Effects of co-ordination number on the nucleation behaviour in many-component self-assembly

Abstract

We report canonical and grand-canonical lattice Monte Carlo simulations of the self-assembly of addressable structures comprising hundreds of distinct component types. The nucleation behaviour, in the form of free-energy barriers to nucleation, changes significantly as the co-ordination number of the building blocks is changed from 4 to 8 to 12. Unlike tetrahedral structures - which roughly correspond to DNA bricks that have been studied in experiments - the shapes of the free-energy barriers of higher co-ordination structures depend strongly on the supersaturation, and such structures require a very significant driving force for structure growth before nucleation becomes thermally accessible. Although growth at high supersaturation results in more defects during self-assembly, we show that high co-ordination number structures can still be assembled successfully in computer simulations and that they exhibit self-assembly behaviour analogous to DNA bricks. In particular, the self-assembly remains modular, enabling in principle a wide variety of nanostructures to be assembled, with a greater spatial resolution than is possible in low co-ordination structures.

Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

“…In contrast to systems with only a few components, the only way to achieve full assembly is to use a cooling protocol, where the system first crosses the nucleation barrier to a partially formed assembly, and further cooling stabilises the full assembly. While our calculations are quantitative for a specific 334 strand SST system, a number of the basic qualitative results above are also found with simpler models [20][21][22][23][24][25] and are likely to generically hold for a wider range of target structures [8][9][10][11][12][13][14] that use the addressable SST assembly method.…”

“…The model used to calculate the thermodynamics of tile association, oxDNA, describes explicitly the polymeric de-grees of freedom of DNA, which makes it more suitable to capture the entropic penalties associated with initiation of a second and subsequent domains during tile association than previous patchy-particles models. 20,21 For the SST system, we show that there exists a narrow temperature regime where the nucleation barrier is low enough to be crossable on experimental time-scales, but large enough to allow a time-scale separation between growth and nucleation. At the same time, the exponentially large design space for DNA means that misbonds do not overwhelm correct assembly at experimentally relevant temperatures.…”

“…This same model was later used to explore the effect of the coordination number on the nucleation barriers, and hence the assembly success. 21 An offlattice model, 22 which provides a somewhat more robust description of the translational and rotational entropy of the single strands, was also found to reproduce the main physical phenomena observed in the simpler lattice model.…”

DNA brick self-assembly with an off-lattice potential

“…2. The underlying behaviour we have proposed for this process in our previous work [12][13][14][15][16] is still predominantly unchanged: self-assembly in such systems is possible over a limited range of temperatures because of a free-energy barrier to nucleation that prevents immediate aggregation and monomer depletion. The structures shown in Fig.…”

“…This permits the large number of distinct DNA molecules to self-assemble into structures comprising potentially thousands of molecules, 4 although there is in principle an upper limit to the target structure size on entropic grounds. 6 To try to explain why selfassembly succeeded for such DNA-based structures whilst it failed for many other, similar -and often even considerably simpler -systems, we have recently developed simulationbased 12,13 and theoretical approaches [14][15][16][17] to studying the problem. The original experiments on DNA bricks 4 entailed short, 32-nucleotide single-stranded DNA molecules.…”