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

Abstract

In conventional research, colloidal particles grafted with singlestranded DNA are allowed to self-assemble, and then the resulting crystal structures are determined. Although this Edisonian approach is useful for a posteriori understanding of the factors governing assembly, it does not allow one to a priori design ssDNA-grafted colloids that will assemble into desired structures. Here we address precisely this design issue, and present an experimentally validated evolutionary optimization methodology that is not only able to reproduce the original phase diagram detailing regions of known crystals, but is also able to elucidate several previously unobserved structures. Although experimental validation of these structures requires further work, our early success encourages us to propose that this genetic algorithm-based methodology is a promising and rational materials-design paradigm with broad potential applications.DNA-grafted colloids | inverse design | nanostructures | crystal lattice predictions | evolutionary algorithm A topic of much interest in the current literature is the selfassembly of colloid particles multiply grafted with ssDNA molecules (1-10). The typical experimental system consists of two types of colloids grafted with complementary ssDNA sequences. Upon cooling, hybridization of the DNA occurs, crosslinking the colloids. Under the right conditions this cross-linking can facilitate the ordering of the colloids into crystal structures. The typical dimensions of colloids result in periodicities comparable to the wavelength of visible length, which have made them attractive for various emergent technologies, e.g., photonic bandgap materials. Classes of plasmonic, light-emitting, and catalytic metamaterials can be realized via the self-assembly of ssDNAgrafted colloids into specified 3D arrays.Although much work has examined the effects of temperature, DNA length, linker DNA groups, size of colloids, etc., on structure formation, it has been largely empirically driven. 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. Crocker and coworker developed a quantitative model based on experimental studies to predict ssDNA-induced particle interactions, the driving force for self-assembly (16). Similarly, Frenkel and coworkers has also defined a general accurate theory of valence-limited colloidal interactions (17). In a similar vein, Mirkin and coworkers proposed a rule-based complementary contact model (CCM) to predict the formation of crystal structures by ssDNA-grafted colloids (7). This model was used to explain the four crystal structures experimentally observed.Althou...

Stoichiometric control of DNA-grafted colloid self-assembly

“…Despite its successes, the CCM still has several deficiencies that need to be addressed. As Srinivasan et al (26) noted, this model does not take into account entropic repulsions due to the chain compression of noncomplementary DNA strands (that cannot base-pair). In the original CCM, the definition of the nearest neighbor(s) is the shortest distance to the colloid with cDNA strands.…”

Binary nanoparticle superlattices of soft-particle systems

“…Explicit calculations (7) (see also ref. 28) have ruled them out as they do not optimally hybridize the DNA shells, but those calculations do not consider the role of entropy and the possibility of coexistence. As the results presented here reveal, they could become equilibrium phases, at either small γ (NaCl), γ ∼ 1 (AuCu 3 ), or when there is an abundance of B particles, that is, x B ∼ 1 (NaZn 13 ).…”

“…Another possibility to target these phases is to modify the DNA shell to include additional AB repulsion forces that compete against hybridizations (28)(29)(30), which is achieved by inclusion of neutral (those that do not form hybridizations) DNA strands into the NP shell (28,30). In those systems, AuCu phases have been found (28,30). SE Systems.…”

Nanoparticle Assembly:A Perspective and some Unanswered Questions

“…(ii) Perhaps the more ambitious means of such a priori design is to use reverse modeling tools, e.g. using genetic algorithm [31][32][33][34] , to design the building blocks that can assemble into a structure with desired function. The current implementation of such ideas has been largely limited to the prediction of colloidal building blocks that assemble into desired ordered structures -in particular, this has been applied to the assembly of colloids grafted with DNA strands, where two colloidal sub-populations have complementary single strands.…”