R: Principal Component Analysis

pca.xyz {bio3d} | R Documentation

## Principal Component Analysis

### Description

Performs principal components analysis (PCA) on a `xyz` numeric data matrix.

### Usage

    ## S3 method for class 'xyz'
    pca(xyz, subset = rep(TRUE, nrow(as.matrix(xyz))),
                     use.svd = FALSE, rm.gaps=FALSE, mass = NULL, ...)

    ## S3 method for class 'pca'
    print(x, nmodes=6, ...)

### Arguments

`xyz` | numeric matrix of Cartesian coordinates with a row per structure.
`subset` | an optional vector of numeric indices that selects a subset of rows (e.g. experimental structures vs molecular dynamics trajectory structures) from the full `xyz` matrix. Note: the full `xyz` is projected onto this subspace.
`use.svd` | logical, if TRUE singular value decomposition (SVD) is called instead of eigenvalue decomposition.
`rm.gaps` | logical, if TRUE gap positions (with missing coordinate data in any input structure) are removed before calculation. This is equivalent to removing NA cols from xyz.
`x` | an object of class `pca`, as obtained from function `pca.xyz`.
`nmodes` | numeric, number of modes to be printed.
`mass` | a ‘pdb’ object or numeric vector of residue/atom masses. By default (`mass=NULL`), mass is ignored. If provided with a ‘pdb’ object, masses of all amino acids obtained from `aa2mass` are used.
`...` | additional arguments to `fit.xyz` (for `pca.xyz`) or to `print` (for `print.pca`).

### Value

Returns a list with the following components:

`L` | eigenvalues.
`U` | eigenvectors (i.e. the x, y, and z variable loadings).
`z` | scores of the supplied `xyz` on the pcs.
`au` | atom-wise loadings (i.e. xyz normalized eigenvectors).
`sdev` | the standard deviations of the pcs.
`mean` | the means that were subtracted.

### Note

If `mass` is provided, mass weighted coordinates will be considered, and iteration of fitting onto the mean structure is performed internally. The extra fitting process is to remove external translation and rotation of the whole system. With this option, a direct comparison can be made between PCs from `pca.xyz` and vibrational modes from `nma.pdb`, with the fact that

A=k[B]TF^-1

, where A is the variance-covariance matrix, F the Hessian matrix, k[B] the Boltzmann's constant, and T the temperature.

### Author(s)

Barry Grant

### References

Grant, B.J. et al. (2006) Bioinformatics 22, 2695–2696.

### See Also

`pca`, `pca.pdbs`, `plot.pca`, `mktrj.pca`, `pca.tor`, `project.pca`

### Examples

    ## Not run:
    #-- Read transducin alignment and structures
    aln <- read.fasta(system.file("examples/transducin.fa",package="bio3d"))
    pdbs <- read.fasta.pdb(aln)

    # Find core
    core <- core.find(pdbs,
                      #write.pdbs = TRUE,
                      verbose=TRUE)

    rm(list=c("pdbs", "core"))

    ## End(Not run)

    #-- OR for demo purposes just read previously saved transducin data
    attach(transducin)

    # Previously fitted coordinates based on sub 1.0A^3 core. See core.find() function.
    xyz <- pdbs$xyz

    #-- Do PCA ignoring gap containing positions
    pc.xray <- pca.xyz(xyz, rm.gaps=TRUE)

    # Plot results (conformer plots & scree plot overview)
    plot(pc.xray, col=annotation[, "color"])

    # Plot a single conformer plot of PC1 v PC2
    plot(pc.xray, pc.axes=1:2, col=annotation[, "color"])

    ## Plot atom wise loadings
    plot.bio3d(pc.xray$au[,1], ylab="PC1 (A)")

    # PDB server connection required - testing excluded

    ## Plot loadings in relation to reference structure 1TAG
    pdb <- read.pdb("1tag")
    ind <- grep("1TAG", pdbs$id)             ## location in alignment

    resno <- pdbs$resno[ind, !is.gap(pdbs)]  ## non-gap residues
    tpdb <- trim.pdb(pdb, resno=resno)

    op <- par(no.readonly=TRUE)
    par(mfrow = c(3, 1), cex = 0.6, mar = c(3, 4, 1, 1))
    plot.bio3d(pc.xray$au[,1], resno, ylab="PC1 (A)", sse=tpdb)
    plot.bio3d(pc.xray$au[,2], resno, ylab="PC2 (A)", sse=tpdb)
    plot.bio3d(pc.xray$au[,3], resno, ylab="PC3 (A)", sse=tpdb)
    par(op)

    ## Not run:
    # Write PC trajectory
    resno = pdbs$resno[1, !is.gap(pdbs)]
    resid = aa123(pdbs$ali[1, !is.gap(pdbs)])

    a <- mktrj.pca(pc.xray, pc=1, file="pc1.pdb",
                   resno=resno, resid=resid )

    b <- mktrj.pca(pc.xray, pc=2, file="pc2.pdb",
                   resno=resno, resid=resid )

    c <- mktrj.pca(pc.xray, pc=3, file="pc3.pdb",
                   resno=resno, resid=resid )

    ## End(Not run)

    detach(transducin)

[Package bio3d version 2.3-4 Index]