NMR relaxation parameters in molecules with internal motion: exact Langevin trajectory results compared with simplified relaxation models

Abstract

The interpretation of NMR relaxation experiments on flexible molecules is explored by use of stochastic dynamics trajectories. The effect of internal motion on the relaxation parameters ( ,, T2, and NOE) of simple alkanes and of aliphatic side chains of proteins is determined. The correlation functions and spectral densities required for the evaluation of 13C NMR relaxation times are evaluated from trajectories lasting up to 100 ns and the results are compared with the predictions of simplified analytical models for the motion. It is shown that for small molecules tumbling in the motional narrowing limit it is possible to approximately separate the NMR relaxation into contributions from tumbling and internal motions. For butane and heptane in aqueous solution, the spin-lattice relaxation times ( ]) are predicted and the gradient in relaxation times along the heptane chain is found to be close to that observed in the pure liquid. Detailed trajectory results are presented for 13C relaxation of an alkane side chain on macromolecules. Wigner functions are used to express the side chain relaxation with respect to the coordinate frame embedded in the macromolecule. Uncoupling the motions about the individual side chain internal rotation axes or introduction of the independent lattice jump model for the motion is shown to describe incorrectly the short-time and long-time relaxation behavior. Nevertheless, for short side chains with barriers to rotation on the order of 3 kcal/mol, both models provide a good approximation for the ,3C NMR relaxation. This suggests that the models can be used for the interpretation of NMR experiments on lipids and aliphatic amino acid side chains protruding into solution, although errors are expected when the motion of the chain under consideration is constrained by the rest of the system.

New view of lipid bilayer dynamics from 2H and 13C NMR relaxation time measurements.

“…Recently, it has been shown by two laboratories that a minimum (35) can be observed in T1 as a function of temperature in certain lipid sytems (36,37). The (6,19,20) but appears consistent with recent stochastic dynamic simulations of model nalkanes (24).…”

“…The interpretation of NMR relaxation times in terms of lipid bilayer dynamics ultimately rests on the introduction of specific motional models, which must lead to experimentally testable predictions before their physical significance can be evaluated. Most recent literature discussions have tended to focus on one or more of the following paradigms: (i) simple isotropic or anisotropic diffusion models (9, 10) modified to include ordering effects (19)(20)(21), (ii) multiple internal rotation models for acyl chain dynamics (22)(23)(24), and (iii) simplified two-motion models in which the fast component is as in (i) and the slow component is identified either with "rigid body motions" (25,26) or with collective bilayer disturbances (12,27,28).…”

Shapes and motions of polysaccharide chains

“…We confine attention here to T1 and note that the inverse of T1 is determined entirely by J(t,v) at the specific frequencies VH, VH + vc, and VH -vc, where vc and VH are the resonance frequencies of 13C and IH at the field strength in question (29). The larger the spectral density at these frequencies, the more power available in the molecular motions for longitudinal relaxation of an excited 13C, and the shorter TI.…”

SPINACH ON THE CEILING: A Theoretical Chemist's Return to Biology

“…Most of these early studies were made by my students at Harvard and focused on the physical aspects of the internal motions and the interpretation of experiments. They include the analysis of fluorescence depolarization of tryptophan residues (45), the role of dynamics in measured NMR parameters (23,83,97) and inelastic neutron scattering (20,113), and the effect of solvent and temperature on protein structure and dynamics (11,29,95). The now widely used simulated annealing methods for X-ray structure refinement (14,15) and NMR structure determination (12, 96) also originated in this period.…”