DNA-coated Colloids Research Articles

Modeling the relative dynamics of DNA-coated colloids.

We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1 μm colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.

Designing disordered materials using DNA-coated colloids of bacteriophage fd and gold.

DNA has emerged as an exciting binding agent for programmable colloidal self-assembly. Its popularity derives from its unique properties: it provides highly specific short-ranged interactions and at the same time it acts as a steric stabilizer against non-specific van der Waals and Coulomb interactions. Because complementary DNA strands are linked only via hydrogen bonds, DNA-mediated binding is thermally reversible: it provides an effective attraction that can be switched off by raising the temperature only by a few degrees. In this article we introduce a new binary system made of DNA-functionalized filamentous fd viruses of ∼880 nm length with an aspect ratio of ∼100, and 50 nm gold nanoparticles (gold NPs) coated with the complementary DNA strands. When quenching mixtures below the melt temperature Tm, at which the attraction is switched on, we observe aggregation. Conversely, above Tm the system melts into a homogenous particulate 'gas'. We present the aggregation behavior of three different gold NP to virus ratios and compare them to a gel made solely of gold NPs. In particular, we have investigated the aggregate structures as a function of cooling rate and determine how they evolve as function of time for given quench depths, employing fluorescence microscopy. Structural information was extracted in the form of an effective structure factor and chord length distributions. Rapid cooling rates lead to open aggregates, while slower controlled cooling rates closer to equilibrium DNA hybridization lead to more fine-stranded gels. Despite the different structures we find that for both cooling rates the quench into the two-phase region leads to initial spinodal decomposition, which becomes arrested. Surprisingly, although the fine-stranded gel is disordered, the overall structure and the corresponding length scale distributions in the system are remarkably reproducible. Such highly porous systems can be developed into new functional materials.

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.

Anomalous lifetime statistics of ligand–receptor binding in a tethered polymer system

.In this paper, motivated by observations of non-exponential decay times in the stochastic binding and release of ligand–receptor systems, exemplified by the work of Rogers et al on optically trapped DNA-coated colloids (Rogers et al 2013 Soft Matter 9 6412), we explore the general problem of polymer-mediated surface adhesion using a simplified model of the phenomenon in which a single polymer molecule, fixed at one end, binds through a ligand at its opposite end to a flat surface a fixed distance L away and uniformly covered with receptor sites. Working within the Wilemski–Fixman approximation to diffusion-controlled reactions, we show that for a flexible Gaussian chain, the predicted distribution of times for which the ligand and receptor are bound is given, for times much shorter than the longest relaxation time of the polymer, by a power law of the form . We also show when the effects of chain stiffness are incorporated into this model (approximately), the structure of is altered to . These results broadly mirror the experimental trends in the work cited above.

Synthetic Strategies Toward DNA-Coated Colloids that Crystallize.

We report on synthetic strategies to fabricate DNA-coated micrometer-sized colloids that, upon thermal annealing, self-assemble into various crystal structures. Colloids of a wide range of chemical compositions, including poly(styrene), poly(methyl methacrylate), titania, silica, and a silica-methacrylate hybrid material, are fabricated with smooth particle surfaces and a dense layer of surface functional anchors. Single-stranded oligonucleotides with a short sticky end are covalently grafted onto particle surfaces employing a strain-promoted alkyne-azide cycloaddition reaction resulting in DNA coatings with areal densities an order of magnitude higher than previously reported. Our approach allows the DNA-coated colloids not only to aggregate upon cooling but also to anneal and rearrange while still bound together, leading to the formation of colloidal crystal compounds when particles of different sizes or different materials are combined.

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.

Direct visualization of conformation and dense packing of DNA-based soft colloids.

Soft colloids--such as polymer-coated particles, star polymers, block-copolymer micelles, microgels--constitute a broad class of materials where microscopic properties such as deformability and penetrability of the particle play a key role in tailoring their macroscopic properties which is of interest in many technological areas. The ability to access these microscopic properties is not yet demonstrated despite its great importance. Here we introduce novel DNA-coated colloids with star-shaped architecture that allows accessing the above local structural information by directly visualizing their intramolecular monomer density profile and arm's free-end locations with confocal fluorescent microscopy. Compression experiments on a two-dimensional hexagonal lattice formed by these macromolecular assemblies reveal an exceptional resistance to mutual interpenetration of their charged corona at pressures approaching the MPa range. Furthermore, we find that this lattice, in a close packing configuration, is surprisingly tolerant to particle size variation. We anticipate that these stimuli-responsive materials could aid to get deeper insight in a wide range of problems in soft matter, including the study and design of biomimetic lubricated surfaces.

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.

Directing assembly of DNA-coated colloids with magnetic fields to generate rigid, semiflexible, and flexible chains.

We report the formation of colloidal macromolecules consisting of chains of micron-sized paramagnetic particles assembled using a magnetic field and linked with DNA. The interparticle spacing and chain flexibility were controlled by varying the magnetic field strength and the linker spring constant. Variations in the DNA lengths allowed for the generation of chains with an improved range of flexibility as compared to previous studies. These chains adopted the rigid-rod, semiflexible, and flexible conformations that are characteristic of linear polymer systems. These assembly techniques were investigated to determine the effects of the nanoscale DNA linker properties on the properties of the microscale colloidal chains. With stiff DNA linkers (564 base pairs) the chains were only stable at moderate to high field strengths and produced rigid chains. For flexible DNA linkers (8000 base pairs), high magnetic field strengths caused the linkers to be excluded from the gap between the particles, leading to a transition from very flexible chains at low field strengths to semiflexible chains at high field strengths. In the intermediate range of linker sizes, the chains exhibited predictable behavior, demonstrating increased flexibility with longer DNA linker length or smaller linking field strengths. This study provides insight into the process of directed assembly using magnetic fields and DNA by precisely tuning the components to generate colloidal analogues of linear macromolecular chains.

Aggregation dynamics, structure, and mechanical properties of bigels

Recently we have introduced bigels, inter-penetrating gels made of two different colloidal species. Even if particles with simple short-range isotropic potential are employed, the selective interactions enable the tunability of the self-assembly, leading to the formation of complex structures. In the present paper, we explore the non-equilibrium dynamics and the phenomenology underlying the kinetic arrest under quench and the formation of bigels. We demonstrate that the peculiar bigel kinetics can be described through an arrested spinodal decomposition driven by demixing of the colloidal species. The role played by the presence of a second colloidal species on the phase diagram, as expanded to account for the increased number of parameters, is clarified both via extensive numerical simulations and experiments. We provide details on the realisation of bigels, by means of DNA-coated colloids (DNACCs), and the consequent imaging techniques. Moreover we evidence, by comparison with the usual one-component gel formation, the emergence of controllable timescales in the aggregation of the bigels, whose final stages are also experimentally studied to provide morphological details. Finally, we use numerical models to simulate the bigel response to mechanical strain, highlighting how such a new material can bear significantly higher stress compared to the usual one-component gel. We conclude by discussing possible technological uses and by providing insights on the viable research steps to undertake for more complex and yet tuneable multi-component colloidal systems.

Multistep kinetic self-assembly of DNA-coated colloids

Equilibrium self-assembly relies on the relaxation of disordered mixtures of building blocks towards an ordered ground state. The main drawback of this traditional approach lies in the kinetic traps that often interrupt the progression of the system towards equilibrium and lead to the formation of arrested phases. The latest techniques to control colloidal interactions open up the possibility of exploiting the tendency to dynamically arrest in order to construct amorphous materials with a specific morphology and local separation between multiple components. Here we propose strategies to direct the gelation of two-component colloidal mixtures by sequentially activating selective interactions. We investigate morphological changes in the structure of the arrested phases both by means of molecular dynamics simulations and experimentally by using DNA-coated colloids. Our approach can be exploited to assemble multicomponent mesoporous materials with possible applications in hybrid photovoltaics, photonics and drug delivery.

Cinnamate-based DNA photolithography

As demonstrated by means of DNA nanoconstructs[1], as well as DNA functionalization of nanoparticles[2-4] and micrometre-scale colloids[5-8], complex self-assembly processes require components to associate with particular partners in a programmable fashion. In many cases the reversibility of the interactions between complementary DNA sequences is an advantage[9]. However, permanently bonding some or all of the complementary pairs may allow for flexibility in design and construction[10]. Here, we show that the substitution of a pair of complementary bases by a cinnamate group provides an efficient, addressable, UV light-based method to covalently bond complementary DNA. To show the potential of this approach, we wrote micrometre-scale patterns on a surface via UV light and demonstrate the reversible attachment of conjugated DNA and DNA-coated colloids. Our strategy enables both functional DNA photolithography and multi-step, specific binding in self-assembly processes.

Communication: A simple analytical formula for the free energy of ligand–receptor-mediated interactions

Recently [P. Varilly, S. Angioletti-Uberti, B. M. Mognetti, and D. Frenkel, "A general theory of DNA-mediated and other valence-limited colloidal interactions," J. Chem. Phys. 137, 094108 (2012)], we presented a general theory for calculating the strength and properties of colloidal interactions mediated by ligand-receptor bonds (such as those that bind DNA-coated colloids). In this Communication, we derive a surprisingly simple analytical form for the interaction free energy, which was previously obtainable only via a costly numerical thermodynamic integration. As a result, the computational effort to obtain potentials of interaction is significantly reduced. Moreover, we can gain insight from this analytic expression for the free energy in limiting cases. In particular, the connection of our general theory to other previous specialised approaches is now made transparent. This important simplification will significantly broaden the scope of our theory.

Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental data

We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying single-stranded DNA of length comparable to the colloids' size. We show that in this regime, the common theoretical approach of assuming pairwise additivity of the colloidal pair interactions leads to quantitatively and sometimes even qualitatively wrong predictions of the phase behaviour of DNA-grafted colloids. Compared to experimental data, we find that our coarse-grained model correctly predicts the equilibrium structure and melting temperature of the formed solids. Due to limited experimental information on the persistence length of single-stranded DNA, some quantitative discrepancies are found in the prediction of spatial quantities. With the availability of better experimental data, the present approach provides a path for the rational design of DNA-functionalised building blocks that can self-assemble into complex, three-dimensional structures.

Developments in understanding and controlling self assembly of DNA-functionalized colloids

In this article we review the latest achievements in understanding and controlling DNA-mediated interactions between colloidal particles. We report the results of experiments, theoretical studies and computer simulations designed to investigate interactions and aggregation/melting behaviour of DNA-functionalized colloids. The unprecedented insight into the physical effects influencing the interactions and their relation with the tunable parameters of the grafted DNA has resulted in innovative DNA coatings, which are expected to solve the decennial issues encountered in the self assembly of DNA-coated colloids.

Kinetics and non-exponential binding of DNA-coated colloids

Transient bridges of DNA have been used to direct the self-assembly of colloidal particles into interesting soft materials, but the particle binding kinetics are often slow or anomalous. Using line optical tweezers, we quantify the dynamics of two DNA-coated microspheres as a function of DNA density and strength of the DNA-induced pair interaction potential. At high DNA density, the binding kinetics is limited by the rate of microsphere diffusion and displays the expected dependence on the interaction potential energy. At low DNA density, the particle binding kinetics is set by single molecular binding events and exhibits bound times having a non-exponential distribution, suggesting that individual DNA bridges may also have intrinsic non-exponential kinetics. A dynamic model that includes such dispersion in the lifetimes of molecular bridges reproduces our observations, while an alternative model based on fluctuations in DNA density does not.

Arrested demixing opens route to bigels

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials--bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

A general theory of DNA-mediated and other valence-limited colloidal interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC.

Re-entrant melting as a design principle for DNA-coated colloids

Colloids functionalized with DNA hold great promise as building blocks for complex self-assembling structures. However, the practical use of DNA-coated colloids (DNACCs) has been limited by the narrowness of the temperature window where the target structures are both thermodynamically stable and kinetically accessible. Here we propose a strategy to design DNACCs, whereby the colloidal suspensions crystallize on cooling and then melt on further cooling. In a phase diagram with such a re-entrant melting, kinetic trapping of the system in non-target structures should be strongly suppressed. We present model calculations and simulations that show that real DNA sequences exist that should bestow this unusual phase behaviour on suitably functionalized colloidal suspensions. We present our results for binary systems, but the concepts that we develop apply to multicomponent systems and should therefore open the way towards the design of truly complex self-assembling colloidal structures.

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

DNA-coated colloids have great potential for the design of complex self-assembling materials. In order to predict the structures that will form, knowledge of the interactions between DNA-functionalized particles is crucial. Here, we report results from Monte Carlo simulations of the pair-interaction between particles coated with single-stranded DNA sticky ends that are connected to the surface by relatively short and stiff surface tethers. We complement our calculations with a study of the interaction between two planar surfaces coated with the same DNA. Based on our simulations we propose analytical expressions for the interaction potentials. These analytical expressions describe the DNA-mediated interactions well for particle sizes ranging from tens of nanometers to a few micrometers and for a wide range of grafting densities. We find that important contributions to both the repulsive and attractive parts of the free energy come from purely entropic effects of the discrete tethered sticky ends. Per bond, these entropic contributions have a magnitude similar to the hybridization free energy of a free pair of sticky ends in solution and they can thus considerably change the effective sticky-end binding strength. Based on the calculated interaction potentials, we expect that stable gas-liquid separation only occurs for particles with radii smaller than a few tens of nanometers, which suggests that nanoparticles and micrometer-sized colloids will follow different routes to crystallization. Finally, we note that the natural statistical nonuniformities in the surface distribution of sticky ends lead to large variations in the binding strength. This phenomenon may compromise the reliability of tests that aim to detect specific DNA targets in diagnostics. In addition to guiding the design of novel self-assembling materials and gene-detection assays, the insights presented here could also shed more light on (multivalent) interactions in other systems with tethered binding groups, for instance in the areas of supramolecular chemistry or ligand-receptor mediated biorecognition.