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

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

(**internal**) structural levels of proteins.

The **quaternary symmetry** of a structure defines the relation and arrangement of the individual chains or groups of chains that are part of a biological assembly.

For a more exhaustive explanation about protein quaternary symmetery and the different types 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 (subunits) that are part of a biological assembly as input, defined by their atomic coordinates, and we are required to find the higest overall symmetry group that

The solution is divided into the following steps:

1. First, we need to identify the chains that are identical (or similar

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

chains and identify **clusters of identical or similar subunits**.

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

3. Afterwards, we try different **symmetry operations** using a grid search to superimpose the chain centroids

and score them using the RMSD.

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

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

5. In case of asymmetric structure, we discard combinatorially a number of chains and try

to detect any **local symmetries** present (symmetry that does not involve all subunits of the biological assembly).

The **quaternary symmetry** detection algorithm is implemented in the biojava class

[QuatSymmetryDetector](http://www.biojava.org/docs/api/org/biojava/nbio/structure/symmetry/core/QuatSymmetryDetector).

An example of how to use it programatically is shown below:

Structure s;

QuatSymmetryParameters parameters = new QuatSymmetryParameters();

SubunitClustererParameters clusterParams = new SubunitClustererParameters();

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](https://github.com/biojava/biojava/blob/885600670be75b7f6bc5216bff52a93f43fff09e/biojava-structure/src/main/java/demo/DemoSymmetry.java#L37-L59) provided in **BioJava** for a real case working example.

The returned `QuatSymmetryResults` object contains all the information of the subunit clustering and structural symmetry.

This object will be used later to obtain axes of symmetry, point group name, stoichiometry or even display the results in Jmol.

The return object of quaternary symmetry (`QuatSymmetryResults`) contains the

In case of asymmetrical structure, the result is a C1 point group.

The return type of the local symmetry is a `List` because there can be multiple valid options of local symmetry.

The list will be empty if there exist no local symmetries in the structure.

In the **global symmetry** mode all chains have to be part of the symmetry result.

In **local symmetry** a number of chains is left out, so that the symmetry only applies to a subset of chains.


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

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

similarity threshold.

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

The **internal symmetry** detection algorithm is implemented in the biojava class

[CeSymm](http://www.biojava.org/docs/api/org/biojava/nbio/structure/symmetry/internal/CeSymm).

It returns a `MultipleAlignment` object, see the explanation of the model in [Data Models](alignment-data-model.md),

that describes the similarity of the internal repeats. In case of no symmetry detected, the

returned alignment represents the optimal self-alignment produced by the first step of the **CE-Symm**

algorithm.

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 merged to obtain the

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

has three chains arranged in a C3 symmetry.

Each chain is internally fourfold symmetric with two levels of symmetry. We can analyze the overall symmetry of the structure by considering together the C3 quaternary symmetry and the fourfold internal symmetry.

In this case, the internal symmetry **augments** the point group of the quaternary symmetry to a D6 overall symmetry, as we can see in the figure below:


An example of how to toggle the **combined symmetry** (quaternary + internal symmetries) programatically is shown below:

Structure s;

QuatSymmetryParameters parameters = new QuatSymmetryParameters();

SubunitClustererParameters clusterParams = new SubunitClustererParameters();

clusterParams.setClustererMethod(SubunitClustererMethod.STRUCTURE);

clusterParams.setInternalSymmetry(true);

clusterParams.setStructureCoverageThreshold(0.75);

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

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

See also the [test](https://github.com/biocryst/biojava/blob/df22da37a86a0dba3fb35bee7e17300d402ab469/biojava-integrationtest/src/test/java/org/biojava/nbio/structure/test/symmetry/TestQuatSymmetryDetectorExamples.java#L167-L192) provided in **BioJava** for a real case working example.