Computation of Overhauser dynamic nuclear polarization processes reveals fundamental correlation between water dynamics, structure, and solvent restructuring entropy

Abstract

Hydration water dynamics, structure, and thermodynamics are crucially important to understand and predict water-mediated properties at molecular interfaces. Yet experimentally and directly quantifying water behavior locally near interfaces at the sub-nanometer scale is challenging, especially at interfaces submerged in biological solutions. Overhauser dynamic nuclear polarization (ODNP) experiments measure equilibrium hydration water dynamics within 8-15 angstroms of a nitroxide spin probe on instantaneous timescales (10 picoseconds to nanoseconds), making ODNP a powerful tool for probing local water dynamics in the vicinity of the spin probe. As with other spectroscopic techniques, concurrent computational analysis is necessary to gain access to detailed molecular level information about the dynamic, structural, and thermodynamic properties of water from experimental ODNP data. We chose a model system that can systematically tune the dynamics of water, a water-glycerol mixture with compositions ranging from 0 to 0.3 mole fraction glycerol. We demonstrate the ability of molecular dynamics (MD) simulations to compute ODNP spectroscopic quantities, and show that translational, rotational, and hydrogen bonding dynamics of hydration water align strongly with spectroscopic ODNP parameters. Moreover, MD simulations show tight correlations between the dynamic properties of water that ODNP captures and the structural and thermodynamic behavior of water. Hence, experimental ODNP readouts of varying water dynamics suggest changes in local structural and thermodynamic hydration water properties.

Figure 1:. Snapshots of simulation boxes for a range of glycerol-water compositions.

Here, OPC water molecules are represented as VDW spheres and glycerol is shown in green (licorice representation). 4-OH-TEMPO is shown in licorice representation with carbons, oxygens, hydrogens, and nitrogens represented in cyan, red, white, and blue, respectively. The water and glycerol molecules closest to the 4-OH-TEMPO are made fully transparent in each panel to make the 4-OH-TEMPO visible amidst the densely packed glycerol mixture.

Figure 2:. Schematic of ODNP spectroscopic quantities calculation from classical MD trajectories.

(a) The snapshot shows 4-OH-TEMPO in a 0.1 mole fraction glycerol mixture at 290K with bulk water represented in VMD as a medium and the hydration waters within 3.5 angstroms of the spin probe in VDW sphere representation. Glycerol molecules are omitted for clarity. The diagram to the right of the snapshot illustrates the ODNP mechanism for the nearest water molecule to the spin probe at some time t. (b) The ODNP time autocorrelation function $C_{ODNP}(t)$ at a glycerol mole fraction of 0.1 (red line) is fit to a tri-exponential model [Equation 3] (black line) as described in the text. (c) The real part of the Fourier transforms of $C_{ODNP,fit}(t)$ gives spectral density function $J(\omega )$. Subsequently, $J(\omega )$ values at radical electron $J\left({\omega }_S\right)$ and proton Larmor frequencies $J\left({\omega }_I\right)$ are identified on the plot by the blue and green vertical lines, respectively. Approximate functional forms of ODNP spectroscopic quantities $k_{\sigma }$ and $\xi$ are in blue and green text, respectively. (d) Based on the Force-Free Hard Sphere model, we depict the expected trends in $k_{\sigma }/k_{\sigma ,bulk}$ (blue line) and $\xi /{\xi }_{bulk}$ (green line). Here, $k_{\sigma ,bulk}$ and ${\xi }_{bulk}$ are the expected bulk values of $k_{\sigma }$ and $\xi$ in pure STP water as defined by Franck et al.

Figure 3:. ODNP spectroscopic quantities measured experimentally and computed from classical MD simulations.

(a) ODNP spectral density functions as a function of glycerol concentration where lighter-colored lines correspond to higher glycerol content with the Larmor precession frequency of the proton and radical electron indicated by the green and blue vertical lines, respectively. Comparing experimentally and computationally determined (b) coupling factor $\xi$, (c) cross-relaxivity $k_{\sigma }$, and (d) $T_{10}[0]$ as a function of glycerol content. ODNP experiments and MD simulations yield spectroscopic quantities with similar trends with increasing glycerol concentration.

Figure 4:. Molecular dynamics probes of hydration water dynamics correlate strongly with ODNP coupling factors.

(a) The survival probability $C_{survival}(t)$ is the fraction of hydration shell waters that remain continuously within the second hydration shell of the spin probe radical oxygen. (b) The orientational autocorrelation function (OACF) $C_{OACF}(t)$ measures the rotation of hydration water dipole vectors away from their initial position. (c) The hydrogen bonding survival probability $C_{HB}(t)$ gives a time scale for water-water hydrogen bond breaking with a hydrogen bond being defined by cutoff radius $r_{cutoff}$ and cutoff angle ${\theta }_{cutoff}$. (d) The ODNP correlation function $C_{ODNP}(t)$ is used to estimate ODNP spectroscopic quantities. We derive characteristic time constants for (e) translational diffusion ${\tau }_{survival}$, (f) rotational diffusion ${\tau }_{OACF}$, (g) hydrogen bond lifetimes, and (h) ODNP diffusion ${\tau }_{ODNP}$ by integrating bi-exponential model fits to the ACFs [(a), (b), (c), and (d), respectively]. Further, these time constants all correlate strongly with relative coupling factor ${\xi }_r$.

Figure 5:. The three-body-angle distribution shows enhanced water tetrahedrality with increasing glycerol concentration.

(a) Increasing glycerol concentration in the mixture increases the incidence of tetrahedrally-coordinated waters relative to pure water $\left[P\left({109.5}^{\circ }\right)-P_{pure}\left({109.5}^{\circ }\right)\right]$ while decreasing the incidence of icosahedrally-coordinated (simple-fluid like) waters $\left[P\left({64}^{\circ }\right)-P_{pure}\left({64}^{\circ }\right)\right]$. The increasing population of tetrahedral waters with glycerol concentration correlates strongly to the relative diffusivity of pure water $D_{H_{2}O}/D_{H_{2}O,pure}$ at a given mixture composition. Characteristic time constants for (b) translational diffusion, ${\tau }_{survival}$, (c) rotational diffusion, ${\tau }_{OACF}$, (d) hydrogen bond lifetimes, ${\tau }_{HB}$, and (e) the ODNP correlation function, ${\tau }_{ODNP}$ correlate strongly with $R^2>0.99$ to the population of tetrahedral waters $p_{tet}={\int }_{{100}^{\circ }}^{{120}^{\circ }}P(\theta )d\theta$.

Figure 6:. Decomposition of the solvation free energy of methane into glycerol-water mixtures.

We calculate the solvation free energy for a methane molecule via expanded ensemble calculations, decomposing the resultant solvation free energy [Figure S10(b)] into (a) enthalpic contribution via the direct energy term ${〈U〉}_{sw}$ and (b) entropy of solution restructuring $S_{res}$. (a) ${〈U〉}_{sw}$ decreases as more glycerol is added to the mixture. (b) $S_{res}$ increases as more glycerol is added to the mixture. (c) We observe a strong correlation $(R^2=0.99)$ between the MD-computed ODNP coupling factor ${\xi }_r$ and $S_{res}$.