# About Crystals, Symmetry and Space
Groups

In a previous chapter you have seen
pictures of protein
crystals and read about how to grow them.
Although you can follow my tutorial up to the chapter on phasing
techniques without knowing about the internal symmetry and space
groups, you should have an idea of the concepts. Serious work
like Heavy Metal Patterson interpretation requires a thorough
knowledge of those subjects. I will only elaborate what is
necessary to follow the following sections of this on-line
tutorial. You can read more about crystal
geometry and space groups
in the first pages 1,
2,
3 of Chapter 5 of my book
Biomolecular Crystallography or
buy the book from Amazon.

### How can proteins self-assemble into a periodic
lattice ?

A crystal is a periodic arrangement of a motif in a lattice.
The** motif **can be a single atom, a small
molecule, a protein or any combination thereof. So here is our
protein, RGFP (Red-Green Fluorescent Protein) serving as a
structural motif :

If we just repeat this motif in three dimensions,
we have realized the most simple way to form a crystal. Very
often the motif, also referred to as to the 'asymmetric unit', is
subjected to a number of symmetry operations yielding differently
oriented copies. Let's just use a 2-fold axis for now :

If there are no additional symmetry operations,
we have already created the contents of the unit cell. The
crystal is build from the unit cells arranged into a
three-dimensional lattice :

So here is our final crystal of RGFP. Once you
have worked through the two next sections, you should be able to
tell what it's space group is. (To
look ahead at a real life example, click here)

The question arises, how many ways are there to build crystals
by combination of symmetry operations and lattice translations ?
Infinite ? A few 1000 ? Time to look at this in more detail.
Click here to go to Introduction
to space groups.

You can read more about crystal
geometry and space groups
in the first pages 1,
2,
3 of Chapter 5 of my book
Biomolecular Crystallography or
buy the book from Amazon.

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**This World Wide Web site conceived and maintained
by Bernhard Rupp. ****
Last revised
Dezember 27, 2009 01:40**