dccm.xyz {bio3d}

Dynamical Cross-Correlation Matrix from Cartesian Coordinates

Description

Determine the cross-correlations of atomic displacements.

Usage

## S3 method for class 'xyz'
dccm(x, reference = NULL, grpby=NULL, method=c("pearson", "lmi"),
                   ncore=1, nseg.scale=1, ...)

Arguments

x

a numeric matrix of Cartesian coordinates with a row per structure/frame.

reference

The reference structure about which displacements are analysed.

grpby

a vector counting connective duplicated elements that indicate the elements of xyz that should be considered as a group (e.g. atoms from a particular residue).

method

method to calculate the cross-correlation. Currently supports Pearson and linear mutual information (LMI).

ncore

number of CPU cores used to do the calculation. ncore=NULL will use all the cores detected.

nseg.scale

split input data into specified number of segments prior to running multiple core calculation. See fit.xyz.

...

Additional arguments to be passed (currently ignored).

Details

The extent to which the atomic fluctuations/displacements of a system are correlated with one another can be assessed by examining the magnitude of all pairwise cross-correlation coefficients (see McCammon and Harvey, 1986).

This function returns a matrix of all atom-wise cross-correlations whose elements, Cij, may be displayed in a graphical representation frequently termed a dynamical cross-correlation map, or DCCM.

If Cij = 1 the fluctuations of atoms i and j are completely correlated (same period and same phase), if Cij = -1 the fluctuations of atoms i and j are completely anticorrelated (same period and opposite phase), and if Cij = 0 the fluctuations of i and j are not correlated.

Typical characteristics of DCCMs include a line of strong cross-correlation along the diagonal, cross-correlations emanating from the diagonal, and off-diagonal cross-correlations. The high diagonal values occur where i = j, where Cij is always equal to 1.00. Positive correlations emanating from the diagonal indicate correlations between contiguous residues, typically within a secondary structure element or other tightly packed unit of structure. Typical secondary structure patterns include a triangular pattern for helices and a plume for strands. Off-diagonal positive and negative correlations may indicate potentially interesting correlations between domains of non-contiguous residues.

If method = "pearson", the conventional Pearson's inner-product correlaiton calculation will be invoked, in which only the diagnol of each atom-atom variance-covariance sub-matrix is considered.

If method = "lmi", then the linear mutual information cross-correlation will be calculated. ‘LMI’ considers both diagnol and off-diagnol entries in the sub-matrices, and so even captures the correlation of atoms moving in orthognal directions.

Value

Returns a cross-correlation matrix with values in a range from -1 to 1 (Pearson) or from 0 to 1 (LMI).

Author(s)

Xin-Qiu Yao, Hongyang Li, Gisle Saelensminde, and Barry Grant

References

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

McCammon, A. J. and Harvey, S. C. (1986) Dynamics of Proteins and Nucleic Acids, Cambridge University Press, Cambridge.

Lange, O.F. and Grubmuller, H. (2006) PROTEINS: Structure, Function, and Bioinformatics 62:1053–1061.

See Also

cor for examining xyz cross-correlations, dccm, dccm.nma, dccm.pca, dccm.enma.

Examples

##-- Read example trajectory file
trtfile <- system.file("examples/hivp.dcd", package="bio3d")
trj <- read.dcd(trtfile)

## Read the starting PDB file to determine atom correspondence
pdbfile <- system.file("examples/hivp.pdb", package="bio3d")
pdb <- read.pdb(pdbfile)

## select residues 24 to 27 and 85 to 90 in both chains
inds <- atom.select(pdb, resno=c(24:27,85:90), elety='CA')

## lsq fit of trj on pdb
xyz <- fit.xyz(pdb$xyz, trj, fixed.inds=inds$xyz, mobile.inds=inds$xyz)

## DCCM (slow to run so restrict to Calpha)
cij <- dccm(xyz)

## Plot DCCM
plot(cij)

## Or
library(lattice)
contourplot(cij, region = TRUE, labels=FALSE, col="gray40",
            at=c(-1, -0.75, -0.5, -0.25, 0.25, 0.5, 0.75, 1),
            xlab="Residue No.", ylab="Residue No.",
            main="DCCM: dynamic cross-correlation map")
            
## LMI matrix
cij <- dccm(xyz, method='lmi')

## Plot LMI matrix
#plot(cij)
col.scale <- colorRampPalette(c("gray95", "cyan"))(5)
plot(cij, at=seq(0.4,1, length=5), col.regions=col.scale)