Most Symmetry puzzles are a type of design puzzle.
In a symmetry puzzle, there are multiple copies of the same protein. Players can work on one copy of the protein, called the monomer or "main chain", in the usual way. The monomer is colored normally, while the other copies of the protein are normally gray.
Changes made to the monomer are automatically reflected in the copies.
The first goal of a symmetry puzzle is to produce a well-folded monomer, just as in a standard design puzzle. The next goal is to assemble the monomer and the copies into an oligomer, or what Foldit usually calls a "complex". The area where the copies connect to each other is called the "interface".
The design goals for a oligomer are generally similar to those for a monomer. For example, the oligomer complex should be tightly packed, ideally with few voids between the monomer and the copies.
Many symmetry puzzles call for the complex to have its own hydrophobic core. This is a tricky requirement, since the hydrophobic residues that go into the the complex's core must be on the surface of the monomer. The exposed residues lead to a worse hiding component of the score for the monomer.
To get around the hiding issue, symmetry puzzles often include a condition which awards a bonus for creating a complex with a hydrophobic core. (And, there's usually a penalty for missing the goal.)
Types of symmetry
There are two main aspects to symmetry in Foldit. The first is the degree of symmetry, or the number of copies of the protein. The puzzle's degree of symmetry is identified in the the title using the somewhat obscure terms listed below.
The other aspect of symmetry involves the geometry of the relation between the copies of the protein. The geometry normally isn't discussed in detail in puzzle descriptions.
Symmetry puzzle geometry
The Foldit symmetry category mentions rotational and translational symmetry, but doesn't explain what these terms mean. There are also occasional references to things like "D2 symmetry" or "C4 symmetry" in puzzle descriptions, but again with little explanation of what these terms mean.
In practical terms, the puzzle's geometry affects what happens when you rotate or move the main chain. Do the other chains rotate in the same way, or in the opposite direction? Can you move the main chain past the copies, or do the ends of the chains stay together? Different symmetry puzzles have different answers to these questions.
See the wikipedia articles molecular symmetry and character tables for 3D point groups for more background on the geometry of symmetry. These articles help to explain why there isn't more discussion of geometry in symmetry: this stuff's complicated!
See symmetry file format for details on how Foldit defines symmetry puzzle geometry.
Degree of symmetry
The proteins in symmetry puzzles are known as oligomers. Oligomers in Foldit have two to six copies of a monomer. Each oligomer has its own -mer name based on the number of copies, so there are dimers, trimers, tetramers, and so on. See oligomer for the complete list.
Symmetry puzzle examples
A symmetry puzzle with a monomer and one copy, for a total of two units.
A symmetry puzzle with a monomer and two copies, for a total of three units.
Symmetric Dimer of Dimers
A symmetry puzzle with a monomer and three copies, for a total of four units. The main chain and one copy form a unit, which then interfaces to the other two copies. See Puzzle 670 for a description of "dimer of dimers" symmetry.
Editors note: this section needs work(!).
Usually taking the shape of a helix. They can be contorted into many different shapes.
We will investigate the theoretical structures of the basic helix and how they interact.
When a helix forms it likes to twist into a right hand twist. A helix with a left hand twist is not a happy helix. When joined together freely into a bundle they will all twist together with a slight left hand twist. This is the same in the making of ropes and twine. This slight counter twist helps the strand hold together and not unravel. Now there can be exceptions, like being restrained by the loops on the ends, that may force the helix to deflect.
Being constructed of helices, it is best to keep them fairly straight and close together. If they become knotted or move far apart it is probably not a good thing.
Tweeking is important in getting the helix aligned properly. Orange in blue out.
Followed by lots of wiggles, shakes, and mutate.