Solvent fluctuations induce non-Markovian kinetics in hydrophobic pocket-ligand binding

TL;DR

This study models how water fluctuations cause non-Markovian, memory effects in the kinetics of hydrophobic pocket-ligand binding, revealing increased friction and slowed binding due to collective hydration dynamics.

Contribution

It introduces a minimalistic stochastic model capturing water fluctuation effects on binding kinetics, linking long-time force autocorrelations to effective friction enhancements.

Findings

Water fluctuations induce non-Markovian effects in binding kinetics.

The model shows increased local friction and decelerated ligand binding.

A generalized Langevin equation with memory function explains the observed dynamics.

Abstract

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.