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For protein residues I know that $C\alpha$ denotes the first carbon atom attached to a functional group. Each subsequent carbon is given a corresponding greek letter ($\beta, \gamma, \delta$) except for one. For example, each residue in a PDB file has a list of atoms that looks something like this:

  • ATOM 32 N AARG
  • ATOM 33 CA AARG
  • ATOM 34 C AARG
  • ATOM 35 O AARG
  • ATOM 36 CB AARG
  • ATOM 37 CG AARG
  • ATOM 38 CD AARG

(A,B,G,D are stand-ins for the greek letters). Why is there just a plain C in this list? What is significant about that carbon?

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In your context, the "plain-C" labelled carbon is the carbon atom in the carbonyl ($\ce{C=O}$) group. In organic chemistry, the alpha carbon is the carbon immediately adjacent to a functional group. In general, the greek letters in alphabetical order denote the distance in increasing order from a functional group. The $\ce{C_\alpha}$ in the case of amino acids is alpha carbon with respect to both the amine and carbonyl.

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  • $\begingroup$ The edit seems to have spoiled your answer. I imagine you can easily edit it to fit the new question that does not mention the phantom C'. $\endgroup$
    – David
    Commented Apr 20, 2018 at 15:10
  • $\begingroup$ @David Done.... $\endgroup$
    – WYSIWYG
    Commented Apr 23, 2018 at 9:41

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