Protein core assembly processes

How does a protein or HP (hydrophobic/polar) copolymer find its globally optimal (native) state without a globally exhaustive search? This is the Levinthal paradox. We consider three routes by which a copolymer might assemble a compact conformation with a maximum number of hydrophobic (HH) contacts: (i) the exhaustive search (ES) process, which assures the global optimum; (ii) a "maximum entropy string" (MES), a series of stepwise decisions each of which explores conformational space exhaustively for given prior contacts; and (iii) a "T-local string," or "hydrophobic zippers" (HZ) process, which makes HH contacts opportunistically based on prior contacts. Using a two-dimensional HP short-chain lattice model, for which the partition function is exactly enumerable, we find that for many HP sequences, T-local strings lead to the globally optimal conformation, offering a resolution to the Levinthal paradox.