pca.xyz. bio3d 2.3-0

Usage

"pca"(xyz, subset = rep(TRUE, nrow(as.matrix(xyz))), use.svd = FALSE, rm.gaps=FALSE, mass = NULL, ...)
"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).

Description

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

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.

Value

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.

References

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

Examples


#-- Read transducin alignment and structures
aln <- read.fasta(system.file("examples/transducin.fa",package="bio3d"))
pdbs <- read.fasta.pdb(aln)

pdb/seq: 1   name: http://www.rcsb.org/pdb/files/1TND.pdb 
pdb/seq: 2   name: http://www.rcsb.org/pdb/files/1TAD.pdb 
pdb/seq: 3   name: http://www.rcsb.org/pdb/files/1TAG.pdb 
pdb/seq: 4   name: http://www.rcsb.org/pdb/files/3V00.pdb 
pdb/seq: 5   name: http://www.rcsb.org/pdb/files/1FQJ.pdb 
pdb/seq: 6   name: http://www.rcsb.org/pdb/files/1FQK.pdb 
pdb/seq: 7   name: http://www.rcsb.org/pdb/files/2XNS.pdb 
   PDB has ALT records, taking A only, rm.alt=TRUE
pdb/seq: 8   name: http://www.rcsb.org/pdb/files/1KJY.pdb 
pdb/seq: 9   name: http://www.rcsb.org/pdb/files/2OM2.pdb 
pdb/seq: 10   name: http://www.rcsb.org/pdb/files/4G5Q.pdb 
   PDB has ALT records, taking A only, rm.alt=TRUE
pdb/seq: 11   name: http://www.rcsb.org/pdb/files/1GP2.pdb 
pdb/seq: 12   name: http://www.rcsb.org/pdb/files/1AGR.pdb 
pdb/seq: 13   name: http://www.rcsb.org/pdb/files/1CIP.pdb 
pdb/seq: 14   name: http://www.rcsb.org/pdb/files/1GFI.pdb 
pdb/seq: 15   name: http://www.rcsb.org/pdb/files/1GIA.pdb 
pdb/seq: 16   name: http://www.rcsb.org/pdb/files/2ZJY.pdb 
pdb/seq: 17   name: http://www.rcsb.org/pdb/files/3ONW.pdb 
pdb/seq: 18   name: http://www.rcsb.org/pdb/files/1BH2.pdb 
pdb/seq: 19   name: http://www.rcsb.org/pdb/files/1GG2.pdb 
pdb/seq: 20   name: http://www.rcsb.org/pdb/files/1GIT.pdb 
pdb/seq: 21   name: http://www.rcsb.org/pdb/files/3QI2.pdb 
pdb/seq: 22   name: http://www.rcsb.org/pdb/files/1SVK.pdb 
   PDB has ALT records, taking A only, rm.alt=TRUE
pdb/seq: 23   name: http://www.rcsb.org/pdb/files/1SVS.pdb 
pdb/seq: 24   name: http://www.rcsb.org/pdb/files/3FFA.pdb 
pdb/seq: 25   name: http://www.rcsb.org/pdb/files/1GIL.pdb 
pdb/seq: 26   name: http://www.rcsb.org/pdb/files/1AS0.pdb 
pdb/seq: 27   name: http://www.rcsb.org/pdb/files/1AS2.pdb 
pdb/seq: 28   name: http://www.rcsb.org/pdb/files/2ODE.pdb 
   PDB has ALT records, taking A only, rm.alt=TRUE
pdb/seq: 29   name: http://www.rcsb.org/pdb/files/2V4Z.pdb 
pdb/seq: 30   name: http://www.rcsb.org/pdb/files/4G5R.pdb 
pdb/seq: 31   name: http://www.rcsb.org/pdb/files/2IHB.pdb 
pdb/seq: 32   name: http://www.rcsb.org/pdb/files/4G5O.pdb 
   PDB has ALT records, taking A only, rm.alt=TRUE


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

 core size 309 of 310  vol = 230.266 
 core size 308 of 310  vol = 205.404 
 core size 307 of 310  vol = 181.373 
 core size 306 of 310  vol = 160.715 
 core size 305 of 310  vol = 144.016 
 core size 304 of 310  vol = 129.352 
 core size 303 of 310  vol = 114.967 
 core size 302 of 310  vol = 104.141 
 core size 301 of 310  vol = 94.073 
 core size 300 of 310  vol = 86.326 
 core size 299 of 310  vol = 79.204 
 core size 298 of 310  vol = 73.164 
 core size 297 of 310  vol = 68.57 
 core size 296 of 310  vol = 64.346 
 core size 295 of 310  vol = 60.377 
 core size 294 of 310  vol = 56.493 
 core size 293 of 310  vol = 53.417 
 core size 292 of 310  vol = 50.379 
 core size 291 of 310  vol = 47.848 
 core size 290 of 310  vol = 45.441 
 core size 289 of 310  vol = 43.448 
 core size 288 of 310  vol = 41.464 
 core size 287 of 310  vol = 39.539 
 core size 286 of 310  vol = 37.874 
 core size 285 of 310  vol = 36.48 
 core size 284 of 310  vol = 35.105 
 core size 283 of 310  vol = 33.999 
 core size 282 of 310  vol = 32.973 
 core size 281 of 310  vol = 32.221 
 core size 280 of 310  vol = 31.472 
 core size 279 of 310  vol = 30.741 
 core size 278 of 310  vol = 30.032 
 core size 277 of 310  vol = 29.33 
 core size 276 of 310  vol = 28.694 
 core size 275 of 310  vol = 28.118 
 core size 274 of 310  vol = 27.536 
 core size 273 of 310  vol = 27.026 
 core size 272 of 310  vol = 26.523 
 core size 271 of 310  vol = 25.986 
 core size 270 of 310  vol = 25.44 
 core size 269 of 310  vol = 24.946 
 core size 268 of 310  vol = 24.593 
 core size 267 of 310  vol = 24.157 
 core size 266 of 310  vol = 23.721 
 core size 265 of 310  vol = 23.324 
 core size 264 of 310  vol = 22.977 
 core size 263 of 310  vol = 22.632 
 core size 262 of 310  vol = 22.297 
 core size 261 of 310  vol = 21.952 
 core size 260 of 310  vol = 21.581 
 core size 259 of 310  vol = 21.241 
 core size 258 of 310  vol = 20.864 
 core size 257 of 310  vol = 20.485 
 core size 256 of 310  vol = 20.143 
 core size 255 of 310  vol = 19.802 
 core size 254 of 310  vol = 19.453 
 core size 253 of 310  vol = 19.101 
 core size 252 of 310  vol = 18.859 
 core size 251 of 310  vol = 18.573 
 core size 250 of 310  vol = 18.271 
 core size 249 of 310  vol = 17.984 
 core size 248 of 310  vol = 17.686 
 core size 247 of 310  vol = 17.371 
 core size 246 of 310  vol = 17.089 
 core size 245 of 310  vol = 16.806 
 core size 244 of 310  vol = 16.535 
 core size 243 of 310  vol = 16.269 
 core size 242 of 310  vol = 16.035 
 core size 241 of 310  vol = 15.806 
 core size 240 of 310  vol = 15.549 
 core size 239 of 310  vol = 15.324 
 core size 238 of 310  vol = 15.102 
 core size 237 of 310  vol = 14.85 
 core size 236 of 310  vol = 14.638 
 core size 235 of 310  vol = 14.422 
 core size 234 of 310  vol = 14.24 
 core size 233 of 310  vol = 14.062 
 core size 232 of 310  vol = 13.858 
 core size 231 of 310  vol = 13.664 
 core size 230 of 310  vol = 13.472 
 core size 229 of 310  vol = 13.274 
 core size 228 of 310  vol = 13.101 
 core size 227 of 310  vol = 12.924 
 core size 226 of 310  vol = 12.736 
 core size 225 of 310  vol = 12.572 
 core size 224 of 310  vol = 12.373 
 core size 223 of 310  vol = 12.197 
 core size 222 of 310  vol = 12.049 
 core size 221 of 310  vol = 11.879 
 core size 220 of 310  vol = 11.673 
 core size 219 of 310  vol = 11.51 
 core size 218 of 310  vol = 11.381 
 core size 217 of 310  vol = 11.196 
 core size 216 of 310  vol = 11.037 
 core size 215 of 310  vol = 10.907 
 core size 214 of 310  vol = 10.765 
 core size 213 of 310  vol = 10.609 
 core size 212 of 310  vol = 10.466 
 core size 211 of 310  vol = 10.327 
 core size 210 of 310  vol = 10.184 
 core size 209 of 310  vol = 10.047 
 core size 208 of 310  vol = 9.896 
 core size 207 of 310  vol = 9.761 
 core size 206 of 310  vol = 9.652 
 core size 205 of 310  vol = 9.523 
 core size 204 of 310  vol = 9.378 
 core size 203 of 310  vol = 9.253 
 core size 202 of 310  vol = 9.159 
 core size 201 of 310  vol = 9.049 
 core size 200 of 310  vol = 8.929 
 core size 199 of 310  vol = 8.799 
 core size 198 of 310  vol = 8.669 
 core size 197 of 310  vol = 8.547 
 core size 196 of 310  vol = 8.41 
 core size 195 of 310  vol = 8.266 
 core size 194 of 310  vol = 8.127 
 core size 193 of 310  vol = 7.991 
 core size 192 of 310  vol = 7.854 
 core size 191 of 310  vol = 7.719 
 core size 190 of 310  vol = 7.59 
 core size 189 of 310  vol = 7.461 
 core size 188 of 310  vol = 7.336 
 core size 187 of 310  vol = 7.217 
 core size 186 of 310  vol = 7.087 
 core size 185 of 310  vol = 6.958 
 core size 184 of 310  vol = 6.842 
 core size 183 of 310  vol = 6.709 
 core size 182 of 310  vol = 6.581 
 core size 181 of 310  vol = 6.456 
 core size 180 of 310  vol = 6.336 
 core size 179 of 310  vol = 6.227 
 core size 178 of 310  vol = 6.129 
 core size 177 of 310  vol = 6.016 
 core size 176 of 310  vol = 5.934 
 core size 175 of 310  vol = 5.847 
 core size 174 of 310  vol = 5.764 
 core size 173 of 310  vol = 5.678 
 core size 172 of 310  vol = 5.6 
 core size 171 of 310  vol = 5.543 
 core size 170 of 310  vol = 5.461 
 core size 169 of 310  vol = 5.374 
 core size 168 of 310  vol = 5.291 
 core size 167 of 310  vol = 5.211 
 core size 166 of 310  vol = 5.133 
 core size 165 of 310  vol = 5.055 
 core size 164 of 310  vol = 4.975 
 core size 163 of 310  vol = 4.891 
 core size 162 of 310  vol = 4.801 
 core size 161 of 310  vol = 4.709 
 core size 160 of 310  vol = 4.644 
 core size 159 of 310  vol = 4.569 
 core size 158 of 310  vol = 4.479 
 core size 157 of 310  vol = 4.408 
 core size 156 of 310  vol = 4.343 
 core size 155 of 310  vol = 4.275 
 core size 154 of 310  vol = 4.191 
 core size 153 of 310  vol = 4.103 
 core size 152 of 310  vol = 4.016 
 core size 151 of 310  vol = 3.936 
 core size 150 of 310  vol = 3.864 
 core size 149 of 310  vol = 3.777 
 core size 148 of 310  vol = 3.687 
 core size 147 of 310  vol = 3.599 
 core size 146 of 310  vol = 3.514 
 core size 145 of 310  vol = 3.434 
 core size 144 of 310  vol = 3.349 
 core size 143 of 310  vol = 3.259 
 core size 142 of 310  vol = 3.18 
 core size 141 of 310  vol = 3.097 
 core size 140 of 310  vol = 3.025 
 core size 139 of 310  vol = 2.952 
 core size 138 of 310  vol = 2.875 
 core size 137 of 310  vol = 2.812 
 core size 136 of 310  vol = 2.729 
 core size 135 of 310  vol = 2.647 
 core size 134 of 310  vol = 2.563 
 core size 133 of 310  vol = 2.489 
 core size 132 of 310  vol = 2.407 
 core size 131 of 310  vol = 2.326 
 core size 130 of 310  vol = 2.26 
 core size 129 of 310  vol = 2.182 
 core size 128 of 310  vol = 2.109 
 core size 127 of 310  vol = 2.051 
 core size 126 of 310  vol = 1.993 
 core size 125 of 310  vol = 1.939 
 core size 124 of 310  vol = 1.883 
 core size 123 of 310  vol = 1.826 
 core size 122 of 310  vol = 1.772 
 core size 121 of 310  vol = 1.716 
 core size 120 of 310  vol = 1.672 
 core size 119 of 310  vol = 1.624 
 core size 118 of 310  vol = 1.581 
 core size 117 of 310  vol = 1.541 
 core size 116 of 310  vol = 1.508 
 core size 115 of 310  vol = 1.465 
 core size 114 of 310  vol = 1.425 
 core size 113 of 310  vol = 1.385 
 core size 112 of 310  vol = 1.35 
 core size 111 of 310  vol = 1.312 
 core size 110 of 310  vol = 1.277 
 core size 109 of 310  vol = 1.248 
 core size 108 of 310  vol = 1.22 
 core size 107 of 310  vol = 1.192 
 core size 106 of 310  vol = 1.159 
 core size 105 of 310  vol = 1.127 
 core size 104 of 310  vol = 1.099 
 core size 103 of 310  vol = 1.071 
 core size 102 of 310  vol = 1.043 
 core size 101 of 310  vol = 1.017 
 core size 100 of 310  vol = 0.993 
 core size 99 of 310  vol = 0.966 
 core size 98 of 310  vol = 0.945 
 core size 97 of 310  vol = 0.921 
 core size 96 of 310  vol = 0.9 
 core size 95 of 310  vol = 0.877 
 core size 94 of 310  vol = 0.854 
 core size 93 of 310  vol = 0.834 
 core size 92 of 310  vol = 0.813 
 core size 91 of 310  vol = 0.793 
 core size 90 of 310  vol = 0.772 
 core size 89 of 310  vol = 0.75 
 core size 88 of 310  vol = 0.73 
 core size 87 of 310  vol = 0.709 
 core size 86 of 310  vol = 0.69 
 core size 85 of 310  vol = 0.671 
 core size 84 of 310  vol = 0.652 
 core size 83 of 310  vol = 0.632 
 core size 82 of 310  vol = 0.613 
 core size 81 of 310  vol = 0.597 
 core size 80 of 310  vol = 0.581 
 core size 79 of 310  vol = 0.565 
 core size 78 of 310  vol = 0.547 
 core size 77 of 310  vol = 0.528 
 core size 76 of 310  vol = 0.512 
 core size 75 of 310  vol = 0.495 
 FINISHED: Min vol ( 0.5 ) reached


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

#-- 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)

NOTE: Removing 49 gap positions with missing coordinate data
      retaining 305 non-gap positions for analysis.


# 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")

  Note: Accessing on-line PDB file

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)


# 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 )

detach(transducin)

Author

Barry Grant

Principal Component Analysis