Theoretical Description of a DNA-Linked Nanoparticle Self-Assembly

Abstract

Nanoparticles tethered with DNA strands are promising building blocks for bottom-up nanotechnology, and a theoretical understanding is important for future development. Here we build on approaches developed in polymer physics to provide theoretical descriptions for the equilibrium clustering and dynamics, as well as the self-assembly kinetics of DNA-linked nanoparticles. Striking agreement is observed between the theory and molecular modeling of DNA tethered nanoparticles.The specificity, directionality, and technological control over base sequence make DNA an attractive linking unit for artificial constructs [1][2][3]. One such approach is to attach DNA strands of designed base sequence onto a nanoparticle (NP), thereby creating "molecules" that self-assemble into highly organized structures through complementary pairings of DNA [4,5]. Recent experiments have demonstrated that uniformly DNAfunctionalized NP can self-assemble into disordered [6][7][8][9] or ordered crystal structures [10][11][12][13]. NPs with a discrete number of attachments are harder to prepare, but they provide possibilities for even more diverse structures [14][15][16][17]. In addition to examining the possible equilibrium structures, it is also vital to develop an understanding for the kinetics of the self-assembly process [8,12,13,18,19], since the pathway to desired structures may depend sensitively on sample preparation.In this Letter, we build on concepts from polymer physics to provide a theoretical framework that describes both the equilibrium properties and the self-assembly kinetics of NPs functionalized with a small number of ss-DNA. We demonstrate the applicability of this theory to molecular simulations of a binary mixture where NPs are functionalized with two or three ssDNA, similar to experimentally realized systems [15].The coarse-grained molecular model we use for the DNA-functionalized NP is a modest modification of a previous model [20]. The inset of fig. 1 provides a graphical representation. The sugar-phosphate backbone is represented by connected beads with only excluded volume interactions; each bead carries an additional "sticky" site that represents a base (A, T, C, or G) and can bond only with another sticky site of complementary type (A-T or C-G pair). The size of the sticky site is small relative to the backbone beads, so that a base can bond to at most one other complementary base. A bending potential between consecutive triplets of backbone beads is included to model the characteristic rigidity of the DNA strands and to maintain the angle between ssDNA attached to the same core (120• for 3-functional NP and 180• for 2-functional NP). A more complete description of the model is provided in Ref. [20]. We consider ssDNA four bases in length with sequence A-C-G-T, chosen to enable complementary pairing between ssDNA on different NPs. To mimic solvent effects on dynamics, we simulate this model using dissipative particle dynamics [21], an algorithm known to ensure correct hydrodynamic behavior. Length is measured in ...

Importance of the DNA “bond” in programmable nanoparticle crystallization

“…We also established that studies of systems where DNA bonds are formed via transient interactions between small sticky ends at the tip of primarily rigid DNA duplexes not only enable more complex superlattice design, but also facilitate fundamental investigations of their crystallization behavior. We therefore encourage both the experimental and theoretical scientific communities to further examine the behavior of these PAEs using techniques that have been previously applied to systems using long DNA overlaps between particles, or primarily singlestranded DNA linkers (9,10,12,21,22,26). Lastly, this work underscores the notion that PAEs present a highly programmable means of studying and controlling crystallization in a more facile and directable manner than their atomic counterparts, and thus are a useful tool for materials synthesis.…”

“…In these systems, however, the identity of the atom and its bonding behavior cannot be independently controlled, limiting our ability to tune material properties at will. In contrast, when a nanoparticle is modified with a dense shell of upright, oriented DNA, it can behave as a programmable atom equivalent (PAE) (1, 2) that can be used to synthesize diverse crystal structures with independent control over composition, scale, and lattice symmetry (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). The thermodynamic product of this crystallization process has been extensively studied by both experimental and theoretical means, and thus a series of design rules has been proposed and validated with a simple geometric model known as the complementary contact model (CCM).…”

Do hierarchical structures assemble best via hierarchical pathways?

“…The connection between underlying thermodynamics and self-assembly dynamics we have made helps us place the model in a broader context: its assembly is similar in certain regards to that of virus capsids, but mostly dissimilar to the assembly of closepacked crystals. Continued classification of the assembly pathways of numerous types of structure [53][54][55][56][57] should eventually reveal whether apparently dissimilar systems can nonetheless be placed in similar categories of behaviors.…”

Designing DNA-grafted particles that self-assemble into desired crystalline structures using the genetic algorithm

“…However, there has been some progress in theory and simulation on understanding this assembly process (5, 6, 11-13). The recent work of Starr and coworkers, for example, has emphasized the complicated phase and assembly behavior of these materials (11,12,14). Travesset and coworkers (5) and Olvera de la Cruz and coworkers (15) have used large-scale molecular dynamics simulations to study equilibrium aspects and the kinetics of self-assembly, including kinetic traps like gel formation.…”