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.

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.

Recent studies aimed at investigating artificial analogues of bacterial colonies have shown that lowdensity suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have a typical size that remains constant (living clusters). In this Letter we address the problem of the formation of living clusters and crystals of active particles in three dimensions. We study two systems: self-propelled particles interacting via a generic attractive potential and colloids that can move towards each other as a result of active agents (e.g. by molecular motors). In both cases fluid-like 'living' clusters form. We explain this general feature in terms of the balance between active forces and regression to thermodynamic equilibrium. This balance can be quantified in terms of a dimensionless number that allows us to collapse the observed clustering behaviour onto a universal curve. We also discuss how active motion affects the kinetics of crystal formation. PACS numbers:Active systems consume energy that keeps them in an out-of-equilibrium state [1,2]. This is typical for many biologically relevant systems which, by exploiting chemical energy, can self-organise into complex structures that lack any equilibrium counterpart. Examples are abundant and exist at different length-scales: from cytoskeleton remodulation during cell mitosis [3] to swarming phenomena in micro-swimmers or flocks of birds [4,5]. The similarity of the patterns displayed by these systems lead many to address the general principles behind their formation using simple models [6]. The reproducibility and robustness of the phenomena under a variety of external conditions motivated a large body of research on selfassembly of active particle as a possible strategy towards the fabrication of new functional nano-and mesoscopic structures [7]. In this respect there have been several efforts to study active self-organisation in a tightly controlled environment; the most studied systems being selfpropelled particles [6,[8][9][10][11] and active gels (e.g. [12]).Recently, two experimental groups have shown how two-dimensional suspensions of self-propelled (SP) colloids (moving through the consumption of an appropriate 'fuel') self-assemble into dynamic clusters that constantly join and split, recombining with each other to reach a steady-state [13,14]. A general understanding of active cluster formation is lacking, but different explanations have been proposed. The authors of Ref.[13] argued that a net attraction between colloids is responsible for clustering. This attraction is due to non-uniformity in the chemical fuel concentration between two colloids. This was confirmed by Ref. [14], that also found a 1/d 2 dependence of the particle-particle attraction ( d being the inter-particle distance). The formation of finite-size clusters has been also observed in low density bacteria/polymer suspensions, at intermediate polymer concentrations just before phase separation [10]. However, in other recent studi...

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.

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.

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 singlestranded 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.

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.

We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure Π of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we extrapolate the low-density expansion outside the dilute regime, obtaining the osmotic pressure for any concentration in the semidilute region.Comparison with field-theoretical predictions and experimental data shows that the obtained expression is quite accurate. The error is approximately 1-2% below the overlap concentration and rises at most to 5-10% in the limit of very large polymer concentrations.