Direct methods (crystallography)
Encyclopedia
In crystallography
, direct methods are a family of methods for estimating the phases of the Fourier transform
of the scattering density from the corresponding magnitudes. The methods generally exploit constraints or statistical correlations between the phases of different Fourier components that result from the fact that the scattering density must be a positive real number.
In two dimensions, it is relatively easy to solve the phase problem directly, but not so in three dimensions. The key step was taken by Hauptman
and Karle
, for which they were awarded the 1985 Nobel prize in Chemistry.
At present, direct methods are the preferred method for phasing crystals of small molecules having up to 1000 atoms in the asymmetric unit. However, they are generally not feasible by themselves for larger molecules such as protein
s.
Several software packages implement direct methods.
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
, direct methods are a family of methods for estimating the phases of the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
of the scattering density from the corresponding magnitudes. The methods generally exploit constraints or statistical correlations between the phases of different Fourier components that result from the fact that the scattering density must be a positive real number.
In two dimensions, it is relatively easy to solve the phase problem directly, but not so in three dimensions. The key step was taken by Hauptman
Herbert A. Hauptman
Herbert Aaron Hauptman was an American mathematician and Nobel laureate. He pioneered and developed a mathematical method that has changed the whole field of chemistry and opened a new era in research in determination of molecular structures of crystallized materials...
and Karle
Jerome Karle
Jerome Karle, born Jerome Karfunkel is an American physical chemist. Jointly with Herbert A. Hauptman, he was awarded the Nobel Prize in Chemistry in 1985, for the direct analysis of crystal structures using X-ray scattering techniques.-Early life and education:Karle was born in New York City on...
, for which they were awarded the 1985 Nobel prize in Chemistry.
At present, direct methods are the preferred method for phasing crystals of small molecules having up to 1000 atoms in the asymmetric unit. However, they are generally not feasible by themselves for larger molecules such as protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
s.
Several software packages implement direct methods.