R: Normal Mode Analysis

nma.pdb {bio3d} | R Documentation

## Normal Mode Analysis

### Description

Perform elastic network model (ENM) C-alpha normal modes calculation of a protein structure.

### Usage

    ## S3 method for class 'pdb'
    nma(pdb, inds = NULL, ff = 'calpha', pfc.fun = NULL,
                      mass = TRUE, temp = 300.0, keep = NULL, hessian = NULL,
                      outmodes = NULL, ... )

    build.hessian(xyz, pfc.fun, fc.weights = NULL, pdb = NULL, ...)

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

### Arguments

`pdb` | an object of class `pdb` as obtained from function `read.pdb`.
`inds` | atom and xyz coordinate indices obtained from `atom.select` that selects the elements of `pdb` upon which the calculation should be based. If not provided the function will attempt to select the calpha atoms automatically (based on function `atom.select`).
`ff` | character string specifying the force field to use: ‘calpha’, ‘anm’, ‘pfanm’, ‘reach’, or ‘sdenm’.
`pfc.fun` | customized pair force constant (‘pfc’) function. The provided function should take a vector of distances as an argument to return a vector of force constants. If provided, 'pfc.fun' will override argument `ff`. See examples below.
`mass` | logical, if TRUE the Hessian will be mass-weighted.
`temp` | numerical, temperature for which the amplitudes for scaling the atomic displacement vectors are calculated. Set ‘temp=NULL’ to avoid scaling.
`keep` | numerical, final number of modes to be stored. Note that all subsequent analyses are limited to this subset of modes. This option is useful for very large structures and cases where memory may be limiting.
`hessian` | hessian matrix as obtained from `build.hessian`. For internal purposes and generally not intended for public use.
`outmodes` | atom indices as obtained from `atom.select`) specifying the atoms to include in the resulting mode object.
`xyz` | a numeric vector of Cartesian coordinates.
`fc.weights` | a numeric matrix of size NxN (where N is the number of calpha atoms) containg scaling factors for the pariwise force constants. See examples below.
`x` | an `nma` object obtained from `nma.pdb`.
`nmodes` | numeric, number of modes to be printed.
`...` | additional arguments to `build.hessian`, `aa2mass`, `pfc.fun`, and `print`. One useful option here for dealing with unconventional residues is ‘mass.custom’, see the `aa2mass` function for details.

### Details

This function calculates the normal modes of a C-alpha model of a protein structure. A number of force fields are implemented all of whhich employ the elastic network model (ENM).

The ‘calpha’ force field - originally developed by Konrad Hinsen - is the recommended one for most applications. It employs a spring force constant differentiating between nearest-neighbour pairs along the backbone and all other pairs. The force constant function was parameterized by fitting to a local minimum of a crambin model using the AMBER94 force field.

See `load.enmff` for details of the different force fields.

By default `nma.pdb` will diagonalize the mass-weighted Hessian matrix. The resulting mode vectors are moreover scaled by the thermal fluctuation amplitudes.

The implementation under default arguments reproduces the calculation of normal modes (VibrationalModes) in the Molecular Modeling Toolkit (MMTK) package. To reproduce ANM modes set `ff='anm'`, `mass=FALSE`, and `temp=NULL`.

### Value

Returns an object of class ‘nma’ with the following components:

`modes` | numeric matrix with columns containing the normal mode vectors. Mode vectors are converted to unweighted Cartesian coordinates when `mass=TRUE`. Note that the 6 first trivial eigenvectos appear in columns one to six.
`frequencies` | numeric vector containing the vibrational frequencies corresponding to each mode (for `mass=TRUE`).
`force.constants` | numeric vector containing the force constants corresponding to each mode (for `mass=FALSE)`).
`fluctuations` | numeric vector of atomic fluctuations.
`U` | numeric matrix with columns containing the raw eigenvectors. Equals to the `modes` component when `mass=FALSE` and `temp=NULL`.
`L` | numeric vector containing the raw eigenvalues.
`xyz` | numeric matrix of class `xyz` containing the Cartesian coordinates in which the calculation was performed.
`mass` | numeric vector containing the residue masses used for the mass-weighting.
`temp` | numerical, temperature for which the amplitudes for scaling the atomic displacement vectors are calculated.
`triv.modes` | number of trivial modes.
`natoms` | number of C-alpha atoms.
`call` | the matched call.

### Note

The current version provides an efficent implementation of NMA with execution time comparable to similar software (when the entire Hessian is diagonalized).

The main (speed related) bottleneck is currently the diagonalization of the Hessian matrix which is performed with the core R function `eigen`. For computing a few (5-20) approximate modes the user can consult package ‘irlba’.

NMA is memory extensive and users should be cautions when running larger proteins (>3000 residues). Use ‘keep’ to reduce the amount of memory needed to store the final ‘nma’ object (the full 3Nx3N Hessian matrix still needs to be allocated).

We thank Edvin Fuglebakk for valuable discussions on the implementation as well as for contributing with testing.

### Author(s)

Lars Skjaerven

### References

Skjaerven, L. et al. (2014) BMC Bioinformatics 15, 399. Grant, B.J. et al. (2006) Bioinformatics 22, 2695–2696. Hinsen, K. et al. (2000) Chemical Physics 261, 25–37.

### See Also

`fluct.nma`, `mktrj.nma`, `dccm.nma`, `overlap`, `rmsip`, `load.enmff`.

### Examples

    ## Fetch stucture
    pdb <- read.pdb( system.file("examples/1hel.pdb", package="bio3d") )

    ## Calculate normal modes
    modes <- nma(pdb)

    ## Print modes
    print(modes)

    ## Plot modes
    plot(modes)

    ## Visualize modes
    #m7 <- mktrj.nma(modes, mode=7, file="mode_7.pdb")

    ## Not run:
    ## Use Anisotropic Network Model
    modes <- nma(pdb, ff="anm", mass=FALSE, temp=NULL, cutoff=15)

    ## Use SSE information and SS-bonds
    sse      <- dssp(pdb, resno=FALSE, full=TRUE)
    ss.bonds <- matrix(c(76,94, 64,80, 30,115, 6,127),
                       ncol=2, byrow=TRUE)

    ## User defined energy function
    ## Note: Must take a vector of distances
    "my.ff" <- function(r) {
       ifelse( r>15, 0, 1 )
    }

    ## Modes with a user defined energy function
    modes <- nma(pdb, pfc.fun=my.ff)

    ## A more manual approach
    sele <- atom.select(pdb, chain='A', elety='CA')
    xyz <- pdb$xyz[sele$xyz]

    hessian <- build.hessian(xyz, my.ff)
    modes <- eigen(hessian)

    ## Dealing with unconventional residues
    pdb <- read.pdb("1xj0")

    ## nma(pdb)
    #modes <- nma(pdb, mass.custom=list(CSX=121.166))

    ## End(Not run)

[Package bio3d version 2.4-0 Index]