Is protein folding really NP-hard and how to show that?
It follows immediately from the fact that protein folding is NP-hard that there exists a reduction from 3SAT to protein folding.   The definition of NP-hard says that there is a reduction from every NP problem to protein folding; and 3SAT is a NP problem.
There are papers in the literature that state that protein folding is NP-hard.  I'm not an expert on them, so I don't know to what extent they do or don't address your specific concerns, but you should be able to find them immediately and review their proof.  See, e.g.,
P. Crescenzi et al. &quot;On the complexity of protein folding.&quot; Journal of computational biology 5.3 (1998): 423-465.
B. Berger et al. &quot;Protein folding in the hydrophobic-hydrophilic (HP) is NP-complete.&quot; Proceedings of the second annual international conference on Computational molecular biology, pp. 30-39. 1998.
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