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I’m not sure how to do precisely what you want out of the box. (As I’m sure you’ve guessed, neither constraints nor abrelax are my areas of expertise).
You seem reasonably comfortable with code. You could modify the RMSDscore scoreterm to work on a subset of Ca – the files are core/scoring/methods/RMS_Energy for the score term and core/scoring/rms_util for the rms calculating utility functions. There are several RMS functions that take maps determining which atoms to align and RMSD over.
I think you could get away with what you want with a large set of AtomPairConstraints – write one constraint per hbond in the secondary structure (either over the hbond or over the CA – if the CA’s are close Rosetta is likely to prefer secondary structure to satisfy the polar groups) plus a few extra CA to CA constraints between secondary structures and from one end of each element to its beginning.