Initial View

Note that the first load can be very slow. Be patient until the molecule loads. (You have have to allow the script to continue if a dialogue tells you that it is too slow. The loaded molecule is in a view of the symmetric unit of the crystal structure of Quinone Reductase (1QRD) Use the mouse to rotate the cell. Note the axes a (Red), b (Green) and c (Blue). Look down the b-axis. Note that the a and c axis are skew. The angle between them is β = 92.6 ° , given by the values in the top left of the molecule frame. Hit next to find out how a two fold axes around the b (Green) axis operates on the asymmetric unit. Note that you can manipulate the view by dragging the mouse as explained here.

Two Fold Axis

Note that the bluish molecules are related to the reddish by a rotation of a half-turn around the green (b) axis. But note also that the red and pink molecules (from different asymmetric units) form a dimer that have a more extensive interface than those within an asymmetric unit. The red-pink molecules are more likely to be biological association than the bluish or reddish dimers.

Two Fold Molecule Translated

The red, pink and greenish molecules are partly in other unit cells. That means that by translation other copies appear in the unit cell we are observing. Here we translate these molecules by one unit cell repeat in a and c. Note that another biological dimer forms between the bluish and a red. Note also that the pink and green appears at the origin of the next unit cell, just as it is seen in the cell shown initially.

Centring Operation on Asymmetric Unit

So far we have seen a two-fold operation and the translations that bring a molecule outside the original unit cell back to within the original unit cell.

Now we see the final type of symmetry operator in this spacegroup, which is body centring. This operation symmetrically places each molecule one-half of a unit cell dimension in each of a, b and c simultaneously.

To appreciate this better, now rotate the unit cell so that the b axis (green) is vertical and the c axis (blue) is horizontal.

The yellow-hued molecules are related to the reddish by this centring operation.

Centring Operation on Two-fold related

Just as body centring operates on the original asymmetric unit (blue-green), it also acts on the red-hued molecules, related to the original by the two fold symmetry.

Use the mouse to drag the unit cell around to appreciate the symmetry

Translations and Centring Operations

The yellow and brown molecules form dimers by their positions in adjacent unit cells.

The green-hued molecules are related to the blue-hued , in the same way as the yellow-hued are to the red-hued

Use the mouse to drag the unit cell around to appreciate the symmetry

Translate middle dimers

The red and blue dimer in the centre of the ac plane is formed by the asymmetric unit partner of the original green molecule at the origin. Notice that the green-pink dimer is two fold-related to the red-blue dimer by a two fold-axis in thw ac plane. This axis doesn't line up with any edge of the unit cell, so it is non-crystallographic. Nevertheless, the position of this dimer is found in the same position (by definition) in the next unit cell above along the b axis. We see by a translation of one unit cell length along b where this dimer lies in the original unit cell.

The yellow-hued molecules are related to the reddish by this centring operation.

Translate edge middle dimers

By the same token, the yellow-brown dimers are related to the red-blue by centring (note that they differ not in orientation but only by translation of half a unit cell along each unit cell direction. Here we also show that these are by translation in the same position in other unit cells in the same ac plane. Here we show how they are replicated in the original unit cell.

The yellow-hued molecules are related to the reddish by this centring operation.

Translation of origin dimer

The dimer between pink and green molecules at the origin, must exist at the origin of bounding units cells. That means it is found at all corners of the ac plane. We have shown one of them by translating the two-fold related molecules. Here we see the other two in the ac plane to make a total of four.(Of course the units cells above the ac plane will also have these dimers by translation - we show that later)

Corner Dimers Translate

As promised in the last section here we show the dimers in each corner of the ac plane translated along the b-axis. They are the dimers at the bottom of the unit cell that lies one unit cell above along the b axis.

The yellow-hued molecules are related to the reddish by this centring operation.

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