Multivalent weak interactions enhance selectivity of interparticle binding

Abstract

Targeted drug delivery critically depends on the binding selectivity of cargo-transporting colloidal particles. Extensive theoretical work has shown that two factors are necessary to achieve high selectivity for a threshold receptor density: multivalency and weak interactions. Here, we study a model system of DNA-coated particles with multivalent and weak interactions that mimics ligand-receptor interactions between particles and cells. Using an optomagnetic cluster experiment, particle aggregation rates are measured as a function of ligand and receptor densities. The measured aggregation rates show that the binding becomes more selective for shorter DNA ligand-receptor pairs, proving that multivalent weak interactions lead to enhanced selectivity in interparticle binding. Simulations confirm the experimental findings and show the role of ligand-receptor dissociation in the selectivity of the weak multivalent binding.

Keywords: multivalency; particles; selectivity.

Fig. 1.

Particle–particle interaction mimics cell–particle interactions. (A) Multivalent binding of a ligand-coated particle to receptors on a cell membrane. (B) Ligand particles are coated with short DNA constructs with a single-stranded overhang, called ligand DNA. Receptor particles are coated with short DNA constructs with a complementary single-stranded overhang, called receptor DNA. The overhang complementarity determines the strength of the ligand–receptor interaction. Filler double-stranded DNA strands, without single-stranded overhang, are inserted to maintain a constant surface charge density. (C) The aggregation rate is measured as a function of the receptor density, for a constant ligand density. Weaker interactions, with fewer complementary nucleotides in the single-stranded overhang of the receptor strand, cause a higher selectivity of interparticle binding. (D) The selectivity parameter α is calculated from the dependence of aggregation rate on receptor density. Weak multivalent interactions yield enhanced selectivity compared to strong multivalent interactions.

Fig. 2.

Aggregation rate as a function of receptor density (σ_R), ligand density (σ_L) and ligand–receptor affinity (bp): (A) 15-bp, (B) 12-bp, (C) 9-bp, (D) 8-bp, (E) 7-bp, and (F) 5-bp complementary between ligand and receptor.

Fig. 3.

Enhanced selectivity for weak multivalent interactions. (A) Measured aggregation rates as a function of receptor density for a constant ligand density of σ_L = (2.2 ± 0.5) 10⁴ μm⁻² for all interaction strengths. Left of the dotted line, on average less than one receptor is present in the interaction area; to the right of the dotted line, on average more than one receptor is present. The 15-, 12-, and 9-bp data are fitted with an exponential function and the 8-, 7-, and 5-bp data are fitted with a sigmoidal function. Details about the fitting can be found in SI Appendix, section S4. (B) Calculated selectivity parameter using Eq. 2, with the fit parameters obtained from A. The weak ligand–receptor interactions (5/7/8 bp) yield an enhanced selectivity compared to the strong ligand–receptor interactions (9/12/15 bp).

Fig. 4.

Simulation results compared to experimental data. (A) Experimental data points accompanied by simulated aggregation rate curves for an interparticle distance Δx = 4 nm and a ligand–receptor binding rate k_LR = 10⁻⁴ μm²s⁻¹. The experimental data of the 15-, 12-, and 9-bp DNA is averaged as these data are very similar. Simulated aggregation rate curves for the other combinations of Δx and k_LR are shown in SI Appendix, Fig. S8. (B) Heat map showing the possible combinations of Δx and k_LR for which the simulation reproduces the experimental data. Small interparticle distance and high ligand receptor binding rates lead to a match between simulation and experiment. The red dot shows the specific combination of Δx and k_LR for the simulation curves in A.