# Pseudo-translation

## What is pseudo-translation?

Pseudo-translation means that two NCS-related molecules are in the same (or similar) orientation. In that case, the Patterson function displays a peak corresponding to the relative displacement of these molecules.

From a posting by Herman Schreuder:

It could also be illuminating to look at what is behind the off-origin peak: it means that you have one molecule (say A) at (0.0.0) and one molecule (say B) at (0,0.5,0.5) which are very similar, but not identical. If they were identical, your off-origin peak would be crystallographic and an origin peak. If you look at the relative phases, the phase of molecule A would be 2pi(h*0+k*0+l*0)=0 whereas the relative phase of molecule B would be 2pi(h*0+0.5*k+0.5*l)=pi(k+l).

The total diffraction is then: Ftotal = FA (cos(0) + isin(0)) + FB (cos(pi(k+l) + isin(k+l)).

For k+l even pi(k+l)= 0 or 2pi and Ftotal = FA (1 + 0) + FB ( 1 + 0) = FA + FB (strong reflections)

For k+l odd pi(k+l)= pi and Ftotal = FA (1 + 0) + FB (-1 + 0) = FA - FB (weak reflections, zero if FA=FB)

This means, you could also discard all k+l reflections by reprocessing the data in the smaller unit cell and run molrep with that data. You will have to search for only one molecule and the final density will be the sum of molecules A and B. This may give you hints how the packing of your larger unit cell may look like. As I said before, these almost crystallographic NCS is extremely trickey and can easily fool automatic programs and crystallographers alike.

## Solving the structure

1. obtain the pseudo-translation vector (PST) from sfcheck/phenix.xtriage/molrep
2. generate a model (2 molecules in 1 pdb file) consisting of one molecule at (0,0,0) and one shifted by the PST in the orientation you found by mol rep and run molecular replacement with that model (note: the molrep program does all of this internally)
3. if that fails, reprocess the data in P1 and try step 2 in all possible spacegroups, including those with lower symmetry (like P1 itself)

## Refinement =

• Due to the bimodal intensity statistics, R-values of a structure with pseudo-translation are higher than usual, e.g. starting R values after molecular replacement could be 70-80%.