achieve self-reconfiguring hierarchical system states is still in its infancy. We introduce modular DSD networks with increasing amounts of regulatory functions, such as negative feedback, signal amplification, and signal thresholding, to cross-regulate the transient polymerization/depolymerization of two self-sorting DNA origami nanofibrils and nanotubes. This is achieved by concatenation of the DSD network with molecular information relays embedded on the origami tips. The two origamis exchange information and display programmable transient states observable by TEM and fluorescence spectroscopy. The programmability on the DSD and the origami level is a viable starting point toward more complex lifelike behavior of colloidal multicomponent systems featuring advanced signal processing functions.

Biocomputing Based on DNA Strand Displacement Reactions

The high sequence specificity and precise base complementary pairing principle of DNA provides a rich orthogonal molecular library for molecular programming, making it one of the most promising materials for developing bio-compatible intelligence. In recent years, DNA has been extensively studied and applied in the field of biological computing. Among them, the toehold-mediated strand displacement reaction (SDR) with properties including enzyme free, flexible design and precise control, have been extensively used to construct biological computing circuits. This review provides a systemic overview of SDR design principles and the applications. Strategies for designing DNA-only, enzymes-assisted, other molecules-involved and external stimuli-controlled SDRs are described. The recently realized computing functions and the application of DNA computing in other fields are introduced. Finally, the advantages and challenges of SDR-based computing are discussed.

Compilation of a Coupled Hyper-Chaotic Lorenz System Based on DNA Strand Displacement Reaction Network

Ideal formal chemical reaction network is an effective programming language to design complex system dynamical behavior. In this article, a coupled hyper-chaotic Lorenz system can be described by the ordinary differential equations of an ideal formal reaction network, which is constructed by catalysis, annihilation and adjust reaction modules, where the variables of system are represented by the difference in concentration of two chemical species. The ideal formal reaction network can be implemented by DNA strand displacement reaction network. Through Lyapunov exponent, we have analyzed hyper-chaotic dynamical behavior of coupled Lorenz system. In discussion and analysis, we have analyzed effect of noise, reaction rate control error and concentration detection error to DNA strand displacement reaction network.

Domain-Specific Programming Languages for Computational Nucleic Acid Systems

The construction of models of system behavior is of great importance throughout science and engineering. In bioengineering and bionanotechnology, these often take the form of dynamic models that specify the evolution of different species over time. To ensure that scientific observations and conclusions are consistent and that systems can be reliably engineered on the basis of model predictions, it is important that models of biomolecular systems can be constructed in a reliable, principled, and efficient manner. This review focuses on efforts to address this need by using domain-specific programming languages as the basis for custom design tools for researchers working on computational nucleic acid devices, where a domain-specific language is simply a programming language tailored to a particular application domain. The underlying thesis of our review is that there is a continuum of practical implementation strategies for computational nucleic acid systems, which can all benefit from appropriate domain-specific languages and software design tools. We emphasize the need for specialized yet flexible tools that can be realized using domain-specific languages that compile to more general-purpose representations.

A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures

Information technologies enable programmers and engineers to design and synthesize systems of startling complexity that nonetheless behave as intended. This mastery of complexity is made possible by a hierarchy of formal abstractions that span from high-level programming languages down to low-level implementation specifications, with rigorous connections between the levels. DNA nanotechnology presents us with a new molecular information technology whose potential has not yet been fully unlocked in this way. Developing an effective hierarchy of abstractions may be critical for increasing the complexity of programmable DNA systems. Here, we build on prior practice to provide a new formalization of 'domain-level' representations of DNA strand displacement systems that has a natural connection to nucleic acid biophysics while still being suitable for formal analysis. Enumeration of unimolecular and bimolecular reactions provides a semantics for programmable molecular interactions, with kinetics given by an approximate biophysical model. Reaction condensation provides a tractable simplification of the detailed reactions that respects overall kinetic properties. The applicability and accuracy of the model is evaluated across a wide range of engineered DNA strand displacement systems. Thus, our work can serve as an interface between lower-level DNA models that operate at the nucleotide sequence level, and high-level chemical reaction network models that operate at the level of interactions between abstract species.

A Logic Programming Language for Computational Nucleic Acid Devices

Computational nucleic acid devices show great potential for enabling a broad range of biotechnology applications, including smart probes for molecular biology research, in vitro assembly of complex compounds, high-precision in vitro disease diagnosis and, ultimately, computational theranostics inside living cells. This diversity of applications is supported by a range of implementation strategies, including nucleic acid strand displacement, localization to substrates, and the use of enzymes with polymerase, nickase, and exonuclease functionality. However, existing computational design tools are unable to account for these strategies in a unified manner. This paper presents a logic programming language that allows a broad range of computational nucleic acid systems to be designed and analyzed. The language extends standard logic programming with a novel equational theory to express nucleic acid molecular motifs. It automatically identifies matching motifs present in the full system, in order to apply a specified transformation expressed as a logical rule. The language supports the definition of logic predicates, which provide constraints that need to be satisfied in order for a given rule to be applied. The language is sufficiently expressive to encode the semantics of nucleic strand displacement systems with complex topologies, together with computation performed by a broad range of enzymes, and is readily extensible to new implementation strategies. Our approach lays the foundation for a unifying framework for the design of computational nucleic acid devices.

Robust chemical circuits

We introduce a new motif for constructing robust digital logic circuits using input/output chemical reaction networks. These chemical circuits robustly handle adversarial manipulation to their input signals, initial concentrations, rate constants, and measurements. In particular, we show that all Boolean circuits and several sequential circuits enjoy this robustness. Our results complement existing literature in the following three ways: (1) our logic gates read their inputs catalytically which make fanout gates unnecessary; (2) formal requirements and rigorous proofs of satisfaction are provided for each circuit; and (3) robustness of every circuit is closed under modular composition.

Thiol-free oligonucleotide surface modification of gold nanoparticles for nanostructure assembly

Gold nanoparticles (AuNPs) decorated with thiol-modified DNA (HS-DNA) strands are an extensively studied, easily adjustable, and highly controllable material for constructing 3D nanostructures with various shapes and functions. However, few reproducible and robust methods involving DNA templates as a key reagent are available for obtaining 3D nanoparticle assemblies. It is still challenging to strictly control the number and location of DNA strands on the AuNP surface. Here, we introduce an efficient approach for the surface modification of AuNPs using unmodified DNA oligonucleotides by building DNA cages that trap the nanoparticles. This enables us to vary the process of nanostructure assembly and create anisotropic nanoparticles that are necessary for directed structure construction. This developed method simplifies the production process in comparison with conventional HS-DNA modification protocols and helps to precisely control the density and position of functional DNA strands designed for further hybridization with other AuNP conjugates.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Individually addressable and dynamic DNA gates for multiplexed cell sorting

The ability to analyze and isolate cells based on the expression of specific surface markers has increased our understanding of cell biology and produced numerous applications for biomedicine. However, established cell-sorting platforms rely on labels that are limited in number due to biophysical constraints, such as overlapping emission spectra of fluorophores in FACS. Here, we establish a framework built on a system of orthogonal and extensible DNA gates for multiplexed cell sorting. These DNA gates label target cell populations by antibodies to allow magnetic bead isolation en masse and then selectively unlock by strand displacement to sort cells. We show that DNA gated sorting (DGS) is triggered to completion within minutes on the surface of cells and achieves target cell purity, viability, and yield equivalent to that of commercial magnetic sorting kits. We demonstrate multiplexed sorting of three distinct immune cell populations (CD8⁺, CD4⁺, and CD19⁺) from mouse splenocytes to high purity and show that recovered CD8⁺ T cells retain proliferative potential and target cell-killing activity. To broaden the utility of this platform, we implement a double positive sorting scheme using DNA gates on peptide-MHC tetramers to isolate antigen-specific CD8⁺ T cells from mice infected with lymphocytic choriomeningitis virus (LCMV). DGS can potentially be expanded with fewer biophysical constraints to large families of DNA gates for applications that require analysis of complex cell populations, such as host immune responses to disease.

The importance of thermodynamics for molecular systems, and the importance of molecular systems for thermodynamics

Improved understanding of molecular systems has only emphasised the sophistication of networks within the cell. Simultaneously, the advance of nucleic acid nanotechnology, a platform within which reactions can be exquisitely controlled, has made the development of artificial architectures and devices possible. Vital to this progress has been a solid foundation in the thermodynamics of molecular systems. In this pedagogical review and perspective, we discuss how thermodynamics determines both the overall potential of molecular networks, and the minute details of design. We then argue that, in turn, the need to understand molecular systems is helping to drive the development of theories of thermodynamics at the microscopic scale.

Enzyme-free nucleic acid dynamical systems

Chemistries exhibiting complex dynamics—from inorganic oscillators to gene regulatory networks—have been long known but either cannot be reprogrammed at will or rely on the sophisticated enzyme chemistry underlying the central dogma. Can simpler molecular mechanisms, designed from scratch, exhibit the same range of behaviors? Abstract chemical reaction networks have been proposed as a programming language for complex dynamics, along with their systematic implementation using short synthetic DNA molecules. We developed this technology for dynamical systems by identifying critical design principles and codifying them into a compiler automating the design process. Using this approach, we built an oscillator containing only DNA components, establishing that Watson-Crick base-pairing interactions alone suffice for complex chemical dynamics and that autonomous molecular systems can be designed via molecular programming languages.

DNA Implementation of Fuzzy Inference Engine: Towards DNA Decision-Making Systems

Decision-making systems are an integral part of any autonomous device. With the recent developments in bio-nanorobots, smart drugs, and engineered viruses, there is an immediate need of decision-making systems which are bio-compatible in nature. DNA is considered a perfect candidate for designing the computing systems in such decision-making systems because of their bio-compatibility and programmability. Complex biological systems can be easily modeled/controlled using fuzzy logic operations with the help of linguistic rules. In this paper, we propose an enzyme-free DNA strand displacement-based architecture of fuzzy inference engine using the fuzzy operators, such as fuzzy intersection and union. The basic building blocks of this architecture are minimum, maximum, and fan-out gates. All these gates are analog in nature, which means that the input/output values of the gates are represented by the concentration of the input/output DNA strands. To demonstrate the performance of the proposed architecture, a detailed design, analysis, and kinetic simulation of each gate were carried out. Finally, the minimum and maximum gates are cascaded according to the pre-defined rules to design the fuzzy inference engine. All these DNA circuits are implemented and simulated in Visual DSD software.

DNA photonic nanowires with tunable FRET signals on the basis of toehold-mediated DNA strand displacement reactions

A DNA photonic nanowire with tunable FRET signals was fabricated on the basis of cascaded toehold-mediated DNA strand displacement reactions. Different DNA inputs were added to trigger the reaction network, and the corresponding FRET signals were obtained. Compared to the direct hybridization, this design is sensitive for 2 nM targets within 20 min and also causes color changes of the solution with blue-light excitation. It could also be applied in live cells to monitor MicroRNA with a simple modification which might become a low-cost method for further application in the future.

Supervised Learning in Adaptive DNA Strand Displacement Networks

The development of engineered biochemical circuits that exhibit adaptive behavior is a key goal of synthetic biology and molecular computing. Such circuits could be used for long-term monitoring and control of biochemical systems, for instance, to prevent disease or to enable the development of artificial life. In this article, we present a framework for developing adaptive molecular circuits using buffered DNA strand displacement networks, which extend existing DNA strand displacement circuit architectures to enable straightforward storage and modification of behavioral parameters. As a proof of concept, we use this framework to design and simulate a DNA circuit for supervised learning of a class of linear functions by stochastic gradient descent. This work highlights the potential of buffered DNA strand displacement as a powerful circuit architecture for implementing adaptive molecular systems.

A strand graph semantics for DNA-based computation

DNA nanotechnology is a promising approach for engineering computation at the nanoscale, with potential applications in biofabrication and intelligent nanomedicine. DNA strand displacement is a general strategy for implementing a broad range of nanoscale computations, including any computation that can be expressed as a chemical reaction network. Modelling and analysis of DNA strand displacement systems is an important part of the design process, prior to experimental realisation. As experimental techniques improve, it is important for modelling languages to keep pace with the complexity of structures that can be realised experimentally. In this paper we present a process calculus for modelling DNA strand displacement computations involving rich secondary structures, including DNA branches and loops. We prove that our calculus is also sufficiently expressive to model previous work on non-branching structures, and propose a mapping from our calculus to a canonical strand graph representation, in which vertices represent DNA strands, ordered sites represent domains, and edges between sites represent bonds between domains. We define interactions between strands by means of strand graph rewriting, and prove the correspondence between the process calculus and strand graph behaviours. Finally, we propose a mapping from strand graphs to an efficient implementation, which we use to perform modelling and simulation of DNA strand displacement systems with rich secondary structure.

Modular verification of chemical reaction network encodings via serializability analysis

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a "commit reaction" that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of "extra tolerance", which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of any system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited.

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks

DNA nanotechnology requires large amounts of highly pure DNA as an engineering material. Plasmid DNA could meet this need since it is replicated with high fidelity, is readily amplified through bacterial culture and can be stored indefinitely in the form of bacterial glycerol stocks. However, the double-stranded nature of plasmid DNA has so far hindered its efficient use for construction of DNA nanostructures or devices that typically contain single-stranded or branched domains. In recent work, it was found that nicked double stranded DNA (ndsDNA) strand displacement gates could be sourced from plasmid DNA. The following is a protocol that details how these ndsDNA gates can be efficiently encoded in plasmids and can be derived from the plasmids through a small number of enzymatic processing steps. Also given is a protocol for testing ndsDNA gates using fluorescence kinetics measurements. NdsDNA gates can be used to implement arbitrary chemical reaction networks (CRNs) and thus provide a pathway towards the use of the CRN formalism as a prescriptive molecular programming language. To demonstrate this technology, a multi-step reaction cascade with catalytic kinetics is constructed. Further it is shown that plasmid-derived components perform better than identical components assembled from synthetic DNA.

DyNAMiC Workbench: an integrated development environment for dynamic DNA nanotechnology

Dynamic DNA nanotechnology provides a promising avenue for implementing sophisticated assembly processes, mechanical behaviours, sensing and computation at the nanoscale. However, design of these systems is complex and error-prone, because the need to control the kinetic pathway of a system greatly increases the number of design constraints and possible failure modes for the system. Previous tools have automated some parts of the design workflow, but an integrated solution is lacking. Here, we present software implementing a three 'tier' design process: a high-level visual programming language is used to describe systems, a molecular compiler builds a DNA implementation and nucleotide sequences are generated and optimized. Additionally, our software includes tools for analysing and 'debugging' the designs in silico, and for importing/exporting designs to other commonly used software systems. The software we present is built on many existing pieces of software, but is integrated into a single package—accessible using a Web-based interface at http://molecular-systems.net/workbench. We hope that the deep integration between tools and the flexibility of this design process will lead to better experimental results, fewer experimental design iterations and the development of more complex DNA nanosystems.

Synthesizing Configurable Biochemical Implementation of Linear Systems from Their Transfer Function Specifications

The ability to engineer synthetic systems in the biochemical context is constantly being improved and has a profound societal impact. Linear system design is one of the most pervasive methods applied in control tasks, and its biochemical realization has been proposed by Oishi and Klavins and advanced further in recent years. However, several technical issues remain unsolved. Specifically, the design process is not fully automated from specification at the transfer function level, systems once designed often lack dynamic adaptivity to environmental changes, matching rate constants of reactions is not always possible, and implementation may be approximative and greatly deviate from the specifications. Building upon the work of Oishi and Klavins, this paper overcomes these issues by introducing a design flow that transforms a transfer-function specification of a linear system into a set of chemical reactions, whose input-output response precisely conforms to the specification. This system is implementable using the DNA strand displacement technique. The underlying configurability is embedded into primitive components and template modules, and thus the entire system is adaptive. Simulation of DNA strand displacement implementation confirmed the feasibility and superiority of the proposed synthesis flow.

Probabilistic Analysis of Localized DNA Hybridization Circuits

Molecular devices made of nucleic acids can perform complex information processing tasks at the nanoscale, with potential applications in biofabrication and smart therapeutics. However, limitations in the speed and scalability of such devices in a well-mixed setting can significantly affect their performance. In this article, we propose designs for localized circuits involving DNA molecules that are arranged on addressable substrates and interact via hybridization reactions. We propose designs for localized elementary logic circuits, which we compose to produce more complex devices, including a circuit for computing the square root of a four bit number. We develop an efficient method for probabilistic model checking of localized circuits, which we implement within the Visual DSD design tool. We use this method to prove the correctness of our circuits with respect to their functional specifications and to analyze their performance over a broad range of local rate parameters. Specifically, we analyze the extent to which our localized designs can overcome the limitations of well-mixed circuits, with respect to speed and scalability. To provide an estimate of local rate parameters, we propose a biophysical model of localized hybridization. Finally, we use our analysis to identify constraints in the rate parameters that enable localized circuits to retain their advantages in the presence of unintended interferences between strands.

Biophysically inspired rational design of structured chimeric substrates for DNAzyme cascade engineering

The development of large-scale molecular computational networks is a promising approach to implementing logical decision making at the nanoscale, analogous to cellular signaling and regulatory cascades. DNA strands with catalytic activity (DNAzymes) are one means of systematically constructing molecular computation networks with inherent signal amplification. Linking multiple DNAzymes into a computational circuit requires the design of substrate molecules that allow a signal to be passed from one DNAzyme to another through programmed biochemical interactions. In this paper, we chronicle an iterative design process guided by biophysical and kinetic constraints on the desired reaction pathways and use the resulting substrate design to implement heterogeneous DNAzyme signaling cascades. A key aspect of our design process is the use of secondary structure in the substrate molecule to sequester a downstream effector sequence prior to cleavage by an upstream DNAzyme. Our goal was to develop a concrete substrate molecule design to achieve efficient signal propagation with maximal activation and minimal leakage. We have previously employed the resulting design to develop high-performance DNAzyme-based signaling systems with applications in pathogen detection and autonomous theranostics.

Cellular signaling circuits interfaced with synthetic, post-translational, negating Boolean logic devices

A negating functionality is fundamental to information processing of logic circuits within cells and computers. Aiming to adapt unutilized electronic concepts to the interrogation of signaling circuits in cells, we first took a bottom-up strategy whereby we created protein-based devices that perform negating Boolean logic operations such as NOT, NOR, NAND, and N-IMPLY. These devices function in living cells within a minute by precisely commanding the localization of an activator molecule among three subcellular spaces. We networked these synthetic gates to an endogenous signaling circuit and devised a physiological output. In search of logic functions in signal transduction, we next took a top-down approach and computationally screened 108 signaling pathways to identify commonalities and differences between these biological pathways and electronic circuits. This combination of synthetic and systems approaches will guide us in developing foundations for deconstruction of intricate cell signaling, as well as construction of biomolecular computers.

Computational design of nucleic acid feedback control circuits

The design of synthetic circuits for controlling molecular-scale processes is an important goal of synthetic biology, with potential applications in future in vitro and in vivo biotechnology. In this paper, we present a computational approach for designing feedback control circuits constructed from nucleic acids. Our approach relies on an existing methodology for expressing signal processing and control circuits as biomolecular reactions. We first extend the methodology so that circuits can be expressed using just two classes of reactions: catalysis and annihilation. We then propose implementations of these reactions in three distinct classes of nucleic acid circuits, which rely on DNA strand displacement, DNA enzyme and RNA enzyme mechanisms, respectively. We use these implementations to design a Proportional Integral controller, capable of regulating the output of a system according to a given reference signal, and discuss the trade-offs between the different approaches. As a proof of principle, we implement our methodology as an extension to a DNA strand displacement software tool, thus allowing a broad range of nucleic acid circuits to be designed and analyzed within a common modeling framework.

Programmable chemical controllers made from DNA

Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on self-organization. To achieve this, molecular control circuits need to be engineered to perform integrated sensing, computation and actuation. Here we report a DNA-based technology for implementing the computational core of such controllers. We use the formalism of chemical reaction networks as a 'programming language' and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors associated with chemically synthesized DNA. We implement several building-block reaction types and then combine them into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving consensus between multiple agents.

DNA-based molecular architecture with spatially localized components

Performing computation inside living cells offers life-changing applications, from improved medical diagnostics to better cancer therapy to intelligent drugs. Due to its bio-compatibility and ease of engineering, one promising approach for performing in-vivo computation is DNA strand displacement. This paper introduces computer architects to DNA strand displacement "circuits", discusses associated architectural challenges, and proposes a new organization that provides practical composability. In particular, prior approaches rely mostly on stochastic interaction of freely diffusing components. This paper proposes practical spatial isolation of components, leading to more easily designed DNA-based circuits. DNA nanotechnology is currently at a turning point, with many proposed applications being realized [20, 9]. We believe that it is time for the computer architecture community to take notice and contribute.

Scaling down DNA circuits with competitive neural networks

DNA has proved to be an exquisite substrate to compute at the molecular scale. However, nonlinear computations (such as amplification, comparison or restoration of signals) remain costly in term of strands and are prone to leak. Kim et al. showed how competition for an enzymatic resource could be exploited in hybrid DNA/enzyme circuits to compute a powerful nonlinear primitive: the winner-take-all (WTA) effect. Here, we first show theoretically how the nonlinearity of the WTA effect allows the robust and compact classification of four patterns with only 16 strands and three enzymes. We then generalize this WTA effect to DNA-only circuits and demonstrate similar classification capabilities with only 23 strands.

Programming the dynamics of biochemical reaction networks

The development of complex self-organizing molecular systems for future nanotechnology requires not only robust formation of molecular structures by self-assembly but also precise control over their temporal dynamics. As an exquisite example of such control, in this issue of ACS Nano, Fujii and Rondelez demonstrate a particularly compact realization of a molecular "predator-prey" ecosystem consisting of only three DNA species and three enzymes. The system displays pronounced oscillatory dynamics, in good agreement with the predictions of a simple theoretical model. Moreover, its considerable modularity also allows for ecological studies of competition and cooperation within molecular networks.

Visual DSD: a design and analysis tool for DNA strand displacement systems

Summary: The Visual DSD (DNA Strand Displacement) tool allows rapid prototyping and analysis of computational devices implemented using DNA strand displacement, in a convenient web-based graphical interface. It is an implementation of the DSD programming language and compiler described by Lakin et al. (2011) with additional features such as support for polymers of unbounded length. It also supports stochastic and deterministic simulation, construction of continuous-time Markov chains and various export formats which allow models to be analysed using third-party tools.

Availability: Visual DSD is available as a web-based Silverlight application for most major browsers on Windows and Mac OS X at http://research.microsoft.com/dna. It can be installed locally for offline use. Command-line versions for Windows, Mac OS X and Linux are also available from the web page.

Contact:aphillip@microsoft.com

Supplementary Information:Supplementary data are available at Bioinformatics online.