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The above article says that DSSP is a hydrogen bond estimation algorithm. Then the article also says that this algorithm is "assigns secondary structure to proteins".

If both are true, how does hydrogen bond estimation helps us to assign secondary structures of proteins?

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"Secondary structure is formally defined by the pattern of hydrogen bonds between the amino hydrogen and carboxyl oxygen atoms in the peptide backbone" (source)

To be more specific: secondary structures are formed explicitly because of hydrogen bonds. So when DSSP says that it estimates hydrogen bonds as a proxy for secondary structure classification, this is likely why.

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