Solvent Fluctuations Induce Non-Markovian Kinetics in Hydrophobic Pocket-Ligand Binding

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. The latter describes the collective hydration behavior of the pocket by bimodal fluctuations of the water-pocket interface that dynamically couples to the diffusive motion of the approaching ligand via the hydrophobic interaction. This leads to a Markovian set of overdamped stochastic equations in 2D-coordinate-space spanned by the interface position and the ligand position. Numerical simulations demonstrate locally increased friction of the ligand, decelerated binding kinetics, and local non-Markovian (memory) effects in a reduced 1D-description along the ligand's reaction (distance) coordinate as found previously in explicit-water simulations. Our minimalistic model elucidates the origin of locally enhanced friction that can be traced back to long-time decays in the force-autocorrelation function induced by a spatially fluctuating interface-ligand interaction. Furthermore, we construct a generalized 1D-Langevin description of ligand binding including a spatially local memory function that reflects the dominant frequencies of the pocket wetting/dewetting process, enabling further interpretation and a semianalytical quantification of our results.