Evaluating the uncertainty in exchange parameters determined from off-resonance R1ρ relaxation dispersion for systems in fast exchange

Abstract

Spin relaxation in the rotating frame (R1ρ) is a powerful NMR technique for characterizing fast microsecond timescale exchange processes directed toward short-lived excited states in biomolecules. At the limit of fast exchange, only kex=k1+k−1 and Φex=pGpE(Δω)2 can be determined from R1ρ data limiting the ability to characterize the structure and energetics of the excited state conformation. Here, we use simulations to examine the uncertainty with which exchange parameters can be determined for two state systems in intermediate-to-fast exchange using off-resonance R1ρ relaxation dispersion. R1ρ data computed by solving the Bloch–McConnell equations reveals small but significant asymmetry with respect to offset (R1ρ (ΔΩ)≠R1ρ (−ΔΩ)), which is a hallmark of slow-to-intermediate exchange, even under conditions of fast exchange for free precession chemical exchange line broadening (kex/Δω>10). A grid search analysis combined with bootstrap and Monte-Carlo based statistical approaches for estimating uncertainty in exchange parameters reveals that both the sign and magnitude of Δω can be determined at a useful level of uncertainty for systems in fast exchange (kex/Δω<10) but that this depends on the uncertainty in the R1ρ data and requires a thorough examination of the multidimensional variation of χ2 as a function of exchange parameters. Results from simulations are complemented by analysis of experimental R1ρ data measured in three nucleic acid systems with exchange processes occurring on the slow (kex/Δω=0.2; pE=∼0.7%), fast (kex/Δω=∼10–16; pE=∼13%) and very fast (kex=39,000s−1) chemical shift timescales.