Projects
Nuclear Magnetic Resonance: What Is It?
The theory of nuclear magnetic resonance (NMR) theory has been extensively developed and is covered in several classic texts that I list at the end of this section. Below, I highlight the most basic aspects of the technique and theory.
The nuclei of many atoms possess an intrinsic property known as “spin” and are described by a spin quantum number, I. A nucleus with spin angular momentum, I, has an associated magnetic dipole moment, μ, modulated by the isotope-specific gyromagnetic ratio, γ: μ = γI =γℏ[I(I+1)]^(1/2).
The gyromagnetic ratio is a way of measuring how magnetic a given isotope is. A nucleus with a nonzero I-value is considered NMR active and will display (2I + 1) degenerate spin states whose degeneracy is broken when placed in an external magnetic field, B0. For a spin-1/2 nucleus, the only type considered herein, the system will split into two spin states, known as the Zeeman splitting, one with lower energy aligned with the field, and one with higher energy aligned against the field (for isotopes with a positive value of γ). The majority of biologically relevant atoms possess at least one isotope with spin-1/2, including 1H, 13C, 15N, and 31P. At natural abundance, nearly 100% of 1H and 31P atoms are NMR active, while 13C and 15N are far more scarce, at 1.11% and 0.37%, respectively, of their respective nuclei.
The effect of a magnetic field on the magnetic moment is to produce a torque on the magnetic moment, leading to a rotation about the field, conventionally defined as the positive z-direction. This rotation is called free precession, and the rate of rotation, or angular velocity, ω0, is known as the Larmor frequency, ω0 =-γB0. The Larmor frequency is related to the energy splitting between the spin states. The signal in NMR is generated when a nucleus is hit with a photon of energy hω0 that matches the energy difference between the α- and β-spin states. Because the α-spin state has slightly lower energy than the β-spin state, the α-state has a higher population, N, resulting in a population difference between the states governed by the Boltzmann constant and temperature. At equilibrium, this population difference creates a bulk magnetization M0 in the sample (even a dilute NMR sample still has ~10^17 spins) that is aligned along the z-axis. It is this bulk magnetization upon which NMR experiments are performed.
To observe magnetization and perform useful experiments, the magnetization of the sample must be brought into the transverse plane, as magnetization along the z-axis is not detectable. This is accomplished by irradiating the sample with radiofrequency wave for a set amount of time. The rf pulse, as it is called, rotates the sample magnetization with angular frequency ω1 into the transverse plane. A 90° pulse along the x-axis, for example, will result in magnetization being rotated to the –y-axis, while a 180° pulse puts magnetization along the –z-axis, which would again be undetectable. Quantum mechanically, we see that the effect of an x- or y-pulse is to create coherent superpostions of spin states, that are no longer eigenstates of the Hamiltonian and therefore evolve in time as described by the time-dependent Schrodinger equation. Again, it is the energy difference between the eigenstates that governs this time-evolution. At the same time, the non-equilibrium magnetization relaxes slowly back to equilibrium, and the rate of return is exploited regularly to determine dynamics of chemical systems.
Excellent NMR Resources
(1) Apperley, D. C.; Harris, R. K.; Hodgkinson, P. Solid State NMR Basic Principles & Practice; Momentum Press, LLC: New York, 2012.
(2) Claridge, T. D. W. High Resolution NMR Techniques in Organic Chemistry; Second ed.; Elsevier, Ltd.: United Kingdom, 2009; Vol. 27.
(3) Keeler, J. Undestanding NMR Spectroscopy; Second ed.; John Wiley & Sons, Ltd: United Kingdom, 2010.
(4) Levitt, M. H. Spin Dynamics: Basics of Nuclear Magnetic Resonance; Second ed.; John Wiley & Sons, Ltd: United Kingdom, 2008.
Ubiquitin
Ubiquitin is a small 76-residue protein that is found ubiquitously in human cells. Ubiquitination and other post-translational modifications play a major role in the proliferation of many neurodegenerative diseases, developmental disorders, and cancers, and as such are subjects of recently increased biochemical interest. The overall goal of the ubiquitin project is to probe and characterize the interaction of ubiquitin with a water-soluble, self-folding, negative cavitand, synthesized by out collaborators in the Hooley Lab at UC Riverside. The synthetic cavitand used in these experiments has already proven useful in biosensing applications, and understanding the nature of its interaction with cationic proteins can shed light on both the binding properties of the protein and the cavitand. Initial experiments will utilize 15N-1H HSQC NMR experiments to determine possible sites of cavitand binding by analyzing the chemical shift changes of the protein’s lysine and arginine motifs. Results may indicate the cavitand’s viability as a biosensor for ubiquitination and other modifications, therefore possibly accelerating diagnostics and disease research as a result.
Ornithine Decarboxylase
Ornithine decarboxylase (ODC) is a 94 kDa homodimer and is responsible for polyamine metabolism in nearly all eukaryotic cells. As a pyridoxal-5′-phosphate (PLP)-dependent enzyme, ODC also joins an extensive class of enzymes reliant on this efficient cofactor. Despite a crystal structure (PDBID: 1D7K) for the wild type enzyme being solved, no NMR structural data have been deposited in the Biologic Magnetic Resonance Data Bank (BMRB). This leaves a gap in the understanding of the dynamic nature of this enzyme and limits studies on how the structure of this enzyme influences its function. We will express and purify ODC and perform 1H-15N HSQC experiments to begin the assignment of the amino acid sequence of the protein. This will pave the way for more detailed studies into the dynamics, relaxation, and mechanism of the enzyme. In addition to our focus on ODC, we will look at other PLP-dependent enzymes to place ODC in its proper context in this enzyme family.
