Electron spin-lattice relaxation in proteins, model heme complexes and ferricyanide solutions at helium temperatures

Abstract

Electron Spin-Lattice relaxation rates are reported for frozen solutions of the blue-copper proteins azurin and plastocyanin, the low-spin iron heme protein cytochrome-c, two (bis)imidazole ferric heme complexes in three different organic solvents and two ferricyanide solutions. Measurements were performed at X-band frequencies and temperatures between 1.4 and 22 K. Relaxation rates show a one-phonon direct process at low temperatures (T $$ 4 K) with a temperature dependence that is approximately characterized by a simple power-law (T$\sp{\rm n}$), with fitted values of n between 4.9 and 7.45. The expected temperature dependence of a two-phonon (Raman) process in simple crystalline systems has been demonstrated to follow a power-law (T$\sp{\rm n}$), with n = 9.0. The anomalously weak temperature dependence for protein systems has been tentatively explained in terms of a fractal model of protein dynamics, where the temperature exponent is n = 4q + 2d - 1 and q = dd$\sb{\varphi}$/D. The localized vibrations (fractons) are characterized by a localization exponent d$\sb{\varphi}$ on an underlying fractal lattice with Hausdorf dimension D and the fracton density of states with a spectral dimension d. A wide variation in the fitted n-values for different solvent conditions of the protein solutions suggests that it may not be possible to conclusively verify the fractal model as it is formulated. Studies of heme complexes and ferricyanide solutions show that the protein backbone is not essential for the observation of an anomalous temperature dependence. Two phenomenological models of a phonon density of states in amorphous systems are discussed and compared to relevant length scales.