From Ramachandran Maps to Tertiary Structures of Proteins

Abstract

Sequence to structure of proteins is an unsolved problem. A possible coarse grained resolution to this entails specification of all the torsional (Φ, Ψ) angles along the backbone of the polypeptide chain. The Ramachandran map quite elegantly depicts the allowed conformational (Φ, Ψ) space of proteins which is still very large for the purposes of accurate structure generation. We have divided the allowed (Φ, Ψ) space in Ramachandran maps into 27 distinct conformations sufficient to regenerate a structure to within 5 Å from the native, at least for small proteins, thus reducing the structure prediction problem to a specification of an alphanumeric string, i.e., the amino acid sequence together with one of the 27 conformations preferred by each amino acid residue. This still theoretically results in 27(n) conformations for a protein comprising "n" amino acids. We then investigated the spatial correlations at the two-residue (dipeptide) and three-residue (tripeptide) levels in what may be described as higher order Ramachandran maps, with the premise that the allowed conformational space starts to shrink as we introduce neighborhood effects. We found, for instance, for a tripeptide which potentially can exist in any of the 27(3) "allowed" conformations, three-fourths of these conformations are redundant to the 95% confidence level, suggesting sequence context dependent preferred conformations. We then created a look-up table of preferred conformations at the tripeptide level and correlated them with energetically favorable conformations. We found in particular that Boltzmann probabilities calculated from van der Waals energies for each conformation of tripeptides correlate well with the observed populations in the structural database (the average correlation coefficient is ∼0.8). An alpha-numeric string and hence the tertiary structure can be generated for any sequence from the look-up table within minutes on a single processor and to a higher level of accuracy if secondary structure can be specified. We tested the methodology on 100 small proteins, and in 90% of the cases, a structure within 5 Å is recovered. We thus believe that the method presented here provides the missing link between Ramachandran maps and tertiary structures of proteins. A Web server to convert a tertiary structure to an alphanumeric string and to predict the tertiary structure from the sequence of a protein using the above methodology is created and made freely accessible at http://www.scfbio-iitd.res.in/software/proteomics/rm2ts.jsp.

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

“…However, while the deviations in statistical coil-like behavior of amino acid residues in intrinsic disordered proteins are interpreted as indicating the transient formation of a secondary structure [72], our results suggest that nearest-neighbor interactions shift conformational propensities of amino acid residues in the protein rather than facilitating formation of regular secondary structures like right-handed helices, β-strands, and polyproline II-like helices. Through the present work, we highlight the relevance of four major types of non-local interactions on protein secondary and tertiary structures, which has been emphasized over the past 60 years [73][74][75][76] and the formation of non-local interactions is a crucial step in the protein-folding process and these interactions might be key drivers to force the residues to adopt certain dihedral angles.…”

A protein sequence fitness function for identifying natural and nonnatural proteins

“…This huge decline in the number of available compact structures and unique 100 residues polypeptides substantiate the possibility of some underlying protein signatures at sequence level that lend the protein with potential of imitating the natural proteins and fold into stable structure. Some of the previous studies have utilized the concept of neighboring effect of amino acid residues in dictating protein secondary and tertiary structures 30‐33 …”

Multidimensional virtual‐system coupled canonical molecular dynamics to compute free‐energy landscapes of peptide multimer assembly

“…An alternative class of generalized-ensemble methods including umbrella sampling, [26,27] adaptive umbrella sampling (AUS), [28][29][30][31] and their variants [13,[32][33][34][35][36][37][38] introduces a structural parameter, for example, intermolecular distance, for the reaction coordinate. In theory, AUS can avoid the oversight described above when major and minor basins can be discriminated on the reaction-coordinate axis.…”