We model all different aspects of μ-opioid receptor activation. This starts with the binding of an opioid to the receptor, followed by conformnational changes, spatio-temporal resolved signaling processes in the cell, the signaling effects, and the internalization and recovering of the μ-opioid receptor via the arrestin route. For this goal we need to model non-reversible molecular and signaling processes. The scientific goal is to estimate missing parameters, characteristic time-scales of the elementary steps, and coherent structures of  non-reversible processes from (also experimental) data.