Heteronuclear proton assisted recoupling

We describe a theoretical framework for understanding the heteronuclear version of the third spin assisted recoupling polarization transfer mechanism and demonstrate its potential for detecting long-distance intramolecular and intermolecular ¹⁵N–¹³C contacts in biomolecular systems. The pulse sequence, proton assisted insensitive nuclei cross polarization (PAIN-CP) relies on a cross term between ¹H–¹⁵N and ¹H–¹³C dipolar couplings to mediate zero- and/or double-quantum ¹⁵N–¹³C recoupling. In particular, using average Hamiltonian theory we derive effective Hamiltonians for PAIN-CP and show that the transfer is mediated by trilinear terms of the form N^±C^∓H_z (ZQ) or N^±C^±H_z (DQ) depending on the rf field strengths employed. We use analytical and numerical simulations to explain the structure of the PAIN-CP optimization maps and to delineate the appropriate matching conditions. We also detail the dependence of the PAIN-CP polarization transfer with respect to local molecular geometry and explain the observed reduction in dipolar truncation. In addition, we demonstrate the utility of PAIN-CP in structural studies with ¹⁵N–¹³C spectra of two uniformly ¹³C,¹⁵N labeled model microcrystalline proteins—GB1, a 56 amino acid peptide, and Crh, a 85 amino acid domain swapped dimer (MW = 2 × 10.4 kDa). The spectra acquired at high magic angle spinning frequencies (ω_r/2π > 20 kHz) and magnetic fields (ω_0H/2π = 700–900 MHz) using moderate rf fields, yield multiple long-distance intramonomer and intermonomer ¹⁵N–¹³C contacts. We use these distance restraints, in combination with the available x-ray structure as a homology model, to perform a calculation of the monomer subunit of the Crh protein.