CaltechAUTHORS
  A Caltech Library Service

An Envelope-based Approach for Direct Phase Determination of Macromolecular Structures

Rees, Douglas C. (1990) An Envelope-based Approach for Direct Phase Determination of Macromolecular Structures. Acta Crystallographica. Section A, Foundations of Crystallography, 46 (11). pp. 915-922. ISSN 0108-7673. https://resolver.caltech.edu/CaltechAUTHORS:20150209-102351401

[img] PDF - Published Version
See Usage Policy.

869Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20150209-102351401

Abstract

An initial electron density distribution for a crystal structure may be directly derived from observed diffraction data by maximizing the product of the observed and calculated Patterson functions with respect to the electron density values within an envelope. This maximization problem may be formulated as an eigenvalue equation, in which potential electron density distributions are obtained as eigendensities (eigenvectors) of a symmetric matrix. Elements of this matrix depend only on the indices and intensities of the observed reflections, and on the coordinates of grid points inside the envelope. Eigendensities are calculated for a set of small envelopes (enclosing about 20% of the molecular volume) covering a unique region of the unit cell whose points are unrelated by space-group operations, origin shifts or changes in enantiomorph. On the basis of correlation coefficients between the observed and calculated values for both the Patterson function and structure factor amplitudes, a small set of eigendensities are selected for combination into a final electron density distribution. This electron density distribution may be Fourier transformed to yield calculated structure factors. Test calculations on lysozyme indicate that phase errors of less than 60° may be obtained for strong low-resolution reflections by this procedure. An extension of this approach to handle crystal structures containing non-crystallographic symmetry is described.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1107/S0108767390006705 DOIArticle
http://scripts.iucr.org/cgi-bin/paper?S0108767390006705PublisherArticle
ORCID:
AuthorORCID
Rees, Douglas C.0000-0003-4073-1185
Additional Information:© 1990 International Union of Crystallography. Received 14 December 1989; accepted 12 June 1990. We thank B. T. Hsu, R. E. Marsh, V. Schomaker, J. N. Franklin, T. O. Yeates and D. E. Malerba for discussions and programs. This work was supported by grants from the NIH, NSF and the Joseph Irvine Equipment Fund. DCR is an A. P. Sloan Research Fellow.
Funders:
Funding AgencyGrant Number
NIHUNSPECIFIED
NSFUNSPECIFIED
Joseph Irvine Equipment FundUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:11
Record Number:CaltechAUTHORS:20150209-102351401
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150209-102351401
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54540
Collection:CaltechAUTHORS
Deposited By: SWORD User
Deposited On:10 Feb 2015 05:28
Last Modified:03 Oct 2019 07:58

Repository Staff Only: item control page