Information and redundancy in the burial folding code of globular proteins within a wide range of shapes and sizes

Recent ab initio folding simulations for a limited number of small proteins have corroborated a previous suggestion that atomic burial information obtainable from sequence could be sufficient for tertiary structure determination when combined to sequence-independent geometrical constraints. Here, we use simulations parameterized by native burials to investigate the required amount of information in a diverse set of globular proteins comprising different structural classes and a wide size range. Burial information is provided by a potential term pushing each atom towards one among a small number L of equiprobable concentric layers. An upper bound for the required information is provided by the minimal number of layers Lmin still compatible with correct folding behavior. We obtain Lmin between 3 and 5 for seven small to medium proteins with 50≤Nr≤110 residues while for a larger protein with Nr=141 we find that L≥6 is required to maintain native stability. We additionally estimate the usable redundancy for a given L≥Lmin from the burial entropy associated to the largest folding-compatible fraction of superfluous atoms, for which the burial term can be turned off or target layers can be chosen randomly. The estimated redundancy for small proteins with L=4 is close to 0.8. Our results are consistent with the above-average quality of burial predictions used in previous simulations and indicate that the fraction of approachable proteins could increase significantly with even a mild, plausible, improvement on sequence-dependent burial prediction or on sequence-independent constraints that augment the detectable redundancy during simulations.