A new approach to visualizing spectral density functions and deriving motional correlation time distributions: Applications to an α-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(ω), as F(ω) = 2ωJ(ω) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(ω) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, ¹⁵N and ¹³C NMR relaxation data have been analyzed for backbone NH and C_αH groups in an α-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(ω) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C_αH bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.