Chapter 1: Introduction to Residual Dipolar Coupling Free

While nuclear magnetic resonance (NMR) spectroscopy started out as a physics discipline in the 30s and 40s of the last century, its potential to exploit the structure, dynamics and interactions of both small and macromolecules turned it into an important tool in chemistry and structural biology. The 1950s witnessed the first measurements of interproton distances and dihedral angles in small molecules. Routine probing of orientational restraints became established in the 1990s. Development of better ways to measure and interpret structural NMR data continues to this day and, beyond any doubt, will also bring about further progress in the future. By combining these structural restraints, NMR spectroscopy enabled the elucidation of many thousands of structures of molecules, spanning a very wide size range from small compounds to proteins and nucleic acids larger than 100 kDa.

The rich information NMR provides is measured through the Hamiltonian of the multi-nuclei molecular spin system. This Hamiltonian comprises terms describing different mechanisms, including the Zeeman interactions, chemical shifts, J couplings and dipolar couplings. Under isotropic conditions, usually prevailing in liquid-state NMR, dipolar couplings are averaged out, although their contribution to nuclear spin relaxation persists. This relaxation, when originating from the proton dipole–dipole interaction, forms the basis of the ¹H–¹H nuclear Overhauser effect (NOE), the most common source of distance information for pairs of protons. Nonzero dipolar couplings are generated if the molecule is partially aligned with respect to the magnetic field and are referred to as residual dipolar couplings (RDCs), the topic of this book. The magnitudes of these couplings depend not only on the distance between the two nuclei involved but also on the orientation of the vector connecting the two nuclei relative to the magnetic field and thus also relative to molecule-fixed frames. Therefore, they offer structural information that is highly complementary to the NOE. The probing of such couplings in aligned small solute molecules has a long history, dating back to the work by Saupe and Englert.¹  However, the molecular alignments generated by the originally used nematic solutions were too strong, which greatly complicated the molecular NMR spectra and limited their application to small molecules, typically containing less than a dozen spins. For molecules that possess substantial paramagnetic or diamagnetic susceptibility anisotropy, dipolar couplings have been measured directly by taking advantage of their self-aligning properties with respect to the magnetic field, with the alignment order parameter S ranging from 10⁻⁵ to 10⁻⁴.²  Such weak alignment simplifies the NMR spectrum, making it similar to that of the unaligned molecule and facilitating the measurement of RDC.

In 1995, Tolman and Prestegard were the first to report residual dipolar couplings for a protein. The system of their choice was cyanometmyoglobin, which encapsulates an iron-complexed heme.³  The anisotropy of the magnetic susceptibility of the heme complex resulted in weak magnetic alignment that generated ¹H–¹⁵N RDCs of backbone amides in the range of −3 to 4.5 Hz at a 17.5 T magnetic field. The alignment order parameter scales with the square of the static magnetic field strength. Thus, one way of generating alignment relies on choosing a paramagnetic metal with suitably large anisotropy of its magnetic susceptibility. The metal can bind either directly to the molecule, as in a metalloprotein, or through a chelator that is covalently attached to the molecule. A limitation is that the presence of a paramagnetic metal broadens the signals of nuclei due to increased transverse relaxation rates, so that spectral peaks from hydrogens proximate to the metal are usually missing and RDCs extracted from paramagnetic samples are therefore often incomplete.

Shortly after the landmark myoglobin study by Tolman and Prestegard, the introduction of a more general way for achieving the optimal extent of molecular alignment catapulted RDCs into a main pier of NMR-based structure determination and characterization of dynamics: by exploiting the weak orientational anisotropy imposed on macromolecules that are immersed in an aqueous suspension of microscopic size particles that are aligned cooperatively relative to the external magnetic field in a liquid crystalline fashion, a tunable degree of alignment could be exerted onto proteins and nucleic acids. While the initial experiments relied on the use of phospholipid bicelles, initially developed by Sanders and Prestegard for a different purpose,⁴  a wide range of other alignment media, such as filamentous bacteriophages and stretched polyacrylamide gels, were quick to follow. The interactions, including the weak electrostatic and steric forces between the target molecule and the strongly aligned medium, align the solute molecules in the magnetic field. Through adjusting the concentration of the medium, an optimal degree of alignment can be achieved for the molecule, where RDCs are sufficiently large that they can be easily measured, but not so large that longer range interactions broaden the spectrum into an intractable mess. The introduction of weak alignments, together with numerous elegantly designed RDC measurement methods, laid the foundation for dipolar coupling studies in biomolecules. Over the past 30 years, the use of RDCs has also expanded beyond proteins and nucleic acids and has become widespread for analysis of small organic molecules, including carbohydrates and natural products.

This book presents a comprehensive overview of the principles and applications of RDCs. It aims at both novices who seek an introduction into the RDC field and experts looking for in-depth treatment of specific aspects.

The first part of the book provides an overview of the RDC fundamentals. In Chapter 2, Ke Ruan and Joel Tolman present the theoretical underpinnings of RDC. Next, various methods for inducing a suitable alignment of target molecules are reviewed. In Chapter 3, Sebastian Meier and Stephan Grzesiek present an overview of commonly used external alignment media, and the alignment of molecules that are paramagnetically tagged is presented by Xun-Cheng Su in Chapter 4. One important approach to interpreting RDC data relates the predicted alignment of proteins and nucleic acids to their three-dimensional shape. The concepts behind such alignment prediction are outlined by Markus Zweckstetter in Chapter 5. In order to fully exploit the large variety of atom pairs between which RDCs can be measured, as well as the different coupling strengths and molecular types in which they occur, the field has witnessed the development of numerous NMR pulse sequences to measure RDCs, targeted to the specific needs of spectroscopists. An overview of such pulse sequences is presented by Nick Fitzkee and Jinfa Ying in Chapter 6. A common purpose of RDC measurement is related to the determination of molecular structures. In Chapter 7, Guillermo Bermejo and Charles Schwieters detail how RDCs can be used for this purpose, also including the treatment of multiple alignment conditions.

The second part of the book is dedicated to applications of RDC measurement and analysis of proteins. There is a push by the NMR community to solve the structures of ever more challenging proteins, expanding to membrane proteins and, more generally, to proteins for which only sparse structural restraints can be collected. In such cases, RDCs have proven to be valuable probes that can greatly extend the limits of solution NMR. In Chapter 8, James Chou reviews the use of RDCs in structure determination of membrane proteins. In Chapter 9, Yang Shen shows how RDCs are an ideal supplement to chemical shifts in structural determination of challenging proteins.

The third part of this book turns to the use of RDCs for the study of molecules other than proteins. Of particular interest are nucleic acids and carbohydrates, but also small molecules that have entered the focus of RDC-based approaches. In Chapter 10, Rohit Roy, Ainan Geng, Supriya Pratihar, Honglue Shi and Hashim Al-Hashimi summarize state-of-the-art RDC methodologies in nucleic acid analysis. The rapidly expanding use of RDCs to study organic molecules is presented by Christina Thiele in Chapter 11. The RDC induced by paramagnetism and its related observable, the pseudocontact shift (PCS), proved useful for the characterization of carbohydrates, as outlined by Angeles Canales, Paola Oquist, Ana Poveda and Jesús Jiménez-Barbero in Chapter 12. Finally, Yizhou, Gary E. Martin, Gao-Wei Li, Xinxiang Lei and R. Thomas Williamson describe in Chapter 13 how RDCs enabled breakthroughs in determining the stereochemical structures of natural products.

In summary, this book highlights the extreme versatility of RDCs and presents a strong promise for further development of the RDC methodology, and thus also for the future exploration of currently uncharted territories in chemistry and structural biology.