Conformation of analysis of macromolecules. IV. Helical structures of poly-L-alanine, poly-L-valine, poly-beta-methyl-L-aspartate, poly-gamma-methyl-L-glutamate, and poly-L-tyrosine.

Abstract

Energy calculations have been carried out for several isolated (single-stranded) homopolymer polyamino acids in order to find the most stable regular (helical) conformations. The energy was expressed as a function of the dihedral angels φ, ψ, and the set of χi's, for rotations about the N–Cα and Cα–C′ bonds of the backbone, and the j single bonds of the side chain, respectively. Torsional, nonbonded, hydrogen-bonded, and dipole—dipole interaction energy contributions were included. For regular structures, the set of φ, ψ, and the χi's is the same in every residue. Energy contours (expressed in kilocalories per mole of monomer) were plotted on ψ-vs-φ diagrams at fixed values of the χi's or on χ2-vs-χ1 diagrams at fixed φ and ψ (and, in some cases, χ3). In addition, the energy was minimized with respect to all of the dihedral angles of the backbone and side chain in the neighborhood of the minima of the contour diagrams, using various minimization procedures, in order to locate the local minima precisely. For poly-L-alanine the left- and right-handed α-helical conformations are those of lowest energy, the right-handed one being more stable than the left-handed one by 0.4 kcal/mole. Similar results were obtained for poly-L-valine, the right-handed α helix being more stable than the left-handed one by 0.5 kcal/mole. In this case, the valyl side chain was found to be rotated around the Cα–Cβ bond by about 10°—15° away from a minimum of the side-chain torsional-potential-energy function. This prediction was verified by recent experiments showing the existence of the α-helical conformation in a block copolymer of D,L-lysine, and L-valine in 98% aqueous methyl alcohol solution. For poly-β-methyl-L-aspartate, analysis of the energy contributions indicated that, whereas the nonbonded energy would favor the right-handed form, the interaction of the dipole of the side-chain ester group with the dipole of the backbone amide group is more repulsive in the right-handed than in the left-handed α helix, thereby destabilizing the right-handed form. In order to demonstrate the importance of this dipole-dipole interaction, the calculations were repeated for several values of the dielectric constant and of the parameters for the nonbonded interaction potential function. As a result of these calculations, it is suggested that the existence of this polyamino acid in the left-handed α-helical form is due to the dipole—dipole interaction between the side chain and the backbone. In contrast, poly-γ-methyl-L-glutamate was found to have a lower energy in the right-handed α-helical form than in the left-handed one. In this polyamino acid, both the nonbonded and the dipole—dipole interaction energies favor the right-handed form, i.e., the additional methylene group in the glutamic acid side chain alters the relative orientations of the side-chain and backbone dipoles so as to lead to a stronger stabilization energy in the right-handed α helix. Poly-L-tyrosine was found to have a lower energy in the right-handed α-helical form than in the left-handed one, the difference in energy between the two forms being 1.8 kcal/mole. The main contribution to the stabilization of the right-handed form is from the nonbonded energy. In summary, in all the cases examined here, the nonbonded interaction energy would favor the right-handed α helix over the left-handed one. However, the dipole—dipole interaction between the side chain and the backbone is apparently of sufficient importance, in the case of the aspartate polymer, to reverse the screw sense.