Pseudo‐Contact NMR Shifts over the Paramagnetic Metalloprotein CoMMP‐12 from First Principles

Abstract

Long-range pseudo-contact NMR shifts (PCSs) provide important restraints for the structure refinement of proteins when a paramagnetic metal center is present, either naturally or introduced artificially. Here we show that ab initio quantum-chemical methods and a modern version of the Kurland-McGarvey approach for paramagnetic NMR (pNMR) shifts in the presence of zero-field splitting (ZFS) together provide accurate predictions of all PCSs in a metalloprotein (high-spin cobalt-substituted MMP-12 as a test case). Computations of 31413 C PCSs via g-and ZFS-tensors based on multi-reference methods provide a reliable bridge between EPRparameter-and susceptibility-based pNMR formalisms. Due to the high sensitivity of PCSs to even small structural differences, local structures based either on X-ray diffraction or on various DFT optimizations could be evaluated critically by comparing computed and experimental PCSs. Many DFT functionals provide insufficiently accurate structures. We also found the available 1RMZ PDB X-ray structure to exhibit deficiencies related to binding of a hydroxamate inhibitor. This has led to a newly refined PDB structure for MMP-12 (5LAB) that provides a more accurate coordination arrangement and PCSs.The anisotropic magnetic susceptibility [1] of paramagnetic metal ions induces the so-called pseudo-contact shifts (PCSs) in NMR spectra, which can be observed for nuclei between 5 Å and 40 Å from the metal center.[2] PCSs provide precious structural information on the biomolecules on which they are measured, both in solution and in the solid state.[3] PCS-based structural restraints have also become important for protein NMR crystallography.[4] Their importance is further enhanced by recent developments in fast magic-angle spinning (MAS) combined with high-field instruments. [4d, 5] While PCSs can thus provide crucial information on the structure of a metalloprotein as a whole, NMR is typically blind to nuclei near the paramagnetic metal center due to fast paramagnetic relaxation. The computation of pNMR shifts by first-principles quantum-chemical (QC) methods, on the other hand, has recently progressed appreciably, in particular by inclusion of the non-contact terms in small to medium-sized molecules, with no fundamental limitations close to the metal center.[6] There has so far been no attempt to access the longrange PCSs in larger biological systems by first-principles calculations, as the molecular sizes needed for an explicit treatment of the hyperfine coupling (HFC) anisotropies appeared prohibitive.Here we show that introduction of the point-dipole approximation (PDA), appropriate for the long-range spin-dipolar HFCs, into modern quantum-chemical pNMR shift machinery can be used to compute long-range PCSs based on accurate multireference ab initio calculations of g-and zero-field splitting (ZFS) D-tensors. Using such a combined approach, we have computed the entire set of 314 previously measured 13 C long-range PCSs [4a] (and further shifts from nuclei closer to the metal cent...

How the Ligand Field in Lanthanide Coordination Complexes Determines Magnetic Susceptibility Anisotropy, Paramagnetic NMR Shift, and Relaxation Behavior

“… Pseudocontact shift fields for [LnL 8a ], reconstructed using Spinach 81 with the “best-fit” magnetic susceptibility tensor. Positive PCS, red; negative, blue.…”

“…Detailed analyses of PCS data have been undertaken for isostructural complexes, with known solution speciation. ,,− A semiautomated combinatorial assignment procedure using PCS data, XRD structure and NMR relaxation rates to limit the combinatorial space (in Spinach) was deployed for [LnL 8a ], enabling assignment of almost every proton resonance . Subsequently, the traceless part of the magnetic susceptibility tensor was obtained by fitting eq to experimental data, giving excellent agreement ( R 2 > 0.99).…”

Quantum-Chemical Approach to NMR Chemical Shifts in Paramagnetic Solids Applied to LiFePO4 and LiCoPO4

“…10−12 Long-range PC shifts are used widely, for example, in the structure refinement of metalloproteins, 13 and we have recently demonstrated the successful ab initio simulation of long-range PC shifts for an entire (cobalt-substituted) metalloprotein domain. 14 In the regime of extended paramagnetic solids, the treatment of such PC contributions is still in its infancy. The first attempts to incorporate them via the electronic g-tensor in a doubletstate formalism were restricted to semilocal DFT functionals, and the effects on the overall shifts were moderate.…”

How Do Nuclei Couple to the Magnetic Moment of a Paramagnetic Center? A New Theory at the Gauntlet of the Experiments

“…33 Indeed, for S > 1/2, quantum mechanics calculations are needed to obtain D and g for PCS calculations using eq 2 or 3. First-principles calculations performed on a macromolecule containing cobalt-(II) as well as on a small cobalt(II) complex 27,30 seem to indicate that the new equation is in better agreement with the experimental data than the old one. Therefore, we thought of turning to an S = 1/2 system with excited states very high in energy, for which D is obviously absent, so that…”

“…5−21 The validity of this approach has been questioned by recent quantum chemistry (QC) work. 22−26 From QC theory, the isotropic average of the nuclear spin−electron spin dipole− dipole interaction in the point dipole and spin Hamiltonian approximations provides the shift 27,28 δ π…”