"Band structure" is a concept of collective excitations in a crystal. The repetition of the crystal, its "point group", dictates many properties of the band structure.
Proteins are very large molecules. We normally speak of the excitations of a molecule as "molecular orbitals". While a protein molecule might be big, it is not so big as to be well described by macroscopic properties like conductor, insulator and semiconductor.
Similarly, while a semiconductor has a fermi level describing which band structure states are occupied, a large molecule would be better described by it HOMO and LUMO - being the highest occupied molecular orbital and the lowest unoccupied molecular orbital.
Now, to be honest, some molecules are just so big that even molecular orbital theory is not useful and one must get .... creative? But, because a molecule is not a crystal, band theory is not the droid that you are looking for.