Observation of a Power-Law Memory Kernel for Fluctuations within a Single Protein Molecule

Abstract

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel $K(t)$, which is proportional to the autocorrelation function of the random fluctuating force. $K(t)$ is a power-law decay, $t^{-0.51\pm 0.07}$ in a broad range of time scales (${10}^{-3}–10\mathrm{s}$). Such a long-time memory effect could have implications for protein functions.