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

Multifarious colloidal structures: new insight into ternary and quadripartite ordered assemblies

DNA-mediated assembly of colloidal particles can be utilized to produce a variety of structures which may have desirable phononic, photonic, or electronic transport properties. Recent developments in linker-mediated assembly processes allow for interactions to be coordinated between many different types of colloidal particles more easily and with fewer unique sequences than direct hybridization. However, the dynamics of colloidal self-assembly becomes increasingly more complex when coordinating interactions between three or more distinct interacting elements. In such cases particle pairs with similar binding energies are allowed to interact unpredictably, and enthalpically degenerate binding sites will be noticeably more present while numerous secondary phases may also result from the self-assembly process. Therefore, it is necessary to develop procedures for predicting feasible superstructure geometries for these systems before they can be implemented in material design. Here we investigate the formation of multifarious ordered structures through self-assembly of multiple types of spherically symmetrical colloidal particles with a variety of interaction matrices. We utilize Molecular Dynamics (MD) simulations to study the growth behavior of systems with different types of interacting elements and different particle sizes, and also predict the formation and stability of the target structures. We also study the phononic spectra of various ternary structures in order to identify the influence of key structural parameters on phonon bandgap frequencies and ranges. Our results provide direct guidelines for designing ternary and quadripartite multifarious colloidal structures, and motivate new directions for future experimental work to target formation of multi-component colloidal superstructures beyond the well-established binary symmetries studied in the past.

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.

Spontaneous emergence of catalytic cycles with colloidal spheres

Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson's notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.

The "sugar" coarse-grained DNA model

More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.

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.

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.

A molecular view of DNA-conjugated nanoparticle association energies

Nanoparticles functionalized with short sequences of DNA represent a promising platform for customizable self assembly. Though much recent research has focused on the phase behavior and assembly of these structures, little has been done to precisely characterize the pairwise interaction between particles. Here we present a detailed calculation of the association between DNA-nanoparticle conjugates using 3SPN.2, a coarse-grained model of DNA that accounts for molecular structure and base-pairing. We compare our results to those obtained experimentally using μm sized particles and analyze the free energy surfaces that characterize interparticle hybridization. Next, we study the importance of three-body effects and their impact on particle association and melting. Lastly, we explore the observation by Park et al. [Nature, 451, 553 (2008)] that DNA-nanoparticle crystallization can be inhibited by the deletion of a single nucleotide. Using our model, we suggest that the role of this nucleotide is to disrupt frustration.

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.

"Crystal-clear" liquid-liquid transition in a tetrahedral fluid

For a model known to exhibit liquid-liquid transitions, we examine how varying the bond orientational flexibility affects the stability of the liquid-liquid transition relative to that of the crystal phases. For very rigidly oriented bonds, the crystal is favored over all amorphous phase transitions. We find that increasing the bond flexibility decreases both the critical temperature Tc for liquid-liquid phase separation and the melting temperature Tm. The effect of increasing flexibility is much stronger for melting, so that the distance between Tc and Tm progressively reduces and inverts sign. Under these conditions, a "naked" liquid-liquid critical point bulges out in the liquid phase and becomes accessible, without the possibility of crystallization. These results confirm that a crystal-clear, liquid-liquid transition can occur as a genuine, thermodynamically stable phenomenon for tetrahedral coordinated particles with flexible bond orientation, but that such a transition is hidden by crystallization when bonds are highly directional.

Size limits of self-assembled colloidal structures made using specific interactions

We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.

Growth dynamics for DNA-guided nanoparticle crystallization

Spherical nucleic acid (SNA) nanostructures assemble into a large variety of well-defined crystalline superlattices via DNA-directed hybridization. Crystallities of SNA with various shapes emerge during the assembly process, which coalesce during coarsening, leading to polycrystalline materials. Here, we investigate the growth dynamics of SNAs into body-centered cubic superlattices and the coalescence of SNA aggregates using a colloidal model formulated from the competition of electrostatic core repulsions and localized DNA hybridization attractions. We find that the growth law of isolated SNA crystallities is well-described by the power law t(1/2), in agreement with experimental observations. At later times, coalescence slows the growth dynamics considerably and is dependent on the orientational mismatch (misorientation angle) of the coalescing crystallites. Molecular dynamics simulations show that the misorientation angle decreases continually during the coalescence, which is a signature of the grain rotation induced coalescence mechanism. This mechanism is followed by the coarsening of a "neck" that develops at the boundary between the coalescing crystallites. Remarkably, we find faster coalescence dynamics for larger SNAs compared to smaller SNAs due to their enhanced surface diffusion, which more effectively reduces curvature at the boundary of two superlattices. These findings provide fundamental insight into the relationship between nanoparticle surface chemistry and its crystallite growth and coalescence.

The self-assembly of particles with isotropic interactions

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, motivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding kinetic effects. It is found that non-trivial morphologies are possible and that, for this effectively one component system, these parallel the phases of diblock copolymer melts for certain parameter choices, despite the absence of connectivity or packing frustration in the model. An explanation for the morphological similarity between these architecturally disparate systems is given. For other parameter choices, it is found that meta-stable and defected phases become more common, and that similarity with block copolymer morphologies decreases.