## Class SymmetryTools

• ```public class SymmetryTools
extends Object```
Utility methods for symmetry (quaternary and internal) detection and result manipulation.
Author:
Spencer Bliven, Aleix Lafita, Peter Rose
• ### Method Summary

All Methods
Modifier and Type Method Description
`static boolean[][]` ```blankOutBreakFlag​(AFPChain afpChain, Atom[] ca2, int rows, int cols, CECalculator calculator, boolean[][] breakFlag, int blankWindowSize)```
`static Matrix` ```blankOutCEOrig​(Atom[] ca2, int rows, int cols, CECalculator calculator, Matrix origM, int blankWindowSize)```
`static Matrix` ```blankOutPreviousAlignment​(AFPChain afpChain, Atom[] ca2, int rows, int cols, CECalculator calculator, Matrix max, int blankWindowSize)```
`static List<List<Integer>>` ```buildSymmetryGraph​(List<AFPChain> afps, Atom[] atoms, boolean undirected)```
Converts a set of AFP alignments into a Graph of aligned residues, where each vertex is a residue and each edge means the connection between the two residues in one of the alignments.
`static org.jgrapht.Graph<Integer,​org.jgrapht.graph.DefaultEdge>` `buildSymmetryGraph​(AFPChain selfAlignment)`
Converts a self alignment into a directed jGraphT of aligned residues, where each vertex is a residue and each edge means the equivalence between the two residues in the self-alignment.
`static List<Structure>` `divideStructure​(CeSymmResult symmetry)`
Method that converts the symmetric units of a structure into different structures, so that they can be individually visualized.
`static MultipleAlignment` ```fromAFP​(AFPChain symm, Atom[] atoms)```
Converts a refined symmetry AFPChain alignment into the standard representation of symmetry in a MultipleAlignment, that contains the entire Atom array of the strcuture and the symmetric repeats are orgaized in different rows in a single Block.
`static double` ```getAngle​(AFPChain afpChain, Atom[] ca1, Atom[] ca2)```
Returns the magnitude of the angle between the first and second blocks of `afpChain`, measured in degrees.
`Matrix` ```getDkMatrix​(Atom[] ca1, Atom[] ca2, int fragmentLength, double[] dist1, double[] dist2, int rows, int cols)```
`static Matrix` ```getDkMatrix​(Atom[] ca1, Atom[] ca2, int k, int fragmentLength)```
`static List<Group>` `getGroups​(Atom[] rAtoms)`
Returns the List of Groups of the corresponding representative Atom array.
`static QuatSymmetryResults` `getQuaternarySymmetry​(CeSymmResult result)`
Given a symmetry result, it calculates the overall global symmetry, factoring out the alignment and detection steps of `QuatSymmetryDetector` algorithm.
`static Atom[]` `getRepresentativeAtoms​(Structure structure)`
Returns the representative Atom Array of the first model, if the structure is NMR, or the Array for each model, if it is a biological assembly with multiple models.
`static List<Integer>` `getValidFolds​(List<Integer> stoichiometry)`
Find valid symmetry orders for a given stoichiometry.
`static Matrix` ```grayOutCEOrig​(Atom[] ca2, int rows, int cols, CECalculator calculator, Matrix origM, int blankWindowSize, double[] gradientPolyCoeff, double gradientExpCoeff)```
Grays out the main diagonal of a duplicated distance matrix.
`static Matrix` ```grayOutPreviousAlignment​(AFPChain afpChain, Atom[] ca2, int rows, int cols, CECalculator calculator, Matrix max, int blankWindowSize, double[] gradientPolyCoeff, double gradientExpCoeff)```
`static MultipleAlignment` `toFullAlignment​(CeSymmResult symm)`
Method that converts a repeats symmetric alignment into an alignment of whole structures.
`static MultipleAlignment` `toRepeatsAlignment​(CeSymmResult result)`
Method that converts a symmetry alignment into an alignment of the repeats only, as new independent structures.
`static void` `updateSymmetryScores​(MultipleAlignment symm)`
Update the scores (TM-score and RMSD) of a symmetry multiple alignment.
`static void` ```updateSymmetryTransformation​(SymmetryAxes axes, MultipleAlignment msa)```
Calculates the set of symmetry operation Matrices (transformations) of the new alignment, based on the symmetry relations in the SymmetryAxes object.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Method Detail

• #### grayOutCEOrig

```public static Matrix grayOutCEOrig​(Atom[] ca2,
int rows,
int cols,
CECalculator calculator,
Matrix origM,
int blankWindowSize,
double[] gradientPolyCoeff,
double gradientExpCoeff)```
Grays out the main diagonal of a duplicated distance matrix.
Parameters:
`ca2` -
`rows` - Number of rows
`cols` - Number of original columns
`calculator` - Used to get the matrix if origM is null
`origM` - starting matrix. If null, uses `CECalculator.getMatMatrix()`
`blankWindowSize` - Width of section to gray out
`gradientPolyCoeff` -
`gradientExpCoeff` -
Returns:
• #### grayOutPreviousAlignment

```public static Matrix grayOutPreviousAlignment​(AFPChain afpChain,
Atom[] ca2,
int rows,
int cols,
CECalculator calculator,
Matrix max,
int blankWindowSize,
double[] gradientPolyCoeff,
double gradientExpCoeff)```
• #### getDkMatrix

```public Matrix getDkMatrix​(Atom[] ca1,
Atom[] ca2,
int fragmentLength,
double[] dist1,
double[] dist2,
int rows,
int cols)```
• #### blankOutPreviousAlignment

```public static Matrix blankOutPreviousAlignment​(AFPChain afpChain,
Atom[] ca2,
int rows,
int cols,
CECalculator calculator,
Matrix max,
int blankWindowSize)```
• #### blankOutCEOrig

```public static Matrix blankOutCEOrig​(Atom[] ca2,
int rows,
int cols,
CECalculator calculator,
Matrix origM,
int blankWindowSize)```
• #### getDkMatrix

```public static Matrix getDkMatrix​(Atom[] ca1,
Atom[] ca2,
int k,
int fragmentLength)```
• #### blankOutBreakFlag

```public static boolean[][] blankOutBreakFlag​(AFPChain afpChain,
Atom[] ca2,
int rows,
int cols,
CECalculator calculator,
boolean[][] breakFlag,
int blankWindowSize)```
• #### getAngle

```public static double getAngle​(AFPChain afpChain,
Atom[] ca1,
Atom[] ca2)```
Returns the magnitude of the angle between the first and second blocks of `afpChain`, measured in degrees. This is always a positive value (unsigned).
Parameters:
`afpChain` -
`ca1` -
`ca2` -
Returns:
• #### buildSymmetryGraph

```public static List<List<Integer>> buildSymmetryGraph​(List<AFPChain> afps,
Atom[] atoms,
boolean undirected)```
Converts a set of AFP alignments into a Graph of aligned residues, where each vertex is a residue and each edge means the connection between the two residues in one of the alignments.
Parameters:
`afps` - List of AFPChains
`atoms` - Atom array of the symmetric structure
`undirected` - if true, the graph is undirected
Returns:
adjacency List of aligned residues
• #### buildSymmetryGraph

`public static org.jgrapht.Graph<Integer,​org.jgrapht.graph.DefaultEdge> buildSymmetryGraph​(AFPChain selfAlignment)`
Converts a self alignment into a directed jGraphT of aligned residues, where each vertex is a residue and each edge means the equivalence between the two residues in the self-alignment.
Parameters:
`selfAlignment` - AFPChain
Returns:
alignment Graph
• #### divideStructure

```public static List<Structure> divideStructure​(CeSymmResult symmetry)
throws StructureException```
Method that converts the symmetric units of a structure into different structures, so that they can be individually visualized.
Parameters:
`symmetry` - CeSymmResult
Throws:
`StructureException`
• #### toFullAlignment

`public static MultipleAlignment toFullAlignment​(CeSymmResult symm)`
Method that converts a repeats symmetric alignment into an alignment of whole structures.

Example: if the structure has repeats A,B and C, the original alignment is A-B-C, and the returned alignment is ABC-BCA-CAB.

Parameters:
`symm` - CeSymmResult
Returns:
MultipleAlignment of the full structure superpositions
• #### toRepeatsAlignment

```public static MultipleAlignment toRepeatsAlignment​(CeSymmResult result)
throws StructureException```
Method that converts a symmetry alignment into an alignment of the repeats only, as new independent structures.

This method changes the structure identifiers, the Atom arrays and re-scles the aligned residues in the Blocks corresponding to those changes.

Application: display superimposed repeats in Jmol.

Parameters:
`result` - CeSymmResult of symmetry
Returns:
MultipleAlignment of the repeats
Throws:
`StructureException`
• #### fromAFP

```public static MultipleAlignment fromAFP​(AFPChain symm,
Atom[] atoms)
throws StructureException```
Converts a refined symmetry AFPChain alignment into the standard representation of symmetry in a MultipleAlignment, that contains the entire Atom array of the strcuture and the symmetric repeats are orgaized in different rows in a single Block.
Parameters:
`symm` - AFPChain created with a symmetry algorithm and refined
`atoms` - Atom array of the entire structure
Returns:
MultipleAlignment format of the symmetry
Throws:
`StructureException`
• #### getQuaternarySymmetry

```public static QuatSymmetryResults getQuaternarySymmetry​(CeSymmResult result)
throws StructureException```
Given a symmetry result, it calculates the overall global symmetry, factoring out the alignment and detection steps of `QuatSymmetryDetector` algorithm.
Parameters:
`result` - symmetry result
Returns:
global symmetry results
Throws:
`StructureException`
• #### getGroups

`public static List<Group> getGroups​(Atom[] rAtoms)`
Returns the List of Groups of the corresponding representative Atom array. The representative Atom array needs to fulfill: no two Atoms are from the same Group and Groups are sequential (connected in the original Structure), except if they are from different Chains.
Parameters:
`rAtoms` - array of representative Atoms (CA, P, etc).
Returns:
List of Groups
• #### updateSymmetryTransformation

```public static void updateSymmetryTransformation​(SymmetryAxes axes,
MultipleAlignment msa)
throws StructureException```
Calculates the set of symmetry operation Matrices (transformations) of the new alignment, based on the symmetry relations in the SymmetryAxes object. It sets the transformations to the input MultipleAlignment and SymmetryAxes objects. If the SymmetryAxes object is null, the superposition of the repeats is done without symmetry constraints.

This method also sets the scores (RMSD and TM-score) after the new superposition has been updated.

Parameters:
`axes` - SymmetryAxes object. It will be modified.
`msa` - MultipleAlignment. It will be modified.
Throws:
`StructureException`
• #### updateSymmetryScores

```public static void updateSymmetryScores​(MultipleAlignment symm)
throws StructureException```
Update the scores (TM-score and RMSD) of a symmetry multiple alignment. This method does not redo the superposition of the alignment.
Parameters:
`symm` - Symmetry Multiple Alignment of Repeats
Throws:
`StructureException`
• #### getRepresentativeAtoms

`public static Atom[] getRepresentativeAtoms​(Structure structure)`
Returns the representative Atom Array of the first model, if the structure is NMR, or the Array for each model, if it is a biological assembly with multiple models.
Parameters:
`structure` -
Returns:
representative Atom[]
• #### getValidFolds

`public static List<Integer> getValidFolds​(List<Integer> stoichiometry)`
Find valid symmetry orders for a given stoichiometry. For instance, an A6B4 protein would give [1,2] because (A6B4)1 and (A3B2)2 are valid decompositions.
Parameters:
`stoichiometry` - List giving the number of copies in each Subunit cluster
Returns:
The common factors of the stoichiometry