Molecular origin of 31P-NMR chemical shifts of phosphate groups with bivalent counter ions

TL;DR

The study investigates the molecular origin of $\delta_{iso}(^{31}P)$ shifts for phosphate groups in DMP$^-$ upon binding bivalent counter ions, combining $^{31}$P-NMR titrations with Mg$^{2+}$/Ca$^{2+}$ and high-level ab initio calculations to distinguish CIP and SSIP contributions. Using umbrella sampling MD and GIAO-DF-LMP2 shielding calculations, the authors show CIP formation induces a characteristic shielding of about $-3.9$ ppm (Mg$^{2+}$) and $-7.6$ ppm (Ca$^{2+}$), with the observed shifts modulated by hydration environment and phosphate geometry; a two-component model yields CIP populations up to ~60% at high Mg$^{2+}$, while Ca$^{2+}$ forms CIP more weakly. A low-dimensional geometric mapping based on P–O bond lengths predicts $\sigma_{iso}(^{31}P)$ with high fidelity, revealing that charge transfer and PO$_2$ polarization, rather than geometric distortions, primarily drive the shielding. These results benchmark ion-phosphate interactions for force-field refinement and provide a quantitative link between CIP/SSIP populations and NMR observables, aiding interpretation of ion atmospheres in nucleic acids.

Abstract

The electrostatic interactions of phosphate groups and counter ions critically affect the structure, function and reactivity of DNA or RNA. We present a joint experimental-theoretical investigation of dimethyl phosphate (DMP-) in aqueous solution, an established model system of the sugar-phosphate backbone. Utilizing 31P-NMR spectroscopy as probe of phosphate-ion association, variations of Mg2+ and Ca2+ content exhibit a systematic shielding of the 31P chemical shift (δiso(31P)) with moderate temperature dependence. Enhanced sampling molecular dynamics (MD) and ab initio (GIAO-DF-LMP2) level of theory are used to reveal the microscopic mechanism. Simulations are performed for a configurational ensemble of DMP-ion geometries and their first solvation shells, demonstrating (i) the spatial convergence of changes of the nuclear shielding constant σiso(31P), (ii) the intramolecular geometric origin of short-timescale σiso(31P) fluctuations and (iii) an average shift of σiso(31P) of about 3-5 ppm upon contact ion pair formation with Mg2+ or Ca2+ ions. A quantitative analysis of δiso(31P) for varying ion content and temperature allows us to extract the temperature-dependent fraction of the contact ion pair species, indicating that solvent separated or free ion pairs are the energetically preferred species. The results impose boundary conditions for improvements of phosphate ion force fields and establish the interactions underlying the changes of δiso(31P).

Figures (6)

• Figure 1: Experimental $\delta_{iso}$($^{31}$P) of DMP- upon titration with Mg^2+. (a) Atomic labeling of DMP-. (b,c) Snapshots of DMP- - Mg^2+ CIP and SSIP from MD simulations. The octahedral solvation shell of Mg^2+ is highlighted in green, i.e., MgO1(H2O)$_5$ and Mg(H2O)$_6$. (d) Experimental ^31P-NMR spectra measured in the range 025 eq. of Mg^2+ at 298K. (e) Peak positions of $\delta_{iso}$($^{31}$P) in a temperature range from 290310 and 025 eq. of Mg^2+.
• Figure 2: Benchmark of hydration shell and basis set. (a) Variation of $\sigma_{iso}$($^{31}$P) in a randomly chosen DMP- - Mg^2+ CIP configuration (red), DMP- - Ca^2+ CIP configuration (blue) and free DMP- (black) with increasing size of the hydration shell (basis: pCVTZ). Dashed vertical lines indicate the first and second hydration shell, consisting of 6 and 36 H_2O (DMP- - Mg^2+ CIP); the largest cluster with 5 water shell considers 60 H_2O. (b) Benchmark of $\sigma_{iso}$($^{31}$P) in the DMP- - Mg^2+ CIP for varying basis size pCVXZ (X=D, T, Q, 5) basis set with a 3.0 (red) and 4.5 water shell (black). Triangles indicate a uniform pCVXZ basis set for all atom types and circles indicate a mixed basis set with pVDZ employed for hydrogen atoms. The right panel shows DMP^- $\times$ N H_2O and DMP- - I^2+ CIP $\times$ N H_2O (I = Mg, Ca) cluster snapshots for hydration shells of varying size.
• Figure 3: (a) Simulated isotropic ^31P shielding constants $\sigma_{iso}$($^{31}$P) as a function of DMP- - Mg^2+ separation. Averages (dots) over sampled 100 configurations are shown together with the standard deviation (bars). Configurations taken from umbrella sampling in the range 2.006.00 (2100 simulations total) consider a 4.5 hydration shell (basis: pCVTZ/pVDZ). (b) Cumulative average of $\sigma_{iso}$($^{31}$P) over 100 configurations for two DMP- - Mg^2+ separations (2. and 6.00). (c) 2D surface of $\sigma_{iso}$($^{31}$P) for the variation of O1/O2-P bond lengths (constant O3/O5-P distance: 1.60). Sampled O1/O2-P bond lengths in umbrella sampling MD simulations are indicated with blue (DMP- - Mg^2+ separation: 2.00) and green dots (DMP- - Mg^2+ separation: 6.00), respectively. (d) 2D surface of $\sigma_{iso}$($^{31}$P) for the variation of O3/O5-P bond lengths (constant O1/O2-P distance: 1.48). Sampled O3/O5-P bond lengths in umbrella sampling MD simulations are indicated with blue (DMP- - Mg^2+ separation: 2.00) and green dots (DMP- - Mg^2+ separation: 6.00), respectively.
• Figure 4: Geometric mapping of isotropic $^{31}$P shielding constants $\sigma_{iso}$($^{31}$P). (a) Correlation of ab initio simulated and predicted $\sigma_{iso}$($^{31}$P) using O1/O2-P and O3/O5-P bond lengths parameters for isolated DMP- shown together with the linear regression (red). (b) Correlation of ab initio simulated and predicted $\sigma_{iso}$($^{31}$P) for free DMP- in a 4.5 Å solvation shell and DMP- - Mg^2+ CIP structures using O1/O2-P and O3/O5-P bond lengths parameters. Red - linear regression of DMP- data points and blue - linear regression of CIP data points. (c) CIP-induced changes of bond lengths in hydration geometries of a DMP- - Mg^2+ CIP. Shown are scans of the O1-P and O2-P bond lengths in the DMP- - Mg^2+ CIP structure (dashed) and the equivalent DMP- solvation structure without the Mg^2+ ion, evaluating the direct impact of the ion on bond length only.
• Figure 5: (a) Relative CIP population $X[CIP]$ (Eq. \ref{['eq:ModelCIP_2']}) for varying Mg^2+ content and temperature in comparison to results from infrared spectroscopySchauss:JPCL:2019_2 (green bars). (b) Basis set dependence of amplitude of simulated chemical shift differences $\Delta\delta_{iso}^{max}$($^{31}$P) of free DMP- and DMP- - Mg^2+ CIP (gas phase simulations), red stars show $\Delta\delta_{iso}^{max}$($^{31}$P) of free DMP- and DMP- - Mg^2+ CIP with water environment obtained with a pCVQZ basis set. (c) Observed chemical shifts $\delta(^{31}\mathrm{P})$ for varying Ca^2+ content (298 K) and derived DMP- - Ca^2+ CIP population $X[CIP]$ (dashed line, lower panel). For comparison results derived from infrared spectroscopy are shown (green bars).