The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis

Abstract

The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H(α) hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen-bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations.

Factors affecting the amplitude of the τ angle in proteins: a revisitation

“…In line with previous reports (Karplus, 1996;Berkholz et al, 2009;Improta et al, 2015b;Esposito et al, 2013;Touw & Vriend, 2010), residues belonging to different secondarystructure elements display large differences in the angle. In particular, as shown in Table 1, the largest values are exhibited by residues belonging to 3 10 -helices, whereas the lowest values Average values with standard deviations and occurrences (number of residues) of the 18 non-Gly/non-Pro amino-acid residues of the data set Data1.6 in -helix, 3 10 -helix, -sheet and polyproline II structures.…”

“…Indeed, it has been shown that several backbone parameters such as bond lengths/angles and indicators of peptide-bond planarity present a remarkable variability (Karplus, 1996;Esposito et al, 2000a;Esposito et al, 2005Esposito et al, , 2013Improta et al, 2011;Berkholz et al, 2009Berkholz et al, , 2010Berkholz et al, , 2012Esposito et al, 2000b;Improta et al, 2015a;MacArthur & Thornton, 1996;Howard et al, 2004;Karplus et al, 2008;Jaskolski et al, 2007;Tickle, 2007). Moreover, recent QM calculations have shown that the variability of these parameters is essentially dictated by local effects (Caballero et al, 2014;Improta et al, 2015b).…”

“…Although the variability of the angle has been well established (Berkholz et al, 2009;Improta et al, 2015b), the factors that modulate it are still under investigation. The very first statistical analysis of protein structure databases, performed by Karplus (1996), suggested that the local backbone conformation plays a major role in dictating the amplitude of the angle.…”

The fully‐extended conformation in peptides and proteins

“…Specifically: (i) the value of τ averaged from the 123 fully‐extended Gly residues is 110.2°, whereas that averaged from 774 Gly residues in conformations other than fully‐extended (selected through the search criterion ϕ,ψ = 0°±160°,0°±160°) found in the CSD is 114.0°; (ii) the value of τ averaged from the fully‐extended C α ‐trisubstituted residues is 108.1°, as compared to the value of 112.6° averaged from 792 helical Ala residues (ϕ,ψ = −60°±20°, −30°±20°) found in the CSD. The sensitivity of the valence geometry of amino acid residues, and in particular of the τ bond angle, to the peptide/protein backbone conformation is a well‐established phenomenon …”

Is there a connection between peptide bond geometry and aminoacid residue conformational preferences?

“…Indeed, although a large number of computational and experimental investigations have highlighted that the different protein residues show distinct conformational propensities, none of the current hypotheses is able to satisfactorily explain these preferences.In the last decades, we and others have clearly demonstrated that several geometrical parameters of protein backbone (bond angles, peptide bond distortions from planarity, and pyramidalization of the carbonyl carbon atom) are heavily dependent on the local conformation (φ/ψ dihedral angles) [1][2][3][4][5][6][7][8]. Moreover, a correlation between bond distances such as CO and CN has been detected in ultrahigh resolution protein structures [9].…”