LAUSR

Carr–Purcell–Meiboom–Gill (CPMG) type relaxation dispersion experiments are now routinely used to characterise protein conformational dynamics that occurs on the μs to millisecond (ms) timescale between a visible major state and ‘invisible’ minor states. The exchange rate(s) ($$ k_{{{\text{ex}}}} $$kex), population(s) of the minor state(s) and the absolute value of the chemical shift difference $$|{\Delta \varpi }|$$|Δϖ| (ppm) between different exchanging states can be extracted from the CPMG data. However the sign of $${\Delta \varpi }$$Δϖ that is required to reconstruct the spectrum of the ‘invisible’ minor state(s) cannot be obtained from CPMG data alone. Building upon the recently developed triple quantum (TQ) methyl $$ ^{1} {\text{H}} $$1H CPMG experiment (Yuwen in Angew Chem 55:11490–11494, 2016) we have developed pulse sequences that use carbon detection to generate and evolve single quantum (SQ), double quantum (DQ) and TQ coherences from methyl protons in the indirect dimension to measure the chemical exchange-induced shifts of the SQ, DQ and TQ coherences from which the sign of $${\Delta \varpi }$$Δϖ is readily obtained for two state exchange. Further a combined analysis of the CPMG data and the difference in exchange induced shifts between the SQ and DQ resonances and between the SQ and TQ resonances improves the estimates of exchange parameters like the population of the minor state. We demonstrate the use of these experiments on two proteins undergoing exchange: (1) the ~ 18 kDa cavity mutant of T4 Lysozyme ($$ k_{{{\text{ex}}}} \sim\,3500{\text{ s}}^{{ - 1}} $$kex∼3500s-1) and (2) the $$\sim\,4.7$$∼4.7 kDa Peripheral Sub-unit Binding Domain (PSBD) from the acetyl transferase of Bacillus stearothermophilus ($$k_{ex} \sim\,13,000\hbox { s}^{-1}$$kex∼13,000s-1).