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

Abstract

Random energy models (REMs) provide a simple description of the energy landscapes that guide protein folding and evolution. The requirement of a large energy gap between the native structure and unfolded conformations, considered necessary for cooperative, protein‐like, folding behavior, indicates that proteins differ markedly from random heteropolymers. It has been suggested, therefore, that natural selection might have acted to choose nonrandom amino acid sequences satisfying this particular condition, implying that a large fraction of possible, unselected random sequences, would not fold to any structure. From an informational perspective, however, this scenario could indicate that protein structures, regarded as messages to be transmitted through a communication channel, would not be efficiently encoded in amino acid sequences, regarded as the communication channel for this transmission, since a large fraction of possible channel states would not be used. Here, we use a combined REM for conformations and sequences, with previously estimated parameters for natural proteins, to explore an alternative possibility in which the appropriate shape of the landscape results mainly from the deviation from randomness of possible native structures instead of sequences. We observe that this situation emerges naturally if the distribution of conformational energies happens to arise from two independent contributions corresponding to sequence‐dependent and ‐independent terms. This construction is consistent with the hypothesis of a protein burial folding code, with native structures being determined by a modest amount of sequence‐dependent atomic burial information with sequence‐independent constraints imposed by unspecific hydrogen bond formation. More generally, an appropriate combination of sequence‐dependent and ‐independent information accommodates the possibility of an efficient structural encoding with the main physical requirement for folding, providing possible insight not only on the folding process but also on several aspects sequence evolution such as neutral networks, conformational coverage, and de novo gene emergence.

Beyond mutations: Accounting for quantitative changes in the analysis of protein evolution

“…A recent study developed a combined random energy model for protein folding and coding under the hypothesis that evolution favors large energy gaps between native and unfolded conformations. These energy levels can potentially be utilized to infer distances [23] .…”

“…Substitution models of evolution describe the process of genetic variation through fixed mutations and constitute a basis of the evolutionary analysis on the molecular level [2] . Yet, the focus on the manifestation of amino acid changes (or amino acid frequencies [29] does not account for the circumstance that selection and self-organization favor certain mutations over others (natural selection could have acted in sequence space to select non-random sequences satisfying the requirement for a large energy gap between native and unfolded conformations [23] . Notably, such accounting has become principally feasible over the past years, in which a substantial body of knowledge has been accrued to describe the physical and chemical properties of amino acids.…”