How to extract R1, R1rho, and R2 rates from the relaxation data

1. Collect intensities after use the same nmrPipe macro to process all spectra with various relaxation delay time points.

2. Normalize to 1 (using relative intensities, every other value divided by the very first value).

3. Fit to exp(-R*t) using excel (set the intercept  = 1), where t is the relaxation delay and R is the rate constant.

4. “Uncertainties in measured peak heights were estimated from baseline noise level and typically < 1% of the peak heights from the first R₁, R_1rho, and R₂ delay points. In general, fitting errors were within 10% of the calculated relaxation rates.” — from Nucleic Acids Research, 2005, 33(7), p2061-2077.

5. To calculate R₂ from R_1rho:

R_1rho = R₂cos²(θ) + R₁sin²(θ),   where θ = tan^-1(2πΔν/γ_NB₁), where Δν is the resonance offset and |γ_NB₁|/2π is the strength of the spin-lock field.

So R₂ = R_1rho /cos²(θ) – R₁*tg²(θ)

= R_1rho(1 + tg²(θ)) – R₁*tg²(θ)

= R_1rho + (R_1rho – R₁)* tg²(θ)

= R_1rho + (R_1rho – R₁)* (Δν*1/(γ_NB₁/2π))²

Foe example, here spin-lock field strength on 600 is 1500Hz, dof2 = 120.1707 ppm at spec = 60.7843 MHz,

So Δν = ($Nppm -120.1707) * 60.7843 (Hz)

tg(θ) =  Δν/1500 = ($Nppm -120.1707) * 60.7843/1500

Where $Nppm is the N¹⁵ chemical shift of each peak in the spectra.

Hongwei created on 4/23/2014