What is a "tail" in the case of the secondary structure of a protein?
How does it influence the "protein assignment" task?
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«Tail» probably is just one word to describe both N-terminus (amino/ammonium group) and C-terminus (carboxylic acid/carboxylate) of a sequence of amino acids/proteins.
The shape of a sequence of amino acids is conformationally constrained depending on the specific amino acids covalently bound together. Empirically, this is described by $\varphi$ and $\psi$ in the Ramanchandran plot.
If the sequence growths, its interaction with e.g., cytoplasma becomes more and more important; thus curling up is one form of energetic optimization. In the form of $\beta$-sheets, coils, etc., some of the conformations eventually lock-in because of the formation of intra- and intermolecular hydrogen bonds. Whenever such ordering interactions are less many, the conformational flexibility of the protein chain increases again, i.e. multiple slightly different folding patterns differ little in energy and thus are «accessible». If the structure of a large protein is resolved by NMR spectroscopy, the description of these regions then is more «more fuzzy». This may happen for the termini. It equally may happen well within the sequence if the consecution of amino acid is not prone to the formation of e.g., $\beta$-sheets.