Geometrically programmed self-limited assembly of tubules using DNA origami colloids

Abstract

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.

Polymorphic self-assembly of helical tubules is kinetically controlled

“…[35] and were shown to be consistent with experiments on DNA origami subunits assembling the tubules in Ref. [9]. A detailed description of how we measure the tubule diameter and the closure size is given in the SI (Fig.…”

“…We now compare the results of our dynamical assembly simulations to recent experiments that motivate our work. We find that the morphology distribution of simulated tubules semi-quantitatively agrees with those observed in the experiments [9], suggesting that the model incorporates the essential physics of the experiments.…”

“…The bevel angles of the edges of each monomer {θ 0 id,i } deter- mine the preferred dihedral angles, which, in turn, set the preferred curvatures of the assembly. The data set against which we compare our simulation results is obtained from an experimental system that resulted in a most probable tubule geometry of (9,4). Since a key unknown parameter from the experiments is the bending modulus B, we performed simulations with a target geometry of (9,4) at four values of the bending modulus: B ∈ {5, 10, 15, 20} k B T .…”

“…A. Discrete equilibrium model Motivated by the high rigidity of DNA origami subunits [8,9], we focus on the regime of high stretching modulus in this work, so that the relative edge length fluctuations are small, k B T /k S l 2 0 1. Thus, in the following calculation we assume that the curvature within a tubule is uniform, and for an assembled geometry (m, n) all the dihedral angles are approximately equal to their ideal value θ (m,n) id,i , with i ∈ 1, 2, 3 as the indices of the three sides of a subunit.…”

Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies

“…In particular, recent approaches to DNA origami particles realize anisotropic, self-assembly particles with anisotropic shapes that defined the relative geometries of bound neighbors [31], but also combine specific (i.e. lock and key type) interactions between specific binding sites [34,35,38], of the type incorporated in the WJ model. Our results hold key lessons for the experimental design of such particle.…”