Details are given in Section 4. Fig. 4a shows four lines corresponding to the four transitions, ν1, ν2, ν6, ν4, ν8,, ν5 ( Fig. 1) with a relative intensity ratio of approximately 1:1:0:1:1, as is expected from Table 5. Also as expected, the central line is not observed because the central transitions ν3, ν7, ν9 are not included in the 2N+Hz density product operator ( Table 1). The linewidths, which are directly proportional to the transverse relaxation check details rates, of the four transitions appear to be very similar and comparison with the simulated
spectra in Fig. 4b shows that the local correlation time, τc, of the DnaK-bound ammonium is shorter than approximately 1 ns. In summary, we have developed the theoretical framework for calculating the 15N relaxation rates of 15N-ammonium. It was assumed that the geometric structure of the ammonium ion is that of a tetrahedron, which in turn means that symmetries of the energy eigenstates fall within the symmetries of the Td point group. We presented the equations that describe the transverse nitrogen relaxations of the ammonium ion in two basis sets, the Zeeman-derived basis and the Cartesian basis, as well as the relaxation rates of the longitudinal spin-density operators in the Cartesian basis. All Selleck PS341 dipole–dipole, auto-
and cross-correlated relaxation mechanisms within the ammonium ion were explicitly included in the calculations and it was also shown how the relaxation of the ammonium protons caused by external spins can be taken into account. An application of the derived equations to the study of the dynamics of enzyme-bound ammonium ions was described, where it was concluded that the local correlation time of ammonium bound to the 41 kDa domain of DnaK is less than ∼1 ns. Thus, the ammonium
ion is rotating rapidly within the cation-binding site of DnaK, since the protein itself is expected to have a rotational correlation time of approximately 25 ns at 298 K. The narrow 15N NMR signals that were observed previously only for protein-bound ammonium ions  can therefore be a consequence of two effects, (i) fast rotation of the ion within the protein binding sites as observed here for the enzyme DnaK or (ii) contributions from cross-correlated relaxation mechanisms originating from the high symmetry of the molecule as outlined in the previous sections. The theoretical framework presented here provides an avenue for further investigations of free and enzyme-bound ammonium ions to elucidate the kinetic and dynamic aspects of monovalent cation binding. Combination of the derived equations with modifications of currently available NMR pulse sequences and experiments will thus shed more light on the local dynamics of ammonium ions in the binding sites of enzymes, thereby allowing more detailed characterisations of monovalent cation:enzyme interactions.