Statement 1: Some iron must be in the Fe³⁺ (ferric) oxidation state.

This is incorrect. For both hemoglobin and myoglobin to bind oxygen effectively, the iron must be in the Fe²⁺ (ferrous) state. Iron in the Fe³⁺ state cannot bind oxygen reversibly.

Statement 2: A coordination bond exists between the nitrogen atom of the proximal histidine and the Fe²⁺ in the heme group.

This is correct. The Fe²⁺ ion in the heme group forms a coordination bond with the nitrogen of the proximal histidine residue in both hemoglobin and myoglobin.

Statement 3: Oxygen only binds to Fe²⁺ in the oxidized state.

This is incorrect. Oxygen binds to Fe²⁺ in its reduced state. The wording here is confusing—oxidation of Fe²⁺ to Fe³⁺ actually prevents oxygen binding.

Statement 4: Histidine (His F8) plays a physiological role in the movement of the heme upon O₂ binding.

This is correct. Histidine F8, also known as the proximal histidine, is directly bonded to the Fe²⁺ ion. When oxygen binds, the heme flattens, and the histidine helps transmit this conformational change, particularly in hemoglobin, facilitating cooperative binding.