Influence of the coupling of interdomain and overall motions on NMR relaxation

Abstract

Most theoretical models for NMR relaxation in liquids assume that overall rotational motion can be described as rotational diffusion with a single diffusion tensor. Such models cannot handle motions (such as between "closed" and "open" states of an enzyme, or between conformers of a partially disordered system) where the shape of the molecule (and hence its rotational diffusion behavior) fluctuates. We provide here a formalism for dealing with such problems. The model involves jumps between discrete conformers with different overall diffusion tensors, and a master (rate) equation to describe the transitions between these conformers. Numerical examples are given for a two-site jump model where global and local motions are concerted, showing how the rate of conformational transitions (relative to the rate of rotational diffusion) affects the observed relaxation parameters.rotation | diffusion | spin T he interpretation of NMR relaxation parameters in terms of molecular parameters has a long and successful history. The "classic" analysis, which is widely used, describes rotational tumbling by a diffusion equation with a single (perhaps anisotropic) diffusion tensor; superimposed on this are internal motions (of various amplitudes and timescales) that are assumed to be independent of overall rotation (1). The internal motions themselves may be modeled as diffusive motion, such as diffusion in a cone or in a more general restraining potential (2, 3), or may be treated as jumps between a set of discrete conformers, where populations and rate constants of conversion among these species are specified in a master equation (4-6).In many interesting cases, however, the assumption that rotational tumbling can be described with a single diffusion tensor is not realistic. These include large-amplitude interdomain motions and proteins that are at least partially disordered. In both cases, there are significant populations of conformations with quite different shapes and hence diffusion tensors. The timescale of such global conformational changes can be similar to that of the overall reorientational dynamics, further complicating the problem.At present, approaches used to analyze NMR relaxation in such systems effectively assume that the overall tumbling and interdomain motions are uncorrelated. The simplest such procedure is to use the extended model-free approach (7), as has been done by Baber et al. for calmodulin (8), where it is assumed that the overall tumbling motion can be described by the diffusion tensor of the dynamically averaged structure and the slow internal motion is identified with the interdomain motions with respect to this frame. More recently, Ryabov and Fushman introduced the ITS (interconversion between two states) model and applied it to di-ubiquitin (9). With respect to overall and interdomain motions, their model is simply a two-site jump model (6, 10) with full anisotropic (but independent) overall motion.In this article we consider the simplest class of models where internal and overall tumbling moti...

Local Isotropic Diffusion Approximation for Coupled Internal and Overall Molecular Motions in NMR Spin Relaxation

“…In isotropic solution C jj ′ q (τ) = (−1) q C jj ′ (τ), therefore, only the correlation function C jj ′ 0 (τ) = C jj ′ (τ) needs to be calculated:Methods for calculating this correlation function have been presented by Wong and co-workers 18 and Ryabov and co-workers. 19 …”

NMR studies of dynamic biomolecular conformational ensembles

“…Physical interpretation of MF parameters requires caution, however, when conditions clearly violate its assumptions; when diffusion of a macromolecule is highly anisotropic (D ‖ >> D ⊥ ), when the spin-interaction tensors are asymmetric, when τ c ≈ τ e or when the overall and internal motions are strongly coupled. Formulations that treat the coupling of overall and internal motions have been developed [13, 69–71]. …”

Coupling between internal dynamics and rotational diffusion in the presence of exchange between discrete molecular conformations

“…15, if one ignores the effect of translational diffusion which are not of interest in the current work, and to the time-domain analog in Ref. 16. To validate our results for the general two-state case in which the diffusion tensors have different principal axes, we numerically inverted the Laplace-transformed Eq.…”

“…Wong et al 16 specified this approach to protein NMR applications in which the rotational diffusion tensor is axially symmetric. Previous work 15,16 contained a serious limitation in that diffusion tensors for the different conformational states were not allowed to be truly independent: the principal axes of the diffusion tensors in the different states were not allowed to change direction, only the magnitudes of these components could vary. In the present work, we generalize these results such that each conformational state can have a unique rotational diffusion tensor whose principal axes take arbitrary, but fixed orientations relative to those of diffusion tensors of the other states.…”