All Atom Normal Mode Analysis

Perform all-atom elastic network model normal modes calculation of a protein structure.

aanma(...)

# S3 method for pdb
aanma(pdb, pfc.fun = NULL, mass = TRUE, temp = 300,
  keep = NULL, hessian = NULL, outmodes = "calpha", rm.wat = TRUE,
  reduced = FALSE, rtb = FALSE, nmer = 1, ...)

rtb(hessian, pdb, mass = TRUE, nmer = 1, verbose = TRUE)

Arguments

...	additional arguments to `build.hessian` and `aa2mass`. One useful option here for dealing with unconventional residues is ‘mass.custom’, see the `aa2mass` function for details.
pdb	an object of class `pdb` as obtained from function `read.pdb`.
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 NULL, the default function ‘aaenm2’ will be employed. (See details 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 limited.
hessian	hessian matrix as obtained from `build.hessian`. For internal purposes and generally not intended for public use.
outmodes	either a character (‘calpha’ or ‘noh’) or atom indices as obtained from `atom.select` specifying the atoms to include in the resulting mode object. (See details below).
rm.wat	logical, if TRUE water molecules will be removed before calculation.
reduced	logical, if TRUE the coarse-grained (‘4-bead’) ENM will be employed. (See details below).
rtb	logical, if TRUE the rotation-translation block based approximate modes will be calculated. (See details below).
nmer	numerical, defines the number of residues per block (used only when `rtb=TRUE`).
verbose	logical, if TRUE print detailed processing message

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.

numeric matrix with columns containing the raw eigenvectors. Equals to the modes component when mass=FALSE and temp=NULL.

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.

Details

This function builds an elastic network model (ENM) based on all heavy atoms of input pdb, and performs subsequent normal mode analysis (NMA) in various manners. By default, the ‘aaenm2’ force field (defining of the spring constants between atoms) is used, which was obtained by fitting to a local energy minimum of a crambin model derived from the AMBER99SB force field. It employs a pair force constant function which falls as r^-6, and specific force constants for covalent and intra-residue atom pairs. See also load.enmff for other force field options.

The outmodes argument controls the type of output modes. There are two standard types of output modes: ‘noh’ and ‘calpha’. outmodes='noh' invokes regular all-atom based ENM-NMA. When outmodes='calpha', an effective Hessian with respect to all C-alpha atoms will be first calculated using the same formula as in Hinsen et al. NMA is then performed on this effective C-alpha based Hessian. In addition, users can provide their own atom selection (see atom.select) as the value of outmodes for customized output modes generation.

When reduced=TRUE, only a selection of all heavy atoms is used to build the ENM. More specifically, three to five atoms per residue constitute the model. Here the N, CA, C atoms represent the protein backbone, and zero to two selected side chain atoms represent the side chain (selected based on side chain size and the distance to CA). This coarse-grained ENM has significantly improved computational efficiency and similar prediction accuracy with respect to the all-atom ENM.

When rtb=TRUE, rotation-translation block (RTB) based approximate modes will be calculated. In this method, each residue is assumed to be a rigid body (or ‘block’) that has only rotational and translational degrees of freedom. Intra-residue deformation is thus ignored. (See Durand et al 1994 and Tama et al. 2000 for more details). N residues per block is also supported, where N=1, 2, 3, etc. (See argument nmer). The RTB method has significantly improved computational efficiency and similar prediction accuracy with respect to the all-atom ENM.

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

Author

Lars Skjaerven & Xin-Qiu Yao

References

Hinsen, K. et al. (2000) Chem. Phys. 261, 25. Durand, P. et al. (1994) Biopolymers 34, 759. Tama, F. et al. (2000) Proteins 41, 1.

Examples

if (FALSE) {
   # All-atom NMA takes relatively long time - Don't run by default.

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

   ## Calculate all-atom normal modes
   modes.aa <- aanma(pdb, outmodes='noh')

   ## Calculate all-atom normal modes with RTB approximation
   modes.aa.rtb <- aanma(pdb, outmodes='noh', rtb=TRUE)

   ## Compare the two modes
   rmsip(modes.aa, modes.aa.rtb)

   ## Calculate C-alpha normal modes.
   modes <- aanma(pdb)

   ## Calculate C-alpha normal modes with reduced ENM.
   modes.cg <- aanma(pdb, reduced=TRUE)

   ## Calculate C-alpha normal modes with RTB approximation
   modes.rtb <- aanma(pdb, rtb=TRUE)

   ## Compare modes
   rmsip(modes, modes.cg)
   rmsip(modes, modes.rtb)

   ## Print modes
   print(modes)

   ## Plot modes
   plot(modes)

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