Fractons and the Fractal Structure of Proteins

We show that a proper description of the temperature dependence of the spin-lattice relaxation rate of low-spin hemoproteins and ferredoxin requires that both the fractal structure of the protein backbone (polypeptide chain) and the cross connections (H bridges) between segments of the folded chain be taken into account. Within this picture the fracton dimensionality $d_{\mathrm{fr}}$ (recently introduced by Alexander and Orbach), the fractal dimensionality $d_f$, and the experimental noninteger exponent $n$ of Stapleton et al. (spin-lattice relaxation rate $\frac{1}{T_1}\propto T^n$) become satisfactorily consistent.