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Molecular replacement: Difference between revisions
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Molecular replacement serves to position one or more known structures (models) in the unit cell of the unknown crystal structure with the goal of providing preliminary phase information. | Molecular replacement serves to position one or more known structures (models) in the unit cell of the unknown crystal structure with the goal of providing preliminary phase information. | ||
For the positioning of a single molecule in the asymmetric unit (ASU), there are 6 degrees of freedom: 3 d.o.f. for rotation (around e.g. the x, y, and z axes), and 3 d.o.f. for translation along (e.g.) x,y,z. | |||
A 6-dimensional search is computationally very demanding if it is performed on a suitable grid. As an example, rotating on a 3-dimensional grid with 10° spacing means almost 14000 unique possibilities (using [[Lattman angles]]); a more exhaustive 5° search would mean 8 times as many possibilities. Translating on a 3-dimensional grid with 1 Å spacing in a 100 * 100 * 100 Å^3 unit cell means 1.000.000 translations. Doing both (a translation search for each rotation, or ''vice versa'') then would lead to a combinatorial explosion of the number of possibilites that have to be evaluated. | |||
It was recognized by Rossmann and Blow (around 1962) (FIXME: give correct reference) that a Patterson function can conceptually be decomposed into those vectors arising from intra-molecular vectors, and those from inter-molecular vectors. | |||
The intra-molecular vectors would change their orientation (but not their length) when the molecule of the ASU would rotate. For a given rotation of that molecule, only the inter-molecular vectors would change upon translation of the molecule through the ASU. | |||
It is thus clear that it is advantageous to first determine the rotation of the molecule, by restricting the comparison between model patterson and crystal patterson to the intra-molecular vectors. When the correct rotation is found, all vectors may then be used to find the correct translation. | |||
== Rotation function (RF) == | |||
=== Fast rotation function (FRF) === | |||
=== scoring functions === | |||
== Translation function == | |||
=== Fast translation function === | |||
=== scoring functions === | |||
== Molecular Replacement Programs == | == Molecular Replacement Programs == | ||