Protein Symmetry using BioJava

BioJava can be used to detect, analyze, and visualize **symmetry** and

**pseudo-symmetry** in the **quaternary** (biological assembly) and tertiary

(**internal**) structural levels.

The **quaternary symmetry** of a structure defines the relations between

its individual chains or groups of chains. For a more extensive explanation

about symmetery visit the [PDB help page](http://www.rcsb.org/pdb/staticHelp.do?p=help/viewers/jmol_symmetry_view.html).

In the **quaternary symmetry** detection problem, we are given a set of chains

in the pseudo-symmetry case). For that, we perform a pairwise alignment of all

chains and determine **clusters of identical chains**.

2. Next, we reduce the each chains to a single point, its **centroid** (center of mass).

3. After that, we try different **symmetry relations** to superimpose the chain centroids

and obtain their RMSD.

4. At last, based on the parameters (cutoffs), we determine the **overall symmetry** of the

structure, with the symmetry relations obtained in the previous step.

QuatSymmetryParameters parameters = new QuatSymmetryParameters();

QuatSymmetryDetector detector = QuatSymmetryDetector(s, parameters, clusterParams);

QuatSymmetryResults globalResults = QuatSymmetryDetector.getGlobalSymmetry(s, parameters, clusterParams);

List<QuatSymmetryResults> localResults = QuatSymmetryDetector.getLocalSymmetries(s, parameters, clusterParams);

See also the demo in the BioJava repo:

The return type are `List` because there can be multiple valid options for the

quaternary symmetry. The local results `List` is empty if there exist no local

symmetry in the structure, and the global results `List` has always size bigger

In **pseudo-symmetry** the chains related by the symmetry are not completely

identical, but they share a sequence similarity above the pseudo-symmetry

similarity threshold.

If we consider hemoglobin, at a 95% sequence identity threshold the alpha and

beta subunits are considered different, which correspond to an A2B2 stoichiometry

and a C2 point group. At the structural similarity level, all four chains are

considered homologous (~45% sequence identity) with an A4 pseudostoichiometry and

D2 pseudosymmetry.


**Internal symmetry** refers to the symmetry present in a single chain, that is,

the tertiary structure. The algorithm implemented in biojava to detect internal

symmetry is called **CE-Symm**.

The **CE-Symm** algorithm was originally developed by [Myers-Turnbull D., Bliven SE.,

Rose PW., Aziz ZK., Youkharibache P., Bourne PE. & Prlić A. in 2014]

(http://www.sciencedirect.com/science/article/pii/S0022283614001557) [](http://www.ncbi.nlm.nih.gov/pubmed/24681267).

As the name of the algorithm explicitly states, **CE-Symm** uses the Combinatorial

Extension (**CE**) algorithm to generate an alignment of the structure chain to itself,

disabling the identity alignment (the diagonal of the **DotPlot** representation of a

structure alignment). This allows the identification of alternative self-alignments,

which are related to symmetry and/or structural repeats inside the chain.

By a procedure called **refinement**, the subunits of the chain that are part of the symmetry

are defined and a **multiple alignment** is created. This process can be thought as to

divide the chain into other subchains, and then superimposing each subchain to each other to

create a multiple alignment of the subunits, respecting the symmetry axes.

To enable some extra features in the display, a `SymmetryDisplay`

class has been created, although the `MultipleAlignmentDisplay` method

can also be used for that purpose (it will not show symmetry axes or

symmetry menus).

Lastly, the `SymmetryGUI` class in the **structure-gui** package

The symmetry display is similar to the **quaternary symmetry**, because

part of the code is shared. See for example this beta-propeller (1U6D),

where the repeated beta-sheets are connected by a linker forming a C6

point group internal symmetry:

One additional feature of the **internal symmetry** display is the representation

of hierarchical symmetries and repeats. Contrary to point groups, some structures

have different **levels** of symmetry. That is, the whole strucutre has, e.g. C2

symmetry and, at the same time, each of the two parts has C2 symmetry, but the axes

of both levels are not related by a point group (i.e. they do not cross to a single

point).

A very clear example are the beta-gamma-crystallins, like 4GCR:

Another feature of the display is the option to show the **multiple alignment** of

the symmetry related subunits created during the **refinement** process. Search for

the option *Subunit Superposition* in the *symmetry* menu of the Jmol window. For

the previous example the display looks like that:


The subunit display highlights the differences and similarities between the symmetry

related subunits of the chain, and helps the user to identify conseved and divergent

regions, with the help of the *Sequence Alignment Panel*.

Finally, the internal and quaternary symmetries can be combined to obtain the global

overall combined symmetry. As we have seen before, the protein 1VYM is a DNA-clamp that

has three chains relates by C3 symmetry. Each chain is internally C2 symmetric, and each

part of the C2 internal symmetry is C2 symmetric, so a case of **hierarchical symmetry**

(C2 + C2). Once we have divided the whole structure into its asymmetric parts, we can

analyze the global symmetry that related each one of them. The interesting result is that

in some cases, the internal symmetry **multiplies** the point group of the quaternary symmetry.

What seemed a C3 + C2 + C2 is combined into a D6 overall symmetry, as we can see in the figure