In the backbone of a polypeptide, you would find amide bonds formed from the amino (NH2) and carboxyl (COOH) groups of two amino acids. Water is lost in this condensation process:
The peptide backbone is considered to simply be the repeating Cα–C–N units. In the peptide shown below (a hexapeptide), the backbone is bolded. The side chains of each amino acid residue (R1, R2, ...) are not part of this backbone.
Amides are only very weakly acidic and very weakly basic, and do not undergo appreciable protonation or deprotonation under aqueous conditions.
Therefore, you only consider the terminal amino and carboxyl groups. So, at pH 2, both the N- and C-termini will be protonated:
Of course, if any of your residues contain a group that could become protonated, you need to consider its pKa as well.