A sequence-compatible amount of native burial information is sufficient for determining the structure of small globular proteins

Abstract

Protein tertiary structures are known to be encoded in amino acid sequences, but the problem of structure prediction from sequence continues to be a challenge. With this question in mind, recent simulations have shown that atomic burials, as expressed by atom distances to the molecular geometrical center, are sufficiently informative for determining native conformations of small globular proteins. Here we use a simple computational experiment to estimate the amount of this required burial information and find it to be surprisingly small, actually comparable with the stringent limit imposed by sequence statistics. Atomic burials appear to satisfy, therefore, minimal requirements for a putative dominating property in the folding code because they provide an amount of information sufficiently large for structural determination but, at the same time, sufficiently small to be encodable in sequences. In a simple analogy with human communication, atomic burials could correspond to the actual "language" encoded in the amino acid "script" from which the complexity of native conformations is recovered during the folding process.protein folding | structure prediction | information theory | folding code D uring the last two decades, a physical picture of the folding process has emerged with the advent of energy landscape theory (1-5) but, despite many recent advances, a general solution to the problem of structure prediction from sequence has remained elusive. Most attempts in this direction have assumed sequences to encode partial information about many structural properties, such as likelihood of tertiary contacts or secondary structure propensities, that could eventually be combined to provide a general predictive algorithm (6-10). An alternative scheme would assume a single (or few) conformational property to be directly encoded in sequences, resulting in a small number of sequence-dependent parameters, whereas other conformational features would arise from sequence-independent constraints. The importance of such constraints has been recently emphasized by Banavar and collaborators (11).The amount of information provided by a putative single property dominating the code should satisfy two conditions: It should be sufficiently large for structural determination but sufficiently small for being encodable in sequences (12). The widely recognized importance of hydrophobic interactions on protein structure formation (13,14) suggests atomic burials to constitute a natural candidate for this putative dominant property. There has been some discussion, in the simplified context of lattice models, on the possibility that intrinsically unspecific hydrophobicity could satisfy the first condition (15), including a dependence on the choice of native conformation (16,17). Encouraging results from recent Monte Carlo simulations, on the other hand, indicate that the first condition is satisfied by atomic burials, as measured by distances from the molecular geometrical center, for small globular proteins represented by off-lattice, geome...

The Evolution of Protein Structures and Structural Ensembles Under Functional Constraint

“…These regions show different rates of amino acid substitution, with the hydrophobic core evolving more slowly than the hydrophilic surface [5]. Quantitatively, core residues evolve up to 10x slower than surface residues [6], and include residues that are the most informative for determining the topology of the native fold [7]. In fact, rates of evolution correlate strongly with fractional residue burial [8].…”

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

“…A comparison with available prediction schemes might be instructive, since our simulations resemble previous schemes that minimize a simplified heuristic energy function containing both sequence‐dependent and sequence‐independent terms. As emphasized in previous reports, however, they stand out in assuming that burial propensities constitute the only information to be obtained from sequence. In particular, there are no sequence‐dependent terms to favor specific tertiary interactions as in most previous schemes, for example, Refs.…”

“…We have been exploring the possibility that atomic burials, as quantified by central distances, could constitute such messages . In terms of a simple analogy with human communication, which is actually similar to the one discussed in Ref.…”

“…, we investigate if the set of viable burial sequences could constitute a “language” capable of expressing structural “ideas” while satisfying the “grammar” of sequence‐independent constraints and being encodable in the “script” generated by the alphabet of amino acids . In this direction, native‐like conformations were obtained in folding simulations guided by burial potentials pushing each atom toward its native central distance, either regarded as a continuous parameter or discretized into a small number L of equiprobable burial layers . This result suggested that atomic burials could indeed be regarded as a practical uniquely decodable code for tertiary structures, at least for the limited number of small proteins that had been investigated.…”

Prediction of functionally important residues in globular proteins from unusual central distances of amino acids

“…The introduction of information-theoretic interpretation of hydrophobicity distributions may lead to valuable insights [84]. One result of the meeting of hydrophobicity and information theory, especially noteworthy in this context, supports our approach by demonstrating improvements in contact potentials tailored to the compositional properties of the sequences of interest [85].…”