Band structure is a concept for periodic system only. As proteins are not periodic structures, they don't have electronic bands.
The fact that you can download a PDB file (or a CIF file) with information about the crystal, it is just due to one of the ways we found to determine the protein structure that is crystalizing the protein and then using single crystal X-ray crystallography.
Very recently, a new technique called cryogenic electron microscopy (cryo-EM) is been using as another way to determine the protein structure without the need of passing through the crystallization process.
In case o non periodic system the molecular orbitals are used instead the electronic bands.
Even molecular orbitals are difficult to calculate for proteins due the high number of atoms (more than 1000 atoms), which make impracticable to use any DFT/ab initio software for the task.
But, you can use semi-empirical software like MOPAC that has implemented a function called MOZYME to do electronic calculations for proteins. Also, you can use the fragment molecular orbital method (FMO), implemented in software like GAMESS-US where you can use DFT/ab initio.
Another way is ti use Quantum Mechanic/Molecular Mechanic (QM/MM), where you divide your protein in two regions: one (smaller, few residues) where you use a quantum mechanic method and the other one (the rest of the protein) where you use molecular mechanics.