493 research outputs found
Noncooperative algorithms in self-assembly
We show the first non-trivial positive algorithmic results (i.e. programs
whose output is larger than their size), in a model of self-assembly that has
so far resisted many attempts of formal analysis or programming: the planar
non-cooperative variant of Winfree's abstract Tile Assembly Model.
This model has been the center of several open problems and conjectures in
the last fifteen years, and the first fully general results on its
computational power were only proven recently (SODA 2014). These results, as
well as ours, exemplify the intricate connections between computation and
geometry that can occur in self-assembly.
In this model, tiles can stick to an existing assembly as soon as one of
their sides matches the existing assembly. This feature contrasts with the
general cooperative model, where it can be required that tiles match on
\emph{several} of their sides in order to bind.
In order to describe our algorithms, we also introduce a generalization of
regular expressions called Baggins expressions. Finally, we compare this model
to other automata-theoretic models.Comment: A few bug fixes and typo correction
Optimal self-assembly of finite shapes at temperature 1 in 3D
Working in a three-dimensional variant of Winfree's abstract Tile Assembly
Model, we show that, for an arbitrary finite, connected shape , there is a tile set that uniquely self-assembles into a 3D
representation of a scaled-up version of at temperature 1 in 3D with
optimal program-size complexity (the "program-size complexity", also known as
"tile complexity", of a shape is the minimum number of tile types required to
uniquely self-assemble it). Moreover, our construction is "just barely" 3D in
the sense that it only places tiles in the and planes. Our
result is essentially a just-barely 3D temperature 1 simulation of a similar 2D
temperature 2 result by Soloveichik and Winfree (SICOMP 2007)
Binary pattern tile set synthesis is NP-hard
In the field of algorithmic self-assembly, a long-standing unproven
conjecture has been that of the NP-hardness of binary pattern tile set
synthesis (2-PATS). The -PATS problem is that of designing a tile assembly
system with the smallest number of tile types which will self-assemble an input
pattern of colors. Of both theoretical and practical significance, -PATS
has been studied in a series of papers which have shown -PATS to be NP-hard
for , , and then . In this paper, we close the
fundamental conjecture that 2-PATS is NP-hard, concluding this line of study.
While most of our proof relies on standard mathematical proof techniques, one
crucial lemma makes use of a computer-assisted proof, which is a relatively
novel but increasingly utilized paradigm for deriving proofs for complex
mathematical problems. This tool is especially powerful for attacking
combinatorial problems, as exemplified by the proof of the four color theorem
by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and
Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by
Konev and Lisitsa using computer programs. We utilize a massively parallel
algorithm and thus turn an otherwise intractable portion of our proof into a
program which requires approximately a year of computation time, bringing the
use of computer-assisted proofs to a new scale. We fully detail the algorithm
employed by our code, and make the code freely available online
Optimal staged self-assembly of linear assemblies
We analyze the complexity of building linear assemblies, sets of linear assemblies, and O(1)-scale general shapes in the staged tile assembly model. For systems with at most b bins and t tile types, we prove that the minimum number of stages to uniquely assemble a 1 n line is (logt n + logb n t + 1). Generalizing to O(1) n lines, we prove the minimum number of stages is O( log n tb t log t b2 + log log b log t ) and
( log n tb t log t b2 ). Next, we consider assembling sets of lines and general shapes using t = O(1) tile types. We prove that the minimum number of stages needed to assemble a set of k lines of size at most O(1) n is O( k log n b2 + k p log n b + log log n) and ( k log n b2 ). In the case that b = O( p k), the minimum number of stages is (log n). The upper bound in this special case is then used to assemble \hefty shapes of at least logarithmic edge-length-to- edge-count ratio at O(1)-scale using O( p k) bins and optimal O(log n) stages
DNA-based Self-Assembly of Chiral Plasmonic Nanostructures with Tailored Optical Response
Surface plasmon resonances generated in metallic nanostructures can be
utilized to tailor electromagnetic fields. The precise spatial arrangement of
such structures can result in surprising optical properties that are not found
in any naturally occurring material. Here, the designed activity emerges from
collective effects of singular components equipped with limited individual
functionality. Top-down fabrication of plasmonic materials with a predesigned
optical response in the visible range by conventional lithographic methods has
remained challenging due to their limited resolution, the complexity of
scaling, and the difficulty to extend these techniques to three-dimensional
architectures. Molecular self-assembly provides an alternative route to create
such materials which is not bound by the above limitations. We demonstrate how
the DNA origami method can be used to produce plasmonic materials with a
tailored optical response at visible wavelengths. Harnessing the assembly power
of 3D DNA origami, we arranged metal nanoparticles with a spatial accuracy of 2
nm into nanoscale helices. The helical structures assemble in solution in a
massively parallel fashion and with near quantitative yields. As a designed
optical response, we generated giant circular dichroism and optical rotary
dispersion in the visible range that originates from the collective
plasmon-plasmon interactions within the nanohelices. We also show that the
optical response can be tuned through the visible spectrum by changing the
composition of the metal nanoparticles. The observed effects are independent of
the direction of the incident light and can be switched by design between left-
and right-handed orientation. Our work demonstrates the production of complex
bulk materials from precisely designed nanoscopic assemblies and highlights the
potential of DNA self-assembly for the fabrication of plasmonic nanostructures.Comment: 5 pages, 4 figure
Fractal assembly of micrometre-scale DNA origami arrays with arbitrary patterns
Self-assembled DNA nanostructures enable nanometre-precise patterning that can be used to create programmable molecular machines and arrays of functional materials. DNA origami is particularly versatile in this context because each DNA strand in the origami nanostructure occupies a unique position and can serve as a uniquely addressable pixel. However, the scale of such structures has been limited to about 0.05 square micrometres, hindering applications that demand a larger layout and integration with more conventional patterning methods. Hierarchical multistage assembly of simple sets of tiles can in principle overcome this limitation, but so far has not been sufficiently robust to enable successful implementation of larger structures using DNA origami tiles. Here we show that by using simple local assembly rules that are modified and applied recursively throughout a hierarchical, multistage assembly process, a small and constant set of unique DNA strands can be used to create DNA origami arrays of increasing size and with arbitrary patterns. We illustrate this method, which we term ‘fractal assembly’, by producing DNA origami arrays with sizes of up to 0.5 square micrometres and with up to 8,704 pixels, allowing us to render images such as the Mona Lisa and a rooster. We find that self-assembly of the tiles into arrays is unaffected by changes in surface patterns on the tiles, and that the yield of the fractal assembly process corresponds to about 0.95^(m − 1) for arrays containing m tiles. When used in conjunction with a software tool that we developed that converts an arbitrary pattern into DNA sequences and experimental protocols, our assembly method is readily accessible and will facilitate the construction of sophisticated materials and devices with sizes similar to that of a bacterium using DNA nanostructures
Biophysical and electrochemical studies of protein-nucleic acid interactions
This review is devoted to biophysical and electrochemical methods used for studying protein-nucleic acid (NA) interactions. The importance of NA structure and protein-NA recognition for essential cellular processes, such as replication or transcription, is discussed to provide background for description of a range of biophysical chemistry methods that are applied to study a wide scope of protein-DNA and protein-RNA complexes. These techniques employ different detection principles with specific advantages and limitations and are often combined as mutually complementary approaches to provide a complete description of the interactions. Electrochemical methods have proven to be of great utility in such studies because they provide sensitive measurements and can be combined with other approaches that facilitate the protein-NA interactions. Recent applications of electrochemical methods in studies of protein-NA interactions are discussed in detail
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