Nanocrystal Assemblies: Current Advances and Open Problems.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Membrane Adhesion through Bridging by Multimeric Ligands.

Ligand/receptor multivalent interactions have been exploited to drive self-assembly of nanoparticles, hard colloids, and, more recently, compliant units including emulsion droplets and lipid vesicles. In deformable liposomes, formation of links between two membranes produces morphological changes depending on the amount of ligands in the environment. Here, we study a proof-of-concept biosensing system in which single lipid vesicles adhere to a flat supported lipid bilayer, both decorated with membrane-anchored biotinylated receptors. Adhesion is driven by multivalent streptavidin (SA) ligands forming bridges between the vesicles and the supported bilayer. Upon changing the concentration of ligands, we characterize the morphological and mechanical changes of the vesicles, including the formation of a stable adhesion patch, membrane tension, and the kinetics of bridge rupture/formation. We observe vesicle binding only within a specific range of ligand concentrations: adhesion does not occur if the amount of SA is either too low or too high. A theoretical model is presented, elucidating the mechanism underlying this observation, particularly, the role of SA multivalency in determining the onset of adhesion. We elaborate on how the behavior of membranes studied here could be exploited in next-generation (bio)molecular analytical devices.

Communication: Free energy of ligand-receptor systems forming multimeric complexes.

Ligand-receptor interactions are ubiquitous in biology and have become popular in materials in view of their applications to programmable self-assembly. Although complex functionalities often emerge from the simultaneous interaction of more than just two linker molecules, state of the art theoretical frameworks enable the calculation of the free energy only in systems featuring one-to-one ligand/receptor binding. In this Communication, we derive a general formula to calculate the free energy of systems featuring simultaneous direct interaction between an arbitrary number of linkers. To exemplify the potential and generality of our approach, we apply it to the systems recently introduced by Parolini et al. [ACS Nano 10, 2392 (2016)] and Halverson and Tkachenko [J. Chem. Phys. 144, 094903 (2016)], both featuring functionalized Brownian particles interacting via three-linker complexes.

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.

Controlling Self-Assembly Kinetics of DNA-Functionalized Liposomes Using Toehold Exchange Mechanism.

The selectivity of Watson-Crick base pairing has allowed the design of DNA-based functional materials bearing an unprecedented level of accuracy. Examples include DNA origami, made of tiles assembling into arbitrarily complex shapes, and DNA coated particles featuring rich phase behaviors. Frequently, the realization of conceptual DNA-nanotechnology designs has been hampered by the lack of strategies for effectively controlling relaxations. In this article, we address the problem of kinetic control on DNA-mediated interactions between Brownian objects. We design a kinetic pathway based on toehold-exchange mechanisms that enables rearrangement of DNA bonds without the need for thermal denaturation, and test it on suspensions of DNA-functionalized liposomes, demonstrating tunability of aggregation rates over more than 1 order of magnitude. While the possibility to design complex phase behaviors using DNA as a glue is already well recognized, our results demonstrate control also over the kinetics of such systems.

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.

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.

Effect of inert tails on the thermodynamics of DNA hybridization.

The selective hybridization of DNA is of key importance for many practical applications such as gene detection and DNA-mediated self-assembly. These applications require a quantitative prediction of the hybridization free energy. Existing methods ignore the effects of non-complementary ssDNA tails beyond the first unpaired base. We use experiments and simulations to show that the binding strength of complementary ssDNA oligomers is altered by these sequences of non-complementary nucleotides. Even a small number of non-binding bases are enough to raise the hybridization free energy by approximately 1 kcal/mol at physiological salt concentrations. We propose a simple analytical expression that accounts quantitatively for this variation as a function of tail length and salt concentration.

Designing stimulus-sensitive colloidal walkers.

Colloidal particles with DNA "legs" that can bind reversibly to receptors on a surface can be made to 'walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how controllable parameters, e.g. coating density and binding strength, affect the dynamics of such colloids. We find that competition between thermodynamic and kinetic trends imply that there is an optimal value for both the binding strength and the number of "legs" for which transport is the fastest. Using available thermodynamic data on DNA binding, we indicate how directionally reversible, temperature-controlled transport of colloidal walkers can be achieved. In particular, the present results should make it possible to design a chromatographic technique that can be used to separate colloids with different DNA functionalizations.

Superselective targeting using multivalent polymers.

Despite their importance for material and life sciences, multivalent interactions between polymers and surfaces remain poorly understood. Combining recent achievements of synthetic chemistry and surface characterization, we have developed a well-defined and highly specific model system based on host/guest interactions. We use this model to study the binding of hyaluronic acid functionalized with host molecules to tunable surfaces displaying different densities of guest molecules. Remarkably, we find that the surface density of bound polymer increases faster than linearly with the surface density of binding sites. Based on predictions from a simple analytical model, we propose that this superselective behavior arises from a combination of enthalpic and entropic effects upon binding of nanoobjects to surfaces, accentuated by the ability of polymer chains to interpenetrate.

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.

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.

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.