Anisotropic rotational diffusion of an α helix and analysis of the internal motion of side chains

Abstract

In order to investigate the anisotropic rotational diffusion of the backbone and the side chains of poly-L-lysine the 13C spin-lattice and spin–spin relaxation times of all carbon atoms with directly bound H atoms have been obtained at a Larmor frequency of 67.89 MHz. The polypeptide was dissolved in a mixed solvent of 40% methanol and 60% water. In this solvent, at pH=11.3, the backbone of poly-L-lysine is in the conformation of an α helix with partially charged side chains. The macromolecule was, therefore, regarded as a rigid rod and the rotational diffusion of the backbone was described by two diffusion constants D1 and D3 which characterize the rotational diffusion of, and around, the symmetry axis, respectively. The rotational motion of the Cβ methylene group with respect to the laboratory coordinate system is characterized by the rotational diffusion of the backbone relative to the laboratory system and by superposed rotations around the Cα–Cβ bond relative to the molecular coordinate system. Simulation of the possible internal motions by using a molecular model has shown that only two rotameric positions of the β methylene group are allowed. Consequently, the model of jumps between two allowed rotamers was applied in the evaluation procedure. The corresponding theory of spin-relaxation was evaluated using Wigner rotation matrices. The diffusion constants of D1=1.0×105 s−1, D3=3.8×107 s−1, and the jump rate of k1=5.0×107 s−1 were evaluated. The rotations of the CγH2, CδH2, and CεH2 methylene groups have been described with the model of one-dimensional diffusion around the corresponding bonds.