Theory
Refinement is an iterative process in which the atomic model is modified, structure factor amplitudes are calculated from the modified model, and the agreement between these calculated structure factor amplitudes (|Fc|) and the experimental or observed ones (|Fobs|) is determined. The goal is to find the model that produces the best agreement between |Fobs| and |Fc|.
It is useful to think of refinement as the problem of finding the minimum of a function that mathematically expresses the agreement between |Fobs| and |Fc|. This function is called a target function, or Exref. A commonly used target function is the crystallographic residual: SUM {(|Fobs| - k|Fc|)2}, where the sum runs over all the reflections in your data set, and k is a scale factor needed to put the Fc on the same scale as the Fobs.
A model consists typically of five parameters for each atom: x,y,z, B, and Q. The triplet (x,y,z) specifies the position of each atom in an orthogonal coordinate system. B is the B-factor or temperature factor of each atom, and it is related to the thermal motion of the atom. But, beware that the B-factor can also contain information about other types of "disorder" including errors that you — the crystallographer — made while constructing and refining your model. Q is the occupancy and it is the fraction of time that the atom spends at position (x,y,z). Typically, Q=1. If one has data better than about 1.8 Å, then occupancies between zero and one are sometimes used. We won't worry too much about occupancies except to say two things. First, setting Q=0 removes an atom's contribution to the calculated structure factors. Verify this fact by examining Eq. 12.9. Second, some files from the Protein Data Bank conain atoms with Q=0. This is an indication that the crystallograher did not know where to place the atom, probably because of poor electron density in that volume of the structure. For completeness, the atoms were included in the model but the user should beware that the (x,y,z) position of any atom with Q=0 is probably highly speculative.
For this module, we'll be concerned with two types of crystallographic
refinement: rigid body and overall B-factor. In rigid
body refinement, big sections of the protein, such as subunits, move
as rigid bodies. In the simplest case, the entire protein is treated
as one rigid body, which results in 6 degrees of freedom. GAPDH
is a homotetramer, so a natural rigid body scheme would be to treat each
subunit as a separate body. Rigid body refinement is useful in the
early stages of structure determination and it is usually done with low
resolution data (15-3Å). Overall
B-factor refinement is useful for finding a ballpark esimate of the
average B-factor of your structure. Like rigid body refinement, it
is done at the early stages of the refinement process. Refinement
of the atomic B-factors is a bit tricky and we will reserve it for
the latter stages of refinement.
Practice
Required files and constants:
Add these aliases to your .cshrc file:Exercisesalias xplor '/du/xplor/object_library/xplor_small_dxml.exe'
alias xplorbig '/du/bin/xploron3851_alpha_osf_exe'
The small version of xplor is dimensioned for 20000 atoms; the big version accommodates 96000 atoms. Fill in the question marks (???) in refi.inp and select the desired refinement options. Read refi.inp and make sure that you know what each line is doing. You will need the X-plor manual, which is available online or in hard copy.
To run X-plor, type
xplor < refi.inp > refi.out &
Hint: type this to see whether errors have occurred:
grep ERR refi.out