Maximum-likelihood density modification

A likelihood‐based approach to density modification is developed that can be applied to a wide variety of cases where some information about the electron density at various points in the unit cell is available. The key to the approach consists of developing likelihood functions that represent the pr...

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Bibliographic Details
Published in:Acta crystallographica. Section D, Biological crystallography. Biological crystallography., 2000-08, Vol.56 (8), p.965-972
Main Author: Terwilliger, Thomas C.
Format: Article
Language:English
Subjects:
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Crystallography, X-Ray
DENSITY
density modification
ELECTRON DENSITY
ELECTRONS
Likelihood Functions
Macromolecular Substances
Models, Molecular
MODIFICATIONS
PROBABILITY
Research Papers
SOLVENTS
Static Electricity
STRUCTURE FACTORS
YIELDS
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Summary:A likelihood‐based approach to density modification is developed that can be applied to a wide variety of cases where some information about the electron density at various points in the unit cell is available. The key to the approach consists of developing likelihood functions that represent the probability that a particular value of electron density is consistent with prior expectations for the electron density at that point in the unit cell. These likelihood functions are then combined with likelihood functions based on experimental observations and with others containing any prior knowledge about structure factors to form a combined likelihood function for each structure factor. A simple and general approach to maximizing the combined likelihood function is developed. It is found that this likelihood‐based approach yields greater phase improvement in model and real test cases than either conventional solvent flattening and histogram matching or a recent reciprocal‐space solvent‐flattening procedure [Terwilliger (1999), Acta Cryst. D55, 1863–1871].
ISSN:1399-0047
0907-4449
1399-0047
DOI:10.1107/S0907444900005072