31P-dephased, 13C-detected REDOR for NMR crystallography at natural isotopic abundance

Abstract

Typically, the process of NMR-based structure determination relies on accurately measuring a large number of internuclear distances to serve as restraints for simulated annealing calculations. In solids, the rotational-echo double-resonance (REDOR) experiment is a widely used approach to determine heteronuclear dipolar couplings corresponding to distances usually in the range of 1.5-8Å. A challenge in the interpretation of REDOR data is the degeneracy of symmetric subunits in an oligomer or equivalent molecules in a crystal lattice, which produce REDOR trajectories that depend explicitly on two or more distances instead of one. This degeneracy cannot be overcome by either spin dilution (for molecules containing ³¹P, ¹⁹F and other highly abundant nuclei) or selective pulses (in the case where there is chemical shift degeneracy). For small, crystalline molecules, such as phosphoserine, we demonstrate that as many as five inter-molecular distances must be considered to model ³¹P-dephased REDOR data accurately. We report excellent agreement between simulation and experiment once lattice couplings, ³¹P chemical shift anisotropy, and radio-frequency field inhomogeneity are all taken into account. We also discuss the systematic inaccuracies that may result from approximations that consider only the initial slope of the REDOR trajectory and/or that utilize a two- or three-spin system. Furthermore, we demonstrate the applicability of ³¹P-dephased REDOR for validation or refinement of candidate crystal structures and show that this approach is especially informative for NMR crystallography of ³¹P-containing molecules.

Keywords: Magic-angle spinning; Phosphorus; Phosphoserine; Simulation; Solid-state NMR.

Figure 1. Applications of ³¹P-dephased REDOR to structural characterization of phosphorus-containing materials

(a–c) Examples of systems that can be characterized using ³¹P-dephased REDOR: (a) Crystal structure of O-phospho-DL-tyrosine, determined by NMR crystallography. (b) Proteins on the surface of and embedded within a lipid bilayer, composed of lipids with phosphate headgroups. (c) Protein bound to the surface of hydroxyapatite, a mineral composed of inorganic phosphate and calcium. (d) The REDOR pulse sequence, which recouples heteronuclear dipolar couplings with a train of rotor-synchronized π pulses. (e) REDOR trajectories of diluted crystalline N-acetyl-valine (left) and natural-abundance O-phospho-serine (right) with fits to Eq. (1) shown as lines.

Figure 2

Chemical structures of compounds investigated in this study, with α, β, and γ carbons specified.

Figure 3. Measurement of B1 field profiles, ³¹P CSA, and multi-spin effects

(a) ³¹P nutation curve of O-phospho-L-serine sample after initial ¹H-³¹P CP. (b) Resultant B1 field profiles for O-phospho-L-serine (black), O-phospho-DL-serine (red), O-phospho-L-serine:Ca²⁺ (blue) and O-phospho-L-threonine (purple) samples. (c) ³¹P sideband pattern of O-phospho-L-serine at 4 kHz spinning with vertically-offset fits in red. (d) X-ray structure of the crystal lattice of O-phospho-L-serine, with phosphate groups of six closest ³¹P nuclei to a given carboxyl carbon emphasized, numbered according to their distance to the carboxyl carbon. (e) Simulated O-phospho-L-serine CO REDOR trajectories including the closest 1, 2, 3, 4, 5, or 6 ³¹P atoms to the CO carbon, as shown in (c). (f) Reduced χ² between CO REDOR data and simulations as a function of the number of included ³¹P spins, with RF inhomogeneity and CSA simulated.

Figure 4. Relative contributions of lattice couplings, CSA, and RF inhomogeneity on simulated ³¹P-dephased REDOR trajectories

(a) Models of increasing complexity used to simulate REDOR trajectories. (b) Comparison of experimental CO REDOR data (symbols) and simulations (solid lines) using different models specified in (a), on various forms of phosphoserine and phosphothreonine. Error bars are standard error on the mean of either 6 or 8 replicates. Reduced χ² between data and simulation is shown for each trajectory.

Figure 5. Discrimination between different forms of phosphoserine and phosphothreonine by REDOR trajectories

REDOR data (circles) for each carbon of O-phospho-L-serine (black), O-phospho-DL-serine (red), O-phospho-L-serine:Ca²⁺ (blue) and O-phospho-L-threonine (purple) compared with simulations (solid lines). For the weaker couplings (CO, C α) the REDOR trajectories for each molecule are easily distinguishable from each other and are reproduced well by simulations. Error bars are standard error on the mean of either 6 or 8 replicates. Reduced χ² between data and simulation is shown for each trajectory.

Figure 6. Discrimination between incorrect candidate structures and published structures by REDOR trajectories

Reduced χ² between REDOR data and simulation is shown for synthetically generated crystal structures (open circles) and published structures (closed circles, O-phospho-L-serine in black, O-phospho-DL-serine in red, O-phospho-L-serine:Ca²⁺ in blue, O-phospho-L-threonine in purple). In each case the lowest χ² corresponds to the published structure.