64,022 research outputs found
Combinatorial optimization problems in self-assembly
Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape.Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a "program" to assemble the shape. We prove that the first problem is NP-complete in general, and polynomial time solvable on trees and squares. In order to prove that the problem is in NP, we present a polynomial time algorithm to verify whether a given tile system uniquely produces a given shape. This algorithm is analogous to a program verifier for traditional computational systems, and may well be of independent interest. For the second problem, we present a polynomial time -approximation algorithm that works for a large class of tile systems that we call partial order systems
Error-proof programmable self-assembly of DNA-nanoparticle clusters
We study theoretically a new generic scheme of programmable self-assembly of
nanoparticles into clusters of desired geometry. The problem is motivated by
the feasibility of highly selective DNA-mediated interactions between colloidal
particles. By analyzing both a simple generic model and a more realistic
description of a DNA-colloidal system, we demonstrate that it is possible to
suppress the glassy behavior of the system, and to make the self-assembly
nearly error-proof. This regime requires a combination of stretchable
interparticle linkers (e.g. sufficiently long DNA), and a soft repulsive
potential. The jamming phase diagram and the error probability are computed for
several types of clusters. The prospects for the experimental implementation of
our scheme are also discussed. PACS numbers: 81.16.Dn, 87.14.Gg, 36.40.EiComment: 6 pages, 4 figures, v2: substantially revised version, added journal
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Self-assembly of the discrete Sierpinski carpet and related fractals
It is well known that the discrete Sierpinski triangle can be defined as the
nonzero residues modulo 2 of Pascal's triangle, and that from this definition
one can easily construct a tileset with which the discrete Sierpinski triangle
self-assembles in Winfree's tile assembly model. In this paper we introduce an
infinite class of discrete self-similar fractals that are defined by the
residues modulo a prime p of the entries in a two-dimensional matrix obtained
from a simple recursive equation. We prove that every fractal in this class
self-assembles using a uniformly constructed tileset. As a special case we show
that the discrete Sierpinski carpet self-assembles using a set of 30 tiles
Evolutionary Dynamics in a Simple Model of Self-Assembly
We investigate the evolutionary dynamics of an idealised model for the robust
self-assembly of two-dimensional structures called polyominoes. The model
includes rules that encode interactions between sets of square tiles that drive
the self-assembly process. The relationship between the model's rule set and
its resulting self-assembled structure can be viewed as a genotype-phenotype
map and incorporated into a genetic algorithm. The rule sets evolve under
selection for specified target structures. The corresponding, complex fitness
landscape generates rich evolutionary dynamics as a function of parameters such
as the population size, search space size, mutation rate, and method of
recombination. Furthermore, these systems are simple enough that in some cases
the associated model genome space can be completely characterised, shedding
light on how the evolutionary dynamics depends on the detailed structure of the
fitness landscape. Finally, we apply the model to study the emergence of the
preference for dihedral over cyclic symmetry observed for homomeric protein
tetramers
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 (Īµ) 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 ā Ī²Īµ^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 ā Ī²Īµ 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
Binding of molecules to DNA and other semiflexible polymers
A theory is presented for the binding of small molecules such as surfactants
to semiflexible polymers. The persistence length is assumed to be large
compared to the monomer size but much smaller than the total chain length. Such
polymers (e.g. DNA) represent an intermediate case between flexible polymers
and stiff, rod-like ones, whose association with small molecules was previously
studied. The chains are not flexible enough to actively participate in the
self-assembly, yet their fluctuations induce long-range attractive interactions
between bound molecules. In cases where the binding significantly affects the
local chain stiffness, those interactions lead to a very sharp, cooperative
association. This scenario is of relevance to the association of DNA with
surfactants and compact proteins such as RecA. External tension exerted on the
chain is found to significantly modify the binding by suppressing the
fluctuation-induced interaction.Comment: 15 pages, 7 figures, RevTex, the published versio
QuASeR -- Quantum Accelerated De Novo DNA Sequence Reconstruction
In this article, we present QuASeR, a reference-free DNA sequence
reconstruction implementation via de novo assembly on both gate-based and
quantum annealing platforms. Each one of the four steps of the implementation
(TSP, QUBO, Hamiltonians and QAOA) is explained with simple proof-of-concept
examples to target both the genomics research community and quantum application
developers in a self-contained manner. The details of the implementation are
discussed for the various layers of the quantum full-stack accelerator design.
We also highlight the limitations of current classical simulation and available
quantum hardware systems. The implementation is open-source and can be found on
https://github.com/prince-ph0en1x/QuASeR.Comment: 24 page
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