Extracting multivalent detachment rates from heterogeneous nanoparticle populations†
Nanoparticles can form multiple bonds with target surfaces, thereby increasing adhesion strength and internalization rate into cells. This property has helped to drive interest in nanoparticles as delivery vehicles for drugs and imaging agents, but significant gaps in our understanding of multivalent adhesion make it difficult to control and optimize binding dynamics. In previous work, we experimentally observed that multivalent nanoparticle adhesion can exhibit a time-dependent detachment rate. However, simulations later indicated that the underlying cause was variability in the number of bonds that formed between individual nanoparticles within the population. Here, we use this insight to develop a simple model to isolate a series of constant detachment rates from such heterogeneous populations. Using simulations of experimental data to train the model, we first classified nanoparticles within a given population based on the most likely equilibrium bond number, which we termed the bond potential. We then assumed that each bond potential category would follow standard first-order kinetics with constant detachment rates. Model results matched the population binding data, but only if we further divided each bond potential category into two sub-components, the second of which did not detach. We then utilized bonding rates from the simulation to estimate detachment rates for the second, slower detaching sub-component. These results confirm our hypothesis that nanoparticle populations can be sub-divided based on bond potential, each of which could be characterized by a constant detachment rate. Finally, we established relationships between the new heterogeneous population detachment model and a time-dependent, empirical detachment model that we developed in previous work. This could make it possible to determine bond potential distributions directly from experimental data without computationally costly simulations, which will be explored in future work.