The sliding motility of the bacilliform virions of Influenza A viruses.

Influenza A virus (IAV) infection relies on the action of the hemagglutinin (HA) and neuraminidase (NA) membrane proteins. The HA ligands anchor the IAV virion to the cell's surface by binding the sialic acid (SA) present on the host's receptors while NA is an enzyme capable of cleaving the SA from the extracellular environment. It is believed that the activity of NA ligands increases the motility of the virions favoring the propagation of the infection. In this work, we develop a numerical framework to study the dynamics of a virion moving across the cell surface for timescales much bigger than the typical ligand-receptor reaction times. We find that the rates controlling the ligand-receptor reactions and the maximal distance at which a pair of ligand-receptor molecules can interact greatly affect the motility of the virions. We also report on how different ways of organizing the two types of ligands on the virions' surface result in different types of motion that we rationalize using general principles. In particular, we show how the emerging motility of the virion is less sensitive to the rate controlling the enzymatic activity when NA ligands are clustered.

DNA-Origami Line-Actants Control Domain Organization and Fission in Synthetic Membranes.

Cells can precisely program the shape and lateral organization of their membranes using protein machinery. Aiming to replicate a comparable degree of control, here we introduce DNA-origami line-actants (DOLAs) as synthetic analogues of membrane-sculpting proteins. DOLAs are designed to selectively accumulate at the line-interface between coexisting domains in phase-separated lipid membranes, modulating the tendency of the domains to coalesce. With experiments and coarse-grained simulations, we demonstrate that DOLAs can reversibly stabilize two-dimensional analogues of Pickering emulsions on synthetic giant liposomes, enabling dynamic programming of membrane lateral organization. The control afforded over membrane structure by DOLAs extends to three-dimensional morphology, as exemplified by a proof-of-concept synthetic pathway leading to vesicle fission. With DOLAs we lay the foundations for mimicking, in synthetic systems, some of the critical membrane-hosted functionalities of biological cells, including signaling, trafficking, sensing, and division.

Sliding across a surface: Particles with fixed and mobile ligands.

A quantitative model of the mobility of ligand-presenting particles at the interface is pivotal to understanding important systems in biology and nanotechnology. In this work, we investigate the emerging dynamics of particles featuring ligands that selectively bind receptors decorating an interface. The formation of a ligand-receptor complex leads to a molecular bridge anchoring the particle to the surface. We consider systems with reversible bridges in which ligand-receptor pairs bind/unbind with finite reaction rates. For a given set of bridges, the particle can explore a tiny fraction of the surface as the extensivity of the bridges is finite. We show how, at timescales longer than the bridges' lifetime, the average position of the particle diffuses away from its initial value. We distill our findings into two analytic equations for the sliding diffusion constant of particles carrying mobile and fixed ligands. We quantitatively validate our theoretical predictions using reaction-diffusion simulations. We compare our findings with results from recent literature studies and discuss the molecular parameters that likely affect the particle's mobility most. Our results, along with recent literature studies, will allow inferring the microscopic parameters at play in complex biological systems from experimental trajectories.

Unfolding of the chromatin fiber driven by overexpression of noninteracting bridging factors.

Nuclear molecules control the functional properties of the chromatin fiber by shaping its morphological properties. The biophysical mechanisms controlling how bridging molecules compactify chromatin are a matter of debate. On the one side, bridging molecules could cross-link faraway sites and fold the fiber through the formation of loops. Interacting bridging molecules could also mediate long-range attractions by first tagging different locations of the fiber and then undergoing microphase separation. Using a coarse-grained model and Monte Carlo simulations, we study the conditions leading to compact configurations both for interacting and noninteracting bridging molecules. In the second case, we report on an unfolding transition at high densities of the bridging molecules. We clarify how this transition, which disappears for interacting bridging molecules, is universal and controlled by entropic terms. In general, chains are more compact in the case of interacting bridging molecules because interactions are not valence limited. However, this result is conditional on the ability of our simulation methodology to relax the system toward its ground state. In particular, we clarify how, unless using reaction dynamics that change the length of a loop in a single step, the system is prone to remain trapped in metastable, compact configurations featuring long loops.

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.

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.

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.

Surface-triggered cascade reactions between DNA linkers direct the self-assembly of colloidal crystals of controllable thickness.

Functionalizing colloids with reactive DNA linkers is a versatile way of programming self-assembly. DNA selectivity provides direct control over colloid-colloid interactions allowing the engineering of structures such as complex crystals or gels. However, the self-assembly of localized and finite structures remains an open problem with many potential applications. In this work, we present a system in which functionalized surfaces initiate a cascade reaction between linkers leading to the self-assembly of crystals with a controllable number of layers. Specifically, we consider colloidal particles functionalized by two families of complementary DNA linkers with mobile anchoring points, as found in experiments using emulsions or lipid bilayers. In bulk, intra-particle linkages formed by pairs of complementary linkers prevent the formation of inter-particle bridges and therefore colloid-colloid aggregation. However, colloids interact strongly with the surface given that the latter can destabilize intra-particle linkages. When in direct contact with the surface, colloids are activated, meaning that they feature more unpaired DNA linkers ready to react. Activated colloids can then capture and activate other colloids from the bulk through the formation of inter-particle linkages. Using simulations and theory, validated by existing experiments, we clarify the thermodynamics of the activation and binding process and explain how particle-particle interactions, within the adsorbed phase, weaken as a function of the distance from the surface. The latter observation underlies the possibility of self-assembling finite aggregates with controllable thickness and flat solid-gas interfaces. Our design suggests a new avenue to fabricate heterogeneous and finite structures.

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.

Translational and rotational dynamics of colloidal particles interacting through reacting linkers.

Much work has studied effective interactions between micron-sized particles carrying linkers forming reversible, interparticle linkages. These studies allowed understanding the equilibrium properties of colloids interacting through ligand-receptor interactions. Nevertheless, understanding the kinetics of multivalent interactions remains an open problem. Here, we study how molecular details of the linkers, such as the reaction rates at which interparticle linkages form or break, affect the relative dynamics of pairs of cross-linked colloids. Using a simulation method tracking single binding and unbinding events between complementary linkers, we rationalize recent experiments and prove that particles' interfaces can move across each other while being cross-linked. We clarify how, starting from diffusing colloids, the dynamics become arrested when increasing the number of interparticle linkages or decreasing the reaction rates. Before getting arrested, particles diffuse through rolling motion. The ability to detect rolling motion will be useful to shed new light on host-pathogen interactions.

Efficient sampling of reversible cross-linking polymers: Self-assembly of single-chain polymeric nanoparticles.

We present a new simulation technique to study systems of polymers functionalized by reactive sites that bind/unbind forming reversible linkages. Functionalized polymers feature self-assembly and responsive properties that are unmatched by the systems lacking selective interactions. The scales at which the functional properties of these materials emerge are difficult to model, especially in the reversible regime where such properties result from many binding/unbinding events. This difficulty is related to large entropic barriers associated with the formation of intra-molecular loops. In this work, we present a simulation scheme that sidesteps configurational costs by dedicated Monte Carlo moves capable of binding/unbinding reactive sites in a single step. Cross-linking reactions are implemented by trial moves that reconstruct chain sections attempting, at the same time, a dimerization reaction between pairs of reactive sites. The model is parametrized by the reaction equilibrium constant of the reactive species free in solution. This quantity can be obtained by means of experiments or atomistic/quantum simulations. We use the proposed methodology to study the self-assembly of single-chain polymeric nanoparticles, starting from flexible precursors carrying regularly or randomly distributed reactive sites. We focus on understanding differences in the morphology of chain nanoparticles when linkages are reversible as compared to the well-studied case of irreversible reactions. Intriguingly, we find that the size of regularly functionalized chains, in good solvent conditions, is non-monotonous as a function of the degree of functionalization. We clarify how this result follows from excluded volume interactions and is peculiar of reversible linkages and regular functionalizations.

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.

Two-parameter model predictions and theta-point crossover for linear-polymer solutions.

We consider the first few virial coefficients of the osmotic pressure, the radius of gyration, the hydrodynamic radius, and the end-to-end distance for a monodisperse polymer solution. We determine the corresponding two-parameter model functions which parametrize the crossover between the good-solvent and the ideal-chain behavior. These results allow us to predict the osmotic pressure and the polymer size in the dilute regime in a large temperature region above the theta point.

Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions.

We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure Pi 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.

Polymer size in dilute solutions in the good-solvent regime.

We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of polymerization), including the leading scaling corrections. Using the expected large-concentration behavior, we extrapolate these low-density expansions outside the dilute regime, obtaining a prediction for the radii for any concentration in the semidilute region. For the radius of gyration, comparison with field-theoretical predictions shows that the relative error should be at most 5% in the limit of very large polymer concentrations.