The effect of finite sampling on the determination of orientational properties: A theoretical treatment with application to interatomic vectors in proteins

D. Fushman, R. Ghose, David Cowburn

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Second-rank tensor properties such as the overall rotational diffusion tensor and the alignment tensor can be determined by NMR methods measuring orientation of interatomic vectors. Here we examine the effect of incomplete sampling of orientation space by interatomic vectors in a molecule on determination of a second-rank tensor. We have developed a quantitative approach to determine (1) how well orientation space is sampled by a particular protein or substructure, (2) to what extent this particular distribution of bond vectors samples the various components of a second-rank tensor and, (3) the ability of this distribution of bond vectors to completely characterize the tensor. This approach is generally applicable to any second-rank tensor property whose determination relies on the sampling of the angular space by the structure or substructure. The theory permits assessment of the expected degree of accuracy of tensor determination using a selected set of interatomic vectors (e.g., NH or C(α)H(α), etc), for a given molecular structure. The sampling properties of real proteins are analyzed using a database of 1736 structures, representing all experimentally determined protein folds. This theoretical approach is applied to the rotational diffusion and alignment tensors obtained from nuclear magnetic resonance data for several systems, including ubiquitin and βARK PH domain. Finally, the proposed sampling characteristics are related to the accuracy of the determination of the rotational diffusion tensor from spin-relaxation data, as an example of an unknown second-rank tensor. Knowing the accuracy of the tensor quantity derived from experimental data assists in optimizing experimental design.

Original languageEnglish (US)
Pages (from-to)10640-10649
Number of pages10
JournalJournal of the American Chemical Society
Volume122
Issue number43
DOIs
StatePublished - Nov 1 2000
Externally publishedYes

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Tensors
Sampling
Proteins
Ubiquitin
Molecular Structure
Information Systems
Research Design
Magnetic Resonance Spectroscopy
Databases
Nuclear magnetic resonance
Design of experiments
Molecular structure
Molecules
Pleckstrin Homology Domains

ASJC Scopus subject areas

  • Chemistry(all)

Cite this

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title = "The effect of finite sampling on the determination of orientational properties: A theoretical treatment with application to interatomic vectors in proteins",
abstract = "Second-rank tensor properties such as the overall rotational diffusion tensor and the alignment tensor can be determined by NMR methods measuring orientation of interatomic vectors. Here we examine the effect of incomplete sampling of orientation space by interatomic vectors in a molecule on determination of a second-rank tensor. We have developed a quantitative approach to determine (1) how well orientation space is sampled by a particular protein or substructure, (2) to what extent this particular distribution of bond vectors samples the various components of a second-rank tensor and, (3) the ability of this distribution of bond vectors to completely characterize the tensor. This approach is generally applicable to any second-rank tensor property whose determination relies on the sampling of the angular space by the structure or substructure. The theory permits assessment of the expected degree of accuracy of tensor determination using a selected set of interatomic vectors (e.g., NH or C(α)H(α), etc), for a given molecular structure. The sampling properties of real proteins are analyzed using a database of 1736 structures, representing all experimentally determined protein folds. This theoretical approach is applied to the rotational diffusion and alignment tensors obtained from nuclear magnetic resonance data for several systems, including ubiquitin and βARK PH domain. Finally, the proposed sampling characteristics are related to the accuracy of the determination of the rotational diffusion tensor from spin-relaxation data, as an example of an unknown second-rank tensor. Knowing the accuracy of the tensor quantity derived from experimental data assists in optimizing experimental design.",
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