On the intractability of protein folding with a finite alphabet of amino acids

We describe a proof of NP-hardness for a lattice protein folding model whose instances contain protein sequences defined with a fixed, finite alphabet that contains 12 amino acid types. This lattice model represents a protein's conformation as a self-avoiding path that is embedded on the three-dimensional cubic lattice. A contact potential is used to determine the energy of a sequence in a given conformation; a pair of amino acids contributes to the conformational energy only if they are adjacent on the lattice. This result overcomes a significant weakness of previous intractability results, which do not examine protein folding models that have a finite alphabet of amino acids together with physically interesting conformations.