Theoretical description of a DNA-linked nanoparticle self-assembly

Programmable Potentials Choreograph Defects in a Colloidal Crystal Shell

Crystallization on spherical surfaces is obliged by topology to induce lattice defects. But controlling the organization of such defects remains a great challenge due to the long-range constraints of the curved geometry. Here, we report on DNA-coated colloids whose programmable interaction potentials can be used to regulate the arrangement of defects and even achieve perfect icosahedral order on a sphere. Combined simulations and theoretical analysis show how the potential can be tuned by changing the temperature, thereby controlling the number of defects. An explicit expression for the effective potential is derived, allowing us to distinguish the effects of entropic repulsion and enthalpic attraction. Altogether, the present findings provide insights into the physics of crystallization on curved spaces and may be used for designing desired crystal geometries.

Optimizing the dynamic and thermodynamic properties of hybridization in DNA-mediated nanoparticle self-assembly

DNA-directed nanoparticle (DNA-NP) systems provide various applications in sensing, medical diagnosis, data storage, plasmonics and photovoltaics. Bonding probability and melting properties are helpful to evaluate the selectivity, thermostability and thermosensitivity of these applications. We investigated the influence of temperature, nanoparticle size, DNA chain length and surface grafting density of DNA on one nanoparticle on the DNA dynamic hybridization percentage and melting properties of DNA-NP assembly systems by molecular dynamics simulation. The high degree of consistency of free energy estimations for DNA hybridization via our theoretical deduction and the nearest-neighbor rule generally used in experiments validates reasonably our DNA model. The melting temperature and thermosensitivity parameter are determined by the sigmoidal melting curves based on hybridization percentage versus temperature. The results indicated that the hybridization percentage presents a downward trend with increasing temperature and nanoparticle size. Applications based on DNA-NP systems with bigger nanoparticle size, such as DNA probes, have better selectivity, thermostability and thermosensitivity. There exist optimal DNA chain length and surface grafting density where the hybridization percentage reaches the maximal value. The melting temperature reaches a maximum at the point of optimal grafting density, while the thermosensitivity parameter presents an upward trend with the increase of grafting density. Several physical quantities consisting of the radial density function, root mean square end-to-end distance, contact distance parameter and effective volume fraction are used to analyse DNA chain conformations and DNA-NP packing in the assembly process. Our findings provide the theoretical basis for the improvement and optimization of applications based on DNA-NP systems.

On the role of flexibility in linker-mediated DNA hydrogels

Three-dimensional DNA networks, composed of tri- or higher valent nanostars with sticky, single-stranded DNA overhangs, have been previously studied in the context of designing thermally responsive, viscoelastic hydrogels. In this work, we use linker-mediated gels, where the sticky ends of two trivalent nanostars are connected through the complementary sticky ends of a linear DNA duplex. We can design this connection to be either rigid or flexible by introducing flexible, non-binding bases. The additional flexibility provided by these non-binding bases influences the effective elasticity of the percolating gel formed at low temperatures. Here we show that by choosing the right length of the linear duplex and non-binding flexible joints, we obtain a completely different phase behaviour to that observed for rigid linkers. In particular, we use dynamic light scattering as a microrheological tool to monitor the self-assembly of DNA nanostars with linear linkers as a function of temperature. While we observe classical gelation when using rigid linkers, the presence of flexible joints leads to a cluster fluid with a much-reduced viscosity. Using both the oxDNA model and a coarse-grained simulation to investigate the nanostar-linker topology, we hypothesise on the possible structure formed by the DNA clusters. Moreover, we present a systematic study of the strong viscosity increase of aqueous solutions in the presence of these DNA building blocks.

Reversible Polymerization-like Kinetics for Programmable Self-Assembly of DNA-Encoded Nanoparticles with Limited Valence

A similarity between the polymerization reaction of molecules and the self-assembly of nanoparticles provides a unique way to reliably predict structural characteristics of nanoparticle ensembles. However, the quantitative elucidation of programmable self-assembly kinetics of DNA-encoded nanoparticles is still challenging due to the existence of hybridization and dehybridization of DNA strands. Herein, a joint theoretical-computational method is developed to explicate the mechanism and kinetics of programmable self-assembly of limited-valence nanoparticles with surface encoding of complementary DNA strands. It is revealed that the DNA-encoded nanoparticles are programmed to form a diverse range of self-assembled superstructures with complex architecture, such as linear chains, sols, and gels of nanoparticles. It is theoretically demonstrated that the programmable self-assembly of DNA-encoded nanoparticles with limited valence generally obeys the kinetics and statistics of reversible step-growth polymerization originally proposed in polymer science. Furthermore, the theoretical-computational method is applied to capture the programmable self-assembly behavior of bivalent DNA-protein conjugates. The obtained results not only provide fundamental insights into the programmable self-assembly of DNA-encoded nanoparticles but also offer design rules for the DNA-programmed superstructures with elaborate architecture.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

Modeling antigen-antibody nanoparticle bioconjugates and their polymorphs

The integration of nanomaterials with biomolecules has recently led to the development of new ways of designing biosensors, and through their assembly, to new hybrid structures for novel and exciting applications. In this work, we develop a coarse-grained model for nanoparticles grafted with antibody molecules and their binding with antigens. In particular, we isolate two possible states for antigen-antibody pairs during the binding process, termed as recognition and anchoring states. Using molecular simulation, we calculate the thermodynamic and structural features of three possible crystal structures or polymorphs, the body-centered cubic, simple cubic, and face-centered cubic phases, and of the melt. This leads us to determine the domain of stability of the three solid phases. In particular, the role played by the switching process between anchoring and recognition states during melting is identified, shedding light on the complex microscopic mechanisms in these systems.

Self-assembly of polymer-linked nanoparticles and scaling behavior in the assembled phase

An entropic depletion-driven phase separation is known to be observed for mixtures of polymers and nanoparticles. While polymer-linked nanoparticles have been synthesized, their phase behavior has only been predicted for chemically specific interactions. We use integral equation theory to determine the structure and phase behavior of chemically isotropic polymer-linked nanoparticles at high densities. When each end of a linear polymer is grafted to a nanoparticle, we predict an entropy-driven microphase separation of locally segregated polymer-rich and nanoparticle-rich domains. The formation of these self-assembled structures is purely a consequence of the shape of the polymer-linked particle species. The depletion-driven demixing of ungrafted polymer-nanoparticle composites (with small amounts of nanoparticles) is enhanced as particle diameter (D) grows compared to the polymer radius of gyration (R_g). However, this study shows that for polymer-linked nanoparticle systems, the transition from a liquid to microphase separated state shifts to higher densities (i.e. is inhibited) as D/R_g increases. The transition volume fractions attain a unique value (of ∼0.69) at D/R_g ∼ 1.13. The repeating length scale (L*) is 1.4-2.2 times the size of the entire species (D + R_g). Surprisingly, L*/(D + R_g) is a non-monotonic function of the polymer radius of gyration. The repeating length scale also displays a remarkable scaling behavior, as a function of the particle diameter and the polymer density. Additionally, our study implies that two different mechanisms of transitioning to the microphase separated state are possible for these systems, which has important implications for the transition density and the kinds of structures formed.

Bond formation kinetics affects self-assembly directed by ligand-receptor interactions

In this paper we study aggregation kinetics in systems of particles functionalised by complementary linkers. Most of the coarse-grained models currently employed to study large-scale self-assembly of these systems rely on effective potentials between particles as calculated using equilibrium statistical mechanics. In these approaches the kinetic aspects underlying the formation of inter-particle linkages are neglected. We show how the rate at which supramolecular linkages form drastically changes the self-assembly pathway. In order to do this we develop a method that combines Brownian dynamics simulations with a Gillespie algorithm accounting for the evolution of inter-particle linkages. If compared with dynamics based on effective potentials, an explicit description of inter-particle linkages results in aggregates that in the early stages of self-assembly have a lower valency. Relaxation towards equilibrium is hampered by the time required to break existing linkages within one cluster and to reorient them toward free particles. This effect is more important at low temperature and high particle diffusion constant. Our results highlight the importance of including kinetic rates into coarse-grained descriptions of ligand-receptor systems.

Diamond family of nanoparticle superlattices

Diamond lattices formed by atomic or colloidal elements exhibit remarkable functional properties. However, building such structures via self-assembly has proven to be challenging because of the low packing fraction, sensitivity to bond orientation, and local heterogeneity. We report a strategy for creating a diamond superlattice of nano-objects via self-assembly and demonstrate its experimental realization by assembling two variant diamond lattices, one with and one without atomic analogs. Our approach relies on the association between anisotropic particles with well-defined tetravalent binding topology and isotropic particles. The constrained packing of triangular binding footprints of truncated tetrahedra on a sphere defines a unique three-dimensional lattice. Hence, the diamond self-assembly problem is solved via its mapping onto two-dimensional triangular packing on the surface of isotropic spherical particles.

Theory and simulation of DNA-coated colloids: a guide for rational design

By exploiting the exquisite selectivity of DNA hybridization, DNA-coated colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the fact that a proper choice of the grafted DNA sequences yields fine control over the colloidal interactions. Theory and simulations have an important role to play in the optimal design of self assembling DNACCs. At present, the powerful model-based design tools are not widely used, because the theoretical literature is fragmented and the connection between different theories is often not evident. In this Perspective, we aim to discuss the similarities and differences between the different models that have been described in the literature, their underlying assumptions, their strengths and their weaknesses. Using the tools described in the present Review, it should be possible to move towards a more rational design of novel self-assembling structures of DNACCs and, more generally, of systems where ligand-receptor are used to control interactions.

Programming macro-materials from DNA-directed self-assembly

DNA is a powerful tool that can be attached to nano- and micro-objects and direct the self-assembly through base pairing. Since the strategy of DNA programmable nanoparticle self-assembly was first introduced in 1996, it has remained challenging to use DNA to make powerful diagnostic tools and to make designed materials with novel properties and highly ordered crystal structures. In this review, we summarize recent experimental and theoretical developments of DNA-programmable self-assembly into three-dimensional (3D) materials. Various types of aggregates and 3D crystal structures obtained from an experimental DNA-driven assembly are introduced. Furthermore, theoretical calculations and simulations for DNA-mediated assembly systems are described and we highlight some typical theoretical models for Monte Carlo and Molecular Dynamics simulations.

Importance of the DNA "bond" in programmable nanoparticle crystallization

If a solution of DNA-coated nanoparticles is allowed to crystallize, the thermodynamic structure can be predicted by a set of structural design rules analogous to Pauling's rules for ionic crystallization. The details of the crystallization process, however, have proved more difficult to characterize as they depend on a complex interplay of many factors. Here, we report that this crystallization process is dictated by the individual DNA bonds and that the effect of changing structural or environmental conditions can be understood by considering the effect of these parameters on free oligonucleotides. Specifically, we observed the reorganization of nanoparticle superlattices using time-resolved synchrotron small-angle X-ray scattering in systems with different DNA sequences, salt concentrations, and densities of DNA linkers on the surface of the nanoparticles. The agreement between bulk crystallization and the behavior of free oligonucleotides may bear important consequences for constructing novel classes of crystals and incorporating new interparticle bonds in a rational manner.

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

In conventional research, colloidal particles grafted with single-stranded 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.

A coarse-grained model for DNA-functionalized spherical colloids, revisited: effective pair potential from parallel replica simulations

We discuss a coarse-grained model recently proposed by Starr and Sciortino [J. Phys.: Condens. Matter 18, L347 (2006)] for spherical particles functionalized with short single DNA strands. The model incorporates two key aspects of DNA hybridization, i.e., the specificity of binding between DNA bases and the strong directionality of hydrogen bonds. Here, we calculate the effective potential between two DNA-functionalized particles of equal size using a parallel replica protocol. We find that the transition from bonded to unbonded configurations takes place at considerably lower temperatures compared to those that were originally predicted using standard simulations in the canonical ensemble. We put particular focus on DNA-decorations of tetrahedral and octahedral symmetry, as they are promising candidates for the self-assembly into a single-component diamond structure. Increasing colloid size hinders hybridization of the DNA strands, in agreement with experimental findings.

DNA-programmed mesoscopic architecture

We study the problem of the self-assembly of nanoparticles (NPs) into finite mesoscopic structures with a programmed local morphology and complex overall shape. Our proposed building blocks are NPs that are directionally functionalized with DNA. The combination of directionality and selectivity of interactions allows one to avoid unwanted metastable configurations, which have been shown to lead to slow self-assembly kinetics even in much simpler systems. With numerical simulations, we show that a variety of target mesoscopic objects can be designed and self-assembled in near perfect yield. They include cubes, pyramids, boxes, and even an Empire State Building model. We summarize our findings with a set of design strategies that leads to the successful self-assembly of a wide range of mesostructures.

Ab initio determination of coarse-grained interactions in double-stranded DNA

We derive the coarse-grained interactions between DNA nucleotides from ab initio total-energy calculations based on density functional theory (DFT). The interactions take into account base and sequence specificity, and are decomposed into physically distinct contributions that include hydrogen bonding, stacking interactions, backbone, and backbone-base interactions. The interaction energies of each contribution are calculated from DFT for a wide range of configurations and are fitted by simple analytical expressions for use in the coarse-grained model, which reduces each nucleotide into two sites. This model is not derived from experimental data, yet it successfully reproduces the stable B-DNA structure and gives good predictions for the persistence length. It may be used to realistically probe dynamics of DNA strands in various environments at the μs time scale and the μm length scale.

Binary heterogeneous superlattices assembled from quantum dots and gold nanoparticles with DNA

Controllable assembly of three-dimensional (3D) superlattices composed of different types of nanoscale objects opens new opportunities for material fabrication. Herein we show the successful assembly of heterogeneous 3D structures from gold nanoparticles (AuNPs) and quantum dots (QDs) using DNA encoding. By applying synchrotron-based small-angle X-ray scattering, we found that AuNPs and QDs are positioned in a body-centered cubic lattice, while each particle type, AuNP and QD, is arranged in a simple-cubic manner. Our studies demonstrate a route for assembly of integrated heterogeneous 3D structures from different nano-objects by DNA-encoded interactions.

DNA-based soft phases

This chapter reviews the state-of-the-art in the study of molecular or colloidal systems whose mutual interactions are mediated by DNA molecules. In the last decade, the robust current knowledge of DNA interactions has enabled an impressive growth of self-assembled DNA-based structures that depend crucially on the properties of DNA-DNA interactions. In many cases, structures are built on design by exploiting the programmable selectivity of DNA interactions and the modularity of their strength. The study of DNA-based materials is definitely an emerging field in condensed matter physics, nanotechnology, and material science. This chapter will consider both systems that are entirely constructed by DNA and hybrid systems in which latex or metal colloidal particles are coated by DNA strands. We will confine our discussion to systems in which DNA-mediated interactions promote the formation of "phases," that is structures extending on length scales much larger than the building blocks. Their self-assembly typically involves a large number of interacting particles and often features hierarchical stages of structuring. Because of the possibility of fine-tuning the geometry and strength of the DNA-mediated interactions, these systems are characterized by a wide variety of patterns of self-assembly, ranging from amorphous, to liquid crystalline, to crystalline in one, two, or three dimensions.