# A complete set of cross-correlated relaxation experiments for determining the protein backbone dihedral angles

## TL;DR

This paper introduces a set of eight NMR experiments to determine protein backbone dihedral angles, even in highly dynamic or disordered proteins.

## Contribution

A novel set of eight cross-correlated relaxation experiments tailored for highly dynamic proteins to determine backbone dihedral angles.

## Key findings

- The eight CCR experiments yield a distribution of backbone dihedral angles for each residue.
- The method was validated on ubiquitin using PDB NMR structures for comparison.
- Peak separation via four chemical shifts enables application to intrinsically disordered proteins.

## Abstract

The investigation of structural propensities of proteins is essential for understanding how they function at the molecular level. NMR, offering atomic-scale information, is often the method of choice. One of the available techniques relies on the cross-correlated relaxation (CCR) effect, whose magnitude is related to local spatial conformation. Application of these methods is difficult if the protein under investigation exhibits high mobility, because NMR observables like CCR rates and chemical shifts present themselves as mere averages of an underlying ensemble distribution. Furthermore, relaxation observables are a convolution of structural and dynamical components. Despite these challenges, it is possible to infer the underlying structural ensemble by combining information from several CCR rates with a different geometrical dependence. In this paper, we present a set of eight CCR experiments tailored for proteins of a highly dynamic nature. Analyzed together, they yield a distribution of backbone dihedral angles for each residue of the protein. The experiments were validated on the folded protein ubiquitin using PDB-deposited NMR structures for comparison. Extraordinary peak separation, achieved by evolving four different chemical shifts, allows for the application of this method to intrinsically disordered proteins in future studies.

The online version contains supplementary material available at 10.1007/s10858-025-00458-x.