theseus - Online in the Cloud

PROGRAM:

NAME

theseus - Maximum likelihood, multiple simultaneous superpositions with statistical
analysis

SYNOPSIS

theseus [options] pdbfile1 [pdbfile2 ...]

and

theseus_align [options] -f pdbfile1 [pdbfile2 ...]

DESCRIPTION

Theseus superposes a set of macromolecular structures simultaneously using the method of
maximum likelihood (ML), rather than the conventional least-squares criterion. Theseus
assumes that the structures are distributed according to a matrix Gaussian distribution
and that the eigenvalues of the atomic covariance matrix are hierarchically distributed
according to an inverse gamma distribution. This ML superpositioning model produces much
more accurate results by essentially downweighting variable regions of the structures and
by correcting for correlations among atoms.

Theseus operates in two main modes: (1) a mode for superimposing structures with identical
sequences and (2) a mode for structures with different sequences but similar structures:

(1) A mode for superpositioning macromolecules with identical sequences and numbers
of residues, for instance, multiple models in an NMR family or multiple structures
from different crystal forms of the same protein.

In this mode, Theseus will read every model in every file on the command line and
superpose them.

Example:

theseus 1s40.pdb

In the above example, 1s40.pdb is a pdb file of 10 NMR models.

(2) An ``alignment'' mode for superpositioning structures with different sequences,
for example, multiple structures of the cytochrome c protein from different species
or multiple mutated structures of hen egg white lysozyme.

This mode requires the user to supply a sequence alignment file of the structures
being superpositioned (see option -A and ``FILE FORMATS'' below). Additionally, it
may be necessary to supply a mapfile that tells theseus which PDB structure files
correspond to which sequences in the alignment (see option -M and ``FILE FORMATS''
below). The mapfile is unnecessary if the sequence names and corresponding pdb
filenames are identical. In this mode, if there are multiple structural models in
a PDB file, theseus only reads the first model in each file on the command line. In
other words, theseus treats the files on the command line as if there were only one
structure per file.

Example 1:

theseus -A cytc.aln -M cytc.filemap d1cih__.pdb d1csu__.pdb d1kyow_.pdb

In the above example, d1cih__.pdb, d1csu__.pdb, and d1kyow_.pdb are pdb files of
cytochrome c domains from the SCOP database.

Example 2:

theseus_align -f d1cih__.pdb d1csu__.pdb d1kyow_.pdb

In this example, the theseus_align script is called to do the hard work for you.
It will calculate a sequence alignment and then superpose based on that alignment.
The script theseus_align takes the same options as the theseus program. Note, the
first few lines of this script must be modified for your system, since it calls an
external multiple sequence alignment program to do the alignment. See the
examples/ directory for more details, including example files.

OPTIONS

Algorithmic options, defaults in {brackets}:
--amber
Do special processing for AMBER8 formatted PDB files

Most people will never need to use this long option, unless you are processing MD
traces from AMBER. AMBER puts the atom names in the wrong column in the PDB file.

-a [selection]
Atoms to include in the superposition. This option takes two types of arguments,
either (1) a number specifying a preselected set of atom types, or (2) an explict
PDB-style, colon-delimited list of the atoms to include.

For the preselected atom type subsets, the following integer options are available:

· 0, alpha carbons for proteins, C1´ atoms for nucleic acids
· 1, backbone
· 2, all
· 3, alpha and beta carbons
· 4, all heavy atoms (no hydrogens)

Note, only the -a0 option is available when superpositioning structures with
different sequences.

To custom select an explicit set of atom types, the atom types must be specified
exactly as given in the PDB file field, including spaces, and the atom-types must
encapsulated in quotation marks. Multiple atom types must be delimited by a colon.
For example,

-a ` N : CA : C : O '

would specify the atom types in the peptide backbone.

-f Only read the first model of a multi-model PDB file

-h Help/usage

-i [nnn]
Maximum iterations, {200}

-p [precision]
Requested relative precision for convergence, {1e-7}

-r [root name]
Root name to be used in naming the output files, {theseus}

-s [n-n:...]
Residue selection (e.g. -s15-45:50-55), {all}

-S [n-n:...]
Residues to exclude (e.g. -S15-45:50-55) {none}

The previous two options have the same format. Residue (or alignment column) ranges
are indicated by beginning and end separated by a dash. Multiple ranges, in any
arbitrary order, are separated by a colon. Chains may also be selected by giving
the chain ID immediately preceding the residue range. For example, -sA1-20:A40-71
will only include residues 1 through 20 and 40 through 70 in chain A. Chains cannot
be specified when superposing structures with different sequences.

-v use ML variance weighting (no correlations) {default}

Input/output options:
-A [sequence alignment file]
Sequence alignment file to use as a guide (CLUSTAL or A2M format)

For use when superposing structures with different sequences. See ``FILE FORMATS''
below.

-E Print expert options

-F Print FASTA files of the sequences in PDB files and quit

A useful option when superposing structures with different sequences. The files
output with this option can be aligned with a multiple sequence alignment program
such as CLUSTAL or MUSCLE, and the resulting output alignment file used as theseus
input with the -A option.

-h Help/usage

-I Just calculate statistics for input file; don't superpose

-M [mapfile]
File that maps PDB files to sequences in the alignment.

A simple two-column formatted file; see ``FILE FORMATS'' below. Used with mode 2.

-n Don't write transformed pdb file

-o [reference structure]
Reference file to superpose on, all rotations are relative to the first model in
this file

For example, 'theseus -o cytc1.pdb cytc1.pdb cytc2.pdb cytc3.pdb' will superpose
the structures and rotate the entire final superposition so that the structure from
cytc1.pdb is in the same orientation as the structure in the original cytc1.pdb PDB
file.

-V Version

Principal components analysis:
-C Use covariance matrix for PCA (correlation matrix is default)

-P [nnn]
Number of principal components to calculate {0}

In both of the above, the corresponding principal component is written in the B-
factor field of the output PDB file. Usually only the first few PCs are of any
interest (maybe up to six).

EXAMPLES theseus 2sdf.pdb

theseus -l -r new2sdf 2sdf.pdb

theseus -s15-45 -P3 2sdf.pdb

theseus -A cytc.aln -M cytc.mapfile -o cytc1.pdb -s1-40 cytc1.pdb cytc2.pdb cytc3.pdb
cytc4.pdb

ENVIRONMENT

You can set the environment variable 'PDBDIR' to your PDB file directory and theseus will
look there after the present working directory. For example, in the C shell (tcsh or
csh), you can put something akin to this in your .cshrc file:

setenv PDBDIR '/usr/share/pdbs/'

FILE FORMATS

Theseus will read standard PDB formatted files (see <http://www.rcsb.org/pdb/>). Every
effort has been made for the program to accept nonstandard CNS and X-PLOR file formats
also.

Two other files deserve mention, a sequence alignment file and a mapfile.

Sequence alignment file
When superposing structures with different residue identities (where the lengths of each
the macromolecules in terms of residues are not necessarily equal), a sequence alignment
file must be included for theseus to use as a guide (specified by the -A option). Theseus
accepts both CLUSTAL and A2M (FASTA) formatted multiple sequence alignment files.

NOTE 1: The residue sequence in the alignment must match exactly the residue sequence
given in the coordinates of the PDB file. That is, there can be no missing or extra
residues that do not correspond to the sequence in the PDB file. An easy way to ensure
that your sequences exactly match the PDB files is to generate the sequences using
theseus' -F option, which writes out a FASTA formatted sequence file of the chain(s) in
the PDB files. The files output with this option can then be aligned with a multiple
sequence alignment program such as CLUSTAL or MUSCLE, and the resulting output alignment
file used as theseus input with the -A option.

NOTE 2: Every PDB file must have a corresponding sequence in the alignment. However, not
every sequence in the alignment needs to have a corresponding PDB file. That is, there can
be extra sequences in the alignment that are not used for guiding the superposition.

PDB -> Sequence mapfile
If the names of the PDB files and the names of the corresponding sequences in the
alignemnt are identical, the mapfile may be omitted. Otherwise, Theseus needs to know
which sequences in the alignment file correspond to which PDB structure files. This
information is included in a mapfile with a very simple format (specified with the -M
option). There are only two columns separated by whitespace: the first column lists the
names of the PDB structure files, while the second column lists the corresponding sequence
names exactly as given in the multiple sequence alignment file.

An example of the mapfile:

cytc1.pdb seq1
cytc2.pdb seq2
cytc3.pdb seq3

SCREEN OUTPUT

Theseus provides output describing both the progress of the superposing and several
statistics for the final result:

Classical LS pairwise <RMSD>:
The conventional RMSD for the superposition, the average RMSD for all pairwise
combinations of structures in the ensemble.

Least-squares <sigma>:
The standard deviation for the superposition, based on the conventional assumption
of no correlation and equal variances. Basically equal to the RMSD from the average
structure.

Maximum Likelihood <sigma>:
The ML analog of the standard deviation for the superposition. When assuming that
the correlations are zero (a diagonal covariance matrix), this is equal to the
square root of the harmonic average of the variances for each atom. In contrast,
the ``Least-squares <sigma>'' given above reports the square root of the arithmetic
average of the variances. The harmonic average is always less than the arithmetic
average, and the harmonic average downweights large values proportional to their
magnitude. This makes sense statistically, because when combining values one should
weight them by the reciprocal of their variance (which is in fact what the ML
superposing method does).

Marginal Log Likelihood:
The final marginal log likelihood of the superposition, assuming the matrix
Gaussian distribution of the structures and the hierarchical inverse gamma
distribution of the eigenvalues of the covariance matrix. The marginal log
likelihood is the likelihood with the covariance matrix integrated out.

AIC: The Akaike Information Criterion for the final superposition. This is an important
statistic in likelihood analysis and model selection theory. It allows an objective
comparison of multiple theoretical models with different numbers of parameters. In
this case, the higher the number the better. There is a tradeoff between fit to the
data and the number of parameters being fit. Increasing the number of parameters
in a model will always give a better fit to the data, but it also increases the
uncertainty of the estimated values. The AIC criterion finds the best combination
by (1) maximizing the fit to the data while (2) minimizing the uncertainty due to
the number of parameters. In the superposition case, one can compare the least
squares superposition to the maximum likelihood superposition. The method (or
model) with the higher AIC is preferred. A difference in the AIC of 2 or more is
considered strong statistical evidence for the better model.

BIC: The Bayesian Information Criterion. Similar to the AIC, but with a Bayesian
emphasis.

Omnibus chi2:
The overall reduced chi2 statistic for the entire fit, including the rotations,
translations, covariances, and the inverse gamma parameters. This is probably the
most important statistic for the superposition. In some cases, the inverse gamma
fit may be poor, yet the overall fit is still very good. Again, it should ideally
be close to 1.0, which would indicate a perfect fit. However, if you think it is
too large, make sure to compare it to the chi2 for the least-squares fit; it's
probably not that bad after all. A large chi2 often indicates a violation of the
assumptions of the model. The most common violation is when superposing two or
more independent domains that can rotate relative to each other. If this is the
case, then there will likely be not just one Gaussian distribution, but several
mixed Gaussians, one for each domain. Then, it would be better to superpose each
domain independently.

Hierarchical var (alpha, gamma) chi2:
The reduced chi2 for the inverse gamma fit of the covariance matrix eigenvalues. As
before, it should ideally be close to 1.0. The two values in the parentheses are
the ML estimates of the scale and shape parameters, respectively, for the inverse
gamma distribtuion.

Rotational, translational, covar chi2:
The reduced chi2 statistic for the fit of the structures to the model. With a good
fit it should be close to 1.0, which indicates a perfect fit of the data to the
statistical model. In the case of least-squares, the assumed model is a matrix
Gaussian distribution of the structures with equal variances and no correlations.
For the ML fits, the assumed model is unequal variances and no correlations, as
calculated with the -v option [default]. This statistic is for the superposition
only, and does not include the fit of the covariance matrix eigenvalues to an
inverse gamma distribution. See ``Omnibus chi2'' below.

Hierarchical minimum var:
The hierarchical fit of the inverse gamma distribution constrains the variances of
the atoms by making large ones smaller and small ones larger. This statistic
reports the minimum possible variance given the inferred inverse gamma parameters.

skewness, skewness Z-value, kurtosis & kurtosis Z-value:
The skewness and kurtosis of the residuals. Both should be 0.0 if the residuals fit
a Gaussian distribution perfectly. They are followed by the P-value for the
statistics. This is a very stringent test; residuals can be very non-Gaussian and
yet the estimated rotations, translations, and covariance matrix may still be
rather accurate.

Data pts, Free params, D/P:
The total number of data points given all observed structures, the number of
parameters being fit in the model, and the data-to-parameter ratio.

Median structure:
The structure that is overall most similar to the average structure. This can be
considered to be the most ``typical'' structure in the ensemble.

Total rounds:
The number of iterations that the algorithm took to converge.

Fractional precision:
The actual precision that the algorithm converged to.

OUTPUT FILES

Theseus writes out the following files:

theseus_sup.pdb
The final superposition, rotated to the principle axes of the mean structure.

theseus_ave.pdb
The estimate of the mean structure.

theseus_residuals.txt
The normalized residuals of the superposition. These can be analyzed for deviations
from normality (whether they fit a standard Gaussian distribution). E.g., the chi2,
skewness, and kurtosis statistics are based on these values.

theseus_transf.txt
The final transformation rotation matrices and translation vectors.

theseus_variances.txt
The vector of estimated variances for each atom.

When Principal Components are calculated (with the -P option), the following files are
also produced:

theseus_pcvecs.txt
The principal component vectors.

theseus_pcstats.txt
Simple statistics for each principle component (loadings, variance explained,
etc.).

theseus_pcN_ave.pdb
The average structure with the Nth principal component written in the temperature
factor field.

theseus_pcN.pdb
The final superposition with the Nth principal component written in the temperature
factor field. This file is omitted when superposing molecules with different
residue sequences (mode 2).

theseus_cor.mat, theseus_cov.mat
The atomic correlation matrix and covariance matrices, based on the final
superposition. The format is suitable for input to GNU's octave. These are the
matrices used in the Principal Components Analysis.

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