Origin of intrinsic 3₁₀‐helix versus strand stability in homopolypeptides and its implications for the accuracy of the Amber force field

Abstract

Current all-atom force fields often fail to recognize the native structure of a protein as the lowest free energy minimum. One possible cause could be the mathematical form of the potential based on the assumption that the conformation of a residue is independent of its neighbors. Here, using quantum mechanical (QM) methods (MP2/6-31g**//HF/6-31g** and MP2/cc-pVDZ//cc-pVDZ//HF/cc-pVDZ), the intrinsic correctness of the gas phase terms (without solvation) of the Amber ff03 and ff99 potentials are examined by testing their ability to reproduce the relative 3 10 -helix versus extended structure stabilities in the gas phase for 1-7-residue alanine, valine, leucine, and isoleucine homopolypeptides. The 3 10 -helix versus extended state stability strongly depends on chain length and less on the amino acid identity. The helical conformation becomes lower in energy than the extended conformation for all tested peptides longer than two residues, and its stability increases with the increase of chain length. The ff03 potential better describes the 3 10 -helix versus extended state energy than ff99 and also reproduces the curvature of the relative helix-extended state energies. Therefore, the mathematical form of the Amber potential is sufficient to describe the local effect of 3 10 -helix versus extended structure stabilization in the gas phase. However, the energy curves are shifted and the backbone geometries differ compared with the QM results. This may cause significant geometric discrepancies between native and predicted structures. Therefore, extant molecular mechanics force fields, such as Amber, need refinement of their parameters to correctly describe helix-extended state energetics and geometry of major conformations.

Helix compactness and stability: Electron structure calculations of conformer dependent thermodynamic functions

“…Results 3.1. Molecular structure I: torsion angles and twisting Molecular structures of both the β-stranded and helical structures of Ala 10 ( Figure 1) are very similar to those calculated previously [1], [16], [17], [18], [19] and [28]. The backbone folds of helices in membrane proteins [φ −60°, ψ −45° [29] and [30] and in water soluble globular proteins [φ −65°, ψ −40° [31] and [32] are close to each other, and are somewhat different from those of 3 10 -helices [φ −68°, ψ −18° [31] and [33].…”

“…Consequently the 3 10 -helix must exhibit the intrinsic properties of the right-handed helical structure, since it is the most stable form when environmental effects are excluded. Several QM computations have been published on 3 10 -helical structures [16], [17], [18] and [19]. However, these studies reported electronic energies rather than thermodynamic functions.…”

Communications: Is quantum chemical treatment of biopolymers accurate? Intramolecular basis set superposition error (BSSE)

“…The error ͑intramolecular BSSE͒ produced by such superposition was found to exceed 4 kcal mol −1 when a medium-sized basis set was used. [35][36][37][38]45,46 This means that this error has the same order of magnitude as the relative energy differences of secondary structure elements of biopolymers reported in recent literature ͓see Fig. 4 and Table I ͑Ref.…”

“…12 ͒ and computational ͑molecular dynamics and quantum chemistry͒ techniques. 3,12,13,38 Their integration is expected to be particularly fruitful. 3,12,13,38 Note that in many cases, modern force fields ͓͑FF͒, e.g., Amber FF03 and FF99͒ fail to recognize the protein native structure.…”

“…Inaccuracy of such fields makes such a structure not the free energy minimum or, at least, not the lowest energy one. 13,38 Unfortunately, there have been critical challenges toward developing a precise quantum chemical treatment of biopolymers: ͑i͒ a large system size and, as a consequence, vast computational requirements; 2,3,14-17 ͑ii͒ the necessity for solvent effect inclusion; 2, [14][15][16][17] and ͑iii͒ the absence of ambiguous experimental ͑especially gas-phase 13,18,38 ͒ data for theoretical result verification. 15,18 Recent progress in density functional theory ͑DFT͒ has enabled the study of many interesting biosystems of medium size ͑such as the simplest biopolymers and natural and artificial peptides͒.…”