The role of multivalency in the association kinetics of patchy particle complexes

A quantitative view on multivalent nanomedicine targeting

Although the concept of selective delivery has been postulated over 100 years ago, no targeted nanomedicine has been clinically approved so far. Nanoparticles modified with targeting ligands to promote the selective delivery of therapeutics towards a specific cell population have been extensively reported. However, the rational design of selective particles is still challenging. One of the main reasons for this is the lack of quantitative theoretical and experimental understanding of the interactions involved in cell targeting. In this review, we discuss new theoretical models and experimental methods that provide a quantitative view of targeting. We show the new advancements in multivalency theory enabling the rational design of super-selective nanoparticles. Furthermore, we present the innovative approaches to obtain key targeting parameters at the single-cell and single molecule level and their role in the design of targeting nanoparticles. We believe that the combination of new theoretical multivalent design and experimental methods to quantify receptors and ligands aids in the rational design and clinical translation of targeted nanomedicines.

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.

Multivalent Patchy Colloids for Quantitative 3D Self-Assembly Studies

We report methods to synthesize sub-micron- and micron-sized patchy silica particles with fluorescently labeled hemispherical titania protrusions, as well as routes to efficiently characterize these particles and self-assemble these particles into non-close-packed structures. The synthesis methods expand upon earlier work in the literature, in which silica particles packed in a colloidal crystal were surface-patterned with a silane coupling agent. Here, hemispherical amorphous titania protrusions were successfully labeled with fluorescent dyes, allowing for imaging by confocal microscopy and super-resolution techniques. Confocal microscopy was exploited to experimentally determine the numbers of protrusions per particle over large numbers of particles for good statistical significance, and these distributions were compared to simulations predicting the number of patches as a function of core particle polydispersity and maximum separation between the particle surfaces. We self-assembled these patchy particles into open percolating gel networks by exploiting solvophobic attractions between the protrusions.

A stochastic view on surface inhomogeneity of nanoparticles

The interactions between and with nanostructures can only be fully understood when the functional group distribution on their surfaces can be quantified accurately. Here we apply a combination of direct stochastic optical reconstruction microscopy (dSTORM) imaging and probabilistic modelling to analyse molecular distributions on spherical nanoparticles. The properties of individual fluorophores are assessed and incorporated into a model for the dSTORM imaging process. Using this tailored model, overcounting artefacts are greatly reduced and the locations of dye labels can be accurately estimated, revealing their spatial distribution. We show that standard chemical protocols for dye attachment lead to inhomogeneous functionalization in the case of ubiquitous polystyrene nanoparticles. Moreover, we demonstrate that stochastic fluctuations result in large variability of the local group density between particles. These results cast doubt on the uniform surface coverage commonly assumed in the creation of amorphous functional nanoparticles and expose a striking difference between the average population and individual nanoparticle coverage.

Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression

To predict the response of a biochemical system, knowledge of the intrinsic and effective rate constants of proteins is crucial. The experimentally accessible effective rate constant for association can be decomposed in a diffusion-limited rate at which proteins come into contact and an intrinsic association rate at which the proteins in contact truly bind. Reversely, when dissociating, bound proteins first separate into a contact pair with an intrinsic dissociation rate, before moving away by diffusion. While microscopic expressions exist that enable the calculation of the intrinsic and effective rate constants by conducting a single rare event simulation of the protein dissociation reaction, these expressions are only valid when the substrate has just one binding site. If the substrate has multiple binding sites, a bound enzyme can, besides dissociating into the bulk, also hop to another binding site. Calculating transition rate constants between multiple states with forward flux sampling requires a generalized rate expression. We present this expression here and use it to derive explicit expressions for all intrinsic and effective rate constants involving binding to multiple states, including rebinding. We illustrate our approach by computing the intrinsic and effective association, dissociation, and hopping rate constants for a system in which a patchy particle model enzyme binds to a substrate with two binding sites. We find that these rate constants increase as a function of the rotational diffusion constant of the particles. The hopping rate constant decreases as a function of the distance between the binding sites. Finally, we find that blocking one of the binding sites enhances both association and dissociation rate constants. Our approach and results are important for understanding and modeling association reactions in enzyme-substrate systems and other patchy particle systems and open the way for large multiscale simulations of such systems.

The magnitude of the intrinsic rate constant: How deep can association reactions be in the diffusion limited regime?

Intrinsic and effective rate constants have an important role in the theory of diffusion-limited reactions. In a previous paper, we provide detailed microscopic expressions for these intrinsic rates [A. Vijaykumar, P. G. Bolhuis, and P. R. ten Wolde, Faraday Discuss. 195, 421 (2016)], which are usually considered as abstract quantities and assumed to be implicitly known. Using these microscopic expressions, we investigate how the rate of association depends on the strength and the range of the isotropic potential and the strength of the non-specific attraction in case of the anisotropic potential. In addition, we determine the location of the interface where these expressions become valid for anisotropic potentials. In particular, by investigating the particles' orientational distributions, we verify whether the interface at which these distributions become isotropic agrees with the interface predicted by the effective association rate constant. Finally, we discuss how large the intrinsic association rate can become, and what are the consequences for the existence of the diffusion limited regime.