614 research outputs found
Programmable Control of Nucleation for Algorithmic Self-Assembly
Algorithmic self-assembly, a generalization of crystal growth processes, has
been proposed as a mechanism for autonomous DNA computation and for bottom-up
fabrication of complex nanostructures. A `program' for growing a desired
structure consists of a set of molecular `tiles' designed to have specific
binding interactions. A key challenge to making algorithmic self-assembly
practical is designing tile set programs that make assembly robust to errors
that occur during initiation and growth. One method for the controlled
initiation of assembly, often seen in biology, is the use of a seed or catalyst
molecule that reduces an otherwise large kinetic barrier to nucleation. Here we
show how to program algorithmic self-assembly similarly, such that seeded
assembly proceeds quickly but there is an arbitrarily large kinetic barrier to
unseeded growth. We demonstrate this technique by introducing a family of tile
sets for which we rigorously prove that, under the right physical conditions,
linearly increasing the size of the tile set exponentially reduces the rate of
spurious nucleation. Simulations of these `zig-zag' tile sets suggest that
under plausible experimental conditions, it is possible to grow large seeded
crystals in just a few hours such that less than 1 percent of crystals are
spuriously nucleated. Simulation results also suggest that zig-zag tile sets
could be used for detection of single DNA strands. Together with prior work
showing that tile sets can be made robust to errors during properly initiated
growth, this work demonstrates that growth of objects via algorithmic
self-assembly can proceed both efficiently and with an arbitrarily low error
rate, even in a model where local growth rules are probabilistic.Comment: 37 pages, 14 figure
An information-bearing seed for nucleating algorithmic self-assembly
Self-assembly creates natural mineral, chemical, and biological structures of great complexity. Often, the same starting materials have the potential to form an infinite variety of distinct structures; information in a seed molecule can determine which form is grown as well as where and when. These phenomena can be exploited to program the growth of complex supramolecular structures, as demonstrated by the algorithmic self-assembly of DNA tiles. However, the lack of effective seeds has limited the reliability and yield of algorithmic crystals. Here, we present a programmable DNA origami seed that can display up to 32 distinct binding sites and demonstrate the use of seeds to nucleate three types of algorithmic crystals. In the simplest case, the starting materials are a set of tiles that can form crystalline ribbons of any width; the seed directs assembly of a chosen width with >90% yield. Increased structural diversity is obtained by using tiles that copy a binary string from layer to layer; the seed specifies the initial string and triggers growth under near-optimal conditions where the bit copying error rate is 17 kb of sequence information. In sum, this work demonstrates how DNA origami seeds enable the easy, high-yield, low-error-rate growth of algorithmic crystals as a route toward programmable bottom-up fabrication
DNA Computing by Self-Assembly
Information and algorithms appear to be central to biological organization
and processes, from the storage and reproduction of genetic information to
the control of developmental processes to the sophisticated computations
performed by the nervous system. Much as human technology uses electronic
microprocessors to control electromechanical devices, biological
organisms use biochemical circuits to control molecular and chemical events.
The engineering and programming of biochemical circuits, in vivo and in
vitro, would transform industries that use chemical and nanostructured
materials. Although the construction of biochemical circuits has been
explored theoretically since the birth of molecular biology, our practical
experience with the capabilities and possible programming of biochemical
algorithms is still very young
Reducing facet nucleation during algorithmic self-assembly
Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex
nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding
interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically reducing yields.
Here we provide experimental evidence that assembly can be made more robust to errors by adding redundant tiles that "proofread" assembly.
We construct DNA tile sets for two methods, uniform and snaked proofreading. While both tile sets are predicted to reduce errors during
growth, the snaked proofreading tile set is also designed to reduce nucleation errors on crystal facets. Using atomic force microscopy to
image growth of proofreading tiles on ribbon-like crystals presenting long facets, we show that under the physical conditions we studied the
rate of facet nucleation is 4-fold smaller for snaked proofreading tile sets than for uniform proofreading tile sets
Toward reliable algorithmic self-assembly of DNA tiles: A fixed-width cellular automaton pattern
Bottom-up fabrication of nanoscale structures relies on chemical processes to direct self-assembly. The complexity, precision, and yield achievable by a one-pot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a one-pot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed structure, then the free tiles grow algorithmically from the seed according to the automaton rules. In our experiments, crystals grew to ~300 nm long, containing ~300 tiles with an initial assembly error rate of ~1.4% per tile. This work provides evidence that programmable molecular self-assembly may be sufficient to create a wide range of complex objects in one-pot reactions
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
Synthesis of crystals with a programmable kinetic barrier to nucleation
A central goal of chemistry is to fabricate supramolecular structures of defined function and composition. In biology, control of supramolecular synthesis is often achieved through precise control over nucleation and growth processes: A seed molecule initiates growth of a structure, but this growth is kinetically inhibited in the seed's absence. Here we show how such control can be systematically designed into self-assembling structures made of DNA tiles. These structures, "zig-zag ribbons," are designed to have a fixed width but can grow arbitrarily long. Under slightly supersaturated conditions, theory predicts that elongation is always favorable but that nucleation rates decrease exponentially with increasing width. We confirm experimentally that although ribbons of different widths have similar thermodynamics, nucleation rates decrease for wider ribbons. It is therefore possible to program the nucleation rate by choosing a ribbon width. The presence of a seed molecule, a stabilized version of the presumed critical nucleus, removes the kinetic barrier to nucleation of a ribbon. Thus, we demonstrate the ability to grow supramolecular structures from rationally designed seeds, while suppressing spurious nucleation. Control over DNA tile nucleation allows for proper initiation of algorithmic crystal growth, which could lead to the high-yield synthesis of micrometer-scale structures with complex programmed features. More generally, this work shows how a self-assembly subroutine can be initiated
Two computational primitives for algorithmic self-assembly: Copying and counting
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length
Proofreading tile sets: Error correction for algorithmic self-assembly
For robust molecular implementation of tile-based algorithmic
self-assembly, methods for reducing errors must be developed. Previous
studies suggested that by control of physical conditions, such as
temperature and the concentration of tiles, errors (Ξ΅) can be reduced
to an arbitrarily low rate - but at the cost of reduced speed (r) for
the self-assembly process. For tile sets directly implementing blocked
cellular automata, it was shown that r β Ξ²Ξ΅^2 was optimal. Here, we
show that an improved construction, which we refer to as proofreading
tile sets, can in principle exploit the cooperativity of tile assembly reactions
to dramatically improve the scaling behavior to r β Ξ²Ξ΅ and better.
This suggests that existing DNA-based molecular tile approaches may be
improved to produce macroscopic algorithmic crystals with few errors.
Generalizations and limitations of the proofreading tile set construction
are discussed
Algorithmic Self-Assembly of DNA Sierpinski Triangles
Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal patternβa Sierpinski triangleβas it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long single-stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100β200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks
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