bio3d (version 2.3-3)

dccm.xyz: DCCM: Dynamical Cross-Correlation Matrix

Description

Determine the cross-correlations of atomic displacements.

Usage

# S3 method for xyz
dccm(x, reference = NULL, grpby=NULL,
ncore=1, nseg.scale=1, …)
cov2dccm(vcov, method = c("pearson", "lmi"), ncore = NULL)

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).

ncore

number of CPU cores used to do the calculation. ncore>1 requires package ‘parallel’ installed.

nseg.scale

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

…

hmm.

vcov

numeric variance-covariance matrix.

method

method to calculate the cross-correlation.

Value

Returns a cross-correlation matrix.

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.

cov2dccm function calculates the N-by-N cross-correlation matrix directly from a 3N-by-3N variance-covariance matrix. If method = "pearson", the conventional Pearson's inner-product correlaiton calculation will be invoked, in which only the diagnol of each residue-residue 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 sub-matrices, and so even grabs the correlation of residues moving on orthognal directions. (See more details in lmi.)

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, lmi, dccm.enma.

Examples

# NOT RUN {
# }
# NOT RUN {
##-- 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")
# }
# NOT RUN {
# }