Comprehensive Analysis of Energy Minima of the 20 Natural Amino Acids

Abstract

Energy minima of the 20 natural amino acids (capped by a peptide bond at both the N and the C termini, CH3-C(═O)-N(H)-(H)Cα(R)-C(═O)-N(H)-CH3), were obtained by ab initio geometry optimization. Starting with a large number of minima, quickly generated by MarvinView, geometry optimization at the HF/6-31G(d,p) level of theory reduced the number of minima, followed by further optimization at the B3LYP/apc-1 and MP2/cc-pVDZ levels, which caused some minima to disappear and some stable minima to migrate on the Ramachandran map. There is a relation between the number of minima and the size and the flexibility of the side chain. The energy minima of the 20 amino acids are mainly located in the regions of βL, γL, δL, and αL of the Ramachandran map. Multipole moments of atoms occurring in the fragment [-NH-Cα-C(═O)-] common to all 20 amino acids were calculated at the three levels of theory mentioned above. The near parallelism in behavior of these moments between levels of theory is beneficial toward estimating moments with the more expensive B3LYP and MP2 methods from data calculated with the cheaper HF method. Finally, we explored the transferability of properties between different amino acids: the bond length and angles of the common fragment [-NH-Cα(HαCβ)-C'(═O)-] in all amino acids except Gly and Pro. All bond lengths are highly transferable between different amino acids, and the standard deviations are small.

The prediction of topologically partitioned intra-atomic and inter-atomic energies by the machine learning method kriging

“…Single-point energy calculations were performed on the resulting structures, outputting the respective molecular wavefunction and Hessian of the potential energy, calculated at the same level. For the capped glycine molecule, we selected the global minimum conformation from the nine known energetic minima described in a previous publication [68]. For glycine, the calculations were performed at B3LYP/apc-1 [69] level of theory, in-keeping with the level of theory used in previous research [68].…”

“…For the capped glycine molecule, we selected the global minimum conformation from the nine known energetic minima described in a previous publication [68]. For glycine, the calculations were performed at B3LYP/apc-1 [69] level of theory, in-keeping with the level of theory used in previous research [68]. Working at B3LYP level complements a recent publication [41] that validates the extension of the IQA approach to the B3LYP density functional.…”

An improved two-rotor function for conformational potential energy surfaces of 20 amino acid diamides

“…A more extensive study by Yuan et al,67 in which all stable amino acid molecular geometries are searched such that there are only small differences between two conformations with respect to all torsion angles, including sidechain dihedral angles. The authors carried out the calculations in three levels of theory, such as HF/6-31G(d,p), B3LYP/apc-1 and MP2/cc-pVDZ.…”

“…It is interesting to compare the energy barrier between the global minimum and the other local minima for each of the amino acids. The energy range, which is defined as the energy difference between the global minimum and the (local) minimum with the highest energy, 67 is shown in Fig. 6.…”

“…Several studies include alanine, [17][18][19][20] valine, 21 glutamic acid, [60][61][62][63][64][65][66][67] As performing quantum chemical calculations is inherently computationally expensive, approximations using analytical fitting methods have been widely used in the construction of PESs. 68,69 For instance, a fitting procedure based on the many-body expansion (MBE) method, 70 amplified by Varandas 71 is widely used in the so-called double many-body expansion (DMBE) method.…”