A method for evaluating correlation times for tumbling and internal motion in macromolecules using cross-relaxation rate constants from proton NMR spectra

A method of estimating the correlation times and extent of internal motion of macromolecules using ¹H NMR is proposed. The method relies on measuring the cross-relaxation rate constant between resolved, identified protons separated by a fixed distance, for example 2, 3 protons of tyrosine residues or 4, 5 protons of tryptophan residues in proteins, and the 5, 6 protons of cytosine residues in DNA. For a rigid body, the cross-relaxation rate constant yields directly an estimate of the tumbling time. Deviation of its dependence on viscosity and temperature from expectations for a rigid body allows one to estimate the degree to which internal motions contribute to the relaxation. The method is illustrated for Ribonuclease A and a 20 base pair fragment of DNA corresponding to the trp operator of Escherichia coli. The calculated correlation time of RNAse A is about 8 ns at 298 K, in good agreement with expectations from hydrodynamic measurements. Tyrosine 25 has significant internal motion, characterized by an apparent amplitude of 50-60°, a correlation time of about 5 ns, and low activation energy. The correlation time of the fragment of DNA is about 6.4 ns at 298 K, in agreement with expectations for a rigid rod. The apparent activation energy was 3.8 kcal/mol, close to the value for the dependence of the viscosity of D₂O on temperature. Further, the same result was obtained regardless of the position of the base in the sequence, indicating that bending motions are of small amplitude on the nanosecond time scale for short fragments of DNA.