NMR lineshape analysis using analytical solutions of multi-state chemical exchange with applications to kinetics of host–guest systems

Abstract

Nuclear magnetic resonance (NMR) lineshape analysis is a powerful tool for the study of chemical kinetics. Here we provide techniques for analysis of the relationship between experimentally observed spin kinetics (transitions between different environments $$A,B,\dots$$ A , B , ⋯ ) and corresponding chemical kinetics (transitions between distinct chemical species; e.g., free host and complexed host molecule). The advantages of using analytical solutions for two-, three- or generally N-state exchange lineshapes (without J-coupling) over the widely used numerical calculation for NMR spectral fitting are presented. Several aspects of exchange kinetics including the generalization of coalescence conditions in two-state exchange, the possibility of multiple processes between two states, and differences between equilibrium and steady-state modes are discussed. ‘Reduced equivalent schemes’ are introduced for spin kinetics containing fast-exchanging states, effectively reducing the number of exchanging states. The theoretical results have been used to analyze a host–guest system containing an oxoporphyrinogen complexed with camphorsulfonic acid and several other literature examples, including isomerization, protein kinetics, or enzymatic reactions. The theoretical treatment and experimental examples present an expansion of the systematic approach to rigorous analyses of systems with rich chemical kinetics through NMR lineshape analysis.

An introduction to one- and two-dimensional lineshape analysis of chemically exchanging systems

“…This expression can be calculated efficiently numerically and integrated into a nonlinear minimisation algorithm to fit experimental data [40,46]. For the case of two-state exchange, an analytical expression for the observed spectrum can also be derived by this approach [47][48][49]:…”

Line Shape Analysis of 19F NMR-Monitored Chemical Denaturation of a Fold-Switching Protein RfaH Reveals Its Slow Folding Dynamics

“…For the spectra in the transition region (3.3–4.8 M urea concentration), peak integration was employed in Topspin to derive p F and p U from the area under the peaks. For the 19 F FL RfaH, the 19 F NMR spectra (Figure ) in the transition region were globally fit to the real part of the analytical solution of the Bloch-McConnell equation (for asymmetric two-site exchange) in the frequency domain ,− using an in-house Python script: Y false( ω false) = C 0 { k ex + p normalF [ R 2 U − i false( ω − ω normalU false) ] + p normalU [ R 2 F + i false( ω − ω normalF false) ] } / { k ex p F false[ R 2 normalF + i ( ω − ω F ) false] + k ex p U false[ R 2 normalU + i ( ω − ω U …”

“…with a common exchange rate k ex between each folded and the single unfolded species with populations p A , p B , and p C , respectively, no chemical exchange ( k ex = 0) between the two folded species and shared parameters R 2 A , R 2 B , and R 2 C across data sets, following the analytical solution described in ref to the equation: Y ( ω ) = C 0 A C + B D B 2 + D 2 where A = p A [ R 2 B R 2 C + R 2 B true( p C k ex true( p A + p C true) + p A k ex true( p A + p C true) + k ex p B true( p B + p C true) true) + R 2 C ( k ex p C ( p B + p C ) ) − ( ω − ω B ) ( ω − ω C ) true] + p B true[ R 2 A …”

“…NMR line shape analysis has been successfully used for the estimation of folding/unfolding/ligand binding kinetics of several proteins. − In these measurements, one or more isolated peaks are monitored over a large temperature/denaturant/ligand concentration range, provided they do not overlap with other peaks. The overlap problem in 1 H NMR spectra was largely alleviated by the site-specific incorporation of 19 F into aromatic amino acids and its large chemical shift dispersion. − Recently, this methodology has gained popularity, in part due to an inexpensive route to 5-fluoro tryptophan incorporation into proteins gradually replacing the traditional expression and growth in auxotrophic bacterial strains. ,− Together with numerical or analytical solutions of the modified Bloch-McConnell equations for multisite chemical exchange, , complex mechanistic information has been derived from dynamic NMR line shape analysis of organic and biochemical reactions.…”

“…14−18 Recently, this methodology has gained popularity, in part due to an inexpensive route to 5-fluoro tryptophan incorporation into proteins gradually replacing the traditional expression and growth in auxotrophic bacterial strains. 13,19−21 Together with numerical or analytical solutions of the modified Bloch-McConnell equations for multisite chemical exchange, 22,23 complex mechanistic information has been derived from dynamic NMR line shape analysis of organic and biochemical reactions.…”