Bio3D[1] is an R package that provides interactive tools for the analysis of bimolecular structure, sequence and simulation data. The aim of this document, termed a vignette[2] in R parlance, is to provide a brief task-oriented introduction to facilities for analyzing protein structure data with Bio3D [@grant06].
Detailed instructions for obtaining and installing the Bio3D package on various platforms can be found in the Installing Bio3D vignette available both online and from within the Bio3D package. To see available vignettes use the command:
vignette(package = "bio3d")
Note that to follow along with this vignette the MUSCLE multiple sequence alignment program and the DSSP secondary structure assignment program must be installed on your system and in the search path for executables. Please see the installation vignette for full details.
Start R, load the Bio3D package and use the command demo("pdb") and
then demo("pca") to get a quick feel for some of the tasks that we
will be introducing in the following sections.
library(bio3d)
demo("pdb")
demo("pca")
You will be prompted to hit the RETURN key at each step of the demos
as this will allow you to see the particular functions being called.
Also note that detailed documentation and example code for each function
can be accessed via the help() and example() commands (e.g.
help(read.pdb)). You can also copy and paste any of the example code
from the documentation of a particular function, or indeed this
vignette, directly into your R session to see how things work. You can
also find this documentation
online.
The code snippet below calls the read.pdb() with a single input
argument, the four letter Protein Data Bank (PDB) identifier code
"1tag". This will cause the read.pdb() function to read directly
from the online RCSB PDB database and return a new object pdb for
further manipulation.
pdb <- read.pdb("1tag")
## Note: Accessing online PDB file
## HEADER GTP-BINDING PROTEIN 23-NOV-94 1TAG
Alternatively, you can read a PDB file directly from your local file
system using the file name (or the full path to the file) as an argument
to read.pdb():
pdb <- read.pdb("myfile.pdb")
pdb <- read.pdb("/path/to/my/data/myfile.pdb")
A short summary of the pdb object can be obtained by simply calling
the function print():
print(pdb)
##
## Call: read.pdb(file = "1tag")
##
## Atom Count: 2890
##
## Total ATOMs#: 2521
## Protein ATOMs#: 2521 ( Calpha ATOMs#: 314 )
## Non-protein ATOMs#: 0 ( residues: )
## Chains#: 1 ( values: A )
##
## Total HETATOMs: 369
## Residues HETATOMs#: 342 ( residues: MG GDP HOH )
## Chains#: 1 ( values: A )
##
## Sequence:
## ARTVKLLLLGAGESGKSTIVKQMKIIHQDGYSLEECLEFIAIIYGNTLQSILAIVRAMTT
## LNIQYGDSARQDDARKLMHMADTIEEGTMPKEMSDIIQRLWKDSGIQACFDRASEYQLND
## SAGYYLSDLERLVTPGYVPTEQDVLRSRVKTTGIIETQFSFKDLNFRMFDVGGQRSERKK
## WIHCFEGVTCIIFIAALSAYDMVLVEDDEVNRMHESLHLFNSICN...<cut>...DIII
##
## + attr: atom, het, helix, sheet, seqres,
## xyz, xyz.models, calpha, call
To examine the contents of the pdb object in more detail we can use
the attributes function:
attributes(pdb)
## $names
## [1] "atom" "het" "helix" "sheet" "seqres"
## [6] "xyz" "xyz.models" "calpha" "call"
##
## $class
## [1] "pdb"
These attributes describe the list components that comprise the pdb
object, and each individual component can be accessed using the $
symbol (e.g. pdb$atom). Their complete description can be found on the
read.pdb() functions help page accessible with the command:
help(read.pdb). Note that the atom component is a matrix consisting
of all atomic coordinate ATOM data, with a row per ATOM and a column per
record type. The column names can be used as a convenient means of data
access, for example to access coordinate data for the first three atoms
in our newly created pdb object:
pdb$atom[1:3, c("resno", "resid", "elety", "x", "y", "z")]
## resno resid elety x y z
## [1,] "27" "ALA" "N" "38.238" "18.018" "61.225"
## [2,] "27" "ALA" "CA" "38.552" "16.715" "60.576"
## [3,] "27" "ALA" "C" "40.042" "16.687" "60.253"
In the example above we used numeric indices to access atoms 1 to 3, and
a character vector of column names to access the specific record types.
In a similar fashion the atom.select() function returns numeric
indices that can be used for accessing desired subsets of the pdb
data. For example:
ca.inds <- atom.select(pdb, "calpha")
The returned ca.inds object is a list containing atom and xyz numeric
indices corresponding to the selection (all C-alpha atoms in this
particular case). The indices can be used to access e.g. the Cartesian
coordinates of the selected atoms (pdb$xyz[ca.inds$xyz]), or residue
numbers and B-factor data for the selected atoms. For example:
resnos <- pdb$atom[ca.inds$atom, "resno"]
bfacts <- pdb$atom[ca.inds$atom, "b"]
plot.bio3d(resnos, bfacts, sse = pdb, ylab = "B-factor", xlab = "Residue", typ = "l")
In the above example we use these indices to plot residue number vs
B-factor along with a basic secondary structure schematic (provided with
the argument sse=pdb; Figure 1). As a further example of data access
lets extract the sequence for the loop region (P-loop) between strand 3
(beta 1) and helix 1 in our pdb object.
loop <- pdb$sheet$end[3]:pdb$helix$start[1]
loop.inds <- atom.select(pdb, resno = loop, elety = "CA")
##
## Build selection from input components
##
## segid chain resno resid eleno elety
## Stest "" "" "35,36,37,38,39,40,41,42" "" "" "CA"
## Natom "2521" "2521" "49" "2521" "2521" "314"
## * Selected a total of: 8 intersecting atoms *
pdb$atom[loop.inds$atom, "resid"]
## [1] "LEU" "GLY" "ALA" "GLY" "GLU" "SER" "GLY" "LYS"
In the above example the residue numbers in the sheet and helix
components of pdb are accessed and used in a subsequent atom
selection, the output of which is used as indices to extract residue
names.
How would you extract the one-letter amino acid sequence for the loop
region mentioned above? HINT The aa321() function converts between
three-letter and one-letter IUPAC amino acid codes.
How would select all backbone or sidechain atoms? HINT: see the example
section of help(atom.select) and the string option.
Consider using the help(combine.sel) function when dealing with more
complicated selections.
The Bio3D package was designed to specifically facilitate the analysis of multiple structures from both experiment and simulation. The challenge with working with these structures is that they are usually different in their composition (i.e. contain differing number of atoms, sequences, chains, ligands, structures, conformations etc. even for the same protein as we will see below) and it is these differences that are frequently of most interest.
For this reason Bio3D contains extensive utilities to enable the reading and writing of sequence and structure data, sequence and structure alignment, performing homologous protein searches, structure annotation, atom selection, re-orientation, superposition, rigid core identification, clustering, torsion analysis, distance matrix analysis, structure and sequence conservation analysis, normal mode analysis across related structures, and principal component analysis of structural ensembles. We will demonstrate some of these utilities in the following sections and in other package vignettes. However, before delving into more advanced analysis lets examine how we can read multiple PDB structures from the RCSB PDB for a particular protein and perform some basic analysis:
## Download some example PDB files
ids <- c("1TND_B", "1AGR_A", "1FQJ_A", "1TAG_A", "1GG2_A", "1KJY_A")
raw.files <- get.pdb(ids)
The get.pdb() function will download the requested files, below we
extract the particular chains we are most interested in with the
function pdbsplit() (note these ids could come from the results of a
blast.pdb() search as described in subsequent sections). The requested
chains are then aligned and their structural data stored in a new object
pdbs that can be used for further analysis and manipulation.
# Extract and align the chains we are interested in
files <- pdbsplit(raw.files, ids)
pdbs <- pdbaln(files)
Below we examine the sequence and structural similarity.
## Calculate sequence identity
seqidentity(pdbs)
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.000 0.693 0.914 1.000 0.690 0.696
## [2,] 0.693 1.000 0.779 0.694 0.997 0.994
## [3,] 0.914 0.779 1.000 0.914 0.776 0.782
## [4,] 1.000 0.694 0.914 1.000 0.691 0.697
## [5,] 0.690 0.997 0.776 0.691 1.000 0.991
## [6,] 0.696 0.994 0.782 0.697 0.991 1.000
## Calculate RMSD
rmsd(pdbs, fit = TRUE)
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.000 0.965 0.609 1.283 1.612 2.100
## [2,] 0.965 0.000 0.873 1.575 1.777 1.914
## [3,] 0.609 0.873 0.000 1.265 1.737 2.042
## [4,] 1.283 1.575 1.265 0.000 1.687 1.841
## [5,] 1.612 1.777 1.737 1.687 0.000 1.879
## [6,] 2.100 1.914 2.042 1.841 1.879 0.000
What effect does setting the fit=TRUE option have in the RMSD
calculation? What would the results indicate if you set fit=FALSE or
disparaged this option? HINT Bio3D functions have various default
options that will be used if the option is not explicitly specified by
the user, see help(rmsd) for an example and note that the input
options with an equals sign (e.g. fit=FALSE) have default values.
A number of example datasets are included with the Bio3D package. The main purpose of including this data (which may be generated by the user by following the extended examples documented within the various Bio3D functions) is to allow users to more quickly appreciate the capabilities of functions that would otherwise require extensive data downloads before execution.
For a number of the examples in the current vignette we will utilize the
included transducin dataset that contains over 50 publicly available
structures. This dataset formed the basis of the work described in
[@yao13] and we refer the motivated reader to this publication and
references therein for extensive background information. Briefly,
heterotrimeric G proteins are molecular switches that turn on and off
intracellular signaling cascades in response to the activation of G
protein coupled receptors (GPCRs). Receptor activation by extracellular
stimuli promotes a cycle of GTP binding and hydrolysis on the G protein
alpha subunit that leads to conformational rearrangements (i.e. internal
structural changes) that activate multiple downstream effectors. The
current dataset consists of transducin (including Gt and Gi/o) alpha
subunit sequence and structural data and can be loaded with the command
data(transducin):
data(transducin)
attach(transducin)
This dataset can be assembled from scratch with commands similar to
those detailed in the next section and those listed in section 2.2. Also
see help(example.data) for a full description of this datasets
contents.
Comparing multiple structures of homologous proteins and carefully analyzing large multiple sequence alignments can help identify patterns of sequence and structural conservation and highlight conserved interactions that are crucial for protein stability and function [@grant07]. Bio3D provides a useful framework for such studies and can facilitate the integration of sequence, structure and dynamics data in the analysis of protein evolution.
In this tutorial, to collect available transducin crystal structures, we first use BLAST to query the PDB database to find similar sequences (and hence structures) to our chosen representative (PDB ID “1tag”):
pdb <- read.pdb("1tag")
seq <- pdbseq(pdb)
blast <- blast.pdb(seq)
Examining the alignment scores and their associated E-values (with the
function plot.blast()) indicates a sensible normalized score
(-log(E-Value)) cutoff of 240 bits (Figure 2).
hits <- plot.blast(blast, cutoff = 240)
## * Possible cutoff values include:
## 709 239 -2
## Yielding Nhits:
## 15 97 240
We can then list a subset of our top hits, for example:
head(hits$hits)
## pdb.id gi.id group
## 1 "1TND_A" "576308" "1"
## 2 "1TND_B" "576309" "1"
## 3 "1TND_C" "576310" "1"
## 4 "1TAD_A" "1065261" "1"
## 5 "1TAD_B" "1065262" "1"
## 6 "1TAD_C" "1065263" "1"
head(hits$pdb.id)
## [1] "1TND_A" "1TND_B" "1TND_C" "1TAD_A" "1TAD_B" "1TAD_C"
pdb.annotate() can fetch detailed information about thecorresponding structures (e.g. title, experimental method, resolution, ligand name(s), citation, etc.). For example:
anno <- pdb.annotate(hits$pdb.id)
## Loading required package: XML
head(anno[, c("resolution", "ligandId", "citation")])
## resolution ligandId citation
## 1AGR 2.8 ALF, CIT, GDP, MG, null Tesmer et al. Cell (1997)
## 1AS0 2.0 GSP, MG, SO4 Raw et al. Biochemistry (1997)
## 1AS2 2.8 GDP, PO4 Raw et al. Biochemistry (1997)
## 1AS3 2.4 GDP, SO4 Raw et al. Biochemistry (1997)
## 1BH2 2.1 GSP, MG Posner et al. J.Biol.Chem. (1998)
## 1BOF 2.2 GDP, MG, SO4 Coleman et al. Biochemistry (1998)
Next we download the complete list of structures from the PDB (with
function get.pdb()), and use function pdbsplit() to split the
structures into separate chains and store them for subsequent access.
Finally, function pdbaln() will extract the sequence of each structure
and perform a multiple sequence alignment to determine residue-residue
correspondences (NOTE: requires external program MUSCLE be in
search path for executables):
unq.ids <- unique(substr(hits$pdb.id, 1, 4))
## - Download and chain split PDBs
raw.files <- get.pdb(unq.ids, path = "raw_pdbs")
files <- pdbsplit(raw.files, ids = hits$pdb.id, path = "raw_pdbs/split_chain")
## - Extract and align sequences
pdbs <- pdbaln(files)
You can now inspect the alignment (the automatically generated “aln.fa” file) with your favorite alignment viewer (we recommend SEAVIEW, available from: http://pbil.univ-lyon1.fr/software/seaview.html).
You may find a number of structures with missing residues (i.e. gaps in the alignment) at sites of particular interest to you. If this is the case you may consider removing these structures from your hit list and generating a smaller, but potentially higher quality, dataset for further exploration.
How could you automatically identify gap positions in your alignment?
HINT: try the command help.search("gap", package="bio3d").
The detailed comparison of homologous protein structures can be used to infer pathways for evolutionary adaptation and, at closer evolutionary distances, mechanisms for conformational change. The Bio3D package employs both conventional methods for structural analysis (alignment, RMSD, difference distance matrix analysis, etc.) as well as refined structural superposition and principal component analysis (PCA) to facilitate comparative structure analysis.
Conventional structural superposition of proteins minimizes the root
mean square difference between their full set of equivalent residues.
This can be performed with Bio3D functions pdbfit() and fit.xyz as
outlined previously. However, for certain applications such a
superposition procedure can be inappropriate. For example, in the
comparison of a multi-domain protein that has undergone a hinge-like
rearrangement of its domains, standard all atom superposition would
result in an underestimate of the true atomic displacement by attempting
superposition over all domains (whole structure superposition). A more
appropriate and insightful superposition would be anchored at the most
invariant region and hence more clearly highlight the domain
rearrangement (sub-structure superposition).
The Bio3D core.find() function implements an iterated superposition
procedure, where residues displaying the largest positional differences
are identified and excluded at each round. The function returns an
ordered list of excluded residues, from which the user can select a
subset of ’core’ residues upon which superposition can be based.
core <- core.find(pdbs)
The plot.core() and print.core() functions allow one to further examine
the output of the core.find() procedure (see below and Figure 3).
col = rep("black", length(core$volume))
col[core$volume < 2] = "pink"
col[core$volume < 1] = "red"
plot(core, col = col)
The print.core() function also returns atom and xyz indices
similar to those returned from the atom.select() function. Below we
use these indices for core superposition and to write a quick PDB file
for viewing in a molecular graphics program such as VMD (Figure 4).
core.inds <- print(core, vol = 1)
## # 88 positions (cumulative volume <= 1 Angstrom^3)
## start end length
## 1 32 52 21
## 2 195 195 1
## 3 216 226 11
## 4 239 239 1
## 5 242 247 6
## 6 260 274 15
## 7 279 279 1
## 8 282 283 2
## 9 295 304 10
## 10 317 336 20
write.pdb(xyz = pdbs$xyz[1, core.inds$xyz], file = "quick_core.pdb")
[htb]
We can now superpose all structures on the selected core indices with
the fit.xyz() or pdbfit() function.
xyz <- pdbfit(pdbs, core.inds)
The above command performs the actual superposition and stores the new
coordinates in the matrix object xyz.
By providing an extra outpath="somedir" argument to pdbfit the
superposed structures can be output for viewing (in this case to the
local directory somedir which you can obviously change). These fitted
structures can then be viewed in your favorite molecular graphics
program (Figure 5).
[htb]
Bio3D contains functions to perform standard structural analysis, such as root mean-square deviation (RMSD), root mean-square fluctuation (RMSF), secondary structure, dihedral angles, difference distance matrices etc. The current section provides a brief exposure to using Bio3D in this vein. However, do feel free to skip ahead to the arguably more interesting section on PCA analysis.
RMSD is a standard measure of structural distance between coordinate sets. Here we examine the pairwise RMSD values and cluster our structures based on these values:
rd <- rmsd(xyz)
hist(rd, breaks = 40, xlab = "RMSD (Å)")
# RMSD clustering
hc.rd <- hclust(as.dist(rd))
plot(hc.rd, labels = pdbs$id, ylab = "RMSD", main = "RMSD Cluster Dendrogram")
How many structure groups/clusters do we have according to this clustering? How would determine which structures are assigned to which cluster? HINT: See help(cutree).
What kind of plot would the command heatmap(rd) produce? How would you label this plot with PDB codes? HINT: labCol and labRow.
RMSF is another often used measure of conformational variance. The Bio3D rmsf() function will return a vector of atom-wise (or residue-wise) variance instead of a single numeric value. For example:
rf <- rmsf(xyz[, gaps.pos$f.inds])
## Error: object 'gaps.pos' not found
plot.bio3d(res.ind, rf, sse = sse, ylab = "RMSF (A)", xlab = "Position", typ = "l")
## Error: object 'res.ind' not found
The conformation of a polypeptide or nucleotide chain can be usefully described in terms of angles of internal rotation around its constituent bonds.
tor <- torsion.pdb(pdb)
# basic Ramachandran plot
plot(tor$phi, tor$psi, xlab = "phi", ylab = "psi")
Lets compare the Calpha atom based pseudo-torsion angles between two structures:
a.xyz <- pdbs$xyz["1TAG_A", ]
b.xyz <- pdbs$xyz["1TND_B", ]
gaps.xyz <- is.gap(pdbs$xyz["1TAG_A", ])
gaps.res <- is.gap(pdbs$ali["1TAG_A", ])
resno <- pdbs$resno["1TAG_A", !gaps.res]
a <- torsion.xyz(a.xyz[!gaps.xyz], atm.inc = 1)
b <- torsion.xyz(b.xyz[!gaps.xyz], atm.inc = 1)
d.ab <- wrap.tor(a - b)
sse2 <- dssp(read.pdb("1tag"))
## Note: Accessing online PDB file
## HEADER GTP-BINDING PROTEIN 23-NOV-94 1TAG
plot.bio3d(resno, abs(d.ab), typ = "h", sse = sse2, xlab = "Residue", ylab = "Angle")
Distance matrices can be calculated with the function dm() and contact
maps with the function cmap(). In the example below we calculate the
differe distance matrix by simply subtracting one distance matrix from
another. Note the vectorized nature of the this calculation (i.e. we do
not have to explicitly iterate through each element of the matrix):
a <- dm(a.xyz[!gaps.xyz])
b <- dm(b.xyz[!gaps.xyz])
plot((a - b), nlevels = 10, grid.col = "gray", resnum.1 = resno, resnum.2 = resno,
xlab = "1tag", ylab = "1tnd (positions relative to 1tag)")
Can you think of the pros and cons of these different analysis methods?
Following core identification and subsequent superposition, PCA can be employed to examine the relationship between different structures based on their equivalent residues. The application of PCA to both distributions of experimental structures and molecular dynamics trajectories, along with its ability to provide considerable insight into the nature of conformational differences is also discussed in the molecular dynamics trajectory analysis vignette.
Briefly, the resulting principal components (orthogonal eigenvectors) describe the axes of maximal variance of the distribution of structures. Projection of the distribution onto the subspace defined by the largest principal components results in a lower dimensional representation of the structural dataset. The percentage of the total mean square displacement (or variance) of atom positional fluctuations captured in each dimension is characterized by their corresponding eigenvalue. Experience suggests that 3–5 dimensions are often sufficient to capture over 70 percent of the total variance in a given family of structures. Thus, a handful of principal components are sufficient to provide a useful description while still retaining most of the variance in the original distribution [@grant06].
The below sequence of commands returns the indices of for gap containing
positions, which we then exclude from subsequent PCA with the
pca.xyz() command.
## Ignore gap containing positions
gaps.res <- gap.inspect(pdbs$ali)
gaps.pos <- gap.inspect(pdbs$xyz)
## – Do PCA
pc.xray <- pca.xyz(xyz[, gaps.pos$f.inds])
Why is the input to function pca.xyz() given as xyz rather than
pdbs$xyz?
Why would you need superposition before using pca.xyz but not need it
for pca.tor?
A quick overview of the results of pca.xyz() can be obtained by
calling plot.pca() (Figure 12).
plot(pc.xray, col = annotation[, "color"])
We can also call plot.bio3d() to examine the contribution of each
residue to the first three principal components with the following
commands (Figure 13).
par(mfrow = c(3, 1), cex = 0.6, mar = c(3, 4, 1, 1))
plot.bio3d(res.ind, pc.xray$au[, 1], sse = sse, ylab = "PC1 (A)")
plot.bio3d(res.ind, pc.xray$au[, 2], sse = sse, ylab = "PC2 (A)")
plot.bio3d(res.ind, pc.xray$au[, 3], sse = sse, ylab = "PC3 (A)")
par(op)
The plots in Figures 12 and 14 display the relationships between different conformers, highlight positions responsible for the major differences between structures and enable the interpretation and characterization of multiple interconformer relationships.
To further aid interpretation, a PDB format trajectory can be produced that interpolates between the most dissimilar structures in the distribution along a given principal cmponent. This involves dividing the difference between the conformers into a number of evenly spaced steps along the principal components, forming the frames of the trajectory. Such trajectories can be directly visualized in a molecular graphics program, such as VMD [@vmd]. Furthermore, the PCA results can be compared to those from simulations (see the molecular dynamics and normal mode analysis vignettes), as well as guiding dynamic network analysis, being analyzed for possible domain and shear movements with the DynDom package [@dyndom], or used as initial seed structures for reaction path refinement methods such as Conjugate Peak Refinement [@cpr].
a <- mktrj.pca(pc.xray, pc = 1, file = "pc1.pdb")
[htb]
Clustering structures in PC space can often enable one to focus on the relationships between individual structures in terms of their major structural displacements, with a controllable the level of dynamic details (via specifying the number of PCs used in the clustering). For example, with clustering along PCs 1 and 2, we can investigate how the X-ray structures of transducin relate to each other with respect to the major conformation change that covers over 65% structural variance (See Figures 12 and 15). This can reveal functional relationships that are often hard to find by conventional pairwise methods such as the RMSD clustering detailed previously. For example in the PC1-PC2 plane, the inactive “GDP” structures (green points in Figure 12) are further split into two sub-groups (Figures 15 and 16). The bottom-right sub-group (blue) exclusively correspond to the structures complexed with GDP dissociation inhibitor (GDPi). This is clearly evident in the PC plot and clustering dendrogram that can be generated with the following commands:
hc <- hclust(dist(pc.xray$z[, 1:2]))
grps <- cutree(hc, h = 30)
cols <- c("red", "green", "blue")
plot(pc.xray$z[, 1:2], typ = "p", pch = 16, col = cols[grps], xlab = "PC1",
ylab = "PC2")
plot(hc, labels = pdbs$id, main = "PC1-2", xlab = "", ylab = "Distance")
abline(h = 30, lty = 3, col = "gray60")
On the PC1 vs PC2 conformer plot in Figure 15 you can interactively
identify and label individual structures by using the identify()
function clicking with your mouse (left to select, right to end). In
this particular case the command would be:
identify(pc.xray$z[, 1], pc.xray$z[, 2], labels = pdbs$id)
Which clustering appears to be most informative, that based on RMSD or that based on PCA? Why might this be the case? HINT: It can be useful to think of PCA as a filter for large scale conformational changes.
Can you find a Bio3D function that would allow you to compare the different clustering results?
If you have read this far, congratulations! We are ready to have some fun and move to other package vignettes that describe more interesting analysis including Correlation Network Analysis (where we will build and dissect dynamic networks form different correlated motion data), enhanced methods for Normal Mode Analysis (where we will explore the dynamics of large protein families and superfamilies using predictive calculations), and advanced Comparative Structure Analysis (where we will mine available experimental data and supplement it with simulation results to map the conformational dynamics and coupled motions of proteins).
This document is shipped with the Bio3D package in both Rnw and PDF formats. All code can be extracted and automatically executed to generate Figures and/or the PDF with the following commands:
knitr::knit("Bio3D_pca.Rnw")
tools::texi2pdf("Bio3D_pca.tex")
sessionInfo()
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Grant, B.J. and Mccammon, A.J. and Caves, L.S.D. and Cross, R.A. (2007) Multivariate Analysis of Conserved Sequence-Structure Relationships in Kinesins: Coupling of the Active Site and a Tubulin-binding Sub-domain. J. Mol. Biol., 5, 1231–1248
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[1]: The latest version of the package, full documentation and further vignettes (including detailed installation instructions) can be obtained from the main Bio3D website: http://thegrantlab.org/bio3d/
[2]: This vignette contains executable examples, see help(vignette)
for further details.