I think one thing to keep in mind is that coming up with these differential equations is an art. Classically it's about balancing simplicity (for human understanding) and being able to recapitulate some of the dynamics of the system.

Receptor dynamics is one subsystem that has been studied well theoretically. We know increasing number of binding sites can generate for example "cooperativity" and bistability dynamics.

Here's a review that discusses this further: https://journals.plos.org/plosone/article?id=10.1371/journal...