Evolution of Multivalent Nanoparticle Adhesion via Specific Molecular Interactions

Abstract

The targeted delivery of nanoparticle carriers holds tremendous potential to transform the detection and treatment of diseases. A major attribute of nanoparticles is the ability to form multiple bonds with target cells, which greatly improves the adhesion strength. However, the multivalent binding of nanoparticles is still poorly understood, particularly from a dynamic perspective. In previous experimental work, we studied the kinetics of nanoparticle adhesion and found that the rate of detachment decreased over time. Here, we have applied the adhesive dynamics simulation framework to investigate binding dynamics between an antibody-conjugated, 200-nm-diameter sphere and an ICAM-1-coated surface on the scale of individual bonds. We found that nano adhesive dynamics (NAD) simulations could replicate the time-varying nanoparticle detachment behavior that we observed in experiments. As expected, this behavior correlated with a steady increase in mean bond number with time, but this was attributed to bond accumulation only during the first second that nanoparticles were bound. Longer-term increases in bond number instead were manifested from nanoparticle detachment serving as a selection mechanism to eliminate nanoparticles that had randomly been confined to lower bond valencies. Thus, time-dependent nanoparticle detachment reflects an evolution of the remaining nanoparticle population toward higher overall bond valency. We also found that NAD simulations precisely matched experiments whenever mechanical force loads on bonds were high enough to directly induce rupture. These mechanical forces were in excess of 300 pN and primarily arose from the Brownian motion of the nanoparticle, but we also identified a valency-dependent contribution from bonds pulling on each other. In summary, we have achieved excellent kinetic consistency between NAD simulations and experiments, which has revealed new insights into the dynamics and biophysics of multivalent nanoparticle adhesion. In future work, we will leverage the simulation as a design tool for optimizing targeted nanoparticle agents.

Figure 1

NAD simulations of nanoparticle detachment. (A) Algorithm for detachment simulations in which nanoparticles were initiated with a single bond. (B) Schematic of the adhesion system. A 210-nm-diameter sphere was coated with monoclonal anti-ICAM-1 antibody (orange), and the substrate was coated with ICAM-1 dimers (gray). (C) Size-scaled depiction of the adhesion molecule system employed. Images are published in the Protein Data Bank: mouse IgG₁ antibody (1IGY), ICAM-1 (combination of 1IAM and 1P53), human IgG₁ Fc (3D03), and protein G (3GB1).

Figure 2

Nanoparticle and bond dynamics. (A,C) Nanoparticle detachment profiles obtained for σ = 0.1 N/m, γ = 0.72 to 1.08 nm, and low ICAM-1 density at (A) low and (C) high antibody density. Time-dependent behavior can clearly be seen at high γ, with an initial rapid decline that transitioned to a more stable regime around ∼5 s. (B,D) Mean bond number increased over time for both (B) low and (D) high antibody density conditions following a similar temporal pattern as nanoparticle detachment. Bond number increased and became more stochastic as fewer nanoparticles remained bound. (E,F) Detachment profiles were fit using eq 7 to obtain (E) β and (F) $k_{\mathrm{D}}^0$ parameters. (E) The temporal parameter β increased with γ until saturating at 0.75, which was the value measured in experiments. There was a slight shift to higher γ as antibody density increased. (F) The magnitude parameter $k_{\mathrm{D}}^0$ progressively increased with γ and decreased with antibody density regardless of β, reflecting overall nanoparticle stability.

Figure 3

Bond biophysics and dynamics. (A) Bond rupture force (F_B,_R) increased with γ before saturating around 95 pN. (B) Mechanical work at bond rupture (γF_B,_R) increased steadily with γ, surpassing the bond chemical energy (dashed line) around 0.9 nm. (C) Bond extension or compression length at rupture (δ_R) was slightly greater than γ until saturating around 0.9 nm. (D,E) Average bond (D) lifetime and (E) formation rate exhibited opposing trends as bonding became more dynamic with increased γ. (F) Mean bond number at the end of simulation (30 s) increased as adhesion became less stable, both in terms of increasing γ and decreasing antibody density. Error bars represent the standard error from 200 simulations.

Figure 4

Bond number distributions and potentials. (A, B) Bond number histograms obtained at the end of simulations (30 s) for σ = 0.1 N/m, γ = 0.72 to 1.08 nm, and a low ICAM-1 density at (A) low and (B) high antibody densities. Detached nanoparticles were categorized under 0 bonds. (C, D) Mean bond potential values as a function of time at (C) low and (D) high antibody densities. The mean bond potential represents the mean bond number determined right after the bond steady state was achieved (0.1 s) and after correcting for nanoparticles that had detached. The mean bond potential did not vary with γ but shifted from ∼1.7 to ∼1.9 with increased antibody density.

Figure 5

Mechanical state diagram. (A) Nanoparticle detachment dynamics at low antibody and medium ICAM-1 densities, assessed across a large range of γ and σ values. The transient regime (blue) corresponds to highly unstable adhesion, defined as <5% of nanoparticles remaining bound after 5 s. The static regime (brown) corresponds to highly stable adhesion, with >95% remaining bound after 5 s. The dynamic regime (red) lies in between, and the red circles indicate the mechanical property combinations that precisely matched experiments. (B) The bond rupture length (δ_R) was slightly less than γ at low F_B,R but became increasingly larger after F_B,R exceeded ∼95 pN. Teal squares denote the matching condition using γ measured with optical tweezers force spectroscopy experiments (0.27 nm) and the best fit σ (0.8 N/m).

Figure 6

Final fitting of experiments for different ICAM-1 clustering conditions. (A) Comparison of $k_{\mathrm{D}}^0$ across all antibody and ICAM-1 densities between experiments and NAD simulations conducted using the final mechanical conditions (γ = 0.27 nm, σ = 0.8 N/m). ICAM-1 was presented in three different configurations: dimers, clustered dimers, and monomers. The clustering of ICAM-1 decreased the nanoparticle stability, particularly at high ICAM-1 density. (B) The mean bond potential was highest for ICAM-1 monomers. Dimer configurations were similar at low and medium ICAM-1, but the clustered dimer surprisingly had elevated mean bond potentials at high ICAM-1. (C) Bond potential histograms for the clustered dimer case. Note the large number of nanoparticles restricted to one or two bonds at low and medium ICAM-1 densities. (D) Mean bond potential versus time for the clustered dimer case, shown only at early time points to illustrate that the bond steady state was reached before 0.1 s at low and medium ICAM-1 densities. At high ICAM-1 density, most bonds formed prior to 0.1 s, but a second, slower bond accumulation phase was also observed out to 0.5 s. (E) $k_{\mathrm{D}}^0$ and mean bond potential closely followed an exponential relationship for all molecular density and ICAM-1 clustering conditions.

Figure 7

Single-tether simulations and valence-state-dependent detachment dynamics. (A) Nanoparticles held by a single tether all detached within 1 s, with a profile that closely resembled the initial phase of rapid detachment observed for multivalent cases. (B) The bond force distribution for the single-tether simulation was nearly identical to the multivalent cases. (C) Bond rupture force distributions were similar between the single tether and low ICAM-1 density cases, but the rupture force shifted to higher values with increased valency. (D–F) Valence-state-dependent detachment dynamics. The mean bond number (black line) is shown over time at low antibody density and either (D) low, (E) medium, or (F) high ICAM-1 density. All detachment events are included in the plot and color-coded on the basis of the maximum bond number achieved: one bond (green), two bonds (orange), or three bonds (purple). The point of detachment is indicated by the triangle (△), and lines then trace back up to the time point at which that nanoparticle was at its maximum bond number, which is indicated by an upside down triangle (▽). Nanoparticles restricted to a single bond detached rapidly, most within the first few seconds. Nanoparticles that detached from the second and third bond states persisted longer and quickly dropped all the way to zero bonds, typically within 0.1 s, limiting the chance for bonds to reform.