Answer:
The modified hemoglobin with free imidazole cannot be expected to show cooperativity in oxygen binding. The movement of iron ion takes place up in the plane of heme when binding of one subunit of hemoglobin takes place with oxygen. One of the iron's and oxygen's axial ligands comprise the proximal histidine's imidazole ring.
With the movement of iron into the hemoglobin ring, the pulling of proximal histidine takes place along with it. Therefore, when binding of oxygen takes place with one subunit, a modification also takes place in the intersubunit associations, this also comprises displacement of the alpha helix. This phenomenon plays an essential role in modifying the hemoglobin's tensed state to the relaxed state. The withdrawal or mutation of the imidazole ring from the histidine residue does not further permit the cooperative binding as it is not associated physically with the alpha-helix.
