John H Reif

• Duke University

Developing intelligent molecular systems for the desired functions is a significant current research topic in the field of nanoscience. Several materials have been explored to construct interesting systems such as molecular motors, molecular walkers, and Boolean logic circuits. Deoxyribonucleic acid (DNA) is one of the most widely used materials as...

DNA strand displacement circuits are powerful tools that can be rationally engineered to implement molecular computing tasks because they are programmable, cheap, robust and predictable. A key feature of these circuits is the use of catalytic gates to amplify signal. Catalytic gates tend to leak, that is, they generate output signal even in the abs...

DNA devices have been shown to be capable of evaluating Boolean logic. Several robust designs for DNA circuits have been demonstrated. Some prior DNA‐based circuits are use‐once circuits since the gate motifs of the DNA circuits get permanently destroyed as a side effect of the computation, and hence cannot respond correctly to subsequent changes i...

The field of DNA computation makes use of DNA reactions to do molecular-scale computation. Most works in DNA computation execute digital computations such as evaluation of Boolean circuits. This chapter surveys novel DNA computation methods that execute analog computations, where the inputs and outputs are real values specified by the concentration...

The field of DNA nanoscience has demonstrated many exquisite DNA nanostructures and intricate DNA nanodevices. However the operation of each step of prior demonstrated DNA nanodevices requires the diffusion of DNA strands, and the speed of these devices is limited by diffusion kinetics. Here we demonstrate chains of localized DNA hybridization reac...

In the past decade, single-molecule imaging has opened new opportunities to understand reaction kinetics of molecular systems. DNA-PAINT uses transient binding of DNA strands to perform super-resolution fluorescence imaging. An interesting challenge in DNA nanoscience and related fields is the unique identification of single-molecules. While wavele...

Theoretical models of localized DNA hybridization reactions on nanoscale substrates indicate potential benefits over conventional DNA hybridization reactions. Recently, a few approaches have been proposed to speed-up DNA hybridization reactions; however, experimental confirmation and quantification of the acceleration factor have been lacking. Here...

DNA based nanostructures and devices are becoming ubiquitous in nanotechnology with rapid advancements in theory and experiments in DNA self-assembly which have led to a myriad of DNA nanodevices. However, the modeling methods used by researchers in the field for design and analysis of DNA nanostructures and nanodevices have not progressed at the s...

DNA self-assembly has been employed non-conventionally to construct nanoscale structures and dynamic nanoscale machines. The technique of hybridization chain reactions by triggered self-assembly has been shown to form various interesting nanoscale structures ranging from simple linear DNA oligomers to dendritic DNA structures. Inspired by earlier t...

Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these exi...

There is a growing need for sensitive and reliable nucleic acid detection methods that are convenient and inexpensive. Responsive and programmable DNA nanostructures have shown great promise as chemical detection systems. Here, we describe a DNA detection system employing the triggered self-assembly of a novel DNA dendritic nanostructure. The detec...

Biomolecular computation includes a diverse set of methods for executing computations at the molecular scale using biomolecules. This chapter overviews the use of DNA-based methods for biomolecular computation.

This Chapter overviews the past and current state of a selected part of the emerging research area of the field of DNA-based biomolecular devices. We particularly emphasize molecular devices that are: • Autonomous: executing steps with no exterior mediation after starting, and • Programmable: the tasks executed can be modified without entirely rede...

Self-reconfigurable robots are composed of many individual modules that can autonomously move to transform the shape and structure of the robot. The task of self-reconfiguration, transforming a set of modules from one arrangement to another specified arrangement, is a key problem for these robots and has been heavily studied. However, consideration...

Molecular computing executed via local interactions of spatially contiguous set of molecules has potential advantages of (i) speed due to increased local concentration of reacting species, (ii) sharper switching behavior due to single molecule interactions, (iii) parallelism since each circuit operates independently of another and (iv) modularity a...

A technique uses DNA strands to perform calculations that can be scaled up in complexity.

Self-assembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano-scale structures. Recent years have seen convergent interest and...

DNA is a useful material for nanoscale construction. Due to highly specific Watson-Crick base pairing, the DNA sequences can be designed to form small tiles or origami. Adjacent helices in such nanostructures are connected via Holliday junction-like crossovers. DNA tiles can have sticky ends which can then be programmed to form large one-dimensiona...

Self-assembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building molecular scale struc- tures. Recent years see convergent interest and...

The hybridization of complementary nucleic acid strands is the most basic of all reactions involving nucleic acids, but has a major limitation: the specificity of hybridization reactions depends critically on the lengths of the complementary pairs of strands and can drop to very low values for sufficiently long strands. This reduction in specificit...

Winfree’s pioneering work led the foundations in the area of error-reduction in algorithmic self-assembly (Winfree and Bekbolatov in DNA Based Computers 9, LNCS, vol. 2943, pp. 126–144, [2004]), but the construction resulted in increase of the size of assembly. Reif et al. (Nanotechnol. Sci. Comput. 79–103, [2006]) contributed further in this area...

Self-reconfigurable robots have an intriguingly flexible design, composing a single robot with many small modules that can autonomously move to transform the robot’s shape and structure. Scaling to a large number of modules is necessary to achieve great flexibility, so each module may only have limited processing and memory resources. This paper in...

Self-repair is essential to all living systems, providing the ability to remain functional in spite of gradual damage. In the context of self-assembly of self-repairing synthetic biomolecular systems, recently Winfree developed a method for transforming a set of DNA tiles into its self-healing counterpart at the cost of increasing the lattice area...

Process algebras are widely used to define the formal semantics of concurrent communicating processes. In this paper, we implement a particularly expressive form of process algebra, known as stochastic π-calculus, at the molecular scale by providing a design for a DNA-based biomolecular device that simulates a process algebraic machine. Our design...

Introduction Introductory Definitions Adelman's Initial Demonstration of a DNA-Based Computation Self-Assembled DNA Tiles and LAT Tices Autonomous Finite-State Computation using Linear DNA Nanostructures Assembling PAT Terned and Addressable 2D DNA LAT Tices Error Correction and Self-Repair at the Molecular Scale Three-Dimensional DNA Lattices Auto...

The conventional tile assembly model (TAM) developed by Winfree using Wang tiles is a powerful, Turing-universal theoretical framework which models varied self-assembly processes. We describe a natural extension to TAM called the probabilistic tile assembly model (PTAM) to model the inherent probabilistic behavior in physically realized self-assemb...

A major challenge in nanoscience is the design of synthetic molecular devices that run autonomously (that is, without externally mediated changes per work-cycle) and are programmable (that is, their behavior can be modified without complete redesign of the device). DNA-based synthetic molecular devices have the advantage of being relatively simple...

Self-assembly is a ubiquitous process in which small objects selforganize into larger and complex structures. In 2000, Rothemund and Winfree proposed a Tile Assembly Model as a mathematical model for theoretical studies of self-assembly.We propose a refined self-assembly model in which the glue strength between two juxtaposed tiles is a function of...

Polymerases are a family of enzymes responsible for copying or replication of nucleic acids (DNA or RNA) templates and hence sustenance of life processes. In this paper, we present a method to exploit a strand-displacing polymerase 29 as a driving force for nanoscale transportation devices. The principal idea behind the device is strong strand disp...

A major challenge in nanoscience is the design of synthetic molecular devices that run autonomously and are programmable. DNA-based synthetic molecular devices have the advantage of being relatively simple to design and engineer, due to the predictable secondary structure of DNA nanostructures and the well-established biochemistry used to manipulat...

Synthesizing molecular tubes with monodisperse, programmable circumferences is an important goal shared by nanotechnology, materials science, and supermolecular chemistry. We program molecular tube circumferences by specifying the complementarity relationships between modular domains in a 42-base single-stranded DNA motif. Single-step annealing res...

Self-assembly has been immensely successful in creating com- plex patterns at the molecular scale. However, the use of self-assembly techniques at the macroscopic level has so far been limited to the for- mation of simple patterns. For example, in a number of prior works, self-assembling units or tiles formed aggregates based on the polarity of mag...

The theoretical basis of computational self-assembly dates back to the idea of Wang tiling models in the early 1960s. 1 More recently, it has been recognized that self-assembly is a promis-ing route to nano-scale computation and there have been many experimental demonstrations of self-assembling DNA tiles performing computation. Winfree 2 proposed...

Whiplash PCR is a novel technique for autonomous molecular computation where a state machine is implemented with a single stranded DNA molecule and state transition is driven by polymerase and thermal cycles. The primary difference between WPCR computation and other forms of molecular computing is that the former is based on local, rather than glob...

As manufacturing and robotics reduces in size scale, there is an increasing need to make use of bottom-up self-assembly techniques rather than conventional top-down assembly techniques. This approach has been very successful at the molecular scale, resulting in com-plex patterning at that scale not previously achievable via conventional methods. Ho...

Recent developments in bio-DNA computer science techniques and methods for the development of autonomous programmable biomolecular devices based on self-assembled DNA nanostructures are reviewed. Molecular-scale devices using DNA nanostructures are engineered to have various capabilities such as execution of molecular-scale computation, use as scaf...

This paper presents several results on some cost-minimizing path problems in polygonal regions. For these types of problems, an approach often used to compute approximate optimal paths is to apply a discrete search algorithm to a graph G(epsilon) constructed from a discretization of the problem; this graph is guaranteed to contain an epsilon-good a...

A self-reconfigurable (SR) robot is one composed of many small modules that autonomously act to change the shape and structure of the robot. In this paper we consider a general class of SR robot modules that have rectilinear shape that can be adjusted between fixed dimensions, can transmit forces to their neighbors, and can apply additional forces...

While algorithmic DNA self-assembly is, in theory, capable of forming complex patterns, its experimental demonstration has been limited by significant assembly errors. In this paper we describe a novel protection/deprotection strategy to strictly enforce the direction of tiling assembly growth to ensure the robustness of the assembly process. Tiles...

The Chapter describes the use of DNA for molecular-scale self-assembly. DNA-nanostructures provide a versatile toolbox with which to organize nanoscale materials. We begin with a discussion of DNA-nanostructures, starting with the self-assembly of various building-blocks known as DNA tiles. We describe how these can be made to self-assemble into tw...

Self-repair is essential to all living systems, providing the ability to remain functional in spite of gradual damage. In the context of self-assembly of self-repairing synthetic biomolecular systems, recently Winfree developed a method for transforming a set of DNA tiles into its self-healing counterpart at the cost of increasing the lattice area...

Recent successes in building large scale DNA nanostructures and in constructing DNA nanomechanical devices have inspired scientists to design more complex nanoscale systems. The design process can be made considerably more efficient and robust with the help of simulators that can model such systems accurately prior to their experimental implementat...

Winfree’s pioneering work led the foundations in the area of error-reduction in algorithmic self-assembly[26], but the construction resulted in increase of the size of assembly. Reif et. al. contributed further in this area with compact error-resilient schemes [15] that maintained the original size of the assemblies, but required certain restrictio...

We consider the problem of finding a minimum length path between two points in 3-dimensional Euclidean space which avoids a set of (not necessarily convex) polyhedral obstacles; we let n denote the number of the obstacle edges and k denote the number of "islands" in the obstacle space. An island is defined to be a maximal convex obstacle surface su...

The main result of this paper is an approximation algorithm for the weighted region optimal path problem. In this problem, a point robot moves in a planar space composed of n triangular regions, each of which is associated with a positive unit weight. The objective is to find, for given source and destination points s and t, a path from s to t with...

Decorated tiles: Self-assembling DNA nanostructures can be used to form addressable, size-controlled nanoarrays with a variety of programmed patterns. Arrays of DNA cross-shaped tiles were decorated with pixels of individual protein molecules. The letters "D", "N", and "A" on self-assembled 4 x 4 arrays (<80-nm square, see picture) were prepared by...

Simulated Annealing is a family of randomized algorithms for solving multivariate global optimization problems. Empirical results from the application of Simulated Annealing algorithms to certain hard problems including certain types of NP-complete problems demonstrate that these algorithms yield better results than known heuristic algorithms. But...

A key problem in medical science and genomics is that of the efficient storage, processing, and retrieval of genetic information and material. This chapter presents an architecture for a Biomolecular Database system that would provide a unique capability in genomics. It completely bypasses the usual transformation from biological material (genomic...

Recent experimental progress in DNA lattice construction, DNA robotics, and DNA computing provides the basis for designing DNA cellular computing devices, i.e. autonomous nano-mechanical DNA computing devices embedded in DNA lattices. Once assembled, DNA cellular computing devices can serve as reusable, compact computing devices that perform (unive...

We propose a self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring posi- tions. We then present an implementation of our model using strand displacement reactions on DNA tiles. Under our model, we can demonstrate and study cataly- sis and self-replication in the tile asse...

We present a DNA nanostructure, the three-helix bundle (3HB), which consists of three double helical DNA domains connected by six immobile crossover junctions such that the helix axes are not coplanar. The 3HB motif presents a triangular cross-section with one helix lying in the groove formed by the other two. By differential programming of sticky-...

We demonstrate the precise control of periodic spacing between individual protein molecules by programming the self-assembly of DNA tile templates. In particular, we report the application of two self-assembled periodic DNA structures, two-dimensional nanogrids, and one-dimensional nanotrack, as template for programmable self-assembly of streptavid...

We discuss the problem of computing optimal paths on terrains for a mobile robot, where the cost of a path is defined to be the energy expended due to both friction and gravity. The physical model used by this problem allows for ranges of impermissible traversal directions caused by overturn danger or power limitations. The model is interesting and...

There's no turning back for an autonomous DNA walker that moves along a self-assembled track, driven by the hydrolysis of ATP. The track contains three anchorages (A, B, C) at which the walker (*), a six-nucleotide DNA fragment, can be bound (see figure). The motion of the walker is unidirectional. At each step it is ligated to the next anchorage,...

In recent years, a number of research groups have begun developing nanofabrication methods based on DNA self‐assembly. Here we review our recent experimental progress to utilize novel DNA nanostructures for self‐assembly as well as for templates in the fabrication of functional nano‐patterned materials. We have prototyped a new DNA nanostructure...

We report on the self-assembly of one- and two-dimensional DNA scaffolds, which serve as templates for the targeted deposition of ordered nanoparticles and molecular arrays. The DNA nanostructures are easy to reprogram, and we demonstrate two distinct conformations: sheets and tubes. The DNA tubes and individual DNA molecules are metallized in solu...

Imagine a host of nanoscale DNA robots move autonomously over a microscale DNA nanostructure, each following a programmable route and serving as a nanoparticle and/or an information carrier. The accomplishment of this goal has many applications in nanorobotics, nano-fabrication, nanoelectronics, nano-diagnostics/therapeutics, and nanocomputing. Rec...

The self-assembly process for bottom-up construction of nanostructures is of key importance to the emerging scientific discipline Nanoscience. However, self-assembly at the molecular scale is prone to a quite high rate of error. Such high error rate is a major barrier to large-scale experimental implementation of DNA tiling. The goals of this paper...

Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nanostructures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step forward: designing autonomous DNA mechanical devices capable...

This paper presents an overview of recent experimental progress by the Duke DNA NanoTech Group in our efforts to utilize novel DNA nanostructures for computational self-assembly as well as for templates in the fabrication of functional nano-patterned materials. We have prototyped a new DNA tile type known as the 4x4 (a cross-like structure composed...

llowing neighboring tiles in an assembly to associate by sticky ends on each side, one could increase the computational complexity of languages generated by linear self-assemblies. Surprisingly sophisticated calculations can be performed with singlelayer linear assemblies when contiguous strings of DNA trace through individual tiles and the entire...

DNA is a crucial construction material for molecular scale objects with nano-scale fea-tures. Diverse synthetic DNA objects hold great potential for applications such as nano-fabrication, nano-robotics, nano-computing, and nano-electronics. The construction of DNA objects is generally carried out via self-assembly. During self-assembly, DNA strands...

We provide designs for the first autonomous DNA nanomechanical devices that execute cycles of motion without external environmental changes. These DNA devices translate along a circular strand of ssDNA and rotate simultaneously. The designs use various energy sources to fuel the movements, include (i) ATP consumption by DNA ligase in conjunction wi...

DNA-based nanotechnology is currently being developed as a general assembly method for nanopatterned materials that may find use in electronics, sensors, medicine, and many other fields. Here we present results on the construction and characterization of DNA nanotubes, a self-assembling superstructure composed of DNA tiles. Triple-crossover tiles m...

Self-assembling DNA tiling lattices represent a versatile system for nanoscale construction. Self-assembled DNA arrays provide an excellent template for spatially positioning other molecules with increased relative precision and programmability. Here we report an experiment using a linear array of DNA triple crossover tiles to controllably template...

Self-assembly is the spontaneous self-ordering of substructures into superstructures driven by the selective affinity of the substructures. DNA pro- vides a molecular scale material for programmable self-assembly, using the selective affinity of pairs of DNA strands to form DNA nanostructures. DNA self-assembly is the most advanced and versatile sy...

Summary This paper presents an overview of recent experimental progress by the Duke DNA NanoTech Group in our efforts to utilize novel DNA nanostructures for computational self-assembly as well as for templates in the fabrication of functional nano-patterned materials. We have prototyped a new DNA tile type known as the 4x4 (a cross-like structure...

Self-assembling DNA nanostructures are an efficient means of executing parallel molecular computations. However, previous experimental demonstrations of computations by DNA tile self-assembly only allowed for one set of distinct input to be processed at a time. Here, we report the multibit, parallel computation of pairwise exclusive-or (XOR) using...

A class of mechanical systems connected by frictional contact linkages between surfaces and their computational power were described. A universal Turing machine (TM) was simulated by a universal frictional mechanical system. It was found that the robotic mover's problem was undecidable when there were frictional linkages. It was also observed that...

A novel approach to inset superimposition in a high-resolution head-mounted display (HMD) is presented. The approach is innovative in its use of optoelectronic, nonmechanical devices in place of scanning mechanical devices commonly adopted previously. A paraxial layout of the overall HMD system is presented, and the benefit of employing hybrid refr...

We consider parallel algorithms for real-time compression of video. Our model of computation is a systolic pipe, where processors are arranged in a linear array (each processor is connected only to its left and right neighbors). The algorithm presented combines quantization techniques with dynamic (adaptive) on-line textual substitution methods for...

A propositional logic of distributed protocols is introduced which includes both the logic of knowledge and temporal logic. Phenomena in distributed computing systems such as asynchronous time, incomplete knowledge by the computing agents in the system, and game-like behavior among the computing agents are all modeled in the logic. Two versions of...

The scope of this paper is to survey randomized parallel algorithms available for various computational problems. We do not claim to give a comprehensive list of all the randomized parallel algorithms that have been discovered so far. We only discuss representative examples which demonstrate the special features of both randomization and paralleliz...

Flashsort [RV83,86] and Samplesort [HC83] are related parallel sorting algorithms proposed in the literature. Both utilize a sophisticated randomized sampling technique to form a splitter set, but Samplesort distributes the splitter set to each processor while Flashsort uses splitter-directed routing.

Potentially, data compression techniques may have a broad impact in computing not only by decreasing storage and communication costs, but also by speeding up computation. For many image processing applications, the use of data compression is so pervasive that we can assume the inputs and outputs are in a compressed domain, and it is intriguing to c...

A DNA nanostructure consisting of four four-arm junctions oriented with a square aspect ratio was designed and constructed. Programmable self-assembly of 4 × 4 tiles resulted in two distinct lattice morphologies: uniform-width nanoribbons and two-dimensional nanogrids, which both display periodic square cavities. Periodic protein arrays were achiev...

Changing the dimensions of the mesh. A robust sequence-dependent DNA device termed a nanoactuator was incorporated into a 2D parallelogram DNA lattice. Conversion of the DNA nanoactuator between two well-defined states (S1 and S2, see picture) results in controlled motion of the lattice.

This paper presents several results on the weighted region optimal path problem. An often-used approach to approximately solve this problem is to apply a discrete search algorithm to a graph G† generated by a discretization of the problem; this graph guarantees to contain an †-approximation of an optimal path between given source and destination po...

The programmed self-assembly of patterned aperiodic molecular structures is a major challenge in nanotechnology and has numerous potential applications for nanofabrication of complex structures and useful devices. Here we report the construction of an aperiodic patterned DNA lattice (barcode lattice) by a self-assembly process of directed nucleatio...

This paper presents several results on the weighted region optimal path problem. An often-used approach to approximately solve this problem is to apply a discrete search algorithm to a graph G generated by a discretization of the problem; this graph guarantees to contain an -approximation of an optimal path between given source and destination poin...

The purpose of this paper is to investigate the properties of a certain class of highly visible spaces. For a given geometric space S containing obstacles speci ed by disjoint subsets of S, the free space F is de ned to be the portion of S not occupied by these obstacles. The space is said to be highly visible if at each point in F a viewer can see...

Two case studies are presented that demonstrate the systematic derivation of efficient algorithms from simple combinatorial definitions. These case studies contribute to an exploration of evolutionary approaches to the explanation, proof, adaptation, and possibly the design of complex algorithms. The algorithms derived are the linear-time depth-fir...

DNA-based nanotechnology is currently being developed for use in biomolecular computation, fabrication of 2D tile lattices, and engineering of 3D periodic matter. Here we present recent results on the construction and characterization of DNA nanotubes - a new self-assembling superstructure composed of DNA tiles. Triple-crossover (TAO) tiles modifie...

The rapidly evolving field of DNA or biomolecular computing uses biotechnological techniques to do computation. In his Perspective, Reif highlights the report by Braich et al. of the largest-scale demonstration to date of the capabilities of DNA computation. The method developed by the authors may have diverse biotechnology and security applicatio...

ently the largest of which has 12 7 microbeads, each carrying approximately 10 7 strands of DNA. This already constitutes by far the largest number of distinct DNA strands synthesized in a library of this type. Following successful completion of the second construction phase, the resulting DNA library will contain 12 14 or 1.28 x 10 15 distinct dat...

We describe our on-going experiments for executing associative search queries within the synthesized DNA databases. These queries are executed by hybridization of a target database strand with a complementary query strand probe. In our initial annealing experiments for processing associative search queries, we employed fluorescently labeled query s...

The usual assumption for proofs of the optimality of lossless encoding is a stationary ergodic source. Dynamic sources with non-stationary probability distributions occur in many practical situations where the data source is formed from a composition of distinct sources, for example, a document with multiple authors, a multimedia document, or the c...

The main theme of this paper is to take inspiration from methods used in computer science and related disciplines, and to apply these to develop improved biotechnology. In particular, our proposed improvements are made by adapting various information theoretic coding techniques which originate in computational and information processing disciplines...

. The first main result of this paper is a novel nonuniform discretization approximation method for the kinodynamic motion-planning problem. The kinodynamic motion-planning problem is to compute a collision-free, time-optimal trajectory for a robot whose accelerations and velocities are bounded. Previous approximation methods are all based on a uni...