Molecular ping-pong Game of Life on a two-dimensional DNA origami array.

We propose a design for programmed molecular interactions that continuously change molecular arrangements in a predesigned manner. We introduce a model where environmental control through laser illumination allows platform attachment/detachment oscillations between two floating molecular species. The platform is a two-dimensional DNA origami array of tiles decorated with strands that provide both, the floating molecular tiles to attach and to pass communicating signals to neighbouring array tiles. In particular, we show how algorithmic molecular interactions can control cyclic molecular arrangements by exhibiting a system that can simulate the dynamics similar to two-dimensional cellular automata on a DNA origami array platform.

Subdiffusion of a sticky particle on a surface.

Conventional diffusion (ΔR2(t))=2Dt gives way to subdiffusion (ΔR2(t))∼t(µ), 0<µ<1 when the waiting time distribution φ(τ) is nonintegrable. We have studied a model system, colloidal particles functionalized with DNA "sticky ends" diffusing on a complementary coated surface. We observe a crossover from subdiffusive to conventional behavior for (ΔR2(t)) and φ(τ) as temperature is increased near the particle-surface melting temperature consistent with a simple Gaussian distribution of sticky ends. Our results suggest that any system with randomness in its binding energy should exhibit subdiffusive behavior as it unbinds. This will strongly affect the kinetics of self-assembly.

Logical computation using algorithmic self-assembly of DNA triple-crossover molecules.

Recent work has demonstrated the self-assembly of designed periodic two-dimensional arrays composed of DNA tiles, in which the intermolecular contacts are directed by 'sticky' ends. In a mathematical context, aperiodic mosaics may be formed by the self-assembly of 'Wang' tiles, a process that emulates the operation of a Turing machine. Macroscopic self-assembly has been used to perform computations; there is also a logical equivalence between DNA sticky ends and Wang tile edges. This suggests that the self-assembly of DNA-based tiles could be used to perform DNA-based computation. Algorithmic aperiodic self-assembly requires greater fidelity than periodic self-assembly, because correct tiles must compete with partially correct tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that can be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits.

Multimerization-cyclization of DNA fragments as a method of conformational analysis.

Ligation of short DNA fragments results in the formation of linear and circular multimers of various lengths. The distribution of products in such a reaction is often used to evaluate fragment bending caused by specific chemical modification, by bound ligands or by the presence of irregular structural elements. We have developed a more rigorous quantitative approach to the analysis of such experimental data based on determination of j-factors for different multimers from the distribution of the reaction products. j-Factors define the effective concentration of one end of a linear chain in the vicinity of the other end. To extract j-factors we assumed that kinetics of the reaction is described by a system of differential equations where j-factors appear as coefficients. The assumption was confirmed by comparison with experimental data obtained here for DNA fragments containing A-tracts. At the second step of the analysis j-factors are used to determine conformational parameters of DNA fragments: the equilibrium bend angle, the bending rigidity of the fragment axis, and the total twist of the fragments. This procedure is based on empirical equations that connect the conformational parameters with the set of j-factors. To obtain the equations, we computed j-factors for a large array of conformational parameters that describe model fragments. The approach was tested on both simulated and actual experimental data for DNA fragments containing A-tracts. A-tract DNA bend angle determined here is in good agreement with previously published data. We have established a set of experimental conditions necessary for the data analysis to be successful.

Direct evidence for spontaneous branch migration in antiparallel DNA Holliday junctions.

The Holliday junction is a central intermediate in genetic recombination. It contains four strands of DNA that are paired into four double helical arms flanking a branch point. In naturally occurring Holliday junctions, the sequence flanking the branch point contains 2-fold (homologous) symmetry. As a consequence of this symmetry, the junction can undergo a conformational isomerization known as branch migration, which relocates the site of branching. In the absence of proteins and in the presence of Mg(2+), the four arms are known to stack in pairs, forming two helical domains whose orientations are antiparallel. Nevertheless, the mechanistic models proposed for branch migration are all predicated on a parallel alignment of helical domains. Here, we have used antiparallel DNA double crossover molecules to demonstrate that branch migration can occur in antiparallel Holliday junctions. We have constructed a DNA double crossover molecule with three crossover points. Two adjacent branch points in this molecule are flanked by symmetric sequences. The symmetric crossover points are held immobile by the third crossover point, which is flanked by asymmetric sequences. Restriction of the helices that connect the immobile junction to the symmetric junctions releases this constraint. The restricted molecule undergoes branch migration, even though it is constrained to an antiparallel conformation.

Cleavage of symmetric immobile DNA junctions by Escherichia coli RuvC.

The Holliday junction is a key DNA intermediate in the process of genetic recombination. It consists of two double-helical domains composed of homologous strands that flank a branch point; two of the strands are roughly helical, and two form the crossover between the helices. RuvC is a Holliday junction resolvase that cleaves the helical strands at a symmetric sequence, leading to the production of two recombinant molecules. We have determined the position of the cleavage site relative to the crossover point by the use of symmetric immobile junctions; these are DNA molecules containing two crossover points, one held immobile by sequence asymmetry and the second a symmetric sequence, but held immobile by torsional coupling to the first junction. We have built five symmetric immobile junctions, in which the tetranucleotide recognition site is moved stepwise relative to the branch point. We have used kinetic analysis of catalysis, gel retardation, and hydroxyl radical hypersensitivity to analyze this system. We conclude that the internucleotide linkage one position 3' to the crossover point is the favored site of cleavage.

Atomic force microscopy of parallel DNA branched junction arrays.

BACKGROUND: The four arms of the Holliday junction are known to stack in pairs forming two helical domains whose orientations are antiparallel, but twisted positively by about 60 degrees, based on electrophoretic, FRET and AFM measurements. Recent gel retardation studies suggest that a bowtie junction (containing 5',5' and 3',3' linkages in its crossover strands) may adopt a parallel conformation. RESULTS: An AFM study of two-dimensional arrays produced by parallelograms of bowtie junctions shows that the angle between helical domains is in the range of -68+/-2 degrees. We demonstrate by AFM that the domains are parallel by constructing V-shaped structures whose arms are separated by approximately 68 degrees and approximately 112 degrees. CONCLUSIONS: The arms of the bowtie junction are parallel rather than antiparallel. The parallel or antiparallel nature of the junction apparently is determined by the local structure of the junction, but the sign of the angle appears to be a consequence of interarm electrostatic interactions.

Two dimensions and two States in DNA nanotechnology.

Abstract The construction of periodic matter and nanomechanical devices are central goals of DNA nanotechnology. The minimal requirements for components of designed crystals are [1] programmable interactions, [2] predictable local intermolecular structures and [3] rigidity. The sticky-ended association of DNA molecules fulfills the first two criteria, because it is specific and diverse, and it results in the formation of B-DNA. Stable branched DNA molecules permit the formation of networks, but individual single branches are too flexible. Antiparallel DNA double crossover (DX) molecules can provide the necessary rigidity, so we use these components to tile the plane. It is possible to include DNA hairpins that act as topographic labels for this 2-D crystalline array, because they protrude from its plane. By altering sticky ends, it is possible to change the topographic features formed by these hairpins, and to detect these changes by means of AFM. We can modify arrays by restricting hairpins or by adding them to sticking ends protruding from the array. Although individual branched junctions are unsuitable for use as crystalline components, parallelograms of four 4-arm junction molecules are sufficiently rigid that they can be used to produce 2D arrays. The arrays contain cavities whose dimensions are readily tuned by changing the edges of their parallelogram components. We have used these arrays to measure directly the angle between the helices of the Holliday junction. The rigidity of the DX motif can also be exploited to produce a nanomechanical device predicated on the B-Z transition. Two DNA double crossover molecules have been joined by a segment of DNAcapable of undergoing the B-Z transition. In the B-conformation, the unconnected helices of the two molecules are on the same side of the connecting helix, whereas in the Z conformation they are on opposite sides, leading to movements of as much as 60Å. This effect is shown by fluorescence resonance energy transfer, because dyes attached to the unconnected helices have different separations in the two states.

No braiding of Holliday junctions in positively supercoiled DNA molecules.

The Holliday junction is a prominent intermediate in genetic recombination that consists of four double helical arms of DNA flanking a branch point. Under many conditions, the Holliday junction arranges its arms into two stacked domains that can be oriented so that genetic markers are parallel or antiparallel. In this arrangement, two strands retain a helical conformation, and the other two strands effect the crossover between helical domains. The products of recombination are altered by a crossover isomerization event, which switches the strands fulfilling these two roles. It appears that effecting this switch from the parallel conformation by the simplest mechanism results in braiding the crossover strands at the branch point. In previous work we showed by topological means that a short, parallel, DNA double crossover molecule with closed ends did not braid its branch point; however, that molecule was too short to adopt the necessary positively supercoiled topology. Here, we have addressed the same problem using a larger molecule of the same type. We have constructed a parallel DNA double crossover molecule with closed ends, containing 14 double helical turns in each helix between its crossover points. We have prepared this molecule in a relaxed form by simple ligation and in a positively supercoiled form by ligation in the presence of netropsin. The positively supercoiled molecule is of the right topology to accommodate braiding. We have compared the relaxed and supercoiled versions for their responses to probes that include hydroxyl radicals, KMnO4, the junction resolvases endonuclease VII and RuvC, and RuvC activation of KMNO4 sensitivity. In no case did we find evidence for a braid at the crossover point. We conclude that Holliday junctions do not braid at their branch points, and that the topological problem created by crossover isomerization in the parallel conformation is likely to be solved by distributing the stress over the helices that flank the branch point.

DNA engineering and its application to nanotechnology.

The combination of branched DNA molecules and 'sticky' ends creates a powerful molecular assembly kit for structural DNA nanotechnology. Polyhedra, complex topological objects, a nanomechanical device and two-dimensional arrays with programmable surface features have already been produced in this way. Future applications range from macromolecular crystallography and new materials to molecular electronics and DNA-based computation.

Parallel helical domains in DNA branched junctions containing 5',5' and 3',3' linkages.

The Holliday junction is a central intermediate in genetic recombination. It contains four strands of DNA that are paired into four double helical arms that flank a branch point. In the presence of Mg2+, the four arms are known to stack in pairs forming two helical domains whose orientations are antiparallel but twisted by about 60 degrees. The basis for the antiparallel orientation of the domains could be either junction structure or the effect of electrostatic repulsion between domains. To discriminate between these two possibilities, we have constructed and characterized an analogue, called a bowtie junction, in which one strand contains a 3',3' linkage at the branch point, the strand opposite it contains a 5',5' linkage, and the other two strands contain conventional 3',5' linkages. Electrostatic effects are expected to lead to an antiparallel structure in this system. We have characterized the molecule in comparison with a conventional immobile branched junction by Ferguson analysis and by observing its thermal transition profile; the two molecules behave virtually identically in these assays. Hydroxyl radical autofootprinting has been used to establish that the unusual linkages occur at the branch point and that the arms stack to form the same domains as the conventional junction. Cooper-Hagerman gel mobility analyses have been used to determine the relative orientations of the helical domains. Remarkably, we find them to be closer to parallel than to antiparallel, suggesting that the preferred structure of the branch point dominates over electrostatic repulsion. We have controlled for the number of available bonds in the branch point, for gel concentration, and for the role of divalent cations. This finding suggests that control of branch point structure alone can lead to parallel domains, which are generally consistent with recombination models derived from genetic data.

A nanomechanical device based on the B-Z transition of DNA.

The assembly of synthetic, controllable molecular mechanical systems is one of the goals of nanotechnology. Protein-based molecular machines, often driven by an energy source such as ATP, are abundant in biology. It has been shown previously that branched motifs of DNA can provide components for the assembly of nanoscale objects, links and arrays. Here we show that such structures can also provide the basis for dynamic assemblies: switchable molecular machines. We have constructed a supramolecular device consisting of two rigid DNA 'double-crossover' (DX) molecules connected by 4.5 double-helical turns. One domain of each DX molecule is attached to the connecting helix. To effect switchable motion in this assembly, we use the transition between the B and Z forms of DNA. In conditions that favour B-DNA, the two unconnected domains of the DX molecules lie on the same side of the central helix. In Z-DNA-promoting conditions, however, these domains switch to opposite sides of the helix. This relative repositioning is detected by means of fluorescence resonance energy transfer spectroscopy, which measures the relative proximity of two dye molecules attached to the free ends of the DX molecules. The switching event induces atomic displacements of 20-60 A.

Sequence dependence of branch migratory minima.

The Holliday junction is a central intermediate in the process of genetic recombination. The position of its branch-point can relocate through an isomerization known as branch migration. This migration occurs because the branch-point is flanked by homologous symmetry. All attempts at modeling the kinetics of branch migration have relied on the assumption that branch migration minima are sequence-independent. We have tested that assumption here, using a competition assay based on symmetric immobile branched junctions; these are junctions that cannot undergo branch migration, despite the fact that they are flanked by homology. The assay used is predicated on the non-association of strands displaced in the assay; we have tested this assumption, and have performed our experiments under conditions where we know that it is true. We have measured the free energy of relocating a branched junction from a fixed non-homologous sequence to all possible dimeric symmetric sequences. We find that the assumption of sequence-independence is often valid, but that it is not universally true. We find that the flanking sequences can have a marked effect on the free energy measured, both for extensions of symmetry and for reversals of flanking nucleotides. We have varied the temperature in our experiments, and have derived both enthalpies and entropies for the different sequences. The entropies are largely unfavorable, whereas the enthalpies are largely favorable; regardless of the signs of these quantities, we see that this is another system where enthalpy-entropy compensation is operative.

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.

DNA nanotechnology: novel DNA constructions.

DNA nanotechnology entails the construction of specific geometrical and topological targets from DNA. The goals include the use of DNA molecules to scaffold the assembly of other molecules, particularly in periodic arrays, with the objects of both crystal facilitation and memory-device construction. Many of these products are based on branched DNA motifs. DNA molecules with the connectivities of a cube and a truncated octahedron have been prepared. A solid-support methodology has been developed to construct DNA targets. DNA trefoil and figure-8 knots have been made, predicated on the relationship between a topological crossing and a half-turn of B-DNA or Z-DNA. The same basis has been used to construct Borromean rings from DNA. An RNA knot has been used to demonstrate an RNA topoisomerase activity. The desire to construct periodic matter held together by DNA sticky ends has resulted in a search for stiff components; DNA double crossover molecules appear to be the best candidates. It appears that novel DNA motifs may be of use in the new field of DNA-based computing.

Non-complementary DNA helical structure induced by positive torsional stress.

We have induced a local conformational transition by positive torsional stress in small synthetic circular DNA molecules containing cruciforms with immobile or tetramobile branched junctions. The immobile species correspond to the extruded and intruded extrema of the tetramobile junction. Under normal conditions the sequences of all the branched species prevent them from being re-absorbed into the circle. We have induced positive stress by addition of ethidium to the circle, in a low ionic strength medium. Alterations in gel electrophoretic mobility under increasing concentrations of ethidium suggest that the cruciforms undergo a transition under torsional stress. The product of this transition contains mispaired nucleotides, but interwound backbones. By comparing the electrophoretic mobilities of circles containing these structures with that of a completely complementary circle of the same length, we conclude that the twist in the mispairing region is similiar to that of completely paired species.

Torsional control of double-stranded DNA branch migration.

DNA branched junctions are analogues of Holliday junction recombination intermediates. Partially mobile junctions contain a limited amount of homology flanking the branch point. A partially mobile DNA branched junction has been incorporated into a synthetic double-stranded circular DNA molecule. The junction is flanked by four homologous nucleotide pairs, so that there are five possible locations for the branch point. Two opposite arms of the branched junction are joined to form the circular molecule, which contains 262 nucleotides to the base of the junction. This molecule represents a system whereby torque applied to the circular molecule can have an impact on the junction, by relocating its branch point. Ligation of the molecule produces two topoisomers; about 87% of the product is a relaxed molecule, and the rest is a molecule with one positive supercoil. The position of the branch point is assayed by cleaving the molecule with endonuclease VII. We find that the major site of the branch point in the relaxed topoisomer is at the maximally extruded position in the relaxed molecule. Upon the addition of ethidium, the major site of the branch point migrates to the minimally extruded position.

A DNA decamer with a sticky end: the crystal structure of d-CGACGATCGT.

The crystal structure of d-CGACGATCGT has been determined to a resolution of 2.6 A. The molecule was synthesized by standard phosphoramidite procedures, and purified by anion-exchange HPLC. Crystals are monolclinic, space group P2(1), with unit cell dimensions, a = 26.45 A, b = 34.66 A, c = 32.17 A, beta = 113.45 degrees and Z = 4, containing a B-DNA double helix in each crystallographic asymmetric unit. The structure was solved using molecular replacement, aided by an isomorphous derivative, in which a bromine atom was attached to the 5 position of cytosine 8. Problems of fit between the search model and the structure ultimately obtained necessitated the use of Patterson correlation procedures between the determination of the orientation and the translation of the molecule. In all, 69 solvent molecules have been identified, and the structure has been refined to an R-factor of 0.214, using the 1421 reflections with F > 2sigma(F), collected at -120 degrees C. The sequence produces a molecule containing eight Watson-Crick base-pairs and a two-nucleotide 5'-sticky end at each end of the duplex. The sticky ends cohere with one another, so the molecules form continuous 10-fold double helices throughout the crystal, with each strand being interrupted by inherent staggered nicks. The relative angular relationships between helices in the structure differ from each other; most of the arrangements differ from Holliday junctions, whose rotational orientations are phased by a crossover and which are modeled to contain double helices that are exactly parallel or antiparallel. However, one helical juxtaposition in this crystal is similar to the alignment of double helices in parallel Holliday junctions. A survey of DNA decamers that also form infinite helices in crystals reveals relationships that approximate both parallel and antiparallel Holliday junction alignments.

Direct evidence for Holliday junction crossover isomerization.

The Holliday junction is a key intermediate in genetic recombination. This is a four-stranded branched DNA structure, whose double-helical arms are stacked in two domains; two of the strands are roughly helical, and the other two cross over between domains. Switching the strands between these two roles is known as crossover isomerization; this postulated reversal is thought to be one of the key transformations that the Holliday junction can undergo, because it can lead to changing the products from patch to splice recombinants. We present direct evidence that this reaction can indeed occur in Holliday junctions in solution. We have constructed a double-crossover molecule containing a branched junction, constrained not to be in its favored conformation. This junction is released from the double-crossover molecule by digestion with restriction endonucleases. We demonstrate by means of hydroxyl radical autofootprinting that the junction changes its crossover isomer spontaneously when released from the double crossover. We control for the possibility that the experimental protocol causes the isomerization. We also exclude dissociation and interaction with other molecules in solution as contributing to the phenomenon. Thus, crossover isomerization is an authentic spontaneous transformation of Holliday junctions.