How To Get The Angle Between Secondary Structure Elements Of A Protein?

I'm recently studying on the tableaux representation of secondary structure elements of proteins. But I don't know how to get the orientations between them from DSSP file. The DSSP file assign helix or strand of sheet to each redisue. Besides, it give some angles such as TCO KAPPA ALPHA PHI PSI. I don't know how to calculate the angle between them. Anyone knows how to do it?

protein

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updated 12.8 years ago by João Rodrigues

• written 12.8 years ago by lylylytc •

1 answer

Calculating orientations between secondary structures could be done, very simply, by assigning a vector to the midpoints of the backbone of the residues of each secondary structure and then calculating their angle. For example, if you have two helices (residues 1-10 and 12-20) you could make two vectors out of them and then calculate the angle between these two vectors.

As for the TCO/KAPPA/etc definitions (taken from the DSSP 'manual'):

TCO

cosine of angle between C=O of residue i and C=O of residue i-1. For alpha-helices, TCO is near +1, for beta-sheets TCO is near -1. Not used for structure definition.
KAPPA

virtual bond angle (bend angle) defined by the three C-alpha atoms of residues i-2,i,i+2. Used to define bend (structure code 'S').
ALPHA

virtual torsion angle (dihedral angle) defined by the four C-alpha atoms of residues i-1,i,i+1,i+2.Used to define chirality (structure code '+' or '-').
PHI PSI

IUPAC peptide backbone torsion angles

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written 12.8 years ago by João Rodrigues

Thanks for your reply. But my question is how to get the numerical value of two vectors of helices. Which attributes ( # RESIDUE AA STRUCTURE BP1 BP2 ACC N-H-->O O-->H-N N-H-->O O-->H-N TCO KAPPA ALPHA PHI PSI X-CA Y-CA Z-CA ) should I use in DSSP result? Given a link as reference: http://mrs.cmbi.ru.nl/m6/entry?db=dssp&nr=29563&rq=2acy

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written 12.8 years ago by lylylytc •

That's not there. But the coordinates of the Ca of each residue are, so you can use a method like I mentioned above. To get a vector out of a helix take the first residue of the helix, select its alpha carbon, take the last residue of the helix, select its alpha carbon, subtract both carbon and you get the vector. For sheets its similar..

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written 12.8 years ago by João Rodrigues

Thanks. And I found that several paper mentioned that use least-square to approximate the axis of helices. Then calculate the angle between them. But now I meet a new problem. How can this angle be from -180 to 180 degree? One paper said: "its sign is defined by the convention that a clockwise retation of the nearer vector with respect to the farther is positive". Arccos function only returns angle between 0 and 180.

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written 12.8 years ago by lylylytc •