A new configurational bias scheme for sampling supramolecular structures

Simulating sticky particles: A Monte Carlo method to sample a stratification

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.

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.

On the interpretation of kinetics and thermodynamics probed by single-molecule experiments

Single-molecule pulling experiments are widely used to extract both thermodynamic and kinetic data on ligand-receptor pairs, typically by fitting different models to the probability distribution of rupture forces of the corresponding bond. Here, a theoretical model is presented that shows how a measurement of the number of binding and unbinding events as a function of the observation time can also give access to both the binding (kon) and the unbinding (koff) rates of bonds, which combined provide a well-defined bond free-energy ΔGbond. The connection between ΔGbond and the ligand-receptor binding constant measured by typical binding essays is critically discussed. The role played by the molecular construct used to tether ligands and receptors to a surface is considered, highlighting the various approximations necessary to derive general expressions that connect its structure to its contribution, termed ΔGcnf, to the bond free-energy. In this way, the validity and the assumptions underpinning widely employed formulas and experimental protocols used to extract binding constants from single-molecule experiments are assessed. Finally, the role of ΔGcnf in processes mediated by ligand-receptor binding is briefly considered, and an experiment to unambiguously measure this quantity proposed.

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.

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.

Influence of Linker Flexibility on the Binding Affinity of Bidentate Binders

The design of responsive nanosensors typically relies on the availability of probes capable of capturing their target with high affinity and specificity. This can be achieved by coupling two or more binding units through a linker. In this work, we study the dependence on the binder architecture of the binding affinity between a target molecule and a semirigid bidentate binder. Using two different binder architectures, central-rigid and extreme-rigid, and modifying the length and the flexibility degree of the linker we generated 153 different architectures. We computed their dissociation free energies by means of Monte Carlo simulations and thermodynamic integration. We found that central-rigid bidentate binders are a poor choice, as they dissociate more easily than analogous fully flexible bidentate binders. On the other hand, molecular architectures presenting extreme-rigid units were shown effective for a wide range of set-ups.

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.

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.

Chelating effect in short polymers for the design of bidentate binders of increased affinity and selectivity

The design of new strong and selective binders is a key step towards the development of new sensing devices and effective drugs. Both affinity and selectivity can be increased through chelation and here we theoretically explore the possibility of coupling two binders through a flexible linker. We prove the enhanced ability of double binders of keeping their target with a simple model where a polymer composed by hard spheres interacts with a spherical macromolecule, such as a protein, through two sticky spots. By Monte Carlo simulations and thermodynamic integration we show the chelating effect to hold for coupling polymers whose radius of gyration is comparable to size of the chelated particle. We show the binding free energy of flexible double binders to be higher than that of two single binders and to be maximized when the binding sites are at distances comparable to the mean free polymer end-to-end distance. The affinity of two coupled binders is therefore predicted to increase non linearly and in turn, by targeting two non-equivalent binding sites, this will lead to higher selectivity.