Spin Relaxation Methods for Characterizing Picosecond-Nanosecond and Microsecond-Millisecond Motions in Proteins

Abstract

Time-dependent conformational fluctuations of proteins and other macromolecules are related by statistical mechanical principles to diverse biophysical phenomena, including thermodynamic stability, folding, molecular recognition, and catalysis. Heteronuclear (2H, 13C, and 15N) NMR spin relaxation spectroscopy constitutes a powerful experimental approach for globally characterizing conformational dynamics of macromolecules in solution, and consequently for probing biological function. Molecular dynamics on picosecond-nanosecond time scales can be characterized using the laboratory frame spin-lattice relaxation rate constant, the spin-spin relaxation rate constant and heteronuclear Overhauser enhancement. The model-free formalism parameterizes the relaxation data in terms of an overall rotational diffusion tensor for the molecule and a generalized order parameter and effective internal correlation time for each nuclear spin. The order parameter and correlation time characterize the amplitude and time scale for reorientational motions of the principal axes of the dipolar, chemical shift anisotropy and quad-rupolar interactions responsible for relaxation of the nuclear spin. The use of the generalized order parameter to investigate entropic contributions to ligand binding and energy landscapes for peptide backbone motions in bovine calbindin D9k, Escherichia coli ribonuclease H, and human fibronectin type III domains are described. Conformational exchange processes occurring on microsecond-millisecond time scales in biological macromolecules can be studied by Carr-Purcell-Meiboom-Gill and R1 experiments. The measurement of exchange rates using these experiments is hindered by the limited range of spin-echo delays that are feasible in the former experiment and the limited range of radiofrequency field strengths accessible in the latter. Nonetheless, the temperature dependence of the transverse relaxation rate constant determined by the Carr-Purcell-Meiboom-Gill technique can be used to define the activation barrier for the exchange process without precise knowledge of the exchange rate constant. Off-resonance R1ρ experiments provide effective fields in the rotating frame that are much larger than the applied radiofrequency field strengt and can be used to measure exchange time constants as short as 10 μs. The methods are applied to Escherichia coli ribonuclease H and the third fibronectin type III domain from human tenascin.