The ‘oxygen paradox’ can be explained as two opposing biological processes with oxygen (O2) as a reactant. On the one hand, oxygen is essential to aerobic metabolism, being used by mitochondria to fuel oxidative phosphorylation. On the other hand, an excess supply of oxygen will generate reactive species which are harmful for the cell. To maintain oxygen homeostasis, the first process should be maximized compared to the second one. We have hypothesized that curved and cholesterol-enriched membrane invaginations called caveolae help maintain the proper oxygen level by taking up oxygen and attenuating its release to the mitochondria. The mechanism by which caveolae may help to buffer the oxygen level in cells is still unclear. Here, we aim to assess how structural aspects of caveolae—namely the curvature and the cholesterol content of the membrane—influence the local oxygen abundance and the membrane permeability. We have modelled liposomes with varying size (curvature) and with varying ratios of phosphatidylcholine (POPC) and cholesterol, using molecular dynamics simulation. Associated changes in the oxygen free energy profile and permeability will be presented.