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Origin of $1/f$ noise transition in hydration dynamics on a lipid membrane surface

Water molecules on lipid membrane surfaces are known to contribute to membrane stability by connecting lipid molecules and acting as a water bridge. Although the number of water molecules near the membrane fluctuates dynamically, the hydration dynamics has been veiled. Here we investigate residence statistics of water molecules on the surface of a lipid membrane using all-atom molecular dynamics simulations. We show that hydration dynamics on the lipid membrane exhibit $1/f^β$ noise with two different power-law exponents, $β_l < 1$ and $β_h > 1$. By constructing a dichotomous process for the hydration dynamics, we find that the process can be regarded as a non-Markov renewal process. The result implies that the origin of the $1/f$ noise transition in hydration dynamics on the membrane surface is a combination of a power-law distribution with cutoff of interoccurrence times of switching events and a long-term correlation between the interoccurrence times.