Analysis of compartmental models of ligand-induced endocytosis

Kinetic models have played a pivotal role in the study of ligand-induced endocytosis. However, an analysis that suggests a systematic way to validate such models is lacking. The current work analyses the base model of ligand-induced endocytosis for three widely used experimental protocols. In protocol I cells initially devoid of ligand are incubated in ligand solution, whereas protocols II and III are desorption experiments in which an initial pool of surface or internalized ligand–receptor complexes, respectively, are released into an elution medium that is initially devoid of ligand. A short-time analysis of protocol I using successive substitutions yielded a corrected pre-factor for the In/Sur plot introduced by Wiley and Cunningham (Cell 25 (1981) 433). In contrast, neglecting the variation in receptor numbers yielded an approximation of protocol I that is valid for long times (e.g. tens of minutes). Similarly, the low cell-concentration limits of protocols II and III are derived by neglecting the concentration of free ligand. The simplicity of these approximations provides a simple and reliable method for estimating the parameters governing ligand kinetics, while their definitive nature implies that they can be used to verify the validity of the base model. This analysis also provides insight on the fast endocytosis and recycling limit of protocol III.