Communication: Simple approach for calculating the binding free energy of a multivalent particle

Biophysical Considerations in the Rational Design and Cellular Targeting of Flexible Polymeric Nanoparticles

How nanoparticle (NP) mechanical properties impact multivalent ligand-receptor-mediated binding to cell surfaces, the avidity, propensity for internalization, and effects due to crowding remains unknown or unquantified. Through computational analyses, the effects of NP composition from soft, deformable NPs to rigid spheres, effect of tethers, the crowding of NPs at the membrane surface, and the cell membrane properties such as cytoskeletal interactions are addressed. Analyses of binding mechanisms of three distinct NPs that differ in type and rigidity (core-corona flexible NP, rigid NP, and rigid-tethered NP) but are otherwise similar in size and ligand surface density are reported; moreover, for the case of flexible NP, NP stiffness is tuned by varying the internal crosslinking density. Biophysical modeling of NP binding to membranes together with thermodynamic analysis powered by free energy calculations is employed, and it is shown that efficient cellular targeting and uptake of NP functionalized with targeting ligand molecules can be shaped by factors including NP flexibility and crowding, receptor-ligand binding avidity, state of the membrane cytoskeleton, and curvature inducing proteins. Rational design principles that confer tension, membrane excess area, and cytoskeletal sensing properties to the NP which can be exploited for cell-specific targeting of NP are uncovered.

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.

Multiscale modeling of protein membrane interactions for nanoparticle targeting in drug delivery

Nanoparticle (NP)-based imaging and drug delivery systems for systemic (e.g. intravenous) therapeutic and diagnostic applications are inherently a complex integration of biology and engineering. A broad range of length and time scales are essential to hydrodynamic and microscopic molecular interactions mediating NP (drug nanocarriers, imaging agents) motion in blood flow, cell binding/uptake, and tissue accumulation. A computational model of time-dependent tissue delivery, providing in silico prediction of organ-specific accumulation of NPs, can be leveraged in NP design and clinical applications. In this article, we provide the current state-of-the-art and future outlook for the development of predictive models for NP transport, targeting, and distribution through the integration of new computational schemes rooted in statistical mechanics and transport. The resulting multiscale model will comprehensively incorporate: (i) hydrodynamic interactions in the vascular scales relevant to NP margination; (ii) physical and mechanical forces defining cellular and tissue architecture and epitope accessibility mediating NP adhesion; and (iii) subcellular and paracellular interactions including molecular-level targeting impacting NP uptake.

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.

Linker-mediated self-assembly of mobile DNA-coated colloids

Developing construction methods of materials tailored for given applications with absolute control over building block placement poses an immense challenge. DNA-coated colloids offer the possibility of realising programmable self-assembly, which, in principle, can assemble almost any structure in equilibrium, but remains challenging experimentally. Here, we propose an innovative system of linker-mediated mobile DNA-coated colloids (mDNACCs), in which mDNACCs are bridged by the free DNA linkers in solution, whose two single-stranded DNA tails can bind with specific single-stranded DNA receptors of complementary sequence coated on colloids. We formulate a mean-field theory efficiently calculating the effective interaction between mDNACCs, where the entropy of DNA linkers plays a nontrivial role. Particularly, when the binding between free DNA linkers in solution and the corresponding receptors on mDNACCs is strong, the linker-mediated colloidal interaction is determined by the linker entropy depending on the linker concentration.

Computational design of probes to detect bacterial genomes by multivalent binding

Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety.

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.

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.

Multivalent Binding of a Ligand-Coated Particle: Role of Shape, Size, and Ligand Heterogeneity

We utilize a multiscale modeling framework to study the effect of shape, size, and ligand composition on the efficacy of binding of a ligand-coated particle to a substrate functionalized with the target receptors. First, we show how molecular dynamics along with steered molecular dynamics calculations can be used to accurately parameterize the molecular-binding free energy and the effective spring constant for a receptor-ligand pair. We demonstrate this for two ligands that bind to the α₅β₁-domain of integrin. Next, we show how these effective potentials can be used to build computational models at the meso- and continuum-scales. These models incorporate the molecular nature of the receptor-ligand interactions and yet provide an inexpensive route to study the multivalent interaction of receptors and ligands through the construction of Bell potentials customized to the molecular identities. We quantify the binding efficacy of the ligand-coated-particle in terms of its multivalency, binding free-energy landscape, and the losses in the configurational entropies. We show that 1) the binding avidity for particle sizes less than 350 nm is set by the competition between the enthalpic and entropic contributions, whereas that for sizes above 350 nm is dominated by the enthalpy of binding; 2) anisotropic particles display higher levels of multivalent binding compared to those of spherical particles; and 3) variations in ligand composition can alter binding avidity without altering the average multivalency. The methods and results presented here have wide applications in the rational design of functionalized carriers and also in understanding cell adhesion.

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.