Viewpoint 6 — characteristic aspects of GG sequences and the importance of constitutional properties for conformational entropies

Abstract

Two consecutive syn-clinal or gauche torsional angles (GG sequence) in a chain of five atoms, A-B-C-D-E, are ubiquitous elements of structural chemistry, occurring in many cyclic and all helical structures. Recent MP2 calculations have shown that GG sequences in hydrocarbons are distinguished by a stabilizing cooperative energy increment that is not found for other torsional sequences, like trans-trans (TT), or trans-gauche (TG). This increment is connected with the ability of GG sequences to effect large changes (greater than 0.15Å) in 1,5-nonbonded distances, between 1,5-CH 3/CH 3,1,5-CH 2/CH 2, and 1,5-CH 2/CH 3 groups in an attractive region of the van der Waals potential, by small changes (less than 5°) in torsional angles (τ). This feature is a specific example of the general phenomenon of the torsional sensitivity (TS) of conformations in structures with several sequential backbone torsional angles: TS is a measure of the extent to which non-bonded distances at a given point in torsional space, and their contributions to non-bonded potential energy, change with changes in backbone torsional angles. TS in a conformational region is high, when small amplitude torsional motions around a given point in torsional space lead to large changes in non-bonded distances and their contributions to non-bonded potential energy. TS is low, when non-bonds are not significantly affected by large amplitude torsional motions. A general analysis of the functional dependence of 1,5-non-bonded distances on torsional angles shows that, in n-pentane-like structures, there are two conformational regions of maximum TS in τ 1 = C1-C2-C3-C4, τ2 = C2-C3-C4-C5 space, situated at (τ1, τ2) equal to (+40°, +40°), or (−40°, −40°), and at (+90°, −90°) or (−90°, + 90°). The former is close to the GG region of hydrocarbons, ( + 60°, + 60°), and to the helical regions of peptides and proteins, (φ(N-C α = −60° and Ψ(C α - C') = −40°), while the latter is encountered in the C7 eq region of peptides, (φ = −80° and Ψ = +80°). Minimum TS is found in the vicinity of (180°, 180°), i.e. in the TT region of hydrocarbons, and close to the C5- or β-regions of peptides (φ = −160°, Ψ = +160°). Thus, molecular conformations can be classified by their TS, i.e. by a constitutional property of their backbone torsional angles. This classification has physical significance because TS is related to conformational entropy. In regions of low TS on a conformational energy surface, potential energy wells are characteristically flat and conformational entropies large. Vice versa, in regions of high TS, potential wells are characteristically steep, and conformational entropies small. Thus, helical minima (GG sequences, high TS) in peptides are constitutionally steep, and the free energy advantages of extended forms in proteins over puckered forms, which have a lower internal energy, are to some extent manifestations of a constitutional property.