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

A bond swap algorithm for simulating dynamically crosslinked polymers

Materials incorporating covalent adaptive networks (CAN), e.g., vitrimers, have received significant scientific attention due to their distinctive attributes of self-healing and stimuli-responsive properties. Different from direct crosslinked systems, bivalent and multivalent systems require a bond swap algorithm that respects detailed balance, considering the multiple equilibria in the system. Here, we propose a simple and robust algorithm to handle bond swap in multivalent and multi-species CAN systems. By including a bias term in the acceptance of Monte Carlo moves, we eliminate the imbalance from the bond swap site selection and multivalency effects, ensuring the detailed balance for all species in the system.

Interpenetrated and Bridged Nanocylinders from Self-Assembled Star Block Copolymers

The design of functional polymeric materials with tunable response requires a synergetic use of macromolecular architecture and interactions. Here, we combine experiments with computer simulations to demonstrate how physical properties of gels can be tailored at the molecular level, using star block copolymers with alternating block sequences as a paradigm. Telechelic star polymers containing attractive outer blocks self-assemble into soft patchy nanoparticles, whereas their mirror-image inverted architecture with inner attractive blocks yields micelles. In concentrated solutions, bridged and interpenetrated hexagonally packed nanocylinders are formed, respectively, with distinct structural and rheological properties. The phase diagrams exhibit a peculiar re-entrance where the hexagonal phase melts upon both heating and cooling because of solvent-block and block-block interactions. The bridged nanostructure is characterized by similar deformability, extended structural coherence, enhanced elasticity, and yield stress compared to micelles or typical colloidal gels, which make them promising and versatile materials for diverse applications.

Self-Assembly of DNA-Grafted Colloids: A Review of Challenges

DNA-mediated self-assembly of colloids has emerged as a powerful tool to assemble the materials of prescribed structure and properties. The uniqueness of the approach lies in the sequence-specific, thermo-reversible hybridization of the DNA-strands based on Watson–Crick base pairing. Grafting particles with DNA strands, thus, results into building blocks that are fully programmable, and can, in principle, be assembled into any desired structure. There are, however, impediments that hinder the DNA-grafted particles from realizing their full potential, as building blocks, for programmable self-assembly. In this short review, we focus on these challenges and highlight the research around tackling these challenges.

Designer Nanomaterials through Programmable Assembly

Nanoparticles have long been recognized for their unique properties, leading to exciting potential applications across optics, electronics, magnetism, and catalysis. These specific functions often require a designed organization of particles, which includes the type of order as well as placement and relative orientation of particles of the same or different kinds. DNA nanotechnology offers the ability to introduce highly addressable bonds, tailor particle interactions, and control the geometry of bindings motifs. Here, we discuss how developments in structural DNA nanotechnology have enabled greater control over 1D, 2D, and 3D particle organizations through programmable assembly. This Review focuses on how the use of DNA binding between nanocomponents and DNA structural motifs has progressively allowed the rational formation of prescribed particle organizations. We offer insight into how DNA-based motifs and elements can be further developed to control particle organizations and how particles and DNA can be integrated into nanoscale building blocks, so-called "material voxels", to realize designer nanomaterials with desired functions.

On the interpretation of kinetics and thermodynamics probed by single-molecule experiments

Single-molecule pulling experiments are widely used to extract both thermodynamic and kinetic data on ligand-receptor pairs, typically by fitting different models to the probability distribution of rupture forces of the corresponding bond. Here, a theoretical model is presented that shows how a measurement of the number of binding and unbinding events as a function of the observation time can also give access to both the binding (kon) and the unbinding (koff) rates of bonds, which combined provide a well-defined bond free-energy ΔGbond. The connection between ΔGbond and the ligand-receptor binding constant measured by typical binding essays is critically discussed. The role played by the molecular construct used to tether ligands and receptors to a surface is considered, highlighting the various approximations necessary to derive general expressions that connect its structure to its contribution, termed ΔGcnf, to the bond free-energy. In this way, the validity and the assumptions underpinning widely employed formulas and experimental protocols used to extract binding constants from single-molecule experiments are assessed. Finally, the role of ΔGcnf in processes mediated by ligand-receptor binding is briefly considered, and an experiment to unambiguously measure this quantity proposed.

Combinatorial-Entropy-Driven Aggregation in DNA-Grafted Nanoparticles

We use computer simulations and experiments to study the interactions between nanoparticles (NPs) grafted with self-complementary DNA strands. Each strand ends with a sticky palindromic single-stranded sequence, allowing it to associate equally favorably with strands grafted on the same particle or on different NPs. Surprisingly we find an attractive interaction between a pair of NPs, and we demonstrate that at low temperature it arises purely from a combinatorial-entropy contribution. We evaluate theoretically and verify numerically this entropic contribution originating from the number of distinct bonding patterns associated with intra- and interparticle binding. This entropic attraction becomes more favorable with decreasing inter-NP distance because more sticky ends can participate in making this choice.

Reconfigurable Self-Assembly and Kinetic Control of Multiprogrammed DNA-Coated Particles

DNA is a unique molecule for storing information, which is used to provide particular biological instructions. Its function is primarily determined by the sequence of its four nucleobases, which have highly specific base-pairing interactions. This unique feature can be applied to direct the self-assembly of colloids by grafting DNA onto them. Due to the sequence-specific interactions, colloids can be programmed with multiple instructions. Here, we show that particles having multiple DNA strands with different melting profiles can undergo multiple phase transitions and reassemble into different crystalline structures in response to temperature. We include free DNA strands in the medium to selectively switch on and off DNA hybridization depending on temperature. We also demonstrate that DNA hybridization kinetics can be used as a means to achieve targeted assembling structure of colloids. These transitions impart a reconfigurability to colloids in which systems can be transformed an arbitrary number of times using thermal and kinetic control.

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, multivalent interactions mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.

Calculation of π and Classification of Self-avoiding Lattices via DNA Configuration

Numerical simulation (e.g. Monte Carlo simulation) is an efficient computational algorithm establishing an integral part in science to understand complex physical and biological phenomena related with stochastic problems. Aside from the typical numerical simulation applications, studies calculating numerical constants in mathematics, and estimation of growth behavior via a non-conventional self-assembly in connection with DNA nanotechnology, open a novel perspective to DNA related to computational physics. Here, a method to calculate the numerical value of π, and way to evaluate possible paths of self-avoiding walk with the aid of Monte Carlo simulation, are addressed. Additionally, experimentally obtained variation of the π as functions of DNA concentration and the total number of trials, and the behaviour of self-avoiding random DNA lattice growth evaluated through number of growth steps, are discussed. From observing experimental calculations of π (π_exp) obtained by double crossover DNA lattices and DNA rings, fluctuation of π_exp tends to decrease as either DNA concentration or the number of trials increases. Based upon experimental data of self-avoiding random lattices grown by the three-point star DNA motifs, various lattice configurations are examined and analyzed. This new kind of study inculcates a novel perspective for DNA nanostructures related to computational physics and provides clues to solve analytically intractable problems.

Hierarchical Crystals Formed from DNA-Functionalized Janus Nanoparticles

Harnessing anisotropic interactions in a DNA-mediated nanoparticle assembly holds great promise as a rational strategy to advance this important area. Here, using molecular dynamics simulations, we report the formation of novel hierarchical crystalline assemblies of Janus nanoparticles functionalized with two types of DNA chains (DNA-JNPs). We find that in addition to the primary nanoparticle crystallization into face-centered cubic (FCC) structure, sequence-specific DNA hybridization events further direct the rotational orientation of the DNA-JNPs to diverse secondary crystalline phases including simple cubic (SC), tetragonally ordered cylinder (P4), and lamella (L) structures, which are mapped in the phase diagrams relating to various asymmetric parameters. The crystallization dynamics of such hierarchical crystals is featured by two consequent processes: entropy-dominated translational order for the primary crystalline structure and enthalpy-dominated rotational order for the secondary crystalline structure. For DNA-JNPs with high asymmetry in DNA sequence length, tetrahedral nanoclusters tend to be favored, which is revealed to be governed by the conformational entropy penalty caused by bounded DNA chains. This work might bear important consequences for constructing new classes of nanoparticle crystals with designed structures and properties at multiple levels and in a predictable manner.

Significance of DNA bond strength in programmable nanoparticle thermodynamics and dynamics

Assembly of nanoparticles (NPs) coated with complementary DNA strands leads to novel crystals with nanosized basic units rather than classic atoms, ions or molecules. The assembly process is mediated by hybridization of DNA via specific base pairing interaction, and is kinetically linked to the disassociation of DNA duplexes. DNA-level physiochemical quantities, both thermodynamic and kinetic, are key to understanding this process and essential for the design of DNA-NP crystals. The melting transition properties are helpful to judge the thermostability and sensitivity of relative DNA probes or other applications. Three different cases are investigated by changing the linker length and the spacer length on which the melting properties depend using the molecular dynamics method. Melting temperature is determined by sigmoidal melting curves based on hybridization percentage versus temperature and the Lindemann melting rule simultaneously. We provide a computational strategy based on a coarse-grained model to estimate the hybridization enthalpy, entropy and free energy from percentages of hybridizations which are readily accessible in experiments. Importantly, the lifetime of DNA bond dehybridization based on temperature and the activation energy depending on DNA bond strength are also calculated. The simulation results are in good agreement with the theoretical analysis and the present experimental data. Our study provides a good strategy to predict the melting temperature which is important for the DNA-directed nanoparticle system, and bridges the dynamics and thermodynamics of DNA-directed nanoparticle systems by estimating the equilibrium constant from the hybridization of DNA bonds quantitatively.

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.

Molecular control over colloidal assembly

Contemporary chemical and material engineering often takes inspiration from nature, targeting for example strong yet light materials and materials composed of highly ordered domains at multiple different lengthscales for fundamental science and applications in e.g. sensing, catalysis, coating technology, and delivery. The preparation of such hierarchically structured functional materials through guided bottom-up assembly of synthetic building blocks requires a high level of control over their synthesis, interactions and assembly pathways. In this perspective we showcase recent work demonstrating how molecular control can be exploited to direct colloidal assembly into responsive materials with mechanical, optical or electrical properties that can be adjusted post-synthesis with external cues.

Annealing cycles and the self-organization of functionalized colloids

The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances in their synthesis. Self-assembly pathways are typically characterized by high energy barriers that hinder access to stable (equilibrium) structures. A possible strategy to tackle this challenge is to perform annealing cycles. By periodically switching on and off the inter-particle bonds, one expects to smooth-out the kinetic pathways and favor the assembly of targeted structures. Preliminary results have shown that the efficiency of annealing cycles depends strongly on their frequency. Here, we study numerically how this frequency-dependence scales with the strength of the directional interactions (size of the patch σ). We use analytical arguments to show that the scaling results from the statistics of a random walk in configurational space.

Interaction Heterogeneity can Favorably Impact Colloidal Crystal Nucleation

Colloidal particles with short-ranged attractions, e.g., micron-scale spheres functionalized with single-stranded DNA oligomers, are susceptible to becoming trapped in disordered configurations even when a crystalline arrangement is the ground state. Moreover, for reasons that are not well understood, seemingly minor variations in the particle formulation can lead to dramatic changes in the crystallization outcome. We demonstrate, using a combination of equilibrium and nonequilibrium computer simulations, that interaction heterogeneity-variations in the energetic interactions among different particle pairs in the population-may favorably impact crystal nucleation. Specifically, interaction heterogeneity is found to lower the free energy barrier to nucleation via the formation of clusters comprised preferentially of strong-binding particle pairs. Moreover, gelation is inhibited by "spreading out over time" the nucleation process, resulting in a reduced density of stable nuclei, allowing each to grow unhindered and larger. Our results suggest a simple and robust approach for enhancing colloidal crystallization near the "sticky sphere" limit, and support the notion that differing extents of interaction heterogeneity arising from various particle functionalization protocols may contribute to the otherwise unexplained variations in crystallization outcomes reported in the literature.

Dynamics of network fluids

Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and nonequilibrium gels. Here, we provide an overview of a selection of their equilibrium and dynamical properties. Recent research efforts towards bridging equilibrium and non-equilibrium studies are discussed, as well as several open questions.

Colloidal joints with designed motion range and tunable joint flexibility

The miniaturization of machines towards the micron and nanoscale requires the development of joint-like elements that enable and constrain motion. We present a facile method to create colloidal joints, that is, anisotropic colloidal particles functionalized with surface mobile DNA linkers that control the motion range of bonded particles. We demonstrate quantitatively that we can control the flexibility of these colloidal joints by tuning the DNA linker concentration in the bond area. We show that the shape of the colloidal joint controls the range of motion of bonded particles through a maximisation of the bond area. Using spheres, cubes, and dumbbells, we experimentally realize spherical joints, planar sliders, and hinges, respectively. Finally we demonstrate the potential of the colloidal joints for programmable bottom-up self-assembly by creating flexible colloidal molecules and colloidal polymers. The reconfigurability and motion constraint offered by our colloidal joints make them promising building blocks for the development of switchable materials and nanorobots.

Directionally Interacting Spheres and Rods Form Ordered Phases

The structures formed by mixtures of dissimilarly shaped nanoscale objects can significantly enhance our ability to produce nanoscale architectures. However, understanding their formation is a complex problem due to the interplay of geometric effects (entropy) and energetic interactions at the nanoscale. Spheres and rods are perhaps the most basic geometrical shapes and serve as convenient models of such dissimilar objects. The ordered phases formed by each of these individual shapes have already been explored, however, when mixed, spheres and rods have demonstrated only limited structural organization to date. Here, we show using experiments and theory that the introduction of directional attractions between rod ends and isotropically interacting spherical nanoparticles (NPs) through DNA base pairing leads to the formation of ordered three-dimensional lattices. The spheres and rods arrange themselves in a complex alternating manner, where the spheres can form either a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, or a disordered phase, as observed by in situ X-ray scattering. Increasing NP diameter at fixed rod length yields an initial transition from a disordered phase to the HCP crystal, energetically stabilized by rod-rod attraction across alternating crystal layers, as revealed by theory. In the limit of large NPs, the FCC structure is instead stabilized over the HCP by rod entropy. We, therefore, propose that directionally specific attractions in mixtures of anisotropic and isotropic objects offer insight into unexplored self-assembly behavior of noncomplementary shaped particles.

Colloidal crystals with diamond symmetry at optical lengthscales

Future optical materials promise to do for photonics what semiconductors did for electronics, but the challenge has long been in creating the structure they require—a regular, three-dimensional array of transparent microspheres arranged like the atoms in a diamond crystal. Here we demonstrate a simple approach for spontaneously growing double-diamond (or B32) crystals that contain a suitable diamond structure, using DNA to direct the self-assembly process. While diamond symmetry crystals have been grown from much smaller nanoparticles, none of those previous methods suffice for the larger particles needed for photonic applications, whose size must be comparable to the wavelength of visible light. Intriguingly, the crystals we observe do not readily form in previously validated simulations; nor have they been predicted theoretically. This finding suggests that other unexpected microstructures may be accessible using this approach and bodes well for future efforts to inexpensively mass-produce metamaterials for an array of photonic applications.

Colloidal crystals arranged in a diamond lattice are desirable for photonic applications, yet are challenging to create. Here, Wang et al. show the self-assembly of a binary system composed of two interlocked diamond structures with lattice spacing comparable to the wavelength of visible light.

Nonequilibrium self-organization of colloidal particles on substrates: adsorption, relaxation, and annealing

Colloidal particles are considered ideal building blocks to produce materials with enhanced physical properties. The state-of-the-art techniques for synthesizing these particles provide control over shape, size, and directionality of the interactions. In spite of these advances, there is still a huge gap between the synthesis of individual components and the management of their spontaneous organization towards the desired structures. The main challenge is the control over the dynamics of self-organization. In their kinetic route towards thermodynamically stable structures, colloidal particles self-organize into intermediate (mesoscopic) structures that are much larger than the individual particles and become the relevant units for the dynamics. To follow the dynamics and identify kinetically trapped structures, one needs to develop new theoretical and numerical tools. Here we discuss the self-organization of functionalized colloids (also known as patchy colloids) on attractive substrates. We review our recent results on the adsorption and relaxation and explore the use of annealing cycles to overcome kinetic barriers and drive the relaxation towards the targeted structures.

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.

Effect of Nonionic Surfactant on Association/Dissociation Transition of DNA-Functionalized Colloids

We report the effect of nonionic surfactants (Pluronics F127 and F88) on the melting transition of micron-sized colloids confined in two dimensions, mediated by complementary single-stranded DNA as a function of the surfactant concentration. Micron-sized silica particles were functionalized with single-stranded DNA using cyanuric chloride chemistry. The existence of covalently linked DNA on particles was confirmed by fluorescence spectroscopy. The nonionic surfactant not only plays a significant role in stabilization of particles, with minimization of nonspecific binding, but also impacts the melting temperature, which increases as a function of the nonionic surfactant concentration. These results suggest that the melting transition for DNA-mediated assembly is sensitive to commonly used additives in laboratory buffers, and that these common solution components may be exploited as a facile and independent handle for tuning the melting temperature and, thus, the assembly and possibly crystallization within these systems.

Melting transition in lipid vesicles functionalised by mobile DNA linkers

We study phase behaviour of lipid-bilayer vesicles functionalised by ligand-receptor complexes made of synthetic DNA by introducing a modelling framework and a dedicated experimental platform. In particular, we perform Monte Carlo simulations that combine a coarse grained description of the lipid bilayer with state of art analytical models for multivalent ligand-receptor interactions. Using density of state calculations, we derive the partition function in pairs of vesicles and compute the number of ligand-receptor bonds as a function of temperature. Numerical results are compared to microscopy and fluorimetry experiments on large unilamellar vesicles decorated by DNA linkers carrying complementary overhangs. We find that vesicle aggregation is suppressed when the total number of linkers falls below a threshold value. Within the model proposed here, this is due to the higher configurational costs required to form inter-vesicle bridges as compared to intra-vesicle loops, which are in turn related to membrane deformability. Our findings and our numerical/experimental methodologies are applicable to the rational design of liposomes used as functional materials and drug delivery applications, as well as to study inter-membrane interactions in living systems, such as cell adhesion.

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

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.

Relaxation dynamics of functionalized colloids on attractive substrates

Particle-based simulations are performed to study the post-relaxation dynamics of functionalized (patchy) colloids adsorbed on an attractive substrate. Kinetically arrested structures that depend on the number of adsorbed particles and the strength of the particle-particle and particle-substrate interactions are identified. The radial distribution function is characterized by a sequence of peaks, with relative intensities that depend on the number of adsorbed particles. The first-layer coverage is a non-monotonic function of the number of particles, with an optimal value around one layer of adsorbed particles. The initial relaxation towards these structures is characterized by a fast (exponential) and a slow (power-law) dynamics. The fast relaxation timescale is a linearly increasing function of the number of adsorbed particles in the submonolayer regime, but it saturates for more than one adsorbed layer. The slow dynamics exhibits two characteristic exponents, depending on the surface coverage.

A new configurational bias scheme for sampling supramolecular structures

We present a new simulation scheme which allows an efficient sampling of reconfigurable supramolecular structures made of polymeric constructs functionalized by reactive binding sites. The algorithm is based on the configurational bias scheme of Siepmann and Frenkel and is powered by the possibility of changing the topology of the supramolecular network by a non-local Monte Carlo algorithm. Such a plan is accomplished by a multi-scale modelling that merges coarse-grained simulations, describing the typical polymer conformations, with experimental results accounting for free energy terms involved in the reactions of the active sites. We test the new algorithm for a system of DNA coated colloids for which we compute the hybridisation free energy cost associated to the binding of tethered single stranded DNAs terminated by short sequences of complementary nucleotides. In order to demonstrate the versatility of our method, we also consider polymers functionalized by receptors that bind a surface decorated by ligands. In particular, we compute the density of states of adsorbed polymers as a function of the number of ligand-receptor complexes formed. Such a quantity can be used to study the conformational properties of adsorbed polymers useful when engineering adsorption with tailored properties. We successfully compare the results with the predictions of a mean field theory. We believe that the proposed method will be a useful tool to investigate supramolecular structures resulting from direct interactions between functionalized polymers for which efficient numerical methodologies of investigation are still lacking.

Crystallization of DNA-coated colloids

DNA-coated colloids hold great promise for self-assembly of programmed heterogeneous microstructures, provided they not only bind when cooled below their melting temperature, but also rearrange so that aggregated particles can anneal into the structure that minimizes the free energy. Unfortunately, DNA-coated colloids generally collide and stick forming kinetically arrested random aggregates when the thickness of the DNA coating is much smaller than the particles. Here we report DNA-coated colloids that can rearrange and anneal, thus enabling the growth of large colloidal crystals from a wide range of micrometre-sized DNA-coated colloids for the first time. The kinetics of aggregation, crystallization and defect formation are followed in real time. The crystallization rate exhibits the familiar maximum for intermediate temperature quenches observed in metallic alloys, but over a temperature range smaller by two orders of magnitude, owing to the highly temperature-sensitive diffusion between aggregated DNA-coated colloids.

DNA-coated colloids have failed to achieve their promise of programmable self-assembly because they stick to each other like Velcro. Here Wang et al. overcome this problem by making clickable smooth colloids that are coated with short single-stranded DNA at high density.

Kinetic interfaces of patchy particles

We study the irreversible adsorption of patchy particles on substrates in the limit of advective mass transport. Recent numerical results show that the interface roughening depends strongly on the particle attributes, such as, patch-patch correlations, bond flexibility and strength of the interactions, uncovering new absorbing phase transitions. Here, we revisit these results and discuss in detail the transitions. In particular, we present new evidence that the tricritical point, observed in systems of particles with flexible patches, is in the tricritical directed percolation universality class. A scaling analysis of the time evolution of the correlation length for the aggregation of patchy particles with distinct bonding energies confirms that the critical regime is in the Kardar-Parisi-Zhang with quenched disorder universality class.

Direct measurement of DNA-mediated adhesion between lipid bilayers

Multivalent interactions between deformable mesoscopic units are ubiquitous in biology, where membrane macromolecules mediate the interactions between neighbouring living cells and between cells and solid substrates. Lately, analogous artificial materials have been synthesised by functionalising the outer surface of compliant Brownian units, for example emulsion droplets and lipid vesicles, with selective linkers, in particular short DNA sequences. This development extended the range of applicability of DNA as a selective glue, originally applied to solid nano and colloidal particles. On very deformable lipid vesicles, the coupling between statistical effects of multivalent interactions and mechanical deformation of the membranes gives rise to complex emergent behaviours, as we recently contributed to demonstrate [Parolini et al., Nat. Commun., 2015, 6, 5948]. Several aspects of the complex phenomenology observed in these systems still lack a quantitative experimental characterisation and a fundamental understanding. Here we focus on the DNA-mediated multivalent interactions of a single liposome adhering to a flat supported bilayer. This simplified geometry enables the estimate of the membrane tension induced by the DNA-mediated adhesive forces acting on the liposome. Our experimental investigation is completed by morphological measurements and the characterisation of the DNA-melting transition, probed by in situ Förster Resonant Energy Transfer spectroscopy. Experimental results are compared with the predictions of an analytical theory that couples the deformation of the vesicle to a full description of the statistical mechanics of mobile linkers. With at most one fitting parameter, our theory is capable of semi-quantitatively matching experimental data, confirming the quality of the underlying assumptions.

Stoichiometric control of DNA-grafted colloid self-assembly

There has been considerable interest in understanding the self-assembly of DNA-grafted nanoparticles into different crystal structures, e.g., CsCl, AlB2, and Cr3Si. 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 Cr3Si structure. However, AlB2 can form when appropriate building blocks are used so that the AlB2 standard-state free energy is low enough to overcome the entropic preference for Cr3Si. 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.

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.

Volume and porosity thermal regulation in lipid mesophases by coupling mobile ligands to soft membranes

Short DNA linkers are increasingly being exploited for driving-specific self-assembly of Brownian objects. DNA-functionalized colloids can assemble into ordered or amorphous materials with tailored morphology. Recently, the same approach has been applied to compliant units, including emulsion droplets and lipid vesicles. The liquid structure of these substrates introduces new degrees of freedom: the tethers can diffuse and rearrange, radically changing the physics of the interactions. Unlike droplets, vesicles are extremely deformable and DNA-mediated adhesion causes significant shape adjustments. We investigate experimentally the thermal response of pairs and networks of DNA-tethered liposomes and observe two intriguing and possibly useful collective properties: negative thermal expansion and tuneable porosity of the liposome networks. A model providing a thorough understanding of this unexpected phenomenon is developed, explaining the emergent properties out of the interplay between the temperature-dependent deformability of the vesicles and the DNA-mediated adhesive forces.

DNA-functionalized particles can aggregate into materials with programmable morphology, but the response of these materials to external stimuli is limited. Here, the authors demonstrate how the structure of DNA-liposome aggregates can be controlled by changing temperature.

Mobile linkers on DNA-coated colloids: valency without patches

Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal "molecules." However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e., the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design principle that exploits many-body effects to control the valency of otherwise isotropic colloids. Using a combination of theory and simulation, we show that we can tune the valency of colloids coated with mobile ssDNA, simply by tuning the nonspecific repulsion between the particles. Our simulations show that the resulting effective interactions lead to low-valency colloids self-assembling in peculiar open structures, very different from those observed in DNACCs with immobile DNA linkers.

Adsorbed films of three-patch colloids: continuous and discontinuous transitions between thick and thin films

We investigate numerically the role of spatial arrangement of the patches on the irreversible adsorption of patchy colloids on a substrate. We consider spherical three-patch colloids and study the dependence of the kinetics on the opening angle between patches. We show that growth is suppressed below and above minimum and maximum opening angles, revealing two absorbing phase transitions between thick and thin film regimes. While the transition at the minimum angle is continuous, in the directed percolation class, that at the maximum angle is clearly discontinuous. For intermediate values of the opening angle, a rough colloidal network in the Kardar-Parisi-Zhang universality class grows indefinitely. The nature of the transitions was analyzed in detail by considering bond flexibility, defined as the dispersion of the angle between the bond and the center of the patch. For the range of flexibilities considered we always observe two phase transitions. However, the range of opening angles where growth is sustained increases with flexibility. At a tricritical flexibility, the discontinuous transition becomes continuous. The practical implications of our findings and the relation to other nonequilibrium transitions are discussed.

Hydrodynamics selects the pathway for displacive transformations in DNA-linked colloidal crystallites

The degree to which DNA-linked particle crystals, particularly those composed of micrometer-scale colloids, are able to dynamically evolve or whether they are kinetically arrested after formation remains poorly understood. Here, we study a recently observed displacive transformation in colloidal binary superlattice crystals, whereby a body-centered cubic to face-centered cubic transformation is found to proceed spontaneously under some annealing conditions. Using a comprehensive suite of computer simulation tools, we develop a framework for analyzing the many displacive transformation pathways corresponding to distinct, but energetically degenerate, random hexagonal close-packed end states. Due to the short-ranged, spherically symmetric nature of the particle interactions the pathways are all barrierless, suggesting that all end states should be equally likely. Instead, we find that hydrodynamic correlations between particles result in anisotropic mobility along the various possible displacive pathways, strongly selecting for pathways that lead to the fcc-CuAu-I configuration, explaining recent experimental observations. This finding may provide clues for discovering new approaches for controlling structure in this emerging class of materials.

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.

A general method for spatially coarse-graining Metropolis Monte Carlo simulations onto a lattice

A recently introduced method for coarse-graining standard continuous Metropolis Monte Carlo simulations of atomic or molecular fluids onto a rigid lattice of variable scale [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012)] is further analyzed and extended. The coarse-grained Metropolis Monte Carlo technique is demonstrated to be highly consistent with the underlying full-resolution problem using a series of detailed comparisons, including vapor-liquid equilibrium phase envelopes and spatial density distributions for the Lennard-Jones argon and simple point charge water models. In addition, the principal computational bottleneck associated with computing a coarse-grained interaction function for evolving particle positions on the discretized domain is addressed by the introduction of new closure approximations. In particular, it is shown that the coarse-grained potential, which is generally a function of temperature and coarse-graining level, can be computed at multiple temperatures and scales using a single set of free energy calculations. The computational performance of the method relative to standard Monte Carlo simulation is also discussed.