Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly.

Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles1-3. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks4-7. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems.

Predicting DNA kinetics with a truncated continuous-time Markov chain method.

Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.

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.

Programming and simulating chemical reaction networks on a surface.

Models of well-mixed chemical reaction networks (CRNs) have provided a solid foundation for the study of programmable molecular systems, but the importance of spatial organization in such systems has increasingly been recognized. In this paper, we explore an alternative chemical computing model introduced by Qian & Winfree in 2014, the surface CRN, which uses molecules attached to a surface such that each molecule only interacts with its immediate neighbours. Expanding on the constructions in that work, we first demonstrate that surface CRNs can emulate asynchronous and synchronous deterministic cellular automata and implement continuously active Boolean logic circuits. We introduce three new techniques for enforcing synchronization within local regions, each with a different trade-off in spatial and chemical complexity. We also demonstrate that surface CRNs can manufacture complex spatial patterns from simple initial conditions and implement interesting swarm robotic behaviours using simple local rules. Throughout all example constructions of surface CRNs, we highlight the trade-off between the ability to precisely place molecules and the ability to precisely control molecular interactions. Finally, we provide a Python simulator for surface CRNs with an easy-to-use web interface, so that readers may follow along with our examples or create their own surface CRN designs.

Author Correction: Diverse and robust molecular algorithms using reprogrammable DNA self-assembly.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Diverse and robust molecular algorithms using reprogrammable DNA self-assembly.

Molecular biology provides an inspiring proof-of-principle that chemical systems can store and process information to direct molecular activities such as the fabrication of complex structures from molecular components. To develop information-based chemistry as a technology for programming matter to function in ways not seen in biological systems, it is necessary to understand how molecular interactions can encode and execute algorithms. The self-assembly of relatively simple units into complex products1 is particularly well suited for such investigations. Theory that combines mathematical tiling and statistical-mechanical models of molecular crystallization has shown that algorithmic behaviour can be embedded within molecular self-assembly processes2,3, and this has been experimentally demonstrated using DNA nanotechnology4 with up to 22 tile types5-11. However, many information technologies exhibit a complexity threshold-such as the minimum transistor count needed for a general-purpose computer-beyond which the power of a reprogrammable system increases qualitatively, and it has been unclear whether the biophysics of DNA self-assembly allows that threshold to be exceeded. Here we report the design and experimental validation of a DNA tile set that contains 355 single-stranded tiles and can, through simple tile selection, be reprogrammed to implement a wide variety of 6-bit algorithms. We use this set to construct 21 circuits that execute algorithms including copying, sorting, recognizing palindromes and multiples of 3, random walking, obtaining an unbiased choice from a biased random source, electing a leader, simulating cellular automata, generating deterministic and randomized patterns, and counting to 63, with an overall per-tile error rate of less than 1 in 3,000. These findings suggest that molecular self-assembly could be a reliable algorithmic component within programmable chemical systems. The development of molecular machines that are reprogrammable-at a high level of abstraction and thus without requiring knowledge of the underlying physics-will establish a creative space in which molecular programmers can flourish.

Effective design principles for leakless strand displacement systems.

Artificially designed molecular systems with programmable behaviors have become a valuable tool in chemistry, biology, material science, and medicine. Although information processing in biological regulatory pathways is remarkably robust to error, it remains a challenge to design molecular systems that are similarly robust. With functionality determined entirely by secondary structure of DNA, strand displacement has emerged as a uniquely versatile building block for cell-free biochemical networks. Here, we experimentally investigate a design principle to reduce undesired triggering in the absence of input (leak), a side reaction that critically reduces sensitivity and disrupts the behavior of strand displacement cascades. Inspired by error correction methods exploiting redundancy in electrical engineering, we ensure a higher-energy penalty to leak via logical redundancy. Our design strategy is, in principle, capable of reducing leak to arbitrarily low levels, and we experimentally test two levels of leak reduction for a core "translator" component that converts a signal of one sequence into that of another. We show that the leak was not measurable in the high-redundancy scheme, even for concentrations that are up to 100 times larger than typical. Beyond a single translator, we constructed a fast and low-leak translator cascade of nine strand displacement steps and a logic OR gate circuit consisting of 10 translators, showing that our design principle can be used to effectively reduce leak in more complex chemical systems.

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.

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.

A cargo-sorting DNA robot.

Two critical challenges in the design and synthesis of molecular robots are modularity and algorithm simplicity. We demonstrate three modular building blocks for a DNA robot that performs cargo sorting at the molecular level. A simple algorithm encoding recognition between cargos and their destinations allows for a simple robot design: a single-stranded DNA with one leg and two foot domains for walking, and one arm and one hand domain for picking up and dropping off cargos. The robot explores a two-dimensional testing ground on the surface of DNA origami, picks up multiple cargos of two types that are initially at unordered locations, and delivers them to specified destinations until all molecules are sorted into two distinct piles. The robot is designed to perform a random walk without any energy supply. Exploiting this feature, a single robot can repeatedly sort multiple cargos. Localization on DNA origami allows for distinct cargo-sorting tasks to take place simultaneously in one test tube or for multiple robots to collectively perform the same task.

Physical principles for DNA tile self-assembly.

DNA tiles provide a promising technique for assembling structures with nanoscale resolution through self-assembly by basic interactions rather than top-down assembly of individual structures. Tile systems can be programmed to grow based on logical rules, allowing for a small number of tile types to assemble large, complex assemblies that can retain nanoscale resolution. Such algorithmic systems can even assemble different structures using the same tiles, based on inputs that seed the growth. While programming and theoretical analysis of tile self-assembly often makes use of abstract logical models of growth, experimentally implemented systems are governed by nanoscale physical processes that can lead to very different behavior, more accurately modeled by taking into account the thermodynamics and kinetics of tile attachment and detachment in solution. This review discusses the relationships between more abstract and more physically realistic tile assembly models. A central concern is how consideration of model differences enables the design of tile systems that robustly exhibit the desired abstract behavior in realistic physical models and in experimental implementations. Conversely, we identify situations where self-assembly in abstract models can not be well-approximated by physically realistic models, putting constraints on physical relevance of the abstract models. To facilitate the discussion, we introduce a unified model of tile self-assembly that clarifies the relationships between several well-studied models in the literature. Throughout, we highlight open questions regarding the physical principles for DNA tile self-assembly.

Determining hydrodynamic forces in bursting bubbles using DNA nanotube mechanics.

Quantifying the mechanical forces produced by fluid flows within the ocean is critical to understanding the ocean's environmental phenomena. Such forces may have been instrumental in the origin of life by driving a primitive form of self-replication through fragmentation. Among the intense sources of hydrodynamic shear encountered in the ocean are breaking waves and the bursting bubbles produced by such waves. On a microscopic scale, one expects the surface-tension-driven flows produced during bubble rupture to exhibit particularly high velocity gradients due to the small size scales and masses involved. However, little work has examined the strength of shear flow rates in commonly encountered ocean conditions. By using DNA nanotubes as a novel fluid flow sensor, we investigate the elongational rates generated in bursting films within aqueous bubble foams using both laboratory buffer and ocean water. To characterize the elongational rate distribution associated with a bursting bubble, we introduce the concept of a fragmentation volume and measure its form as a function of elongational flow rate. We find that substantial volumes experience surprisingly large flow rates: during the bursting of a bubble having an air volume of 10 mm(3), elongational rates at least as large as [Formula: see text] s(-1) are generated in a fragmentation volume of [Formula: see text] [Formula: see text]. The determination of the elongational strain rate distribution is essential for assessing how effectively fluid motion within bursting bubbles at the ocean surface can shear microscopic particles and microorganisms, and could have driven the self-replication of a protobiont.

Increasing Redundancy Exponentially Reduces Error Rates during Algorithmic Self-Assembly.

While biology demonstrates that molecules can reliably transfer information and compute, design principles for implementing complex molecular computations in vitro are still being developed. In electronic computers, large-scale computation is made possible by redundancy, which allows errors to be detected and corrected. Increasing the amount of redundancy can exponentially reduce errors. Here, we use algorithmic self-assembly, a generalization of crystal growth in which the self-assembly process executes a program for growing an object, to examine experimentally whether redundancy can analogously reduce the rate at which errors occur during molecular self-assembly. We designed DNA double-crossover molecules to algorithmically self-assemble ribbon crystals that repeatedly copy a short bitstring, and we measured the error rate when each bit is encoded by 1 molecule, or redundantly encoded by 2, 3, or 4 molecules. Under our experimental conditions, each additional level of redundancy decreases the bitwise error rate by a factor of roughly 3, with the 4-redundant encoding yielding an error rate less than 0.1%. While theory and simulation predict that larger improvements in error rates are possible, our results already suggest that by using sufficient redundancy it may be possible to algorithmically self-assemble micrometer-sized objects with programmable, nanometer-scale features.

Thermodynamics and kinetics of DNA nanotube polymerization from single-filament measurements.

DNA nanotubes provide a programmable architecture for molecular self-assembly and can serve as model systems for one-dimensional biomolecular assemblies. While a variety of DNA nanotubes have been synthesized and employed as models for natural biopolymers, an extensive investigation of DNA nanotube kinetics and thermodynamics has been lacking. Using total internal reflection microscopy, DNA nanotube polymerization was monitored in real time at the single filament level over a wide range of free monomer concentrations and temperatures. The measured polymerization rates were subjected to a global nonlinear fit based on polymerization theory in order to simultaneously extract kinetic and thermodynamic parameters. For the DNA nanotubes used in this study, the association rate constant is (5.99 ± 0.15) × 105 M-1 s-1, the enthalpy is 87.9 ± 2.0 kcal mol-1, and the entropy is 0.252 ± 0.006 kcal mol-1 K-1. The qualitative and quantitative similarities between the kinetics of DNA nanotubes, actin filaments, and microtubules polymerization highlight the prospect of building complex dynamic systems from DNA molecules inspired by biological architecture.

Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator.

In vitro compartmentalization of biochemical reaction networks is a crucial step towards engineering artificial cell-scale devices and systems. At this scale the dynamics of molecular systems becomes stochastic, which introduces several engineering challenges and opportunities. Here we study a programmable transcriptional oscillator system that is compartmentalized into microemulsion droplets with volumes between 33 fl and 16 pl. Simultaneous measurement of large populations of droplets reveals major variations in the amplitude, frequency and damping of the oscillations. Variability increases for smaller droplets and depends on the operating point of the oscillator. Rather than reflecting the stochastic kinetics of the chemical reaction network itself, the variability can be attributed to the statistical variation of reactant concentrations created during their partitioning into droplets. We anticipate that robustness to partitioning variability will be a critical challenge for engineering cell-scale systems, and that highly parallel time-series acquisition from microemulsion droplets will become a key tool for characterization of stochastic circuit function.

On the biophysics and kinetics of toehold-mediated DNA strand displacement.

Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

Integrating DNA strand-displacement circuitry with DNA tile self-assembly.

DNA nanotechnology has emerged as a reliable and programmable way of controlling matter at the nanoscale through the specificity of Watson-Crick base pairing, allowing both complex self-assembled structures with nanometer precision and complex reaction networks implementing digital and analog behaviors. Here we show how two well-developed frameworks, DNA tile self-assembly and DNA strand-displacement circuits, can be systematically integrated to provide programmable kinetic control of self-assembly. We demonstrate the triggered and catalytic isothermal self-assembly of DNA nanotubes over 10 µm long from precursor DNA double-crossover tiles activated by an upstream DNA catalyst network. Integrating more sophisticated control circuits and tile systems could enable precise spatial and temporal organization of dynamic molecular structures.

Direct atomic force microscopy observation of DNA tile crystal growth at the single-molecule level.

While the theoretical implications of models of DNA tile self-assembly have been extensively researched and such models have been used to design DNA tile systems for use in experiments, there has been little research testing the fundamental assumptions of those models. In this paper, we use direct observation of individual tile attachments and detachments of two DNA tile systems on a mica surface imaged with an atomic force microscope (AFM) to compile statistics of tile attachments and detachments. We show that these statistics fit the widely used kinetic Tile Assembly Model and demonstrate AFM movies as a viable technique for directly investigating DNA tile systems during growth rather than after assembly.

Robust self-replication of combinatorial information via crystal growth and scission.

Understanding how a simple chemical system can accurately replicate combinatorial information, such as a sequence, is an important question for both the study of life in the universe and for the development of evolutionary molecular design techniques. During biological sequence replication, a nucleic acid polymer serves as a template for the enzyme-catalyzed assembly of a complementary sequence. Enzymes then separate the template and complement before the next round of replication. Attempts to understand how replication could occur more simply, such as without enzymes, have largely focused on developing minimal versions of this replication process. Here we describe how a different mechanism, crystal growth and scission, can accurately replicate chemical sequences without enzymes. Crystal growth propagates a sequence of bits while mechanically-induced scission creates new growth fronts. Together, these processes exponentially increase the number of crystal sequences. In the system we describe, sequences are arrangements of DNA tile monomers within ribbon-shaped crystals. 99.98% of bits are copied correctly and 78% of 4-bit sequences are correct after two generations; roughly 40 sequence copies are made per growth front per generation. In principle, this process is accurate enough for 1,000-fold replication of 4-bit sequences with 50% yield, replication of longer sequences, and darwinian evolution. We thus demonstrate that neither enzymes nor covalent bond formation are required for robust chemical sequence replication. The form of the replicated information is also compatible with the replication and evolution of a wide class of materials with precise nanoscale geometry such as plasmonic nanostructures or heterogeneous protein assemblies.

Ensemble Bayesian analysis of bistability in a synthetic transcriptional switch.

An overarching goal of synthetic and systems biology is to engineer and understand complex biochemical systems by rationally designing and analyzing their basic component interactions. Practically, the extent to which such reductionist approaches can be applied is unclear especially as the complexity of the system increases. Toward gradually increasing the complexity of systematically engineered systems, programmable synthetic circuits operating in cell-free in vitro environments offer a valuable testing ground for principles for the design, characterization, and analysis of complex biochemical systems. Here we illustrate this approach using in vitro transcriptional circuits ("genelets") while developing an activatable transcriptional switch motif and configuring it as a bistable autoregulatory circuit, using just four synthetic DNA strands and three essential enzymes, bacteriophage T7 RNA polymerase, Escherichia coli ribonuclease H, and ribonuclease R. Fulfilling the promise of predictable system design, the thermodynamic and kinetic constraints prescribed at the sequence level were enough to experimentally demonstrate intended bistable dynamics for the synthetic autoregulatory switch. A simple mathematical model was constructed based on the mechanistic understanding of elementary reactions, and a Monte Carlo Bayesian inference approach was employed to find parameter sets compatible with a training set of experimental results; this ensemble of parameter sets was then used to predict a test set of additional experiments with reasonable agreement and to provide a rigorous basis for confidence in the mechanistic model. Our work demonstrates that programmable in vitro biochemical circuits can serve as a testing ground for evaluating methods for the design and analysis of more complex biochemical systems such as living cells.