In a preliminary exploration of the dummy model for diiron proteins, random-acceleration molecular dynamics (RAMD) revealed that a pure four-helix bundle structure, like hemerythrin, constitutes an efficient cage for dioxygen (O ), which can only leave from defined, albeit very broad, gates. However, this well ordered structure does not constitute an archetype on which to compare O permeation of other diiron proteins, like the complex of soluble methane monooxygenase hydroxylase with the regulatory protein (sMMOH-MMOB). The reason is that with this complex, unlike hemerythrin, the four helices of the four-helix bundle are heavily bent, and RAMD showed that most traps for O lie outside them. It was also observed that, in spite of a nearly identical van der Waals radius for O and the natural substrate CH , the latter behaves under RAMD as a bulkier molecule than O , requiring a higher external force to be brought out of sMMOH-MMOB along trajectories of viable length. All that determined with sMMOH-MMOB multiple gates and multiple pathways to each of them through several binding pockets, for both O and CH . Of the two equally preferred pathways for O , at right angle with one another, one proved to be in accordance with the Xe-atom mapping for sMMOH. In contrast, none of the pathways identified for CH proved to be in accordance with such mapping, CH looking for more open avenues instead.