Dielectric response of frustrated water down to a single‐molecule contribution

Abstract

A theory of dielectric response of water under nanoscale confinement was long overdue. This work addresses the problem by establishing a relation between dielectric response and hydrogen-bond frustration subsumed in a non-Debye polarization term. The results hold down to the single-molecule contribution and are validated vis-à-vis experimental measurements on a system where dielectric modulation entails removal of a single water molecule. The frustrated dielectric response down to molecular scales is assessed by contrasting two enantiomeric ligands in association with the same protein, with the complexes differing in the removal of a single interfacial water molecule.

Stickiness of the Hydrogen Bond

“…Yet, the effective wrapping drag exerted by the hydrogen bond down to the effect of a single‐molecule removal has been measured experimentally utilizing a molecular force probe, as shown in Figure , and lies within the confidence band of a previous experimental estimation . To validate the nanoscale dielectric theory, our scope here is to compute the wrapping drag, and thus interpret the experimental underpinning of the nanoscale stickiness of the hydrogen bond.…”

“…The computation of the nanoscale stickiness exploits a local molecular descriptor of the water fluxional structure. To that effect, we introduce a “frustration scalar field” parametrically dependent on test hydrophobe position , that indicates the expected number of missed hydrogen‐bond opportunities of a test water molecule at spatial location relative to the quasi‐tetrahedral saturating coordination associated with bulk water . The frustration field is defined as , where is the expected number of hydrogen bonds engaging a water molecule visiting a sphere of radius r = 4 Å centered at position for a minimum time period τ = 1 ps around time t , a permanence time typically associated with the relaxation timescale for a decoupled water lattice .…”

“…This scheme, subsumed into the permittivity coefficient ε, has been often adopted with scant justification to treat water partially confined in nanocavities at the interface with protein structure or with other materials featuring nano‐detailed surfaces . The extrapolation is probably unwarranted since the Debye ansatz breaks down under nanoscale confinement mostly due to the frustration of water hydrogen bonding possibilities . Reconciling the discrete behavior of nano‐confined water with the continuum equations that govern dielectric response requires a nontrivial extension of the latter .…”

“…The extrapolation is probably unwarranted since the Debye ansatz breaks down under nanoscale confinement mostly due to the frustration of water hydrogen bonding possibilities . Reconciling the discrete behavior of nano‐confined water with the continuum equations that govern dielectric response requires a nontrivial extension of the latter . Accordingly, this work identifies the nanoscale stickiness of water‐embedded preformed hydrogen bonds as the kind of phenomena that is not encompassed by the classical continuum laws governing dielectric response but can be quantitatively predicted and interpreted within a nanoscale dielectric theory holding down to molecular dimensions.…”

“…Heuristically, this motion is predicted to lower the “local dielectric permittivity” with the net effect of enhancing the underlying electrostatics. Locating the center of coordinates at the hydrogen‐bond shared proton, the wrapping drag , exerted by a hydrogen bond on a test hydrophobe at position , is orthogonal to the Coulombic field ( Figure ) and can be heuristically written as , where U C, 0 is the in vacuo Coulomb energy of the hydrogen‐bond underlying electrostatic interaction and is the nanoscale Debye component of the dielectric permittivity along the direction of the electrostatic field . The standard continuum treatment of electrostatics does not enable the computation of the wrapping drag, since the ‐dependence of the permittivity is not available.…”