SUMMARY Polymerization and phase separation of proteins containing low-complexity (LC) domains are important factors in gene expression, mRNA processing and trafficking, and localization of translation. We have used solid state nuclear magnetic resonance methods to characterize the molecular structure of self-assembling fibrils formed by the LC domain of the fused in sarcoma (FUS) RNA-binding protein. From the 214-residue LC domain of FUS (FUS-LC), a segment of only 57 residues forms the fibril core, while other segments remain dynamically disordered. Unlike pathogenic amyloid fibrils, FUS-LC fibrils lack hydrophobic interactions within the core and are not polymorphic at the molecular structural level. Phosphorylation of core-forming residues by DNA-dependent protein kinase blocks binding of soluble FUS-LC to FUS-LC hydrogels and dissolves phase-separated, liquid-like FUS-LC droplets. These studies offer a structural basis for understanding LC domain self-assembly, phase separation, and regulation by post-translational modification.

We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T(1e) is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.

Accurate determination of sample temperatures in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) can be problematic, particularly because frictional heating and heating by radio-frequency irradiation can make the internal sample temperature significantly different from the temperature outside the MAS rotor. This paper demonstrates the use of 79 Br chemical shifts and spin-lattice relaxation rates in KBr powder as temperature-dependent parameters for the determination of internal sample temperatures. Advantages of this method include high signalto-noise, proximity of the 79 Br NMR frequency to that of 13 C, applicability from 20 K to 320 K or higher, and simultaneity with adjustment of the MAS axis direction. We show that spin-lattice relaxation in KBr is driven by a quadrupolar mechanism. We demonstrate a simple approach to including KBr powder in hydrated samples, such as biological membrane samples, hydrated amyloid fibrils, and hydrated microcrystalline proteins, that allows direct assessment of the effects of frictional and radio-frequency heating under experimentally relevant conditions.