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I am studying protein structures and in alpha helix I found out that one amino acid residue's carbonyl oxygen is linked to the nitrogen of amino group of 4 residues ahead.. However the first and last amino acids are not H bonded.. My question is why so? Shouldn't the first amino acid's carbonyl oxygen 5th residue's amino nitrogen like every other one.

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In general, an absence of the alpha-helical backbone hydrogen-bonding interactions in an X-ray crystal structure of a protein can be due to (1) incorrect detection of the beginning and end of the alpha-helix, (2) local structural disturbance in the regularity of the alpha-helix, (3) low resolution of the X-ray crystal structure, (4) incorrectly modeled atomic coordinates into the electron density map.

But none of the above is your case . . .

The picture below shows the first alpha-helix in an X-ray structure of human DNA polymerase beta (PDB code: 2FMP). The alpha-helix is composed of 18 amino-acid residues (Asn-12 to Val-29), here numbered 1 to 18. All the "CO"..."HN" hydrogen-bonding interactions (black dashed lines) are present (blue, "N"; red, "O"), i.e., only the first four "N" and the last four "O" atoms are not involved in the hydrogen-bonding, because there are no -3 to 0 and 19 to 22 partners for them (because those amino acid residues do not belong to the alpha-helix).

PDB code: 2FMP - alpha-helix Asn12 to Val29

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Hydrogen bomd forms between alpha carbonyl group of 1st peptide bond with alpha amino group of n+th amino acid residues away towards c terminal direction. Each and every amino acid residues in alpha helix should be inolved in H bonding it is the first 4 alpha NH2 group and last four alpha carbonyl groups which are not involved because for first four alpha amino group there is no preceding carbonyl groups and also for there is no alpha amino group for last four carbonyl groups.

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