In assemblies, the geometric frustration of a locally preferred packing motif leads to anomalous behaviours, from self-limiting growth to defects in the ground state. Here, we demonstrate that geometric frustration selects the equilibrium morphology of cohesive bundles of chiral filaments, an assembly motif critical to a broad range of biological and synthetic nanomaterials. Frustration of inter-filament spacing leads to optimal shapes of self-twisting bundles that break the symmetries of packing and of the underlying inter-filament forces, paralleling a morphological instability in spherical two-dimensional crystals. Equilibrium bundle morphology is controlled by a parameter that characterizes the relative costs of filament bending and the straining of cohesive bonds between filaments. This parameter delineates the boundaries between stable, isotropic cylindrical bundles and anisotropic, twisted-tape bundles. We also show how the mechanical and interaction properties of constituent amyloid fibrils may be extracted from the mesoscale dimensions of the anisotropic bundles that they form.

Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are needed. To address this challenge, we explore the trade-offs between addressable assembly and self-closing assembly of a specific class of self-limiting structures: cylindrical tubules. We make triangular subunits using DNA origami that have specific, valencelimited interactions and designed binding angles, and study their assembly into tubules that have a self-limited width that is much larger than the size of an individual subunit. In the simplest case, the tubules are assembled from a single component by geometrically programming the dihedral angles between neighboring subunits. We show that the tubules can reach many micrometers in length and that their average width can be prescribed through the dihedral angles. We find that there is a distribution in the width and the chirality of the tubules, which we rationalize by developing a model that considers the finite bending rigidity of the assembled structure as well as the mechanism of self-closure. Finally, we demonstrate that the distributions of tubules can be further sculpted by increasing the number of subunit species, thereby increasing the assembly complexity, and demonstrate that using two subunit species successfully reduces the number of available end states by half. These results help to shed light on the roles of assembly complexity and geometry in self-limited assembly and could be extended to other self-limiting architectures, such as shells, toroids, or triply-periodic frameworks.

Abstract-A testable EXOR-Sum-of-Products (ESOP) circuit realization and a simple, universal test set which detects all single stuck-at faults in the internal lines and the primary inputs/outputs of the realization are given. Since ESOP is the most general form of AND-EXOR representations, our realization and test set are more versatile than those described by other researchers for the restricted GRM, FPRM, and PPRM forms of AND-EXOR circuits. Our circuit realization requires only two extra inputs for controllability and one extra output for observability. The cardinality of our test set for an input circuit is ( +6). For Built-in Self Test (BIST) applications, we show that our test set can be generated internally as easily as a pseudo-random pattern, and that it provides 100% single stuck-at fault coverage. In addition, our test set requires a much shorter test cycle than a comparable pseudo-exhaustive or pseudo-random test set.Index Terms-Universal test set, AND-EXOR realizations, Reed-Muller expressions, single stuck-at fault model, easily testable combinational networks, Design for Testing (DFT), self testable circuits, Built-in Self Test (BIST), test pattern generation.

Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure-finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. 'frustration escape'). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

Hydroxyapatite (HA) coated iron oxide (Fe(3)O(4)) magnetic nanoparticles have been shown to enhance osteoblast (bone forming cells) proliferation and osteoblast differentiation into calcium depositing cells (through increased secretion of alkaline phosphatase, collagen and calcium deposition) compared to control samples without nanoparticles. Such nanoparticles are, thus, very promising for numerous orthopedic applications including magnetically directed osteoporosis treatment. The objective of the current study was to elucidate the mechanisms of the aforementioned improved osteoblast responses in the presence of HA coated Fe(3)O(4) nanoparticles. Results demonstrated large amounts of fibronectin (a protein known to increase osteoblast functions) adsorption on HA coated Fe(3)O(4) nanoparticles. Specifically, fibronectin adsorption almost doubled when HA coated Fe(3)O(4) nanoparticle concentrations increased from 12.5 to 100 μg ml(-1), and from 12.5 to 200 μg ml(-1), a four fold increase was observed. Results also showed greater osteoblast gene regulation (specifically, osteocalcin, type I collagen and cbfa-1) in the presence of HA coated Fe(3)O(4) nanoparticles. Collectively, these results provide a mechanism for the observed enhanced osteoblast functions in the presence of HA coated iron oxide nanoparticles, allowing their further investigation for a number of orthopedic applications.