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

Amphiphilic DNA nanostructures for bottom-up synthetic biology

DNA nanotechnology enables the construction of sophisticated biomimetic nanomachines that are increasingly central to the growing efforts of creating complex cell-like entities from the bottom-up. DNA nanostructures have been proposed as both structural and functional elements of these artificial cells, and in many instances are decorated with hydrophobic moieties to enable interfacing with synthetic lipid bilayers or regulating bulk self-organisation. In this feature article we review recent efforts to design biomimetic membrane-anchored DNA nanostructures capable of imparting complex functionalities to cell-like objects, such as regulated adhesion, tissue formation, communication and transport. We then discuss the ability of hydrophobic modifications to enable the self-assembly of DNA-based nanostructured frameworks with prescribed morphology and functionality, and explore the relevance of these novel materials for artificial cell science and beyond. Finally, we comment on the yet mostly unexpressed potential of amphiphilic DNA-nanotechnology as a complete toolbox for bottom-up synthetic biology - a figurative and literal scaffold upon which the next generation of synthetic cells could be built.

Statistical physics of DNA hybridization

Deoxyribonucleic acid (DNA) hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number N of strings and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N→∞) of our description, which provides a full justification for the extra entropic contribution that in classic hybridization modeling was required to correctly describe within the same framework the melting of sequences either self-complementary or not. We thus provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.

Adaptable DNA interactions regulate surface triggered self assembly

DNA-mediated multivalent interactions between colloidal particles have been extensively applied for their ability to program bulk phase behaviour and dynamic processes. Exploiting the competition between different types of DNA-DNA bonds, here we experimentally demonstrate the selective triggering of colloidal self-assembly in the presence of a functionalised surface, which induces changes in particle-particle interactions. Besides its relevance to the manufacturing of layered materials with controlled thickness, the intrinsic signal-amplification features of the proposed interaction scheme make it valuable for biosensing applications.

Combinatorial entropy behaviour leads to range selective binding in ligand-receptor interactions

From viruses to nanoparticles, constructs functionalized with multiple ligands display peculiar binding properties that only arise from multivalent effects. Using statistical mechanical modelling, we describe here how multivalency can be exploited to achieve what we dub range selectivity, that is, binding only to targets bearing a number of receptors within a specified range. We use our model to characterise the region in parameter space where one can expect range selective targeting to occur, and provide experimental support for this phenomenon. Overall, range selectivity represents a potential path to increase the targeting selectivity of multivalent constructs.

Self-assembly of finite-sized colloidal aggregates

One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures. Microfluidic platforms address this problem by loading into single droplets the exact amount of colloids entering the targeted aggregate. Using theory and simulations, in this paper, we validate a more versatile design allowing us to fabricate different types of finite-sized aggregates, including colloidal molecules or core-shell clusters, starting from finite density suspensions of isotropic colloids in bulk. In our model, interactions between particles are mediated by DNA linkers with mobile tethering points, as found in experiments using DNA oligomers tagged with hydrophobic complexes immersed into supported bilayers. By fine-tuning the strength and number of the different types of linkers, we prove the possibility of controlling the morphology of the aggregates, in particular, the valency of the molecules and the size of the core-shell clusters. In general, our design shows how multivalent interactions can lead to microphase separation under equilibrium conditions.

Self-Assembly and Crystallization of DNA-Coated Colloids via Linker-Encoded Interactions

Coating colloidal particles with DNA is a promising strategy to make functional nanoscale materials because the particles can be programmed to spontaneously self-assemble into complex, ordered structures. In this Article, we explore the phase behavior and types of structures that can be formed when interactions between DNA-coated colloids are specified by linker DNA strands dispersed in solution. We show that linker-mediated interactions direct the self-assembly of colloids into equilibrium crystal structures. Furthermore, we demonstrate how different linker sequences and concentrations produce different crystal lattices, whose symmetry and compositional order are encoded exclusively by the linker-mediated interactions. These results illustrate how linkers can be used to separate the assembly instructions, encoded in the linkers, from the colloids themselves. We also examine the phase behavior of asymmetric linkers, which bind more strongly to one colloidal species than the other. We find that asymmetry strongly influences the concentration dependence of the colloidal interactions, which we explain using a mean-field model. We also find evidence that asymmetric linkers might help to reduce kinetic bottlenecks to colloidal crystallization. Together, our findings expand the design rules of linker-mediated self-assembly and make connections between the various schemes for programming assembly of DNA-coated colloids reported in the literature.

First-order 'hyper-selective' binding transition of multivalent particles under force

Multivalent particles bind to targets via many independent ligand-receptor bonding interactions. This microscopic design spans length scales in both synthetic and biological systems. Classic examples include interactions between cells, virus binding, synthetic ligand-coated micrometer-scale vesicles or smaller nano-particles, functionalised polymers, and toxins. Equilibrium multivalent binding is a continuous yet super-selective transition with respect to the number of ligands and receptors involved in the interaction. Increasing the ligand or receptor density on the two particles leads to sharp growth in the number of bound particles at equilibrium. Here we present a theory and Monte Carlo simulations to show that applying mechanical force to multivalent particles causes their adsorption/desorption isotherm on a surface to become sharper and more selective, with respect to variation in the number of ligands and receptors on the two objects. When the force is only applied to particles bound to the surface by one or more ligands, then the transition can become infinitely sharp and first-order-a new binding regime which we term 'hyper-selective'. Force may be imposed by, e.g. flow of solvent around the particles, a magnetic field, chemical gradients, or triggered uncoiling of inert oligomers/polymers tethered to the particles to provide a steric repulsion to the surface. This physical principle is a step towards 'all or nothing' binding selectivity in the design of multivalent constructs.

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.

Kinetics of Nanoparticle-Membrane Adhesion Mediated by Multivalent Interactions

Multivalent adhesive interactions mediated by a large number of ligands and receptors underpin many biological processes, including cell adhesion and the uptake of particles, viruses, parasites, and nanomedical vectors. In materials science, multivalent interactions between colloidal particles have enabled unprecedented control over the phase behavior of self-assembled materials. Theoretical and experimental studies have pinpointed the relationship between equilibrium states and microscopic system parameters such as the ligand-receptor binding strength and their density. In regimes of strong interactions, however, kinetic factors are expected to slow down equilibration and lead to the emergence of long-lived out-of-equilibrium states that may significantly influence the outcome of self-assembly experiments and the adhesion of particles to biological membranes. Here we experimentally investigate the kinetics of adhesion of nanoparticles to biomimetic lipid membranes. Multivalent interactions are reproduced by strongly interacting DNA constructs, playing the role of both ligands and receptors. The rate of nanoparticle adhesion is investigated as a function of the surface density of membrane-anchored receptors and the bulk concentration of nanoparticles and is observed to decrease substantially in regimes where the number of available receptors is limited compared to the overall number of ligands. We attribute such peculiar behavior to the rapid sequestration of available receptors after initial nanoparticle adsorption. The experimental trends and the proposed interpretation are supported by numerical simulations.

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.

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.

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.