Erik Winfree

Design and self-assembly of two-dimensional DNA crystals

Molecular self-assembly presents a ‘bottom-up’ approach to the fabrication of objects specified with nanometre precision. DNA molecular structures and intermolecular interactions are particularly amenable to the design and synthesis of complex molecular objects. We report the design and observation of two-dimensional crystalline forms of DNA that self-assemble from synthetic DNA double-crossover molecules. Intermolecular interactions between the structural units are programmed by the design of ‘sticky ends’ that associate according to Watson–Crick complementarity, enabling us to create specific periodic patterns on the nanometre scale. The patterned crystals have been visualized by atomic force microscopy.

Enzyme-free nucleic acid logic circuits.

Biological organisms perform complex information processing and control tasks using sophisticated biochemical circuits, yet the engineering of such circuits remains ineffective compared with that of electronic circuits. To systematically create complex yet reliable circuits, electrical engineers use digital logic, wherein gates and subcircuits are composed modularly and signal restoration prevents signal degradation. We report the design and experimental implementation of DNA-based digital logic circuits. We demonstrate AND, OR, and NOT gates, signal restoration, amplification, feedback, and cascading. Gate design and circuit construction is modular. The gates use single-stranded nucleic acids as inputs and outputs, and the mechanism relies exclusively on sequence recognition and strand displacement. Biological nucleic acids such as microRNAs can serve as inputs, suggesting applications in biotechnology and bioengineering.

Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades

Scalability and noise control are demonstrated in a molecular computer built from DNA. To construct sophisticated biochemical circuits from scratch, one needs to understand how simple the building blocks can be and how robustly such circuits can scale up. Using a simple DNA reaction mechanism based on a reversible strand displacement process, we experimentally demonstrated several digital logic circuits, culminating in a four-bit square-root circuit that comprises 130 DNA strands. These multilayer circuits include thresholding and catalysis within every logical operation to perform digital signal restoration, which enables fast and reliable function in large circuits with roughly constant switching time and linear signal propagation delays. The design naturally incorporates other crucial elements for large-scale circuitry, such as general debugging tools, parallel circuit preparation, and an abstraction hierarchy supported by an automated circuit compiler.

Control of DNA Strand Displacement Kinetics Using Toehold Exchange

DNA is increasingly being used as the engineering material of choice for the construction of nanoscale circuits, structures, and motors. Many of these enzyme-free constructions function by DNA strand displacement reactions. The kinetics of strand displacement can be modulated by toeholds, short single-stranded segments of DNA that colocalize reactant DNA molecules. Recently, the toehold exchange process was introduced as a method for designing fast and reversible strand displacement reactions. Here, we characterize the kinetics of DNA toehold exchange and model it as a three-step process. This model is simple and quantitatively predicts the kinetics of 85 different strand displacement reactions from the DNA sequences. Furthermore, we use toehold exchange to construct a simple catalytic reaction. This work improves the understanding of the kinetics of nucleic acid reactions and will be useful in the rational design of dynamic DNA and RNA circuits and nanodevices.

Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA

Artificial biochemical circuits are likely to play as large a role in biological engineering as electrical circuits have played in the engineering of electromechanical devices. Toward that end, nucleic acids provide a designable substrate for the regulation of biochemical reactions. However, it has been difficult to incorporate signal amplification components. We introduce a design strategy that allows a specified input oligonucleotide to catalyze the release of a specified output oligonucleotide, which in turn can serve as a catalyst for other reactions. This reaction, which is driven forward by the configurational entropy of the released molecule, provides an amplifying circuit element that is simple, fast, modular, composable, and robust. We have constructed and characterized several circuits that amplify nucleic acid signals, including a feedforward cascade with quadratic kinetics and a positive feedback circuit with exponential growth kinetics.

Molecular robots guided by prescriptive landscapes

Traditional robots rely for their function on computing, to store internal representations of their goals and environment and to coordinate sensing and any actuation of components required in response. Moving robotics to the single-molecule level is possible in principle, but requires facing the limited ability of individual molecules to store complex information and programs. One strategy to overcome this problem is to use systems that can obtain complex behaviour from the interaction of simple robots with their environment. A first step in this direction was the development of DNA walkers, which have developed from being non-autonomous to being capable of directed but brief motion on one-dimensional tracks. Here we demonstrate that previously developed random walkers—so-called molecular spiders that comprise a streptavidin molecule as an inert ‘body’ and three deoxyribozymes as catalytic ‘legs’—show elementary robotic behaviour when interacting with a precisely defined environment. Single-molecule microscopy observations confirm that such walkers achieve directional movement by sensing and modifying tracks of substrate molecules laid out on a two-dimensional DNA origami landscape. When using appropriately designed DNA origami, the molecular spiders autonomously carry out sequences of actions such as ‘start’, ‘follow’, ‘turn’ and ‘stop’. We anticipate that this strategy will result in more complex robotic behaviour at the molecular level if additional control mechanisms are incorporated. One example might be interactions between multiple molecular robots leading to collective behaviour; another might be the ability to read and transform secondary cues on the DNA origami landscape as a means of implementing Turing-universal algorithmic behaviour.

Neural network computation with DNA strand displacement cascades

The impressive capabilities of the mammalian brain—ranging from perception, pattern recognition and memory formation to decision making and motor activity control—have inspired their re-creation in a wide range of artificial intelligence systems for applications such as face recognition, anomaly detection, medical diagnosis and robotic vehicle control. Yet before neuron-based brains evolved, complex biomolecular circuits provided individual cells with the ‘intelligent’ behaviour required for survival. However, the study of how molecules can ‘think’ has not produced an equal variety of computational models and applications of artificial chemical systems. Although biomolecular systems have been hypothesized to carry out neural-network-like computations in vivo and the synthesis of artificial chemical analogues has been proposed theoretically, experimental work has so far fallen short of fully implementing even a single neuron. Here, building on the richness of DNA computing and strand displacement circuitry, we show how molecular systems can exhibit autonomous brain-like behaviours. Using a simple DNA gate architecture that allows experimental scale-up of multilayer digital circuits, we systematically transform arbitrary linear threshold circuits (an artificial neural network model) into DNA strand displacement cascades that function as small neural networks. Our approach even allows us to implement a Hopfield associative memory with four fully connected artificial neurons that, after training in silico, remembers four single-stranded DNA patterns and recalls the most similar one when presented with an incomplete pattern. Our results suggest that DNA strand displacement cascades could be used to endow autonomous chemical systems with the capability of recognizing patterns of molecular events, making decisions and responding to the environment.

DNA as a universal substrate for chemical kinetics

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior.

The program-size complexity of self-assembled squares (extended abstract)

Molecular self-assembly gives rise to a great diversity of complex forms, from crystals and DNA helices to microtubules and holoenzymes. We study a formal model of pseudocrystalline self-assembly, called the Tile Assembly Model, in which a tile may be added to the growing object when the total interaction strength with its neighbors exceeds a parameter Τ. This model has been shown to be Turing-universal. Thus, self-assembled objects can be studied from the point of view of computational complexity. Here, we define the program size complexity of an NxN square to be the minimum number of distinct tiles required to self-assemble the square and no other objects. We study this complexity under the Tile Assembly Model and find a dramatic decrease in complexity, from N^2 tiles to O(log N) tiles, as Τ is increased from 1 (where bonding is noncooperative) to 2 (allowing cooperative bonding). Further, we find that the size of the largest square uniquely produced by a set of n tiles grows faster than any computable function.

An autonomous polymerization motor powered by DNA hybridization

We present a synthetic molecular motor capable of autonomous nanoscale transport in solution. Inspired by bacterial pathogens such as Rickettsia rickettsii, which locomote by inducing the polymerization of the protein actin at their surfaces to form ‘comet tails’1, the motor operates by polymerizing a double-helical DNA tail2. DNA strands are propelled processively at the living end of the growing polymers, demonstrating autonomous locomotion powered by the free energy of DNA hybridization.