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Water molecules on lipid membrane surfaces are known to contribute tomembrane stability by connecting lipid molecules and acting as a water bridge.Although the number of water molecules near the membrane fluctuatesdynamically, the hydration dynamics has been veiled. Here we investigateresidence statistics of water molecules on the surface of a lipid membraneusing all-atom molecular dynamics simulations. We show that hydration dynamicson the lipid membrane exhibit $1/f^\beta$ noise with two different power-lawexponents, $\beta_l < 1$ and $\beta_h > 1$. By constructing a dichotomousprocess for the hydration dynamics, we find that the process can be regarded asa 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 combinationof a power-law distribution with cutoff of interoccurrence times of switchingevents and a long-term correlation between the interoccurrence times.

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