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Single-Dimer Formation Rate Reveals Heterogeneous Particle Surface Reactivity

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.


S1) Substrate functionalization
To verify the immobilization strategy of primary particles on the substrate, two experiments were performed. In the first experiment the number of immobilized primary particles on the substrate was counted for different concentrations of the goat-anti-mouse IgG on the substrate. Fig. S1a shows a curve with saturation at a concentration of 200 nM. Given the Ab concentration during incubation with the substrate, the amount of antibodies on the particles, and the curvature of the particle, it can be calculated that around 10 2 molecular bonds are formed between a single particle and the substrate.
In the second experiment, the substrate was functionalized and particles were immobilized as described above. Thereafter, the substrate was blocked with different concentrations of polyclonal mouse IgG, after which a second incubation step with primary particles was done. Fig. S1b shows that the goat-anti-mouse IgG was blocked by incubation with 100 nM mouse IgG, demonstrating that the particles were indeed bound to goat-anti-mouse IgG molecules on the substrate.

Fig. S3 Raw data analysis software: (a) Typical microscope image showing a full field of view filled with primary particles.
Zoom shows a single primary particle. (b) Zoomed microscope image of a single secondary particle trapped on a single primary particle in a tilted out-of-plane magnetic field.

S4) Statistics of the time-to-aggregation
The available observation time per dimer is limited by the time between the moment the secondary particle gets trapped, which is random, and the moment when an additional particle gets trapped on that same dimer, resulting in the formation of a trimer and the end of the dimer experiment. It is possible to optimize the number of aggregation events per dimer by varying the particle concentration in solution, but it is a trade-off. At low secondary particle concentration in solution only few secondary particles are trapped on primary particles; at high secondary particle concentration, a dimer experiment has a short duration due to faster formation of a trimer.
The range of times-to-aggregation that can be measured with the single-dimer aggregation experiment is limited by several experimental constraints. The rotation angle per frame (field rotation frequency/frame rate) needs to be large enough to detect with the software. It is possible to increase the framerate, however, increasing the field rotation frequency is not preferred because the particle should be able to follow the field rotation in the free state. Therefore the shortest measureable time-to-aggregation (~0.4 s) is determined by the maximum field rotation frequency. The longest time-to-aggregation depends again on the time between the secondary particle gets trapped, which is random, and the time that another secondary particle gets trapped on that same dimer (< 10 min).

Fig. S5 Varying antibody coverage: Histograms of the time-to-aggregation including the extracted rate constant from the single exponential fit for secondary particles with (a) PEG only, (b) low [Ab] + PEG and (c) high [Ab] + PEG.
S6

S6) Aggregation rate as a function of particle surface chemistry
To investigate the influence of the surface chemistry of the particles on the aggregation process three experiments are performed with different particle coatings: Firstly, a primary particle coated with a-cTnI Ab1 + 5kPEG and secondary particle coated with a-cTnI Ab1 + 5kPEG + 5% BSA physisorption (Fig. S6a). Secondly, a primary particle coated with a-cTnI Ab1 + 5kPEG and bare secondary particle with carboxyl groups (Fig. S6b). Thirdly, a primary particle coated with a-cTnI Ab2 + 5kPEG and secondary particle coated with a-cTnI Ab2 + 5kPEG (Fig. S6c). The variations in the obtained aggregation rate are small. The error in the aggregation rate is the fit error. However, the real error in the measurement also depends on the amount of statistics.

Fig. S6 Varying surface chemistry:
Histograms of the time-to-aggregation measured with the single-dimer aggregation experiment for 500 nm particles with different surface chemistries: (a) Primary particle coated with a-cTnI Ab1 + 5kPEG and secondary particle coated with a-cTnI Ab1 + 5kPEG + 5% BSA physisorption. (b) Primary particle coated with a-cTnI Ab1 + 5kPEG and bare secondary particle with carboxyl groups. (a) Primary particle coated with a-cTnI Ab2 + 5kPEG and secondary particle coated with a-cTnI Ab2 + 5kPEG.