Abstract
Stokes’s law for the friction of a sphere in water has been argued to work down to molecular scales, provided the effective hydrodynamic radius includes the hydration layer. In interpretations of experiments and in theoretical models, it is tacitly assumed that the solvent friction experienced by a solute does not depend on whether an external confinement potential acts on the solute. Using a novel method to extract the friction memory function from molecular dynamics simulations, we show that the solvent friction of a strongly harmonically confined methane molecule in water increases by 60% compared to its free-solution value, which is caused by an amplification of the slowest component of the memory function. The friction enhancement occurs for potential strengths typical of physical and chemical bonds and is accompanied by a significant slowing-down of the hydration water dynamics. Thus, the solvent friction acting on molecular solutes is not determined by solvent properties and solute-solvent interactions alone but results from the coupling between solute and solvent dynamics and thereby can be tuned by an external potential acting on the solute. This also explains why simulations of positionally constrained solutes do not reproduce free-solution diffusivities. Dynamic scaling arguments suggest similar effects also for macromolecular solutes provided the solution viscosity is sufficiently enhanced.
Highlights
Friction sets the fundamental time scale for all processes that occur in a solvent, ranging from molecular diffusion [1], macromolecular conformational changes [2,3], and chemical reactions [4], to protein folding [5,6]
Our results demonstrate a direct consequence of this coupling between solute and hydration shell dynamics: By a detailed analysis of the solute friction memory function, which we extract from our simulation trajectories using a novel method, we show that solute diffusivity and hydration shell kinetics are coupled and both influenced by the inherent time scale of solute motion, in our simulation model set by the external potential strength K
The friction coefficient γ of a methane molecule is shown to significantly depend on the confinement potential strength K, which constitutes a generic and unexpected modification of Stokes’s law γ 1⁄4 6πηR. This reflects, on the one hand, that friction coefficients of fixed solutes differ from free solutes, as suggested previously [43]; on the other hand, it means that freesolution friction coefficients and memory functions cannot be obtained from confined or frozen simulations, contrary to common practice
Summary
Friction sets the fundamental time scale for all processes that occur in a solvent, ranging from molecular diffusion [1], macromolecular conformational changes [2,3], and chemical reactions [4], to protein folding [5,6]. In this paper we discuss a different modification of Stokes’s law, demonstrated by molecular dynamics (MD) simulations of a single methane in water that is subject to a harmonic confinement potential of strength K. There are various consequences of our findings: In simulation studies, it is common practice to constrain the position of a solute in order to determine spatially dependent solvation properties in inhomogeneous systems, for example, in hydrated lipid bilayer systems [9] While this is unproblematic for static properties such as free-energy profiles, our results show that this procedure potentially perturbs kinetic properties such as the diffusivity profile.
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