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, powering oxidative phosphorylation in mitochondria. On the other hand, an excess supply of oxygen will generate reactive species which are harmful for the cell. In healthy tissues, the first process must be maximized relative 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, the curvature of the membrane, influence the local oxygen abundance and the membrane partitioning. We have modelled a flat bilayer and a liposome composed of dipalmitoylphosphatidylcholine (DPPC), using molecular dynamics simulation. Associated changes in the membrane-level oxygen partition coefficient and free energy profiles will be presented.