Fluctuations of conformational states in biological molecules: Theory for anomalous spectral diffusion dynamics

An anomalous power law behavior of spectral diffusion broadening of persistent holes is found in large biological molecules dissolved in a glassy host at very low temperature. We argue that this is caused by the internal degrees of freedom of the biomolecule itself rather than by excitations of the glassy host. To explain the observed universal time dependence of the hole width w ∼ t^1/4, we propose a stochastic model of protein dynamics close to the equilibrium, which describes this process in terms of the quasi-one-dimensional diffusion of proteins in conformation space. Assuming that each step of diffusive motion changes the electronic excitation energy randomly, we derive the observed time behavior of the spectral hole. The physical mechanisms involved are discussed.