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

Abstract

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 L(min) still compatible with correct folding behavior. We obtain L(min) 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 ≥ L(min) 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.

Constrained Layer Assignment for the Protein Burial Folding Code Accounting for Chain Connectivity

“…It is apparent in any case that different native structures of similar size might require different amounts of burial information for appropriate folding behavior. More information, or larger L values, is also expected to be required for larger proteins, as previously observed for three proteins between 100 and 150 residues in length, namely 2hsy, 1ifr and 1oz9 . As L increases, the average thickness of layers must decrease and the atoms become appropriately more constrained within thinner layers.…”

“…For other two proteins in the same size range, all-β 1shf and all-α 3zr8, L = 4 turned out to be required. Furthermore, most folding trajectories for 1enh and 3fil arrived at the native-like ensemble already for L = 3 while a large fraction of trajectories for 1shf, 3zr8, and also 1c9o, arrived at non-native ensembles even for L = 4, in which case the native-like ensemble was distinguishable by an appropriately lower energy . For three of these proteins, 3zr8, 3fil and 1c9o, prediction of L = 4 burial layers from sequence with the HMM turned out to be sufficiently accurate.…”

“…In previous computational experiments either native or predicted burial information was included in molecular dynamics folding simulations by a tailored energy function that contained a burial term pushing each atom toward a specific burial level, or “layer”, determined by a given range of central distance values, among a small number L of disjoint equally populated possibilities. A gradually increasing unspecific penalty for the burial of backbone CO and N–H groups not forming hydrogen bonds, independent of partner, was also enforced. , Appropriate folding behavior, as determined by the accessibility and stability of a native-like ensemble, was observed with native burials even for L = 3 for three small globular proteins between 50 and 70 residues, all-α 1enh, all-β 1c9o, and α/β 3fil, as identified by their pdb codes . For other two proteins in the same size range, all-β 1shf and all-α 3zr8, L = 4 turned out to be required.…”

“…While simulations using native burial information in the form of a small number of burial levels, or “layers”, have corroborated the first hypothesis, regarding sufficiency, the validity of the second hypothesis, regarding obtainability, is still under investigation. , Prediction of burial layers from a sequence with a Hidden Markov Model (HMM), which explicitly accounts for local correlations between burial symbols, has actually provided appropriate burial estimates for some examples . Resulting estimates for most proteins, however, appear to be insufficiently accurate . Local burial correlations are accounted because the HMM uses fragments of adjacent burial symbols as hidden states while transitions between adjacent states are accompanied by the emission of an amino acid symbol.…”

“…Here we investigate to what extent appropriate folding behavior can still be observed in this explicitly constrained scenario using atomic burials obtained from the native structure, as in ref , but with a nonuniform, structure-dependent layer assignment. The assignment is intended to produce the largest number of layers, L , or the smallest average layer thickness weighted by the number of C α atoms inside each layer, in order to provide the largest amount of burial information still compatible with the imposed constraint on adjacent burials.…”