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During a discussion of NMR, my lecturer told me to think about which amino acids contain protons in an aromatic ring, and whether any are likely to be affected by changes in pH.

The 4 aromatic amino acids are His, Phe, Tyr and Trp. I've marked Histidine as such in my notes, but can't remember why I thought this at the time. Contrary to this, Wikipedia states explicitly that “the imidazole ring of histidine is aromatic at all pH values”.

I also marked Histidine as "+ve" (as in, positive) but I'm stumped as to what I meant by it

I can't find any information on the others, but am guessing perhaps the fact that these have phenyl (rather than imidazole) rings means it's possible they respond differently to changing pH?

Any advice or hints would be appreciated, as I can't find any further information online and nothing in the structures jumps out at me to suggest an answer.

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There are two nitrogen atoms in the imidazole ring in histidine, but the $sp^2$ nitrogen is significantly more basic than the $sp^3$ nitrogen, as the electron pair in the latter is delocalized over the ring. Protonating the $sp^3$ nitrogen would destroy the aromaticity, but that would require very strongly acidic conditions, possibly not attainable in aqueous solution. Protonating the $sp^2$ nitrogen does not affect aromaticity because the electron pair is approximately perpendicular to the plane of the ring, meaning it cannot overlap with other orbitals in the ring and therefore does not participate in mesomerism.

Tryptophan also has a $sp^3$ nitrogen atom in an aromatic ring, but like in the imidazole ring it is not very basic.

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In proteins, amino acid residues of histidine have pKas near 6 and tyrosine side chains near 10. The protonated form of histidine is positive, and there can be a substantial fraction protonated at physiological pH in a given protein depending upon the exact pK value.

NMR has been used to determine the pKas of particular residues in particular proteins, with interest in deviation from the usual values. In metalloenzymes, the oxidation state of a metal ion can be coupled to the protonation state a side chain.

This is probably what the lecturer wanted you to think about, which pKas would be interesting to try to observe by NMR? not which ones change aromaticity necessarily.

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