814 research outputs found
Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model
We consider the self-assembly of fractals in one of the most well-studied
models of tile based self-assembling systems known as the Two-handed Tile
Assembly Model (2HAM). In particular, we focus our attention on a class of
fractals called discrete self-similar fractals (a class of fractals that
includes the discrete Sierpi\'nski carpet). We present a 2HAM system that
finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1.
Moreover, the 2HAM system that we give lends itself to being generalized and we
describe how this system can be modified to obtain a 2HAM system that finitely
self-assembles one of any fractal from an infinite set of fractals which we
call 4-sided fractals. The 2HAM systems we give in this paper are the first
examples of systems that finitely self-assemble discrete self-similar fractals
at scale factor 1 in a purely growth model of self-assembly. Finally, we show
that there exists a 3-sided fractal (which is not a tree fractal) that cannot
be finitely self-assembled by any 2HAM system
Self-assembly, modularity and physical complexity
We present a quantitative measure of physical complexity, based on the amount
of information required to build a given physical structure through
self-assembly. Our procedure can be adapted to any given geometry, and thus to
any given type of physical system. We illustrate our approach using
self-assembling polyominoes, and demonstrate the breadth of its potential
applications by quantifying the physical complexity of molecules and protein
complexes. This measure is particularly well suited for the detection of
symmetry and modularity in the underlying structure, and allows for a
quantitative definition of structural modularity. Furthermore we use our
approach to show that symmetric and modular structures are favoured in
biological self-assembly, for example of protein complexes. Lastly, we also
introduce the notions of joint, mutual and conditional complexity, which
provide a useful distance measure between physical structures.Comment: 9 pages, submitted for publicatio
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
GP-9s Are Ubiquitous Proteins Unlikely Involved in Olfactory Mediation of Social Organization in the Red Imported Fire Ant, Solenopsis invicta
The red imported fire ant (RIFA), Solenopsis invicta, is an invasive species, accidentally introduced in the United States that can cause painful (sometimes life-threatening) stings to human, pets, and livestock. Their colonies have two social forms: monogyne and polygyne that have a single and multiple functional queens, respectively. A major gene (Gp-9), identified as a putative pheromone-binding protein on the basis of a modest amino acid sequence identity, has been suggested to influence the expression of colony social organization. Monogyne queens are reported to possess only the GP-9B alleles, whereas polygyne queens possess both GP-9B and GP-9b. Thus, both social forms are reported to express GP-9B, with GP-9b being a marker expressed in polygynes but it is absent in monogynes. Here, we report two types of polygyne colonies, one that does not express GP-9b (monogyne-like) and the other expressing both proteins, GP-9B and GP-9b. Given their expression pattern, GP-9s are hemolymph proteins, which are more likely to be involved in the transport of lipids and small ligands within the homocoel. GP-9B existed in two forms, one of them is phosphorylated. The helical-rich content of the protein resembles the secondary structures of a beetle hemolymph protein and moth pheromone-binding proteins. An olfactory role is unlikely given the lack of specific expression in the sensillar lymph. In marked contrast to GP-9s, a chemosensory protein, SinvCSP, is demonstrated to be specifically expressed in the antennae. Within the antennae, expression of SinvCSP is restricted to the last two segments, which are known to house olfactory sensilla
One Tile to Rule Them All: Simulating Any Tile Assembly System with a Single Universal Tile
In the classical model of tile self-assembly, unit square tiles translate in the plane and attach edgewise to form large crystalline structures. This model of self-assembly has been shown to be capable of asymptotically optimal assembly of arbitrary shapes and, via information-theoretic arguments, increasingly complex shapes necessarily require increasing numbers of distinct types of tiles.
We explore the possibility of complex and efficient assembly using systems consisting of a single tile. Our main result shows that any system of square tiles can be simulated using a system with a single tile that is permitted to flip and rotate. We also show that systems of single tiles restricted to translation only can simulate cellular automata for a limited number of steps given an appropriate seed assembly, and that any longer-running simulation must induce infinite assembly
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
Programmable disorder in random DNA tilings
Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures
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