The chemical properties of heme proteins largely reflect the electronic properties of their heme group. Often, the polphyrin ring of the heme exhibits significant distortions from its isolated structure, but the impact of these distortions on the chemical properties of the heme is yet uncertain. A systematic study focused on the effects of the distortion of the macrocycle on the binding affinity for oxygen is presented. The results show that out-of-plane distortions decrease the binding affinity, while in-plane distortions can increase or decrease it. Among in-plane distortions, only the breathing mode, which involves the symmetric compression expansion of the porphyrin ring, strongly modulates the binding affinity. These findings shed light into the peculiar binding affinity of Methanosarcina acetivorans protoglobin, a protein that contains a highly distorted heme. Overall, the results highlight that in-plane distortions might be exploited by certain classes of heme proteins to modulate the ligand affinity.