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

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

The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.Comment: 11 pages 4 figure

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Genome-wide interaction study of early-life smoking exposure on time-to-asthma onset in childhood

BACKGROUND: Asthma, a heterogeneous disease with variable age of onset, results from the interplay between genetic and environmental factors. Early-life tobacco smoke (ELTS) exposure is a major asthma risk factor. Only a few genetic loci have been reported to interact with ELTS exposure in asthma. OBJECTIVE: Our aim was to identify new loci interacting with ELTS exposure on time-to-asthma onset (TAO) in childhood. METHODS: We conducted genome-wide interaction analyses of ELTS exposure on time-to-asthma onset in childhood in five European-ancestry studies (totaling 8,273 subjects) using Cox proportional-hazard model. The results of all five genome-wide analyses were meta-analyzed. RESULTS: The 13q21 locus showed genome-wide significant interaction with ELTS exposure (P=4.3x10-8 for rs7334050 within KLHL1 with consistent results across the five studies). Suggestive interactions (P<5x10-6 ) were found at three other loci: 20p12 (rs13037508 within MACROD2; P=4.9x10-7 ), 14q22 (rs7493885 near NIN; P=2.9x10-6 ) and 2p22 (rs232542 near CYP1B1; P=4.1x10-6 ). Functional annotations and the literature showed that the lead SNPs at these four loci influence DNA methylation in the blood and are located nearby CpG sites reported to be associated with exposure to tobacco smoke components, which strongly support our findings. CONCLUSION AND CLINICAL RELEVANCE: We identified novel candidate genes interacting with ELTS exposure on time-to-asthma onset in childhood. These genes have plausible biological relevance related to tobacco smoke exposure. Further epigenetic and functional studies are needed to confirm these findings and to shed light on the underlying mechanisms. This article is protected by copyright. All rights reserved

Polymorphisms in the WNK1 gene are asociated with blood pressure variation and urinary potassium excretion

WNK1 - a serine/threonine kinase involved in electrolyte homeostasis and blood pressure (BP) control - is an excellent candidate gene for essential hypertension (EH). We and others have previously reported association between WNK1 and BP variation. Using tag SNPs (tSNPs) that capture 100% of common WNK1 variation in HapMap, we aimed to replicate our findings with BP and to test for association with phenotypes relating to WNK1 function in the British Genetics of Hypertension (BRIGHT) study case-control resource (1700 hypertensive cases and 1700 normotensive controls). We found multiple variants to be associated with systolic blood pressure, SBP (7/28 tSNPs min-p = 0.0005), diastolic blood pressure, DBP (7/28 tSNPs min-p = 0.002) and 24 hour urinary potassium excretion (10/28 tSNPs min-p = 0.0004). Associations with SBP and urine potassium remained significant after correction for multiple testing (p = 0.02 and p = 0.01 respectively). The major allele (A) of rs765250, located in intron 1, demonstrated the strongest evidence for association with SBP, effect size 3.14 mmHg (95%CI:1.23–4.9), DBP 1.9 mmHg (95%CI:0.7–3.2) and hypertension, odds ratio (OR: 1.3 [95%CI: 1.0–1.7]).We genotyped this variant in six independent populations (n = 14,451) and replicated the association between rs765250 and SBP in a meta-analysis (p = 7×10−3, combined with BRIGHT data-set p = 2×10−4, n = 17,851). The associations of WNK1 with DBP and EH were not confirmed. Haplotype analysis revealed striking associations with hypertension and BP variation (global permutation p10 mmHg reduction) and risk for hypertension (OR<0.60). Our data indicates that multiple rare and common WNK1 variants contribute to BP variation and hypertension, and provide compelling evidence to initiate further genetic and functional studies to explore the role of WNK1 in BP regulation and EH

Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal Dali alignments for the very first time

Environmental controls on observed spatial variability of soil pore water geochemistry in small headwater catchments underlain with permafrost

Soil pore water (SPW) chemistry can vary substantially across multiple scales in Arctic permafrost landscapes. The magnitude of these variations and their relationship to scale are critical considerations for understanding current controls on geochemical cycling and for predicting future changes. These aspects are especially important for Arctic change modeling where accurate representation of sub-grid variability may be necessary to predict watershed-scale behaviors. Our research goal is to characterize intra- and inter-watershed soil water geochemical variations at two contrasting locations in the Seward Peninsula of Alaska, USA. We then attempt to identify the key factors controlling concentrations of important pore water solutes in these systems. The SPW geochemistry of 18 locations spanning two small Arctic catchments was examined for spatial variability and its dominant environmental controls. The primary environmental controls considered were vegetation, soil moisture and/or redox condition, water–soil interactions and hydrologic transport, and mineral solubility. The sampling locations varied in terms of vegetation type and canopy height, presence or absence of near-surface permafrost, soil moisture, and hillslope position. Vegetation was found to have a significant impact on SPW NO3- concentrations, associated with the localized presence of nitrogen-fixing alders and mineralization and nitrification of leaf litter from tall willow shrubs. The elevated NO3- concentrations were, however, frequently equipoised by increased microbial denitrification in regions with sufficient moisture to support it. Vegetation also had an observable impact on soil-moisture-sensitive constituents, but the effect was less significant. The redox conditions in both catchments were generally limited by Fe reduction, seemingly well-buffered by a cache of amorphous Fe hydroxides, with the most reducing conditions found at sampling locations with the highest soil moisture content. Non-redox-sensitive cations were affected by a wide variety of water–soil interactions that affect mineral solubility and transport. Identification of the dominant controls on current SPW hydrogeochemistry allows for qualitative prediction of future geochemical trends in small Arctic catchments that are likely to experience warming and permafrost thaw. As source areas for geochemical fluxes to the broader Arctic hydrologic system, geochemical processes occurring in these environments are particularly important to understand and predict with regards to such environmental changes.</p