Mathematical modeling of the receptor-mediated endocytosis process of targeted therapeutic agents in drug delivery systems

Abstract

In this paper, we propose mathematical models to describe receptor-mediated endocytosis processes. One is a stochastic differential model for the agent-target binding process. The mean extinction time and a standard variation over time profile are evaluated. The other is an age-structured model for demonstrating endocytosis and lysosome processes. A targeted drug delivery system has a complex process in how it is to deliver drug molecules in terms of administration, transportation in blood and across membranes to intracellular space, and inhibition to microtubule polymerization. In particular, receptor-mediated endocytosis of targeted therapeutic agents, such as antibody drug conjugates or ligand-targeted liposome encapsulated nanoparticles, is a key step in understanding the drug delivery mechanism. We discuss stochastic quasi steady state approximation when agent-target complex does not appreciably vary compared with the free agents. This reduces the number of the systems and the parameters; however, an initial time phase cannot be captured. In addition, we discuss the strengths and weaknesses when the age-structured model induces the reduced model compared with the full model that considers endocytosis and lysosome processes. If the total mean retention time until payload release in intracellular space is known, then the age-structured model with the Erlang distribution may fairly predict data of the released payload over time profile with far fewer parameters; however, induced compartments lose their physical meaning and describe only a delay.