Protein core assembly processes

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Abstract
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.