  We investigate the impact of water fluctuations on the key-lock association
kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock)
by means of a minimalistic stochastic model system. It describes the collective
hydration behavior of the pocket by bimodal fluctuations of a water-pocket
interface that dynamically couples to the diffusive motion of the approaching
ligand via the hydrophobic interaction. This leads to a set of overdamped
Langevin equations in 2D-coordinate-space, that is Markovian in each dimension.
Numerical simulations demonstrate locally increased friction of the ligand,
decelerated binding kinetics, and local non-Markovian (memory) effects in the
ligand's reaction coordinate as found previously in explicit-water molecular
dynamics studies of model hydrophobic pocket-ligand binding [1,2]. Our
minimalistic model elucidates the origin of effectively enhanced friction in
the process that can be traced back to long-time decays in the
force-autocorrelation function induced by the effective, spatially fluctuating
pocket-ligand interaction. Furthermore, we construct a generalized 1D-Langevin
description including a spatially local memory function that enables further
interpretation and a semi-analytical quantification of the results of the
coupled 2D-system.
