Predictions of peptide and protein backbone structural parameters from first principles. IV: Systematic comparisons of calculated N—C(α)—C′ angles with peptide crystal structures

Abstract

SUMMARYFor some fifty oligopeptides for which high resolution crystal structures have been deposited in the Cambridge Crystallographic Data File, the crystallographic N-C(α)-C angles, cryst α i , were compared with values calculated on the basis of first principles. Crystal structures of cyclic and non-cyclic peptides were included in this comparison, with sizes ranging from six to sixteen residues, if they were refined to an R-factor of at least 0.08 or better. The calculated values were obtained using an algorithm which employs spline-function representations of ab initio dipeptide conformational geometry maps to predict backbone bond lengths and angles in oligopeptides and proteins as functions of the φ[N - • grid and region-average values calculated, the average rms deviation between the two sets in the most populated regions is 1.52• . As in the previous protein studies, helix compression is found in the oligopeptides. The analysis reveals that the φ/ψ-torsional dependence of N-C(α)-C in oligopeptides is similar to that previously found for proteins. We expect the computational procedure to be useful for establishing flexible geometry functions for use in empirical peptide and protein modeling and protein crystallography.KEY WORDS peptide and protein background geometries; conformationally dependent geometry trends; comparison of ab initio peptide geometries and crystal structures; standard geometry functions; ideal geometries for protein crystallography.

Ab Initio Geometry Determinations of Proteins. 1. Crambin

“…Thus, the helix compression effect, ∼1.5°, 9,10 is significantly above the error limits of the computational procedures. A similar phenomenon, -expansion, is also found in polypeptide systems, [6][7][8][9] but crambin does not have a sizable fragment in this exact conformational region that would clearly illustrate this effect.…”

“…Some time ago Cao et al − described a program that calculates the HF/4-21G backbone bond lengths and angles of the model dipeptide N -acetyl- N ‘-methylalaninamide at any arbitrary point in its φ,ψ-space. Using this program, the HF/4-21G dipeptide values of N−C(α), C(α)−C‘, and N−C(α)−C‘) were calculated for the current study at the φ and ψ angles of the residues of crambin obtained by the HF/4-21G geometry refinement of the entire molecule.…”

“…For the R R -helical regions, residues 7-16 and 23-29, the average value of the N-C(R)-C′ angles in the HF/4-21G dipeptide structures (112.6°) is 1.8°larger than the average angle (110.8°) in the HF/4-21G structure calculated for the molecule as a whole. The two values demonstrate helix compression [6][7][8][9][10] in the polymer chain compared to the single (dipeptide) residue. That is, due to cooperative effects, the N-C(R)-C′ angles in elongated R-helices are compressed compared to single residues.…”

“…Ab initio geometry optimizations of peptides are a valuable source of information on the structural properties of peptides and proteins. Even the earliest studies , of this kind, involving HF/4-21G gradient , geometry optimizations of the N -acetyl- N ‘-methyl derivatives of glycine 1 and alanine 2 revealed unexpected details of the flexibility of peptide geometries in close agreement with the crystal structures of oligopeptides , and proteins. − In the meantime many similar studies have been performed − employing various basis sets and ab initio computational techniques.…”