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

Abstract

The connection between protein sequences and tertiary structures has intrigued investigators for decades. A plausible hypothesis for the coding scheme postulates that atomic burial information obtainable from the sequence could be sufficient for structural determination when combined to sequence-independent constraints. Accordingly, folding simulations using native burial information expressed by atomic central distances, discretized into a small number L of equiprobable burial layers, have indeed been successful in reaching and distinguishing the native structure of several globular proteins. Attempted predictions of layers from sequence, however, turned out to be insufficiently accurate for most proteins. Here we explore the possibility that a nonuniform assignment of layers, which is intended to account for constraints imposed by chain connectivity, might provide a more efficient burial encoding of tertiary structures. We consider the condition that adjacent Cα-atoms along the sequence cannot occupy nonadjacent layers, in which case the information required to specify sequences of burials would be smaller. It is shown that appropriate folding behavior can still be observed in this explicitly more constrained scenario with a structure-dependent assignment intended to produce the thinnest possible layers still compatible with the imposed burial constraint. This thinnest assignment turns out to be sufficiently restrictive for the observed examples and provides appropriately thinner layers or, equivalently, a larger number of layers, for examples previously observed to indeed require more restrictive constraints when compared to counterparts of similar size, as well as the appropriate increase in number of layers for larger proteins. Implications for the general understanding of the protein folding code are discussed.

Sequence‐dependent and ‐independent information in a combined random energy model for protein folding and coding

“…We also consider that normally distributed conformational energies might result from the sum of two normally distributed contributions with different mean values, corresponding to stabilizing sequence-dependent and destabilizing sequence-independent terms. This combination is consistent with the hypothesis of a protein burial folding code, as has been investigated by folding simulations of geometrically realistic protein models, [9][10][11][12][13] with native structures being determined by a modest amount of sequence-dependent atomic burial information combined to sequence-independent constraints imposed by unspecific hydrogen bond formation. The required gap in total energy can emerge in this case even in the absence of any gap in each of the two separate contributions.…”

“…Folding occurs with the hiding from the aqueous environment of hydrophobic surface, to which sequence‐dependent side chains strongly contribute, while satisfying hydrogen bonds mainly from the sequence‐independent peptide backbone 21,22 . This simple physical picture was incorporated in the hypothesis of a burial folding code, as has been investigated by simulations of geometrically realistic protein models with an effective atomic burial potential, 9–13 and a modest amount of atomic burial information was found to be sufficient for structural determination. In a recent study, this required information was actually suggested to be less than bits/residue, 13 which is consistent with the presently used estimate for , in the middle of the range obtained in Ref.…”

“…This simple physical picture was incorporated in the hypothesis of a burial folding code, as has been investigated by simulations of geometrically realistic protein models with an effective atomic burial potential, 9–13 and a modest amount of atomic burial information was found to be sufficient for structural determination. In a recent study, this required information was actually suggested to be less than bits/residue, 13 which is consistent with the presently used estimate for , in the middle of the range obtained in Ref. 6, as seen above.…”