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Universal correlation between energy gap and foldability for the random energy model and lattice proteins

The random energy model, originally used to analyze the physics of spin glasses, has been employed to explore what makes a protein a good folder versus a bad folder. In earlier work, the ratio of the folding temperature over the glass–transition temperature was related to a statistical measure of protein energy landscapes denoted as the foldability F. It was posited and subsequently established by simulation that good folders had larger foldabilities, on average, than bad folders. An alternative hypothesis, equally verified by protein folding simulations, was that it is the energy gap Δ between the native state and the next highest energy that distinguishes good folders from bad folders. This duality of measures has led to some controversy and confusion with little done to reconcile the two. In this paper, we revisit the random energy model to derive the statistical distributions of the various energy gaps and foldability. The resulting joint distribution allows us to explicitly demonstrate the positive c...