Single-Dimer Formation Rate Reveals Heterogeneous Particle Surface Reactivity

Abstract

Biofunctionalized micro- and nanoparticles are important for a wide range of applications, but methodologies to measure, modulate, and model interactions between individual particles are scarce. Here, we describe a technique to measure the aggregation rate of two particles to a single dimer, by recording the trajectory that a particle follows on the surface of another particle as a function of time. The trajectory and the interparticle potential are controlled by a magnetic field. Particles were studied with and without conjugated antibodies in a wide range of pH conditions. The data shows that the aggregation process strongly depends on the particle surface charge density and hardly on the antibody surface coverage. Furthermore, microscopy videos of single particle dimers reveal the presence of reactive patches and thus heterogeneity in the particle surface reactivity. The aggregation rates measured with the single-dimer experiment are compared to data from an ensemble aggregation experiment. Quantitative agreement is obtained using a model that includes the influence of surface heterogeneity on particle aggregation. This single-dimer experiment clarifies how heterogeneities in particle reactivity play a role in colloidal stability.

Figure 1

Single-dimer aggregation (SDA) experiment. (a) Experimental concept: single particles are immobilized on a glass substrate, called primary particles. In the presence of a rotating (precessing) magnetic field, a secondary particle is trapped on the primary particle by magnetic dipole–dipole interactions. The secondary particle follows the rotating field, making a circular motion path on top of the primary particle. Upon particle aggregation, the secondary particle becomes immobilized and stops following the rotating magnetic field. (b) Microscopy image of a quarter of a full field of view of primary particles. (c) Microscope images showing how a single secondary particle is trapped onto a primary particle (upper row) and how a circulating secondary particle stops circulating upon aggregation (lower row). The full recording is given in Supporting Information Video S1. (d) Cumulative number of rotations for a single dimer. In the free state, the dimer follows the field. In the aggregated state, the dimer shows a wiggling behavior, because the secondary particle still has limited freedom of motion. (e) Time trace of the rotation speed of a single dimer, showing 12 aggregation and dissociation events, including a fit of the data by the analysis software. The small spikes in the time trace originate from particles in solution that diffuse into the imaged region, thereby perturbing the image analysis. (f) Survival plot of the times-to-aggregation of 19 single dimers in a field of view. Data is fitted as:. The fit to the data gives k_agg = 0.10 ± 0.02 s^–1.

Figure 2

Single-dimer aggregation experiment as a function of surface charge. (a) ζ-Potential of the 0.5 and 1.0 μm particles measured as a function of pH of the citric acid buffer (ionic strength 150 mM). (b) Schematic representation of the two dimer systems: the equal-particle dimer system consists of two antibody-coated 0.5 μm particles, and the different-particle dimer system consists of both an antibody-coated 0.5 μm particle and a carboxylated 1.0 μm particle. (c) Measured aggregation rate for both dimer systems at different pH of the citric acid buffer (ionic strength 150 mM).

Figure 3

Single-dimer aggregation experiment using two 0.5 μm particles, as a function of antibody coverage on the secondary particles. (a) Antibody coverage on the secondary particle as a function of antibody concentration during particle functionalization. The right y-axis shows the calculated antibody surface density. (b) ζ-Potential of the secondary particles before and after functionalization with antibodies and PEG. Measurements were performed in PBS at pH 7.4. (c) Aggregation rate measured with the single-dimer experiment for three surface coverages of the secondary particle: zero Ab coverage, ∼10% Ab coverage, and ∼100% Ab coverage. The number of dimers N_d and the number of measured events N_e are shown for each Ab coverage. The data show that the aggregation rate hardly depends on the antibody surface coverage.

Figure 4

Heterogeneous binding orientations: a measured time trace of single-dimer (dis)aggregation. Colored dots at each binding event indicate the orientation of the dimer, showing that the primary particle has preferential aggregation locations on its surface.

Figure 5

Simulation of aggregation in the case of heterogeneous surface reactivity. (a) Heterogeneity in surface reactivity is simulated as N reactive patches on a nonreactive particle. An interaction volume is defined by two spherical caps centered around the contact point between particles. Aggregation can only occur when the interaction area on both particles contains at least one reactive patch. (b) Total probed interaction area on both particles depends on the experiment type and the motion of the secondary particle. For the SDA experiment, a rolling secondary particle probes more area on the secondary particle compared to the shoving case. In the OMC experiment, only the two initial spherical interaction areas have interaction. (c) Simulated aggregation rate as a function of the coverage of reactive patches on the particles, with R_patch = 2.5 nm, R_particle = 250 nm, and k_patch = 1 s^–1. Experimental results for the system of particles with a 10% Ab coverage are indicated by the horizontal bars.