An Efficient Computational Method for Predicting Rotational Diffusion Tensors of Globular Proteins Using an Ellipsoid Representation

Ryabov, Yaroslav; Geraghty, C; Varshney, and Amitabh; Fushman, David

doi:10.1021/ja062715t

Cited by 53 publications

(84 citation statements)

References 72 publications

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“…Rather, the challenge is to find circumstances where enough is known about the number of states, and their detailed (anisotropic) rotational diffusion tensors to warrant applying such detailed models. One promising avenue exploits the significant recent improvements in the ability to compute rotational diffusion tensors from structure (14,15). The input required to apply the theory described here would then consist of two or more structural models and the rate constants for interconversion between them.…”

Section: Discussionmentioning

confidence: 99%

“…Formally, our approach is based on an equation describing the composite conformational exchange-rotational diffusion process (11)(12)(13), which provides the total correlation function characterizing laboratory frame reorientation of the vector of interest. Although some of the quantities needed to make use of the formalism (such as the diffusion tensor of each state) may be difficult to determine experimentally, theory [e.g., hydrodynamic modeling (14,15) of putative structures of the interconverting species] may provide some of the missing input.…”

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confidence: 99%

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

Wong

Case²,

Szabó³

2009

Proc. Natl. Acad. Sci. U.S.A.

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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...

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Wong

Case²,

Szabó³

2009

Proc. Natl. Acad. Sci. U.S.A.

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“…His observation was confirmed in both numerical studies and experiments. [18][19][20][21][22][23][24][25][26][27] Proteins have also been modeled by anisotropic ellipsoidal shapes known as inertial, momental, or Cauchy ellipsoids 28,29 having the same inertial properties as the corresponding proteins. A numerical measure of this anisotropy, the asphericity, is derived from the eigenvalues of the inertial tensor associated to a frozen momentary configuration adopted by the polymer chain.…”

Section: Introductionmentioning

confidence: 99%

“…34 In their study of diffusion of proteins in solution, Ryabov et al 27 employed a more complex method to define an enveloping ellipsoid of a protein in which they first use software that identifies the protein surface exposed to solvent molecules of a given radius ͑see also Ref analysis to identify the axes and dimensions of an ellipsoid. They note that diffusion characteristics are important factors in limiting reactions and in the interpretation of data from experiments involving proteins in solutions.…”

Section: Introductionmentioning

confidence: 99%

Effect of knotting on polymer shapes and their enveloping ellipsoids

Millett

Plunkett

Piatek

et al. 2009

The Journal of Chemical Physics

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Effect of knotting on polymer shapes and their enveloping ellipsoidsWe simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

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“…Diffusion tensors can be calculated directly from molecular structures, 25 and then Eq. (22) can be combined with expressions for relaxation rates 23 to back-calculate values to be directly compared with experiment.…”

Section: Discussionmentioning

confidence: 99%

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

Ryabov

Clore

Schwieters

2012

The Journal of Chemical Physics

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We present a general formalism for the computation of orientation correlation functions involving a molecular system undergoing rotational diffusion in the presence of transitions between discrete conformational states. In this formalism, there are no proscriptions on the time scales of conformational rearrangement relative to that for rotational diffusion, and the rotational diffusion tensors of the different states can be completely arbitrary. Although closed-form results are limited to the frequency domain, this is generally useful for many spectroscopic observables as the result allows the computation of the spectral density function. We specialize the results for the computation of the frequency-domain correlation function associated with the NMR relaxation.

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An Efficient Computational Method for Predicting Rotational Diffusion Tensors of Globular Proteins Using an Ellipsoid Representation

Cited by 53 publications

References 72 publications

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

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

Effect of knotting on polymer shapes and their enveloping ellipsoids

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

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