Numerical study of DNA-functionalized microparticles and nanoparticles: Explicit pair potentials and their implications for phase behavior

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...

Section: Significancementioning

confidence: 99%

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

Srinivasan

Zhang

et al. 2013

“…A large number of theories and simulations have been developed to delineate the hybridization interactions between two interacting DNA-NPs (9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). Despite the success of these theories in providing insights into the ground-state free energy, they are generally limited to enumerating interactions at the twoparticle level.…”

mentioning

confidence: 99%

“…Despite the success of these theories in providing insights into the ground-state free energy, they are generally limited to enumerating interactions at the twoparticle level. They also ignore any entropic effects relevant to this self-assembly process (9)(10)(11)(12)(17)(18)(19)(20)(21). Molecular dynamics simulations avoid these difficulties and extend this analysis to superlattice self-assembly so as to provide a detailed understanding of the effects of kinetics (13), DNA sequence (14), and electrostatics (15,16,22) on lattice stability.…”

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confidence: 99%

Stoichiometric control of DNA-grafted colloid self-assembly

Venkatasubramanian

Kumar

et al. 2015

There has been considerable interest in understanding the selfassembly of DNA-grafted nanoparticles into different crystal structures, e.g., CsCl, AlB 2 , and Cr 3 Si. Although there are important exceptions, a generally accepted view is that the right stoichiometry of the two building block colloids needs to be mixed to form the desired crystal structure. To incisively probe this issue, we combine experiments and theory on a series of DNA-grafted nanoparticles at varying stoichiometries, including noninteger values. We show that stoichiometry can couple with the geometries of the building blocks to tune the resulting equilibrium crystal morphology. As a concrete example, a stoichiometric ratio of 3:1 typically results in the Cr 3 Si structure. However, AlB 2 can form when appropriate building blocks are used so that the AlB 2 standard-state free energy is low enough to overcome the entropic preference for Cr 3 Si. These situations can also lead to an undesirable phase coexistence between crystal polymorphs. Thus, whereas stoichiometry can be a powerful handle for direct control of lattice formation, care must be taken in its design and selection to avoid polymorph coexistence. colloidal interactions | functional particle | superlattice engineering | molecular design | modeling O ver the past several decades, there has been increasing interest in programmable self-assembly for materials fabrication. Rather than using traditional methods of shaping bulk materials, the emerging concept is to focus on the design of nanoscale building blocks that self-organize into desired structures. This "design" philosophy has led to the development of novel techniques such as DNA origami, where specific interactions are used to direct the folding of oligonucleotides into a variety of assemblies (1-6). Another vein of research is to focus on the directed assembly of DNA-grafted nanoparticles (DNA-NPs) into superlattices with well-defined crystal morphologies. These systems have unusual photonic and plasmonic properties with applications in spectroscopy, surface imaging, and optical sensors (7,8).A large number of theories and simulations have been developed to delineate the hybridization interactions between two interacting DNA-NPs (9-20). Despite the success of these theories in providing insights into the ground-state free energy, they are generally limited to enumerating interactions at the twoparticle level. They also ignore any entropic effects relevant to this self-assembly process (9-12, 17-21). Molecular dynamics simulations avoid these difficulties and extend this analysis to superlattice self-assembly so as to provide a detailed understanding of the effects of kinetics (13), DNA sequence (14), and electrostatics (15, 16, 22) on lattice stability. We particularly highlight the work of Li et al. (16), who explicitly considered the role of stoichiometry on the crystal morphology formed. They selected several stoichiometries, i.e., 1:1, 2:1, and 3:1. We focus here on one specific case, 2:1. As the size and linker ratios of ...

“…Several groups have reported interaction models (9,(11)(12)(13)(14)(15), all based on capturing the entropic contributions and hybridization thermodynamics of individual grafted DNA molecules. While these models qualitatively describe the existing interaction measurements based on the temperature-dependent aggregation-disaggregation transition of DNA-labeled nanoparticles (16), microparticles (12,14,(17)(18)(19), and polymers (20), or direct measurements with optical tweezers (9), they typically overpredict the interaction strength by roughly two orders of magnitude, corresponding to an unexpectedly large hybridization free energy difference of ∼5 k B T per DNA bridge.…”

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confidence: 99%

Direct measurements of DNA-mediated colloidal interactions and their quantitative modeling

Rogers

Crocker

2011

171

210

DNA bridging can be used to induce specific attractions between small particles, providing a highly versatile approach to creating unique particle-based materials having a variety of periodic structures. Surprisingly, given the fact that the thermodynamics of DNA strands in solution are completely understood, existing models for DNA-induced particle interactions are typically in error by more than an order of magnitude in strength and a factor of two in their temperature dependence. This discrepancy has stymied efforts to design the complex temperature, sequence and time-dependent interactions needed for the most interesting applications, such as materials having highly complex or multicomponent microstructures or the ability to reconfigure or self-replicate. Here we report high-spatial resolution measurements of DNA-induced interactions between pairs of polystyrene microspheres at binding strengths comparable to those used in self-assembly experiments, up to 6 k B T . We also describe a conceptually straightforward and numerically tractable model that quantitatively captures the separation dependence and temperature-dependent strength of these DNA-induced interactions, without empirical corrections. This model was equally successful when describing the more complex and practically relevant case of grafted DNA brushes with self-interactions that compete with interparticle bridge formation. Together, our findings motivate a nanomaterial design approach where unique functional structures can be found computationally and then reliably realized in experiment.colloidal iteractions | functional particles | nucleic acids | polymer entropy | optical tweezers A promising route to forming unique nanoparticle-based materials is directed self-assembly-where the interactions among multiple species of suspended particles are intentionally designed to favor the self-assembly of a specific cluster arrangement or nanostructure. DNA provides a natural tool (1-3) for directed particle assembly because DNA double helix formation is chemically specific-particles with short single-stranded DNAgrafted on their surfaces will be bridged together if and only if those strands have complementary base sequences, allowing the two strands to spontaneously hybridize to form double-stranded DNA. Moreover, the temperature-dependent stability of such DNA bridges allows the resulting attraction to be modulated (1, 2) from negligibly weak to effectively irreversible over a convenient range of temperatures. Several groups have recently used such interactions to drive the assembly of three-dimensional (3D), crystalline structures from nanoscopic (4-8) and microscopic (9, 10) particles. Ultimately, we envision a highly versatile nanomaterial design protocol in which a user-designed matrix of specific interactions among multiple particle species leads to sequential or even hierarchical assembly of complex particle structures, controlled by a user-designed thermal program. Unlike this vision of designable, sequential, and hierarchical assembly among a s...