Sequence-structure relationships in proteins and copolymers

We model proteins as copolymer chains of H (hydrophobic) and P (polar) monomers configured as self-avoiding flights on three-dimensional simple-cubic lattices. The HH interaction is favorable. The folding problem is to find the ''native'' conformation(s) (lowest free energy) for an HP sequence. Using geometric proofs for self-avoiding lattice chains, we develop equations relating a monomer sequence to its native structures. These constraint relations can be used for two purposes: (1) to compute a tight lower bound on the free energy of the native state for HP sequences of any length, which is useful for testing conformational search strategies, and (2) to develop a search strategy. In its present implementation, the search strategy finds native states for HP lattice chains up to 36 monomers in length, which is a speedup of 5-15 orders of magnitude over existing brute-force exhaustive-search methods.