Mean-Field HP Model, Designability and Alpha-Helices in Protein Structures

Abstract

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with large number of switch backs between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha-helices.PACS number: 87.10.+e, 87.15.By The three-dimensional structure of proteins is a complex physical and mathematical problem of prime importance in molecular biology, medicine and pharmacology [1]. It is believed that the folding instruction of a protein is encoded in its amino acid sequence [2] and from model studies much has been learned about protein structure and folding kinetics [3][4][5][6]. Yet much still remains to be understood. This simple fact is already intriguing: the number of possible globular structures for a peptide of typical length -about 300 amino acids -is practically infinite; the number of proteins whose structures are known empirically or hypothetically is more than a hundred thousand and is growing rapidly with time; the number of classes of native protein structures is about five hundred and is believed unlikely to exceed a thousand in the long run [1,7]. Numerical simulations based on lattice models have shown that structures of exceptionally high designability -those that attract a large number of protein sequences to conform to it -do exist [5,6,8]. Why such structures would emerge is however not well understood. Protein folding also has an outstanding temporal feature: the initial collapse to globular shape and the formation of α-helices are completed in less than 10 −7 seconds [10], while the rest of the folding takes up to ten seconds to complete.In this report, based on results from a mean-field lattice model we observe that structures with high designability are preponderant in a type of substructure that suggests α-helices in real proteins and we explain the reason for this phenomenon. This notion is supported by global comparisons of model structural sequences with (binary) sequences constructed from sets of proteins of known structure: the Protein Data Bank (PDB) [9] and the Dali Domain Dictionary (DDD) [7]. Since the meanfield in the model represents the hydrophobic potential that is known to cause the initial collapse of a peptide to a globular shape, the results may explain why the initial collapse and the formation of α-helices occur essentially simultaneously and rapidly, and are temporally separated from other slower folding processes that are driven by far-neighbor inter-residual interactions.In the minimal model for protein folding, the HP model of Dill et al. [3], the 20 kinds of amino acids are divided into two types, hydrophobic and polar. This reduces a peptide chain of length N to a binary "pepti...

Shape-dependent designability studies of lattice proteins

“…In past studies of protein designability, amino acid sequences were threaded onto all possible compact conformations of a given shape and for each threading the total energy of the fold was computed based on a specified energy function (19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35). If there is a conformation that has a total energy lower than all other conformations, we assume that the sequence will fold to that specific conformation.…”

Simplification of complexity in protein molecular systems by grouping amino acids: a view from physics

“…The sequence-structure relationship is clearly exemplified for the four-helix-bundle fold, which demonstrates the power of the simplification of amino acid alphabet. Later, some bioinformatic and modeling studies also discovered HP patterns on the regular secondary structures (helix and strand) [64]. These directly prove the redundancy of the natural alphabet of amino acids as well as the possible simplifications for protein composition, and greatly benefit the design of protein designs [65].…”

Geometric and statistical properties of the mean-field hydrophobic-polar model, the large-small model, and real protein sequences

“…In this paper, expanding on claims made in an earlier letter [10], the highly designable structures in the meanfield HP model will be characterized -they are those that have the largest number of surface-core switchbacks, and it will be shown that highly foldable peptides have a high similarity with real protein sequences in general and with segments of sequences that fold to α helices in particular.…”

“…Another issue clarified by simple lattice models is the designability of "topological" classes of protein conformations [6,7,10]. The designability of a conformation class is the number of proteins whose native conformations belong to the class.…”

“…A mean-field version of the model that yields tremendous simplification was used to study the designability problem, and it was found that the designabilities of structures vary greatly (the terms structures and conformation classes will be used interchangeably in this paper), and that only a tiny portion of structures are highly designable. Moreover, it was noted that highly designable structures seem to have patterns that emulates secondary structural motifs [6,7,10].…”