Dipolar nuclear spin relaxation of 19F in multispin systems. Application to 19F labeled proteins

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Abstract
A theoretical description of 19F–1H dipolar nuclear spin relaxation in multispin systems is presented which serves to explain the relaxation behavior of 19F in fluorine‐labeled proteins when the protons are not irradiated. The complete solution of the two‐spin 1H–19F spin–lattice relaxation is discussed for the various experimental pulse techniques commonly employed in Fourier transform NMR. Recovery curves following a single 90° pulse applied to 19F in spin systems containing several protons are simulated by using a digital computer to calculate the time development of the complete set of differential equations for z‐magnetizations. Steady‐state experiments such as progressive saturation were also examined. The simulated 19F relaxation curves for two‐spin and several‐spin systems (when the protons are not irradiated) are compared to the behavior expected if the relaxation followed an ’’ideal’’ single exponential with T1 given by the standard ’’unlike’’ spins formula. These calculations were performed for various values of the correlation time τc for isotropic tumbling, and significant deviation from the ’’ideal’’ T1 behavior was observed, especially for slow tumbling times where ω0τc ≳ 1. This deviation was less in systems of several spins, and a generalized model for the spin system of a fluorine‐labeled protein was developed which showed that for large spin systems the dipolar relaxation behavior of 19F will in fact exhibit the ’’ideal’’ T1 behavior whether or not the protons are irradiated. The effect of the over‐all molecular tumbling as well as internal motions on T1 and the nuclear Overhauser enhancement (NOE) is discussed. Finally, a spin temperature argument is described which complements the more formal theoretical treatment and also explains all of the experimental observations that have been made on the protein fluorotyrosine alkaline phosphatase from E. coli. The treatment presented here can also be applied to other problems where dilute spins (e.g., 13C, 31P, 15N) interact with abundant spins.

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