The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photo-induced electron transfer, and found to be a stationary, time-reversible and non-Markovian Gaussian process. Within the generalized Langevin equation (GLE) 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 ± 0.07 in a broad range of time-scales (10-3 s -10s. Such a long time memory effect, which is associated with sub-diffusion within a harmonic bound, has implications to protein functions.
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