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What data structure is used in representing protein structures in computers so that we can apply algorithms?

Matrix or Graph or tree?

P.S. I am absolutely new to Bioinformatics.

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You don't specify what the algorithms shall do. If represented does not equal to visualization, then a the structures may be stored, transferred and processed via the atomic coordinates of the protein. For proteins, the .pdb format is quite common. After a header, the (x,y,z) are described in a block like

ATOM      1  N   PRO A   1       8.316  21.206  21.530  1.00 17.44           N
ATOM      2  CA  PRO A   1       7.608  20.729  20.336  1.00 17.44           C
ATOM      3  C   PRO A   1       8.487  20.707  19.092  1.00 17.44           C
ATOM      4  O   PRO A   1       9.466  21.457  19.005  1.00 17.44           O
ATOM      5  CB  PRO A   1       6.460  21.723  20.211  1.00 22.26           C

(loc. cit.)

in the first three columns with entries of type real (not integer, nor character) with the implicit unit of Angstrom (i.e., $\pu{10^{-10} m}$). Note that the format equally supports D instead of H to describe the deuterium isotope (reference). If you need to familiarize yourself with this file fomat, visit e.g., Jmol's public set of reference files here.

If the algorithms are about determining similarity between molecules stored in a database, then likely fingerprints are more suitable for you.

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    $\begingroup$ This does not really explain how the "tertiary" part of tertiary protein structure is represented. In other words, even if I have a snapshot of a protein structure in terms of Cartesian coordinates, what does that tell me about the persistence of atomic contacts? $\endgroup$
    – Buck Thorn
    Jul 20 at 10:22
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    $\begingroup$ I'm pretty sure pdb uses residue definitions to specify covalent connections between atoms. Those definition files give meaning to the third and fourth columns, eg CA PRO means the alpha carbon of a proline structure. $\endgroup$
    – Andrew
    Jul 20 at 13:26

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