Synthesis of crystals with a programmable kinetic barrier to nucleation

Abstract

A central goal of chemistry is to fabricate supramolecular structures of defined function and composition. In biology, control of supramolecular synthesis is often achieved through precise control over nucleation and growth processes: A seed molecule initiates growth of a structure, but this growth is kinetically inhibited in the seed's absence. Here we show how such control can be systematically designed into self-assembling structures made of DNA tiles. These structures, "zig-zag ribbons," are designed to have a fixed width but can grow arbitrarily long. Under slightly supersaturated conditions, theory predicts that elongation is always favorable but that nucleation rates decrease exponentially with increasing width. We confirm experimentally that although ribbons of different widths have similar thermodynamics, nucleation rates decrease for wider ribbons. It is therefore possible to program the nucleation rate by choosing a ribbon width. The presence of a seed molecule, a stabilized version of the presumed critical nucleus, removes the kinetic barrier to nucleation of a ribbon. Thus, we demonstrate the ability to grow supramolecular structures from rationally designed seeds, while suppressing spurious nucleation. Control over DNA tile nucleation allows for proper initiation of algorithmic crystal growth, which could lead to the high-yield synthesis of micrometer-scale structures with complex programmed features. More generally, this work shows how a self-assembly subroutine can be initiated.

Fig. 1.

Zig-zag ribbon design. (a) DNA tiles used to construct the four-tile-wide zig-zag ribbon, ZZ4. Single tiles (top two rows) each consist of four strands, and double tiles (bottom two rows) consist of six strands. Every strand has a unique sequence; colors distinguish the strands. Arrows indicate the 3′ (vs. 5′) ends of strands. Tile cores are double-stranded; their structures form because Watson–Crick complementary subsequences prefer to hybridize. Helix ends are single-stranded sticky ends that can hybridize to sticky ends on other tiles. Along the edges of the ribbon, the double tiles have noninteracting ends. Each tile has one of two orientations: The sticky ends on the top helix have either 3′ or 5′ ends. In subsequent diagrams, tiles are depicted by rectangle and claw diagrams. Colors of tile cores distinguish tile types. Claws with the same color represent complementary sticky ends. (b) Tiles bind by hybridization of their sticky ends. (c) ZZ4 tile structure. The dashed box encloses the six tile types in each repeating unit. Arrows show the zig-zag growth pattern of favorable assembly at each end of the ribbon. (d) Energetics of the standard sequence for nucleation and growth of ZZ4. Nucleation steps (at left) culminate in the critical nucleus (at top), followed by growth (at right). A monomer tile is added to the crystal at each reaction step. Large black arrows depict forward-biased reaction steps, and small red arrows depict unfavorable reaction steps.

Fig. 2.

Tile sets for ZZ3–ZZ6 (a–d Upper) and AFM images of ZZ3–ZZ6 (a–d Lower). Ribbons sometimes rip during sample deposition, leaving ribbon fragments stuck to the surface. [Scale bars: 500 nm (Left); 25 nm (Right).]

Fig. 3.

Temperature-ramp anneals and melts. (a) Temperature-ramp experiment using zig-zag tiles with (green) and without (black) sticky ends. To adjust for cuvette and stoichiometry variations, the black trace was normalized so that the traces line up at 90°C and 42°C. The dashed box encloses the area shown in b and c. (b) Width dependence for ZZ3–ZZ6 at 50 nM. To approximate the fraction of unbound tiles, we normalized differential absorbance (the difference in absorbance between samples with and without sticky ends) to 0 at 15°C, where virtually all tiles were assembled into ribbons, and to 1 after melting to 42°C, where virtually all tiles were assumed to be unbound. Formation and melting temperatures are marked with black squares. (c) Concentration dependence for ZZ4 at 25, 50, 100, and 200 nM. Black squares as in b. (d) Formation and melting temperatures. Points are staggered so error bars are visible. Here and elsewhere, error bars are 95% confidence intervals, determined by bootstrapping, and are omitted for a few samples with insufficient data.

Fig. 4.

Growth and melting at constant temperatures. (a–c) Growth and melting of 50 nM ZZ4 at three different temperatures. Absorbances are normalized as described in d–i. (d–i) Absorbances at the beginning (blue and cyan) and end (red and magenta) of temperature holds for anneals and melts, respectively. Points plot individual measurements, and lines connect averages for each temperature. Arrows indicate the direction of absorbance changes during holds. Gray regions show the hysteresis remaining after 24 h. Dashed lines indicate the estimated temperature-dependent absorbance for unbound tiles in solution. Black squares mark the formation and melting temperatures. Absorbances are normalized so that the largest absorbance after the 24-h anneal hold has value 1, and the absorbance at the end of the hold at 15°C has value 0. (j) Formation temperatures determined from temperature-hold experiments. (k) Determination of ΔH° and ΔS° from melting temperatures in temperature-hold experiments.

Fig. 5.

Hysteresis in ribbon formation disappears when crystal seeds are present. (a) A designed nucleus for ZZ4. The size of the helical regions and placement of crossover points are the same as in the tile lattice. (b) AFM image of the crystal seeds. (Scale bar: 25 nm.) Both intact and incomplete structures are seen. (c) Putative growth from a crystal seed: at every step, tiles can bind favorably (by two sticky ends) to produce the structure shown at right, which can then grow through zig-zag growth. (d) Hysteresis of 50 nM ZZ4 with (Lower) and without (Upper) crystal seeds at 34°C over 12 h. The higher absorbance during the melt in the sample with seeds is due to the added material.