Evaluating the influence of initial magnetization conditions on extracted exchange parameters in NMR relaxation experiments: applications to CPMG and CEST

Practical considerations for the measurement of near-surface electrostatics based on solvent paramagnetic relaxation enhancements

Electrostatic interactions can play important roles in regulating various biological processes. Quantifying surface electrostatics of biomolecules is, therefore, of significant interest. Recent advances in solution NMR spectroscopy have enabled site-specific measurements of de novo near-surface electrostatic potentials (ϕ_ENS) based on a comparison of solvent paramagnetic relaxation enhancements generated from differently charged paramagnetic co-solutes with similar structures. Although the NMR-derived near-surface electrostatic potentials have been shown to agree with theoretical calculations in the context of folded proteins and nucleic acids, such benchmark comparisons may not always be possible, particularly in cases where high-resolution structural models are lacking, such as in the study of intrinsically disordered proteins. Cross-validation of ϕ_ENS potentials can be achieved by comparing values obtained using three pairs of paramagnetic co-solutes, each with a different net charge. Notably we have found cases where agreement of ϕ_ENS potentials between the three pairs is poor and herein we investigate the source of this discrepancy in some detail. We show that for the systems considered here ϕ_ENS potentials obtained from cationic and anionic co-solutes are accurate and that the use of paramagnetic co-solutes with different structures can be a viable option for validation, although the optimal choice of paramagnetic compounds depends on the system of interest.

Measurement of 1Hα transverse relaxation rates in proteins: application to solvent PREs

It has recently been demonstrated that accurate near surface electrostatic potentials can be calculated for proteins from solvent paramagnetic relaxation enhancements (PREs) of amide protons measured using spin labels of similar structures but different charges (Yu et al. in Proc Natl Acad Sci 118(25):e2104020118, 2021). Here we develop methodology for extending such measurements to intrinsically disordered proteins at neutral pH where amide spectra are of very poor quality. Under these conditions it is shown that accurate PRE values can be measured using the haCONHA experiment that has been modified for recording ¹H^α transverse relaxation rates. The optimal pulse scheme includes a spin-lock relaxation element for suppression of homonuclear scalar coupled evolution for all ¹H^α protons, except those derived from Ser and Thr residues, and minimizes the radiation damping field from water magnetization that would otherwise increase measured relaxation rates. The robustness of the experiment is verified by developing a second approach using a band selective adiabatic decoupling scheme for suppression of scalar coupling modulations during ¹H^α relaxation and showing that the measured PRE values from the two methods are in excellent agreement. The near surface electrostatic potential of a 103-residue construct comprising the C-terminal intrinsically disordered region of the RNA-binding protein CAPRIN1 is obtained at pH 5.5 using both ¹H^N and ¹H^α-based relaxation rates, and at pH 7.4 where only ¹H^α rates can be quantified, with very good agreement between potentials obtained under all experimental conditions.

QUESP and QUEST revisited - fast and accurate quantitative CEST experiments

PURPOSE

Chemical exchange saturation transfer (CEST) NMR or MRI experiments allow detection of low concentrated molecules with enhanced sensitivity via their proton exchange with the abundant water pool. Be it endogenous metabolites or exogenous contrast agents, an exact quantification of the actual exchange rate is required to design optimal pulse sequences and/or specific sensitive agents.

METHODS

Refined analytical expressions allow deeper insight and improvement of accuracy for common quantification techniques. The accuracy of standard quantification methodologies, such as quantification of exchange rate using varying saturation power or varying saturation time, is improved especially for the case of nonequilibrium initial conditions and weak labeling conditions, meaning the saturation amplitude is smaller than the exchange rate (γB₁  < k).

RESULTS

The improved analytical 'quantification of exchange rate using varying saturation power/time' (QUESP/QUEST) equations allow for more accurate exchange rate determination, and provide clear insights on the general principles to execute the experiments and to perform numerical evaluation. The proposed methodology was evaluated on the large-shift regime of paramagnetic chemical-exchange-saturation-transfer agents using simulated data and data of the paramagnetic Eu(III) complex of DOTA-tetraglycineamide.

CONCLUSIONS

The refined formulas yield improved exchange rate estimation. General convergence intervals of the methods that would apply for smaller shift agents are also discussed. Magn Reson Med 79:1708-1721, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C^α, H^α, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.