Heteronuclear transverse and longitudinal relaxation in AX4 spin systems: Application to 15N relaxations in 15NH4+

摘要

class="kwd-title">Keywords: AX4 spin systems, Nuclear spin relaxation, Ammonium class="head no_bottom_margin" id="idm140425980646752title">AbstractThe equations that describe the time-evolution of transverse and longitudinal ¹⁵N magnetisations in tetrahedral ammonium ions, ¹⁵NH4⁺, are derived from the Bloch-Wangsness-Redfield density operator relaxation theory. It is assumed that the relaxation of the spin-states is dominated by (1) the intra-molecular ¹⁵N–¹H and ¹H–¹H dipole–dipole interactions and (2) interactions of the ammonium protons with remote spins, which also include the contribution to the relaxations that arise from the exchange of the ammonium protons with the bulk solvent. The dipole–dipole cross-correlated relaxation mechanisms between each of the ¹⁵N–¹H and ¹H–¹H interactions are explicitly taken into account in the derivations. An application to ¹⁵N-ammonium bound to a 41 kDa domain of the protein DnaK is presented, where a comparison between experiments and simulations show that the ammonium ion rotates rapidly within its binding site with a local correlation time shorter than approximately 1 ns. The theoretical framework provided here forms the basis for further investigations of dynamics of AX4 spin systems, with ammonium ions in solution and bound to proteins of particular interest.