Theoretical and computational framework for the analysis of the relaxation properties of arbitrary spin systems. Application to high-resolution relaxometry

Abstract

A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in the course of the experiment, such as dissolution dynamic nuclear polarization or high-resolution relaxometry. Understanding the relaxation properties of nuclear spin systems over orders of magnitude of magnetic fields is essential to rationalize the results of these experiments. For example, during a high-resolution relaxometry experiment, the absence of control of nuclear spin relaxation pathways during the sample transfers and relaxation delays leads to systematic deviations of polarization decays from an ideal mono-exponential decay with the pure longitudinal relaxation rate. These deviations have to be taken into account to describe quantitatively the dynamics of the system. Here, we present computational tools to (1) calculate analytical expressions of relaxation rates for a broad variety of spin systems and (2) use these analytical expressions to correct the deviations arising in high-resolution relaxometry experiments. These tools lead to a better understanding of nuclear spin relaxation, which is required to improve the sensitivity of many pulse sequences, and to better characterize motions in macromolecules.

Detection of Metabolite-Protein Interactions in Complex Biological Samples by High-Resolution Relaxometry: Towards Interactomics by NMR

“…Note that decay rates in high-resolution relaxometry experiments deviate from longitudinal relaxation rates by as much as 15% in proteins. 72,[98][99] Here, our analysis assumes that the decay rates are the longitudinal relaxation rates, which should minimally impact the obtained values of correlation times. 72 Finally, we were also able to identify competitive binding of small molecules to serum albumin in human blood serum, which could prove to be a new approach for performing fragment-based drug design directly in a complex biological fluid.…”

Two-Field Transverse Relaxation-Optimized Spectroscopy for the Study of Large Biomolecules – an in Silico Investigation

“…We considered pairs of directly bound 13 C and 19 F nuclei, with the physical properties of a specifically labelled side chain of 3-Fluorotyrosine (3F-Tyr) as previously used. 15 Analytical calculations of the relaxation rates (reported in the Supplementary Materials) for an isolated 13 C- 19 F spin pair were performed using the program RedKite 22 with a bond length of 133.8 picometers. 15 The 13 C-and 19 F-CSA tensors from Ref.…”

“…The simulation of the evolution of the density operator during the shuttle transfers was performed as previously described. 22 Briefly, we used the existing prototype of a two-field NMR spectrometer operating at 14.1 T and 0.33 T to model the design of other two-field NMR systems. The field profiles were assumed to be identical to the one of our current system apart from a scaling factor ( G ) where B0 is the high-field value and a is a dimensionless function of the magnetic field B: ( ) = 14.1 ⁄ (Fig.…”

“…We report here relaxation rates of each of these operators and cross-relaxation between them, as calculated using RedKite [1]. They are also shown in Fig.…”

“…The use of advanced isotopic labeling methods has facilitated the study of large biomolecules and biomolecular complexes by focusing on a limited number of well-defined spin systems, such as methyl groups in aliphatic side-chains. 1,2 Selective isotope labeling is optimally suited to the investigation of large systems when combined with transverse relaxation-optimized spectroscopy (TROSY) methods. First introduced for backbone 15 N-1 H pairs in deuterated proteins, 3 and a variety of similar two-spin one half systems in protein sidechains and nucleic acids, [4][5][6] the concept of TROSY was later successfully extended to methyl groups as encountered in protein side-chains 7,8 or methylated nucleic acids.…”