StructureFactor Extrapolation using the Scalar Approximation: Theory, Applications and Limitations
Abstract
For many experiments in macromolecular crystallography, the overall structure of the protein/nucleic acid is already known and the aim of the experiment is to determine the effect a chemical or physical perturbation/activation has on the structure of the molecule. In a typical experiment, an experimenter will collect a data set from a crystal in the unperturbed state, perform the perturbation (i.e. soaking a ligand into the crystal or activating the sample with light) and finally collect a data set from the perturbed crystal. In many cases the perturbation fails to activate all molecules, so that the crystal contains a mix of molecules in the activated and native states. In these cases, it has become common practice to calculate a data set corresponding to a hypothetical fully activated crystal by linear extrapolation of structurefactor amplitudes. These extrapolated data sets often aid greatly in the interpretation of electrondensity maps. However, the extrapolation of structurefactor amplitudes is based on a mathematical shortcut that treats structure factors as scalars, not vectors. Here, a full derivation is provided of the error introduced by this approximation and it is determined how this error scales with key experimental parameters. The perhaps surprising result of this analysis ismore »
 Authors:
 Publication Date:
 Research Org.:
 Brookhaven National Laboratory (BNL) National Synchrotron Light Source
 Sponsoring Org.:
 Doe  Office Of Science
 OSTI Identifier:
 959549
 Report Number(s):
 BNL825352009JA
TRN: US201016%%693
 DOE Contract Number:
 DEAC0298CH10886
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Acta Crystallographica Section D: Biological Crystallography; Journal Volume: 63
 Country of Publication:
 United States
 Language:
 English
 Subject:
 59 BASIC BIOLOGICAL SCIENCES; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; AMPLITUDES; APPROXIMATIONS; CRYSTALLOGRAPHY; ELECTRON DENSITY; EXTRAPOLATION; PROTEINS; RESOLUTION; SCALARS; STRUCTURE FACTORS; VECTORS; national synchrotron light source
Citation Formats
Genick,U. StructureFactor Extrapolation using the Scalar Approximation: Theory, Applications and Limitations. United States: N. p., 2007.
Web. doi:10.1107/S0907444907038164.
Genick,U. StructureFactor Extrapolation using the Scalar Approximation: Theory, Applications and Limitations. United States. doi:10.1107/S0907444907038164.
Genick,U. Mon .
"StructureFactor Extrapolation using the Scalar Approximation: Theory, Applications and Limitations". United States.
doi:10.1107/S0907444907038164.
@article{osti_959549,
title = {StructureFactor Extrapolation using the Scalar Approximation: Theory, Applications and Limitations},
author = {Genick,U.},
abstractNote = {For many experiments in macromolecular crystallography, the overall structure of the protein/nucleic acid is already known and the aim of the experiment is to determine the effect a chemical or physical perturbation/activation has on the structure of the molecule. In a typical experiment, an experimenter will collect a data set from a crystal in the unperturbed state, perform the perturbation (i.e. soaking a ligand into the crystal or activating the sample with light) and finally collect a data set from the perturbed crystal. In many cases the perturbation fails to activate all molecules, so that the crystal contains a mix of molecules in the activated and native states. In these cases, it has become common practice to calculate a data set corresponding to a hypothetical fully activated crystal by linear extrapolation of structurefactor amplitudes. These extrapolated data sets often aid greatly in the interpretation of electrondensity maps. However, the extrapolation of structurefactor amplitudes is based on a mathematical shortcut that treats structure factors as scalars, not vectors. Here, a full derivation is provided of the error introduced by this approximation and it is determined how this error scales with key experimental parameters. The perhaps surprising result of this analysis is that for most structural changes encountered in protein crystals, the error introduced by the scalar approximation is very small. As a result, the extrapolation procedure is largely limited by the propagation of experimental uncertainties of individual structurefactor amplitudes. Ultimately, propagation of these uncertainties leads to a reduction in the effective resolution of the extrapolated data set. The program XTRA, which implements SASFE (scalar approximation to structurefactor extrapolation), performs errorpropagation calculations and determines the effective resolution of the extrapolated data set, is further introduced.},
doi = {10.1107/S0907444907038164},
journal = {Acta Crystallographica Section D: Biological Crystallography},
number = ,
volume = 63,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

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