In glassy polymer membranes, experimental sorption isotherms for light gases are usually found to be concave to the pressure axis. In the present work, oxygen (O2) transport through a fully atomistic polyimide membrane has been studied using large-scale molecular dynamics (MD) simulations under five different conditions of applied external gas pressure. The concave behavior is well reproduced by the model and the natural gas uptake is linked to two distinct mobility modes. Because of a strong chemical potential gradient, the penetrants first undergo a rapid adsorption at the polymer surface at the very start of the simulations, which results in a complete saturation of the interfacial region. The average gas concentration at the interface then hardly changes with time and a quasi dynamic equilibrium is established with the gas phase. This is followed by a second slower and diffusion-limited uptake mode, with the diffusion coefficient for the penetrant in the membrane being independent of the applied external pressure. Results are analyzed and discussed in order to provide a molecular foundation to the sorption isotherms. Although the uptake vs pressure curves are well described by the popular dual-mode (DMS) sorption model, there is no evidence of two different populations of sorbed species at the molecular level Boltzmann weighted probability densities of test-particle insertion energies are found to be described by single Gaussian distributions, thus supporting the site-distribution (SD) model