771 research outputs found
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)
Reflections on Tiles (in Self-Assembly)
We define the Reflexive Tile Assembly Model (RTAM), which is obtained from
the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across
their horizontal and/or vertical axes. We show that the class of directed
temperature-1 RTAM systems is not computationally universal, which is
conjectured but unproven for the aTAM, and like the aTAM, the RTAM is
computationally universal at temperature 2. We then show that at temperature 1,
when starting from a single tile seed, the RTAM is capable of assembling n x n
squares for n odd using only n tile types, but incapable of assembling n x n
squares for n even. Moreover, we show that n is a lower bound on the number of
tile types needed to assemble n x n squares for n odd in the temperature-1
RTAM. The conjectured lower bound for temperature-1 aTAM systems is 2n-1.
Finally, we give preliminary results toward the classification of which finite
connected shapes in Z^2 can be assembled (strictly or weakly) by a singly
seeded (i.e. seed of size 1) RTAM system, including a complete classification
of which finite connected shapes be strictly assembled by a "mismatch-free"
singly seeded RTAM system.Comment: New results which classify the types of shapes which can
self-assemble in the RTAM have been adde
Self-replication and evolution of DNA crystals
Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required
Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions
The field of algorithmic self-assembly is concerned with the design and
analysis of self-assembly systems from a computational perspective, that is,
from the perspective of mathematical problems whose study may give insight into
the natural processes through which elementary objects self-assemble into more
complex ones. One of the main problems of algorithmic self-assembly is the
minimum tile set problem (MTSP), which asks for a collection of types of
elementary objects (called tiles) to be found for the self-assembly of an
object having a pre-established shape. Such a collection is to be as concise as
possible, thus minimizing supply diversity, while satisfying a set of stringent
constraints having to do with the termination and other properties of the
self-assembly process from its tile types. We present a study of what we think
is the first practical approach to MTSP. Our study starts with the introduction
of an evolutionary heuristic to tackle MTSP and includes results from extensive
experimentation with the heuristic on the self-assembly of simple objects in
two and three dimensions. The heuristic we introduce combines classic elements
from the field of evolutionary computation with a problem-specific variant of
Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte
The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM),
which is a slight extension to the abstract Tile Assembly Model (aTAM) that
allows for not only the standard square tiles, but also "duple" tiles which are
rectangles pre-formed by the joining of two square tiles. We show that the
addition of duples allows for powerful behaviors of self-assembling systems at
temperature 1, meaning systems which exclude the requirement of cooperative
binding by tiles (i.e., the requirement that a tile must be able to bind to at
least 2 tiles in an existing assembly if it is to attach). Cooperative binding
is conjectured to be required in the standard aTAM for Turing universal
computation and the efficient self-assembly of shapes, but we show that in the
DaTAM these behaviors can in fact be exhibited at temperature 1. We then show
that the DaTAM doesn't provide asymptotic improvements over the aTAM in its
ability to efficiently build thin rectangles. Finally, we present a series of
results which prove that the temperature-2 aTAM and temperature-1 DaTAM have
mutually exclusive powers. That is, each is able to self-assemble shapes that
the other can't, and each has systems which cannot be simulated by the other.
Beyond being of purely theoretical interest, these results have practical
motivation as duples have already proven to be useful in laboratory
implementations of DNA-based tiles
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
Controlled assembly of SNAP-PNA-fluorophore systems on DNA templates to produce fluorescence resonance energy transfer
The SNAP protein is a widely used self-labeling tag that can be used for tracking protein localization and trafficking in living systems. A model system providing controlled alignment of SNAP-tag units can provide a new way to study clustering of fusion proteins. In this work, fluorescent SNAP-PNA conjugates were controllably assembled on DNA frameworks forming dimers, trimers, and tetramers. Modification of peptide nucleic acid (PNA) with the O6-benzyl guanine (BG) group allowed the generation of site-selective covalent links between PNA and the SNAP protein. The modified BG-PNAs were labeled with fluorescent Atto dyes and subsequently chemo-selectively conjugated to SNAP protein. Efficient assembly into dimer and oligomer forms was verified via size exclusion chromatography (SEC), electrophoresis (SDS-PAGE), and fluorescence spectroscopy. DNA directed assembly of homo- and hetero-dimers of SNAP-PNA constructs induced homo- and hetero-FRET, respectively. Longer DNA scaffolds controllably aligned similar fluorescent SNAP-PNA constructs into higher oligomers exhibiting homo-FRET. The combined SEC and homo-FRET studies indicated the 1:1 and saturated assemblies of SNAP-PNA-fluorophore:DNA formed preferentially in this system. This suggested a kinetic/stoichiometric model of assembly rather than binomially distributed products. These BG-PNA-fluorophore building blocks allow facile introduction of fluorophores and/or assembly directing moieties onto any protein containing SNAP. Template directed assembly of PNA modified SNAP proteins may be used to investigate clustering behavior both with and without fluorescent labels which may find use in the study of assembly processes in cells
Single-molecule derivation of salt dependent base-pair free energies in DNA
Accurate knowledge of the thermodynamic properties of nucleic acids is
crucial to predicting their structure and stability. To date most measurements
of base-pair free energies in DNA are obtained in thermal denaturation
experiments, which depend on several assumptions. Here we report measurements
of the DNA base-pair free energies based on a simplified system, the mechanical
unzipping of single DNA molecules. By combining experimental data with a
physical model and an optimization algorithm for analysis, we measure the 10
unique nearest-neighbor base-pair free energies with 0.1 kcal mol-1 precision
over two orders of magnitude of monovalent salt concentration. We find an
improved set of standard energy values compared with Unified Oligonucleotide
energies and a unique set of 10 base-pair-specific salt-correction values. The
latter are found to be strongest for AA/TT and weakest for CC/GG. Our new
energy values and salt corrections improve predictions of DNA unzipping forces
and are fully compatible with melting temperatures for oligos. The method
should make it possible to obtain free energies, enthalpies and entropies in
conditions not accessible by bulk methodologies.Comment: Main text: 27 pages, 4 figures, 2 tables. Supporting Information: 51
pages, 19 figures, 4 table
Random, blocky and alternating ordering in supramolecular polymers of chemically bidisperse monomers
As a first step to understanding the role of molecular or chemical
polydispersity in self-assembly, we put forward a coarse-grained model that
describes the spontaneous formation of quasi-linear polymers in solutions
containing two self-assembling species. Our theoretical framework is based on a
two-component self-assembled Ising model in which the bidispersity is
parameterized in terms of the strengths of the binding free energies that
depend on the monomer species involved in the pairing interaction. Depending
upon the relative values of the binding free energies involved, different
morphologies of assemblies that include both components are formed, exhibiting
paramagnetic-, ferromagnetic- or anti ferromagnetic-like order,i.e., random,
blocky or alternating ordering of the two components in the assemblies.
Analyzing the model for the case of ferromagnetic ordering, which is of most
practical interest, we find that the transition from conditions of minimal
assembly to those characterized by strong polymerization can be described by a
critical concentration that depends on the concentration ratio of the two
species. Interestingly, the distribution of monomers in the assemblies is
different from that in the original distribution, i.e., the ratio of the
concentrations of the two components put into the system. The monomers with a
smaller binding free energy are more abundant in short assemblies and monomers
with a larger binding affinity are more abundant in longer assemblies. Under
certain conditions the two components congregate into separate supramolecular
polymeric species and in that sense phase separate. We find strong deviations
from the expected growth law for supramolecular polymers even for modest
amounts of a second component, provided it is chemically sufficiently distinct
from the main one.Comment: Submitted to Macromolecules, 6 figures. arXiv admin note: substantial
text overlap with arXiv:1111.176
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