A Comparison of the CHARMM, AMBER and ECEPP Potentials for Peptides. II. φ-ψ Maps for N-Acetyl Alanine N′-Methyl Amide: Comparisons, Contrasts and Simple Experimental Tests

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Abstract
φ-ψ maps of N-acetyl alanine N′-methyl amide have been computed using the CHARMM potential, the all-atom AMBER potential, and the ECEPP/2 potential, before and after adiabatic relaxation. Maps using the CHARMM and AMBER potentials were determined with values of 1.0 and 4.0 for the dielectric constant ε, and with a distance dependent dielectric constant. Adiabatic relaxation was carried out using flexible geometry for the CHARMM and AMBER potentials, and using rigid geometry for the AMBER and ECEPP potentials. In all cases, the lowest energy was found in the C7 eq region (φ −70°, ψ ∼ 70°). The maps with CHARMM and AMBER with ε = 4.0 and with ECEPP, without adiabatic relaxation, were broadly similar but differed in the relative energies allotted to high-energy regions of the map. After adiabatic relaxation with rigid geometry, the map with ECEPP, and the map with AMBER using a distance-dependent dielectric constant, agreed fairly well apart from differences in the relative energies of the αR, αL and C7 ax regions. After adiabatic relaxation with flexible geometry, the maps with CHARMM and AMBER became very similar; the lowest energies were observed in the C7 eq region, the C5 region (φ ∼ −150°, ψ ∼ 150°) and the C7 ax region (φ ∼ 70°, ψ 70°). Breakdown of the energies, after adiabatic relaxation, into electrostatic, nonbonded, and geometric (including torsional) contributions, showed that (1) with fixed geometry, the nonbonded and torsional contribution to the ECEPP and AMBER potentials were very similar, but the electrostatic contributions were markedly different; (2) with flexible geometry, the nonbonded contribution to the CHARMM and AMBER potentials did not vary greatly over the whole map. The φ-ψ maps were subjected to three simple comparisons with experiment. (1) The maps were used to predict the characteristic ratio for poly-L-alanine, and the results were compared with experimental findings (D.A. Brant and P.J. Flory, J. Amer. Chem. Soc. 87, 2788-2791, 1965). The agreement with experiment was acceptable for ECEPP, and for CHARMM after adiabatic relaxation, marginal for AMBER after adiabatic relaxation, and unsatisfactory for CHARMM or AMBER without adiabatic relaxation. (2) Deviations of bond angles from their equilibrium values, in energy-minimized conformations, were compared with values deduced from crystals of terminally-blocked amino acids. With both the CHARMM and AMBER potentials using flexible geometry, one or more excessive deviations was observed in the C7 ax local minimum. (3) Distributions of φ and ψ among residues other than glycine and proline, taken from the coordinates of high-resolution crystals of 16 non-homologous proteins, were plotted for those residues that had zero, one, two, or three hydrogen bonds, respectively, involving a backbone atom. Comparison of the plots with the φ-ψ maps generated using CHARMM or AMBER with flexible geometry showed that, in the plots based on the X-ray data, far more residues had φ-ψ values in the αR region, and far fewer had φ-ψ values in the C7 ax region, than would be expected from those calculated maps. Comparison of the plots with the maps generated using ECEPP, or AMBER with fixed geometry and ε = 4.0, showed much better agreement; however, some discrepancies remained. It is concluded that none of these potentials leads to predictions that are completely compatible with all the experimental results, although ECEPP, and AMBER with fixed geometry and ε = 4.0, come closer than the other variants of the potentials. Although the potentials have often performed satisfactorily in other tests with small peptides, there is a need to develop a more accurate potential for large peptides and proteins, which should almost certainly embody new functional forms.