Spectral density function mapping using ¹⁵N relaxation data exclusively

Summary

A method is presented for the determination of values of the spectral density function, J(ω), describing the dynamics of amide bond vectors from ¹⁵N relaxation parameters alone. Assuming that the spectral density is given by the sum of Lorentzian functions, the approach allows values of J(ω) to be obtained at ω=0, ω_N and 0.870ω_H, where ω_N and ω_H are Larmor frequencies of nitrogen and proton nuclei, respectively, from measurements of ¹⁵N T₁, T₂ and ¹H−¹⁵N steady-state NOE values at a single spectrometer frequency. Alternatively, when measurements are performed at two different spectrometer frequencies of i and j MHz, J(ω) can be mapped at ω=0, ωⁱ _N, ω^j _N, 0.870ωⁱ _H and 0.870ω^j _H, where ωⁱ _N, for example, is the ¹⁵N Larmor frequency for a spectrometer operating at i MHz. Additionally, measurements made at two different spectrometer frequencies enable contributions to trasverse relaxation from motions on millisecond-microsecond time scales to be evaluated and permit assessment of whether a description of the internal dynamics is consistent with a correlation function consisting of a sum of exponentials. No assumptions about the specific form of the spectral density function describing the dynamics of the ¹⁵N−NH bond vector are necessary, provided that dJ(ω)/dω is relatively constant between ω=ω_H+ω_N to ω=ω_H−ω_N. Simulations demonstrate that the method is accurate for a wide range of protein motions and correlation times, and experimental data establish the validity of the methodology. Results are presented for a folded and an unfolded form of the N-terminal SH3 domain of the protein drk.