In road2stat/protr: Generating Various Numerical Representation Schemes for Protein Sequences
knitr::opts_chunk$set(
comment = "#>",
collapse = TRUE
)
Introduction
The protr package offers a unique and comprehensive toolkit
for generating various numerical representation schemes of protein
sequences. The descriptors included are extensively utilized in
bioinformatics and chemogenomics research.
The commonly used descriptors listed in protr include amino acid composition,
autocorrelation, CTD, conjoint traid, quasi-sequence order,
pseudo amino acid composition, and profile-based descriptors
derived by Position-Specific Scoring Matrix (PSSM).
The descriptors for proteochemometric (PCM) modeling, includes the
scales-based descriptors derived by principal components analysis,
factor analysis, multidimensional scaling, amino acid properties
(AAindex), 20+ classes of 2D and 3D molecular descriptors
(Topological, WHIM, VHSE, etc.), and BLOSUM/PAM matrix-derived descriptors.
The protr package also implemented parallelized similarity computation
derived by pairwise protein sequence alignment and Gene Ontology (GO)
semantic similarity measures. ProtrWeb, the web application built on
protr, can be accessed from http://protr.org.
If you find protr useful in your research, please feel free to cite our paper:
Nan Xiao, Dong-Sheng Cao, Min-Feng Zhu, and Qing-Song Xu. (2015). protr/ProtrWeb: R package and web server for generating various numerical representation schemes of protein sequences. _Bioinformatics_ 31 (11), 1857-1859.
BibTeX entry:
@article{Xiao2015,
author = {Xiao, Nan and Cao, Dong-Sheng and Zhu, Min-Feng and Xu, Qing-Song.},
title = {protr/{ProtrWeb}: {R} package and web server for generating various numerical representation schemes of protein sequences},
journal = {Bioinformatics},
year = {2015},
volume = {31},
number = {11},
pages = {1857--1859},
doi = {10.1093/bioinformatics/btv042}
}
An example predictive modeling workflow
Here we use the subcellular localization dataset of human proteins presented
in @chou2008cell to demonstrate the basic usage of protr.
The complete dataset includes 3,134 protein sequences (2,750 different
proteins), classified into 14 human subcellular locations. We selected
two classes of proteins as our benchmark dataset. Class 1 contains 325
extracell proteins, and class 2 includes 307 mitochondrion
proteins. Here we aim to build a random forest classification model
to classify these two types of proteins.
First, we load the protr package, then read the protein sequences
stored in two separated FASTA files with readFASTA():
library("protr")
# load FASTA files
# (system.file is for accessing example file in protr package,
# replace it with your path)
extracell <- readFASTA(system.file(
"protseq/extracell.fasta",
package = "protr"
))
mitonchon <- readFASTA(system.file(
"protseq/mitochondrion.fasta",
package = "protr"
))
To read protein sequences stored in PDB format files, use readPDB() instead.
The loaded sequences will be stored as two lists in R, and each
component in the list is a character string representing one protein sequence.
In this case, there are 325 extracell protein sequences and
306 mitonchon protein sequences:
length(extracell)
## [1] 325
length(mitonchon)
## [1] 306
To ensure that the protein sequences only have the 20 standard amino acid
types which is usually required for the descriptor computation, we use the
protcheck() function to do the amino acid type sanity check and
remove the non-standard sequences:
extracell <- extracell[(sapply(extracell, protcheck))]
mitonchon <- mitonchon[(sapply(mitonchon, protcheck))]
length(extracell)
## [1] 323
length(mitonchon)
## [1] 304
Two protein sequences were removed from each class.
For the remaining sequences, we calculate the Type II PseAAC descriptor,
i.e., the amphiphilic pseudo amino acid composition (APseAAC) descriptor
[@chouapaac] and make class labels for classification modeling.
# calculate APseAAC descriptors
x1 <- t(sapply(extracell, extractAPAAC))
x2 <- t(sapply(mitonchon, extractAPAAC))
x <- rbind(x1, x2)
# make class labels
labels <- as.factor(c(rep(0, length(extracell)), rep(1, length(mitonchon))))
In protr, the functions of commonly used descriptors for protein
sequences and proteochemometric (PCM) modeling descriptors are named
after extract...().
Next, we will split the data into a 75% training set and a 25% test set.
set.seed(1001)
# split training and test set
tr.idx <- c(
sample(1:nrow(x1), round(nrow(x1) * 0.75)),
sample(nrow(x1) + 1:nrow(x2), round(nrow(x2) * 0.75))
)
te.idx <- setdiff(1:nrow(x), tr.idx)
x.tr <- x[tr.idx, ]
x.te <- x[te.idx, ]
y.tr <- labels[tr.idx]
y.te <- labels[te.idx]
We will train a random forest classification model on the training set
with 5-fold cross-validation, using the randomForest package.
library("randomForest")
rf.fit <- randomForest(x.tr, y.tr, cv.fold = 5)
rf.fit
The training result is:
## Call:
## randomForest(x = x.tr, y = y.tr, cv.fold = 5)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 8
##
## OOB estimate of error rate: 25.11%
## Confusion matrix:
## 0 1 class.error
## 0 196 46 0.1900826
## 1 72 156 0.3157895
With the model trained on the training set, we predict on the test set
and plot the ROC curve with the pROC package, as is shown
in Figure 1.
# predict on test set
rf.pred <- predict(rf.fit, newdata = x.te, type = "prob")[, 1]
# plot ROC curve
library("pROC")
plot.roc(y.te, rf.pred, grid = TRUE, print.auc = TRUE)
The area under the ROC curve (AUC) is:
## Call:
## plot.roc.default(x = y.te, predictor = rf.pred, col = "#0080ff",
## grid = TRUE, print.auc = TRUE)
##
## Data: rf.pred in 81 controls (y.te 0) > 76 cases (y.te 1).
## Area under the curve: 0.8697
Figure 1: ROC curve for the test set of protein subcellular localization data
Package overview
The protr package [@Xiao2015] implemented most of the
state-of-the-art protein sequence descriptors with R.
Generally, each type of the descriptors (features) can be calculated
with a function named extractX() in the protr package,
where X stands for the abbrevation of the descriptor name.
The descriptors are:
- Amino acid composition
extractAAC() - Amino acid compositionextractDC() - Dipeptide compositionextractTC() - Tripeptide composition
- Autocorrelation
extractMoreauBroto() - Normalized Moreau-Broto autocorrelationextractMoran() - Moran autocorrelationextractGeary() - Geary autocorrelation
- CTD descriptors
extractCTDC() - CompositionextractCTDT() - TransitionextractCTDD() - Distribution
- Conjoint triad descriptors
extractCTriad() - Conjoint triad descriptors
- Quasi-sequence-order descriptors
extractSOCN() - Sequence-order-coupling numberextractQSO() - Quasi-sequence-order descriptors
- Pseudo-amino acid composition
extractPAAC() - Pseudo-amino acid composition (PseAAC)extractAPAAC() - Amphiphilic pseudo-amino acid composition (APseAAC)
- Profile-based descriptors
extractPSSM()extractPSSMAcc()extractPSSMFeature()
The descriptors commonly used in Proteochemometric Modeling (PCM)
implemented in protr include:
extractScales(), extractScalesGap() - Scales-based descriptors derived by Principal Components Analysis
extractProtFP(), extractProtFPGap() - Scales-based descriptors derived by amino acid properties from AAindex (a.k.a. Protein Fingerprint)extractDescScales() - Scales-based descriptors derived by 20+ classes of 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.)
extractFAScales() - Scales-based descriptors derived by Factor AnalysisextractMDSScales() - Scales-based descriptors derived by Multidimensional ScalingextractBLOSUM() - BLOSUM and PAM matrix-derived descriptors
The protr package integrates the function of parallelized similarity score
computation derived by local or global protein sequence alignment between
a list of protein sequences, the sequence alignment computation is
provided by Biostrings, the corresponding functions listed in the
protr package include:
twoSeqSim() - Similarity calculation derived by sequence alignment
between two protein sequencesparSeqSim() - Parallelized pairwise similarity calculation with a
list of protein sequences (in-memory version)parSeqSimDisk() - Parallelized pairwise similarity calculation with a
list of protein sequences (disk-based version)crossSetSim() - Parallelized pairwise similarity calculation between
two sets of protein sequences (in-memory version)
The protr package also integrates the function of parallelized similarity
score computation derived by Gene Ontology (GO) semantic similarity measures
between a list of GO terms / Entrez Gene IDs, the GO similarity computation
is provided by GOSemSim, the corresponding functions listed
in the protr package include:
twoGOSim() - Similarity calculation derived by GO-terms
semantic similarity measures between two GO terms / Entrez Gene IDs;parGOSim() - Pairwise similarity calculation with a
list of GO terms / Entrez Gene IDs.
To use the parSeqSim() function, we suggest the users to install
the packages foreach and doParallel first, in order to make
the parallelized pairwise similarity computation available.
In the following sections, we will introduce the descriptors and function
usage in this order.
Commonly used descriptors
Note: Users need to intelligently evaluate the underlying details
of the descriptors provided, instead of using protr with their data blindly,
especially for the descriptor types with more flexibility.
It would be wise for the users to use some negative and positive control
comparisons where relevant to help guide interpretation of the results.
A protein or peptide sequence with $N$ amino acid residues can be generally
represented as ${\,R_1, R_2, \ldots, R_n\,}$, where $R_i$ represents the
residue at the $i$-th position in the sequence. The labels $i$ and $j$ are
used to index amino acid position in a sequence, and $r$, $s$, $t$ are used
to represent the amino acid type. The computed descriptors are roughly
categorized into 4 groups according to their major applications.
A protein sequence can be partitioned equally into segments.
The descriptors designed for the complete sequence, can be often
applied to each individual segment.
Amino acid composition descriptor
The amino acid composition describes the fraction of each amino acid type
within a protein sequence. The fractions of all 20 natural amino acids
are calculated as:
$$
f(r) = \frac{N_r}{N} \quad r = 1, 2, \ldots, 20.
$$
where $N_r$ is the number of the amino acid type $r$ and $N$ is the length
of the sequence.
As was described above, we can use the function extractAAC() to
extract the descriptors (features) from protein sequences:
library("protr")
x <- readFASTA(system.file(
"protseq/P00750.fasta",
package = "protr"
))[[1]]
extractAAC(x)
Here, with the function readFASTA() we loaded a single protein sequence
(P00750, Tissue-type plasminogen activator) from a FASTA format file.
Then extracted the AAC descriptors with extractAAC().
The result returned is a named vector, whose elements are tagged
with the name of each amino acid.
Dipeptide composition descriptor
Dipeptide composition gives a 400-dimensional descriptor, defined as:
$$
f(r, s) = \frac{N_{rs}}{N - 1} \quad r, s = 1, 2, \ldots, 20.
$$
where $N_{rs}$ is the number of dipeptide represented by amino acid
type $r$ and type $s$. Similar to extractAAC(),
here we use extractDC() to compute the descriptors:
dc <- extractDC(x)
head(dc, n = 30L)
Here we only showed the first 30 elements of the result vector and omitted
the rest of the result. The element names of the returned vector are
self-explanatory as before.
Tripeptide composition descriptor
Tripeptide composition gives a 8000-dimensional descriptor, defined as:
$$
f(r, s, t) = \frac{N_{rst}}{N - 2} \quad r, s, t = 1, 2, \ldots, 20
$$
where $N_{rst}$ is the number of tripeptides represented by amino acid type
$r$, $s$, and $t$. With function extractTC(), we can easily obtain
the length-8000 descriptor, to save some space, here we also omitted
the long outputs:
tc <- extractTC(x)
head(tc, n = 36L)
Autocorrelation descriptors
Autocorrelation descriptors are defined based on the distribution of amino
acid properties along the sequence. The amino acid properties used here are
various types of amino acids index (Retrieved from the
AAindex database,
see @aaindex1999, @aaindex2000, and @aaindex2008; see Figure 2
for an illustrated example). Three types of autocorrelation
descriptors are defined here and described below.
All the amino acid indices are centralized and standardized before
the calculation, i.e.
$$
P_r = \frac{P_r - \bar{P}}{\sigma}
$$
where $\bar{P}$ is the average of the property of the 20 amino acids:
$$
\bar{P} = \frac{\sum_{r=1}^{20} P_r}{20} \quad \textrm{and} \quad \sigma = \sqrt{\frac{1}{2} \sum_{r=1}^{20} (P_r - \bar{P})^2}
$$
Figure 2: An illustrated example in the AAIndex database
Normalized Moreau-Broto autocorrelation descriptors
For protein sequences, the Moreau-Broto autocorrelation descriptors
can be defined as:
$$
AC(d) = \sum_{i=1}^{N-d} P_i P_{i + d} \quad d = 1, 2, \ldots, \textrm{nlag}
$$
where $d$ is called the lag of the autocorrelation; $P_i$ and $P_{i+d}$
are the properties of the amino acids at position $i$ and $i+d$;
$\textrm{nlag}$ is the maximum value of the lag.
The normalized Moreau-Broto autocorrelation descriptors are defined as:
$$
ATS(d) = \frac{AC(d)}{N-d} \quad d = 1, 2, \ldots, \textrm{nlag}
$$
The corresponding function for this descriptor is extractMoreauBroto().
A typical call would be:
moreau <- extractMoreauBroto(x)
head(moreau, n = 36L)
The eight default properties used here are:
- AccNo. CIDH920105 - Normalized Average Hydrophobicity Scales
- AccNo. BHAR880101 - Average Flexibility Indices
- AccNo. CHAM820101 - Polarizability Parameter
- AccNo. CHAM820102 - Free Energy of Solution in Water, kcal/mole
- AccNo. CHOC760101 - Residue Accessible Surface Area in Tripeptide
- AccNo. BIGC670101 - Residue Volume
- AccNo. CHAM810101 - Steric Parameter
- AccNo. DAYM780201 - Relative Mutability
Users can change the property names of AAindex database with the argument
props. The AAindex data shipped with protr can be loaded by
data(AAindex), which has the detailed information of each property.
With the argument customprops and nlag, users can specify
their own properties and lag value to calculate with. For example:
# Define 3 custom properties
myprops <- data.frame(
AccNo = c("MyProp1", "MyProp2", "MyProp3"),
A = c(0.62, -0.5, 15), R = c(-2.53, 3, 101),
N = c(-0.78, 0.2, 58), D = c(-0.9, 3, 59),
C = c(0.29, -1, 47), E = c(-0.74, 3, 73),
Q = c(-0.85, 0.2, 72), G = c(0.48, 0, 1),
H = c(-0.4, -0.5, 82), I = c(1.38, -1.8, 57),
L = c(1.06, -1.8, 57), K = c(-1.5, 3, 73),
M = c(0.64, -1.3, 75), F = c(1.19, -2.5, 91),
P = c(0.12, 0, 42), S = c(-0.18, 0.3, 31),
T = c(-0.05, -0.4, 45), W = c(0.81, -3.4, 130),
Y = c(0.26, -2.3, 107), V = c(1.08, -1.5, 43)
)
# Use 4 properties in the AAindex database, and 3 cutomized properties
moreau2 <- extractMoreauBroto(
x,
customprops = myprops,
props = c(
"CIDH920105", "BHAR880101",
"CHAM820101", "CHAM820102",
"MyProp1", "MyProp2", "MyProp3"
)
)
head(moreau2, n = 36L)
About the standard input format of props and customprops,
see ?extractMoreauBroto for details.
Moran autocorrelation descriptors
For protein sequences, the Moran autocorrelation descriptors can be defined as:
$$
I(d) = \frac{\frac{1}{N-d} \sum_{i=1}^{N-d} (P_i - \bar{P}') (P_{i+d} - \bar{P}')}{\frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P}')^2} \quad d = 1, 2, \ldots, 30
$$
where $d$, $P_i$, and $P_{i+d}$ are defined in the same way as in
the first place; $\bar{P}'$ is the considered property $P$ along
the sequence, i.e.,
$$
\bar{P}' = \frac{\sum_{i=1}^N P_i}{N}
$$
$d$, $P$, $P_i$ and $P_{i+d}$, $\textrm{nlag}$ have the same meaning as above.
With extractMoran() (which has the identical parameters as
extractMoreauBroto()), we can compute the Moran autocorrelation
descriptors (only print out the first 36 elements):
# Use the 3 custom properties defined before
# and 4 properties in the AAindex database
moran <- extractMoran(
x,
customprops = myprops,
props = c(
"CIDH920105", "BHAR880101",
"CHAM820101", "CHAM820102",
"MyProp1", "MyProp2", "MyProp3"
)
)
head(moran, n = 36L)
Geary autocorrelation descriptors
Geary autocorrelation descriptors for protein sequences can be defined as:
$$
C(d) = \frac{\frac{1}{2(N-d)} \sum_{i=1}^{N-d} (P_i - P_{i+d})^2}{\frac{1}{N-1} \sum_{i=1}^{N} (P_i - \bar{P}')^2} \quad d = 1, 2, \ldots, 30
$$
where $d$, $P$, $P_i$, $P_{i+d}$, and $\textrm{nlag}$ have the same
meaning as above.
For each amino acid index, there will be $3 \times \textrm{nlag}$
autocorrelation descriptors. The usage of extractGeary() is
exactly the same as extractMoreauBroto() and extractMoran():
# Use the 3 custom properties defined before
# and 4 properties in the AAindex database
geary <- extractGeary(
x,
customprops = myprops,
props = c(
"CIDH920105", "BHAR880101",
"CHAM820101", "CHAM820102",
"MyProp1", "MyProp2", "MyProp3"
)
)
head(geary, n = 36L)
Composition/Transition/Distribution
The CTD descriptors are developed by @dubchak1 and @dubchak2.
Figure 3: The sequence of a hypothetic protein indicating
the construction of composition, transition, and distribution descriptors
of a protein. Sequence index indicates the position of an amino acid in
the sequence. The index for each type of amino acids in the sequence
(1, 2 or 3) indicates the position of the first, second, third,
... of that type of amino acid. 1/2 transition indicates the position
of 12 or 21 pairs in the sequence (1/3 and 2/3 are defined
in the same way).
Step 1: Sequence Encoding
The amino acids are categorized into three classes according to its attribute,
and each amino acid is encoded by one of the indices 1, 2, 3 according to which
class it belongs. The attributes used here include hydrophobicity,
normalized van der Waals volume, polarity, and polarizability.
The corresponding classification for each attribute is listed in Table 1.
**Group 1** **Group 2** **Group 3**
Hydrophobicity Polar Neutral Hydrophobicity
R, K, E, D, Q, N G, A, S, T, P, H, Y C, L, V, I, M, F, W
Normalized van der Waals Volume 0-2.78 2.95-4.0 4.03-8.08
G, A, S, T, P, D, C N, V, E, Q, I, L M, H, K, F, R, Y, W
Polarity 4.9-6.2 8.0-9.2 10.4-13.0
L, I, F, W, C, M, V, Y P, A, T, G, S H, Q, R, K, N, E, D
Polarizability 0-1.08 0.128-0.186 0.219-0.409
G, A, S, D, T C, P, N, V, E, Q, I, L K, M, H, F, R, Y, W
Charge Positive Neutral Negative
K, R A, N, C, Q, G, H, I, L, M, F, P, S, T, W, Y, V D, E
Secondary Structure Helix Strand Coil
E, A, L, M, Q, K, R, H V, I, Y, C, W, F, T G, N, P, S, D
Solvent Accessibility Buried Exposed Intermediate
A, L, F, C, G, I, V, W R, K, Q, E, N, D M, S, P, T, H, Y
: Table 1: Amino acid attributes, and the three-group classification of
the 20 amino acids by each attribute
For example, for a given sequence MTEITAAMVKELRESTGAGA, it will be
encoded as 32132223311311222222 according to its hydrophobicity.
Step 2: Compute Composition, Transition, and Distribution Descriptors
Three types of descriptors, Composition (C), Transition (T),
and Distribution (D) can be calculated for a given attribute as follows.
Composition
Composition is defined as the global percentage for each encoded class
in the protein sequence. In the above example using the hydrophobicity
classification, the numbers for encoded classes 1, 2, 3 are 5, 10, and 5,
so that the compositions for them will be $5/20=25\%$, $10/20=10\%$,
and $5/20=25\%$, where 20 is the length of the protein sequence.
The composition descriptor can be expressed as
$$
C_r = \frac{n_r}{n} \quad r = 1, 2, 3
$$
where $n_r$ is the number of amino acid type $r$ in the encoded
sequence; $N$ is the length of the sequence.
An example for extractCTDC():
extractCTDC(x)
The result shows the elements who are named as PropertyNumber.GroupNumber
in the returned vector.
Transition
A transition from class 1 to 2 is the percent frequency with which 1 is
followed by 2 or 2 is followed by 1 in the encoded sequences.
The transition descriptor can be computed as
$$
T_{rs} = \frac{n_{rs} + n_{sr}}{N - 1} \quad rs = \text{12}, \text{13}, \text{23}
$$
where $n_{rs}$, $n_{sr}$ are the numbers of dipeptide encoded as rs and
sr in the sequence; $N$ is the length of the sequence.
An example for extractCTDT():
extractCTDT(x)
Distribution
The distribution descriptor describes the distribution of each attribute
in the sequence.
There are five "distribution" descriptors for each attribute and they are
the position percents in the whole sequence for the first residue, 25%
residues, 50% residues, 75% residues, and 100% residues for a certain
encoded class. For example, there are 10 residues encoded
as 2 in the above example, the positions for the first residue 2,
the 2nd residue 2 (25% * 10 = 2), the 5th 2 residue (50% * 10 = 5),
the 7th 2 (75% * 10 = 7) and the 10th residue 2 (100% * 10)
in the encoded sequence are 2, 5, 15, 17, 20, so that
the distribution descriptors for 2 are: 10.0 (2/20 * 100),
25.0 (5/20 * 100), 75.0 (15/20 * 100), 85.0 (17/20 * 100),
100.0 (20/20 * 100).
To compute the distribution descriptor, use extractCTDD():
extractCTDD(x)
Conjoint triad descriptors
Conjoint triad descriptors are proposed by @shenjw.
The conjoint triad descriptors were used to model protein-protein
interactions based on the classification of amino acids. In this approach,
each protein sequence is represented by a vector space consisting of
descriptors of amino acids. To reduce the dimensions of vector space,
the 20 amino acids were clustered into several classes according to
their dipoles and volumes of the side chains. The conjoint triad
descriptors are calculated as follows:
Step 1: Classification of Amino Acids
Electrostatic and hydrophobic interactions dominate protein-protein
interactions. These two kinds of interactions may be reflected by
the dipoles and volumes of the side chains of amino acids, respectively.
Accordingly, these two parameters were calculated by using the
density-functional theory method B3LYP/6-31G and molecular
modeling approach. Based on the dipoles and volumes of the side chains,
the 20 amino acids can be clustered into seven classes (See Table 2).
Amino acids within the same class likely involve synonymous mutations
because of their similar characteristics.
No. Dipole Scale$^1$ Volume Scale$^2$ Class
1 $-$ $-$ Ala, Gly, Val
2 $-$ $+$ Ile, Leu, Phe, Pro
3 $+$ $+$ Tyr, Met, Thr, Ser
4 $++$ $+$ His, Asn, Gln, Tpr
5 $+++$ $+$ Arg, Lys
6 $+'+'+'$ $+$ Asp, Glu
7 $+^3$ $+$ Cys
: Table 2: Classification of amino acids based on dipoles and volumes of the
side chains
1 Dipole Scale (Debye): $-$, Dipole < 1.0;
$+$, 1.0 < Dipole < 2.0; $++$, 2.0 < Dipole < 3.0; $+++$, Dipole > 3.0;
$+'+'+'$, Dipole > 3.0 with opposite orientation.
2 Volume Scale
($\overset{\lower.5em\circ}{\mathrm{A}}\lower.01em^3$):
$-$, Volume < 50; $+$, Volume > 50.
3 Cys is separated from class 3
because of its ability to form disulfide bonds.
Step 2: Conjoint Triad Calculation
The conjoint triad descriptors considered the properties of one amino acid
and its vicinal amino acids and regarded any three continuous amino acids
as a unit. Thus, the triads can be differentiated according to the classes
of amino acids, i.e., triads composed by three amino acids belonging to
the same classes, such as ART and VKS, can be treated identically.
To conveniently represent a protein, we first use a binary space
$(\mathbf{V}, \mathbf{F})$ to represent a protein sequence. Here,
$\mathbf{V}$ is the vector space of the sequence features, and
each feature $v_i$ represents a sort of triad type; $\mathbf{F}$
is the frequency vector corresponding to $\mathbf{V}$, and the value
of the $i$-th dimension of $\mathbf{F} (f_i)$ is the frequency of type
$v_i$ appearing in the protein sequence. For the amino acids that have
been catogorized into seven classes, the size of $\mathbf{V}$ should be
$7 \times 7 \times 7$; thus $i = 1, 2, \ldots, 343$. The detailed
description for ($\mathbf{V}$, $\mathbf{F}$) is illustrated
in Figure 4.
Figure 4: Schematic diagram for constructing the
vector space ($\mathbf{V}$, $\mathbf{F}$) of protein sequences.
$\mathbf{V}$ is the vector space of the sequence features;
each feature ($v_i$) represents a triad composed of three
consecutive amino acids; $\mathbf{F}$ is the frequency vector
corresponding to $\mathbf{V}$, and the value of the $i$-th
dimension of $\mathbf{F} (f_i)$ is the frequency that $v_i$
triad appeared in the protein sequence.
Clearly, each protein correlates to the length (number of amino acids)
of protein. In general, a long protein would have a large value of $f_i$,
which complicates the comparison between two heterogeneous proteins.
Thus, we defined a new parameter, $d_i$, by normalizing $f_i$ with the
following equation:
$$
d_i = \frac{f_i - \min{\,f_1, f_2 , \ldots, f_{343}\,}}{\max{\,f_1, f_2, \ldots, f_{343}\,}}
$$
The numerical value of $d_i$ of each protein ranges from 0 to 1, which
thereby enables the comparison between proteins. Accordingly, we obtain
another vector space (designated $\mathbf{D}$) consisting of $d_i$ to
represent protein.
To compute conjoint triads of protein sequences, we can simply use:
ctriad <- extractCTriad(x)
head(ctriad, n = 65L)
by which we only outputted the first 65 of total 343 dimension to save space.
Quasi-sequence-order descriptors
The quasi-sequence-order descriptors are proposed by @chouqsoe.
They are derived from the distance matrix between the 20 amino acids.
Sequence-order-coupling number
The $d$-th rank sequence-order-coupling number is defined as:
$$
\tau_d = \sum_{i=1}^{N-d} (d_{i, i+d})^2 \quad d = 1, 2, \ldots, \textrm{maxlag}
$$
where $d_{i, i+d}$ is the distance between the two amino acids at position
$i$ and $i+d$.
Note: maxlag is the maximum lag and the length of the protein
must be not less than $\textrm{maxlag}$.
The function extractSOCN() is used for computing the
sequence-order-coupling numbers:
extractSOCN(x)
Users can also specify the maximum lag value with the nlag argument.
Note: In addition to Schneider-Wrede physicochemical distance
matrix [@wrede] used by Kuo-Chen Chou, another chemical distance
matrix by @grantham is also used here. So the descriptors dimension
will be nlag * 2. The quasi-sequence-order descriptors described
next also utilized the two matrices.
Quasi-sequence-order descriptors
For each amino acid type, a quasi-sequence-order descriptor can be defined as:
$$
X_r = \frac{f_r}{\sum_{r=1}^{20} f_r + w \sum_{d=1}^{\textrm{maxlag}} \tau_d} \quad r = 1, 2, \ldots, 20
$$
where $f_r$ is the normalized occurrence for amino acid type $i$ and $w$
is a weighting factor ($w=0.1$). These are the first 20 quasi-sequence-order
descriptors. The other 30 quasi-sequence-order are defined as:
$$
X_d = \frac{w \tau_{d-20}}{\sum_{r=1}^{20} f_r + w \sum_{d=1}^{\textrm{maxlag}} \tau_d} \quad d = 21, 22, \ldots, 20 + \textrm{maxlag}
$$
Figure 5: A schematic drawing to show (a) the 1st-rank, (b) the 2nd-rank, and (3) the 3rd-rank sequence-order-coupling mode along a protein sequence. (a) Reflects the coupling mode between all the most contiguous residues, (b) that between all the 2nd most contiguous residues, and (c) that between all the 3rd most contiguous residues. This figure is from @chouqsoe.
A minimal example for extractQSO():
extractQSO(x)
where users can also specify the maximum lag with the argument nlag
and the weighting factor with the argument w.
Pseudo-amino acid composition (PseAAC)
This group of descriptors are proposed by @choupaac. PseAAC descriptors
are also named as the type 1 pseudo-amino acid composition. Let $H_1^o (i)$,
$H_2^o (i)$, $M^o (i)$ ($i=1, 2, 3, \ldots, 20$) be the original hydrophobicity
values, the original hydrophilicity values and the original side chain masses
of the 20 natural amino acids, respectively. They are converted to following
qualities by a standard conversion:
$$
H_1 (i) = \frac{H_1^o (i) - \frac{1}{20} \sum_{i=1}^{20} H_1^o (i)}{\sqrt{\frac{\sum_{i=1}^{20} [H_1^o (i) - \frac{1}{20} \sum_{i=1}^{20} H_1^o (i) ]^2}{20}}}
$$
$H_2^o (i)$ and $M^o (i)$ are normalized as $H_2 (i)$ and $M (i)$ in the same way.
Figure 6: A schematic drawing to show (a) the first-tier, (b) the second-tier, and (3) the third-tiersequence order correlation mode along a protein sequence. Panel (a) reflects the correlation mode between all the most contiguous residues, panel (b) that between all the second-most contiguous residues, and panel (c) that between all the third-most contiguous residues. This figure is from @choupaac.
Then, a correlation function can be defines as
$$
\Theta (R_i, R_j) = \frac{1}{3} \bigg{ [ H_1 (R_i) - H_1 (R_j) ]^2 + [ H_2 (R_i) - H_2 (R_j) ]^2 + [ M (R_i) - M (R_j) ]^2 \bigg}
$$
This correlation function is actually an average value for the three amino
acid properties: hydrophobicity value, hydrophilicity value and side chain
mass. Therefore, we can extend this definition of correlation functions for
one amino acid property or for a set of $n$ amino acid properties.
For one amino acid property, the correlation can be defined as:
$$
\Theta (R_i, R_j) = [H_1 (R_i) - H_1(R_j)]^2
$$
where $H (R_i)$ is the amino acid property of amino acid $R_i$ after
standardization.
For a set of n amino acid properties, it can be defined as: where $H_k (R_i)$
is the $k$-th property in the amino acid property set for amino acid $R_i$.
$$
\Theta (R_i, R_j) = \frac{1}{n} \sum_{k=1}^{n} [H_k (R_i) - H_k (R_j)]^2
$$
where $H_k(R_i)$ is the $k$-th property in the amino acid property set
for amino acid $R_i$.
A set of descriptors named sequence order-correlated factors are defined as:
\begin{align}
\theta_1 & = \frac{1}{N-1} \sum_{i=1}^{N-1} \Theta (R_i, R_{i+1})\
\theta_2 & = \frac{1}{N-2} \sum_{i=1}^{N-2} \Theta (R_i, R_{i+2})\
\theta_3 & = \frac{1}{N-3} \sum_{i=1}^{N-3} \Theta (R_i, R_{i+3})\
& \ldots \
\theta_\lambda & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} \Theta (R_i, R_{i+\lambda})
\end{align}
$\lambda$ ($\lambda < L$) is a parameter to be specified. Let $f_i$ be the
normalized occurrence frequency of the 20 amino acids in the protein
sequence, a set of $20 + \lambda$ descriptors called the pseudo-amino
acid composition for a protein sequence can be defines as:
$$
X_c = \frac{f_c}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{\lambda} \theta_j} \quad (1 < c < 20)
$$
$$
X_c = \frac{w \theta_{c-20}}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{\lambda} \theta_j} \quad (21 < c < 20 + \lambda)
$$
where $w$ is the weighting factor for the sequence-order effect and is
set to $w = 0.05$ in protr as suggested by Kuo-Chen Chou.
With extractPAAC(), we can compute the PseAAC descriptors directly:
extractPAAC(x)
The extractPAAC() fucntion also provides the additional arguments
props and customprops, which are similar to those arguments for
Moreau-Broto/Moran/Geary autocorrelation descriptors. For their minor
differences, please see ?extracPAAC. Users can specify the lambda
parameter and the weighting factor with arguments lambda and w.
Note: In the work of Kuo-Chen Chou, the definition for "normalized
occurrence frequency" was not given. In this work, we define it as the
occurrence frequency of amino acid in the sequence normalized to 100%
and hence our calculated values are not the same as values by them.
Amphiphilic pseudo-amino acid composition (APseAAC)
Amphiphilic Pseudo-Amino Acid Composition (APseAAC) was proposed in
@choupaac. APseAAC is also recognized as the type 2 pseudo-amino
acid composition. The definitions of these qualities are similar to the
PAAC descriptors. From $H_1 (i)$ and $H_2 (j)$ defined before,
the hydrophobicity and hydrophilicity correlation functions are
defined as:
\begin{align}
H_{i, j}^1 & = H_1 (i) H_1 (j)\
H_{i, j}^2 & = H_2 (i) H_2 (j)
\end{align}
From these qualities, sequence order factors can be defines as:
\begin{align}
\tau_1 & = \frac{1}{N-1} \sum_{i=1}^{N-1} H_{i, i+1}^1\
\tau_2 & = \frac{1}{N-1} \sum_{i=1}^{N-1} H_{i, i+1}^2\
\tau_3 & = \frac{1}{N-2} \sum_{i=1}^{N-2} H_{i, i+2}^1\
\tau_4 & = \frac{1}{N-2} \sum_{i=1}^{N-2} H_{i, i+2}^2\
& \ldots \
\tau_{2 \lambda - 1} & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} H_{i, i+\lambda}^1\
\tau_{2 \lambda} & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} H_{i, i+\lambda}^2
\end{align}
Figure 7: A schematic diagram to show (a1/a2) the first-rank, (b1/b2) the second-rank and (c1/c2) the third-rank sequence-order-coupling mode along a protein sequence through a hydrophobicity/hydrophilicity correlation function, where $H_{i, j}^1$ and $H_{i, j}^2$ are given by Equation (3). Panel (a1/a2) reflects the coupling mode between all the most contiguous residues, panel (b1/b2) that between all the second-most contiguous residues and panel (c1/c2) that between all the third-most contiguous residues. This figure is from @chouapaac.
Then a set of descriptors called Amphiphilic Pseudo-Amino Acid Composition (APseAAC) are defined as:
$$
P_c = \frac{f_c}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{2 \lambda} \tau_j} \quad (1 < c < 20)
$$
$$
P_c = \frac{w \tau_u}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{2 \lambda} \tau_j} \quad (21 < u < 20 + 2 \lambda)
$$
where $w$ is the weighting factor. Its default value is set to $w = 0.5$ in protr.
A minimal example for extracAPAAC() is:
extractAPAAC(x)
This function has the same arguments as extractPAAC().
Profile-based descriptors
The profile-based descriptors for protein sequences are available in
the protr package. The feature vectors of profile-based methods
were based on the PSSM by running PSI-BLAST, and often show good performance.
See @ye2011assessment and @rangwala2005profile for details.
The functions extractPSSM(), extractPSSMAcc() and
extractPSSMFeature() are used to generate these descriptors.
Users need to install the NCBI-BLAST+ software package first to make
the functions fully functional.
Proteochemometric modeling descriptors
Proteochemometric (PCM) modeling utilizes statistical modeling techniques
to model ligand-target interaction space. The below descriptors implemented
in protr are extensively used in Proteochemometric modeling.
-
Scales-based descriptors derived by Principal Components Analysis
- Scales-based descriptors derived by Amino Acid Properties from AAindex (Protein Fingerprint)
- Scales-based descriptors derived by 20+ classes of 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.)
-
Scales-based descriptors derived by Factor Analysis
- Scales-based descriptors derived by Multidimensional Scaling
- BLOSUM and PAM matrix-derived descriptors
Note that each of the scales-based descriptor functions are freely to combine
with the more than 20 classes of 2D and 3D molecular descriptors to construct
highly customized scales-based descriptors. Of course, these functions are
designed to be flexible enough that users can provide totally self-defined
property matrices to construct scales-based descriptors.
For example, to compute the "topological scales" derived by PCA
(using the first 5 principal components),
one can use extractDescScales():
x <- readFASTA(system.file(
"protseq/P00750.fasta",
package = "protr"
))[[1]]
descscales <- extractDescScales(
x,
propmat = "AATopo",
index = c(37:41, 43:47),
pc = 5, lag = 7, silent = FALSE
)
the argument propmat involkes the AATopo dataset shipped with the
protr package, and the argument index selects the 37 to 41 and the
43 to 47 columns (molecular descriptors) in the AATopo dataset to use,
the parameter lag was set for the Auto Cross Covariance (ACC) for
generating scales-based descriptors of the same length. At last,
we printed the summary of the first 5 principal components (standard
deviation, proportion of variance, cumulative proportion of variance).
The result is a length 175 named vector, which is consistent with the
descriptors before:
length(descscales)
head(descscales, 15)
For another example, to compute the descriptors derived by
the BLOSUM62 matrix and use the first 5 scales, one can use:
x <- readFASTA(system.file(
"protseq/P00750.fasta",
package = "protr"
))[[1]]
blosum <- extractBLOSUM(
x,
submat = "AABLOSUM62",
k = 5, lag = 7, scale = TRUE, silent = FALSE
)
The result is a length 175 named vector:
length(blosum)
head(blosum, 15)
Dealing with gaps. In proteochemometrics, (sequence alignment)
gaps can be very useful, since a gap in a certain position contains information.
The protr package has built-in support for such gaps. We deal with
the gaps by using a dummy descriptor to code for the 21st type
of amino acid. The function extractScalesGap() and extractProtFPGap()
can be used to deal with such gaps. See ?extractScalesGap and
?extractProtFPGap for details.
Similarity calculation by sequence alignment
Similarity computation derived by local or global protein sequence alignment
between a list of protein sequences is of great need in protein research.
However, this type of pairwise similarity computation often computationally
intensive, especially when there exists many protein sequences.
Luckily, this process is also highly parallelizable, the protr package
integrates the function of parallelized similarity computation derived
by local or global protein sequence alignment between a list of protein sequences.
The function twoSeqSim() calculates the alignment result between
two protein sequences. The function parSeqSim() calculates
the pairwise similarity with a list of protein sequences in parallel:
s1 <- readFASTA(system.file("protseq/P00750.fasta", package = "protr"))[[1]]
s2 <- readFASTA(system.file("protseq/P08218.fasta", package = "protr"))[[1]]
s3 <- readFASTA(system.file("protseq/P10323.fasta", package = "protr"))[[1]]
s4 <- readFASTA(system.file("protseq/P20160.fasta", package = "protr"))[[1]]
s5 <- readFASTA(system.file("protseq/Q9NZP8.fasta", package = "protr"))[[1]]
plist <- list(s1, s2, s3, s4, s5)
psimmat <- parSeqSim(plist, cores = 4, type = "local", submat = "BLOSUM62")
psimmat
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.00000000 0.11825938 0.10236985 0.04921696 0.03943488
## [2,] 0.11825938 1.00000000 0.18858241 0.12124217 0.06391103
## [3,] 0.10236985 0.18858241 1.00000000 0.05819984 0.06175942
## [4,] 0.04921696 0.12124217 0.05819984 1.00000000 0.05714638
## [5,] 0.03943488 0.06391103 0.06175942 0.05714638 1.00000000
Similarly, the function crossSetSim() calculates the pairwise
similarity between two sets of protein sequences in parallel.
Note that for a small number of proteins, calculating their
pairwise similarity scores derived by sequence alignment in parallel may
not significantly reduce the overall computation time, since each of the
task only requires a relatively small time to finish, thus, computational
overheads may exist and affect the performance. In our benchmarks, we used
about 1,000 protein sequences on 64 CPU cores, and observed significant
performance improvement comparing to the sequential computation.
Scaling up for a large number of sequences
batches.
A useful argument for reducing the memory usage is batches.
It splits the similarity computations into smaller batches.
A larger batch number reduces the memory need for each parallel process,
but also adds the overhead of forking new processes. This is a trade-off
between time (CPU) and space (memory). Also, use verbose = TRUE
to print the computation progress.
parSeqSimDisk().
For similarity computations over an even larger number of protein sequences,
please try parSeqSimDisk() and set batches to a large number.
Unlike the in-memory version, this disk-based function caches the
partial results in each batch to the hard drive and merges all the
results together in the end, which further reduces the memory usage.
Example.
Let's assume we have 20,000 sequences. By setting cores = 64 and
batches = 10000 in parSeqSimDisk(), the workload will be
around 20000^2/2/64/10000 = 312.5 alignments per batch per core.
This could give you a relatively quick feedback about if the memory
size is going to be sufficient, and how long the computation will
take in total, after the first few batches.
Similarity calculation by GO semantic similarity measures
The protr package also integrates the function of similarity score
computation derived by Gene Ontology (GO) semantic similarity measures
between a list of GO terms or Entrez Gene IDs.
The function twoGOSim() calculates the similarity derived by GO-terms
semantic similarity measures between two GO terms / Entrez Gene IDs, and the
function parGOSim() calculates the pairwise similarity with a list
of GO terms / Entrez Gene IDs:
# By GO Terms
go1 <- c(
"GO:0005215", "GO:0005488", "GO:0005515",
"GO:0005625", "GO:0005802", "GO:0005905"
) # AP4B1
go2 <- c(
"GO:0005515", "GO:0005634", "GO:0005681",
"GO:0008380", "GO:0031202"
) # BCAS2
go3 <- c(
"GO:0003735", "GO:0005622", "GO:0005840",
"GO:0006412"
) # PDE4DIP
golist <- list(go1, go2, go3)
parGOSim(golist, type = "go", ont = "CC", measure = "Wang")
## [,1] [,2] [,3]
## [1,] 1.000 0.344 0.17
## [2,] 0.344 1.000 0.24
## [3,] 0.170 0.240 1.00
# By Entrez gene id
genelist <- list(c("150", "151", "152", "1814", "1815", "1816"))
parGOSim(genelist, type = "gene", ont = "BP", measure = "Wang")
## 150 151 152 1814 1815 1816
## 150 1.000 0.702 0.725 0.496 0.570 0.455
## 151 0.702 1.000 0.980 0.456 0.507 0.551
## 152 0.725 0.980 1.000 0.460 0.511 0.538
## 1814 0.496 0.456 0.460 1.000 0.687 0.473
## 1815 0.570 0.507 0.511 0.687 1.000 0.505
## 1816 0.455 0.551 0.538 0.473 0.505 1.000
Miscellaneous tools
In this section, we will briefly introduce some useful tools provided by the protr package.
Retrieve protein sequences from UniProt
This function getUniProt() gets protein sequences from uniprot.org
by protein ID(s). The input ID is a character vector specifying
the protein ID(s). The returned sequences are stored in a list:
ids <- c("P00750", "P00751", "P00752")
prots <- getUniProt(ids)
prots
## [[1]]
## [1] "MDAMKRGLCCVLLLCGAVFVSPSQEIHARFRRGARSYQVICRDEKTQMIYQQHQSWLRPVLRSNRVEYCWCN
## SGRAQCHSVPVKSCSEPRCFNGGTCQQALYFSDFVCQCPEGFAGKCCEIDTRATCYEDQGISYRGTWSTAESGAECT
## NWNSSALAQKPYSGRRPDAIRLGLGNHNYCRNPDRDSKPWCYVFKAGKYSSEFCSTPACSEGNSDCYFGNGSAYRGT
## HSLTESGASCLPWNSMILIGKVYTAQNPSAQALGLGKHNYCRNPDGDAKPWCHVLKNRRLTWEYCDVPSCSTCGLRQ
## YSQPQFRIKGGLFADIASHPWQAAIFAKHRRSPGERFLCGGILISSCWILSAAHCFQERFPPHHLTVILGRTYRVVP
## GEEEQKFEVEKYIVHKEFDDDTYDNDIALLQLKSDSSRCAQESSVVRTVCLPPADLQLPDWTECELSGYGKHEALSP
## FYSERLKEAHVRLYPSSRCTSQHLLNRTVTDNMLCAGDTRSGGPQANLHDACQGDSGGPLVCLNDGRMTLVGIISWG
## LGCGQKDVPGVYTKVTNYLDWIRDNMRP"
##
## [[2]]
## [1] "MGSNLSPQLCLMPFILGLLSGGVTTTPWSLARPQGSCSLEGVEIKGGSFRLLQEGQALEYVCPSGFYPYPVQ
## TRTCRSTGSWSTLKTQDQKTVRKAECRAIHCPRPHDFENGEYWPRSPYYNVSDEISFHCYDGYTLRGSANRTCQVNG
## RWSGQTAICDNGAGYCSNPGIPIGTRKVGSQYRLEDSVTYHCSRGLTLRGSQRRTCQEGGSWSGTEPSCQDSFMYDT
## PQEVAEAFLSSLTETIEGVDAEDGHGPGEQQKRKIVLDPSGSMNIYLVLDGSDSIGASNFTGAKKCLVNLIEKVASY
## GVKPRYGLVTYATYPKIWVKVSEADSSNADWVTKQLNEINYEDHKLKSGTNTKKALQAVYSMMSWPDDVPPEGWNRT
## RHVIILMTDGLHNMGGDPITVIDEIRDLLYIGKDRKNPREDYLDVYVFGVGPLVNQVNINALASKKDNEQHVFKVKD
## MENLEDVFYQMIDESQSLSLCGMVWEHRKGTDYHKQPWQAKISVIRPSKGHESCMGAVVSEYFVLTAAHCFTVDDKE
## HSIKVSVGGEKRDLEIEVVLFHPNYNINGKKEAGIPEFYDYDVALIKLKNKLKYGQTIRPICLPCTEGTTRALRLPP
## TTTCQQQKEELLPAQDIKALFVSEEEKKLTRKEVYIKNGDKKGSCERDAQYAPGYDKVKDISEVVTPRFLCTGGVSP
## YADPNTCRGDSGGPLIVHKRSRFIQVGVISWGVVDVCKNQKRQKQVPAHARDFHINLFQVLPWLKEKLQDEDLGFL"
##
## [[3]]
## [1] "APPIQSRIIGGRECEKNSHPWQVAIYHYSSFQCGGVLVNPKWVLTAAHCKNDNYEVWLGRHNLFENENTAQF
## FGVTADFPHPGFNLSLLKXHTKADGKDYSHDLMLLRLQSPAKITDAVKVLELPTQEPELGSTCEASGWGSIEPGPDB
## FEFPDEIQCVQLTLLQNTFCABAHPBKVTESMLCAGYLPGGKDTCMGDSGGPLICNGMWQGITSWGHTPCGSANKPS
## IYTKLIFYLDWINDTITENP"
Read FASTA files
The function readFASTA() provides a convenient way to read protein
sequences stored in FASTA format files. See ?readFASTA for details.
The returned sequences are stored in a named list, whose components are
named with the protein sequences' names.
Read PDB files
The Protein Data Bank (PDB) file format is a text file
format describing the three dimensional structures of protein.
The function readPDB() provides the function to read
protein sequences stored in PDB format files.
See ?readPDB for details.
Sanity check for amino acid types
The protcheck() function checks if the protein sequence's amino acid
types are in the 20 default types, which returns a TRUE if all the
amino acids in the sequence belongs to the 20 default types:
x <- readFASTA(system.file("protseq/P00750.fasta", package = "protr"))[[1]]
# a real sequence
protcheck(x)
# an artificial sequence
protcheck(paste(x, "Z", sep = ""))
Remove gaps from sequences
The removeGaps() function allows us to remove/replace gaps (-) or any
"irregular" characters from amino acid sequences, to prepare them for
feature extraction or sequence alignment based similarity computation.
Protein sequence partition
The protseg() function partitions the protein sequences to create
sliding windows. This is usually required when creating feature vectors
for machine learning tasks. Users can specify a sequence x, and
a character aa, one of the 20 amino acid types, and a positive
integer k, which controls the window size (half of the window).
This function returns a named list, each component contains one of the
segmentations (a character string), names of the list components are
the positions of the specified amino acid in the sequence.
See the example below:
protseg(x, aa = "M", k = 5)
Auto cross covariance computation
Auto Cross Covariance (ACC) is extensively used in the scales-based
descriptors computation, this approach calculates the auto covariance
and auto cross covariance for generating scale-based descriptors of
the same length. Users can write their own scales-based descriptor
functions with the help of acc() function in the protr package.
Pre-computed 2D and 3D descriptor sets for the 20 amino acids
The protr package ships with more than 20 pre-computed 2D and 3D
descriptor sets for the 20 amino acids to use with the scales-based
descriptors. Please use data(package = "protr") to list all
the datasets included in the protr package.
BLOSUM and PAM matrices for the 20 amino acids
The BLOSUM and PAM matrices for the 20 amino acids can be used to calculate
BLOSUM and PAM matrix-derived descriptors with function extractBLOSUM(),
the datasets are named in AABLOSUM45, AABLOSUM50,
AABLOSUM62, AABLOSUM80, AABLOSUM100, AAPAM30,
AAPAM40, AAPAM70, AAPAM120, and AAPAM250.
Metadata of the 20 amino acids
As the reference, the AAMetaInfo dataset includes the meta information
of the 20 amino acids used for the 2D and 3D descriptor calculation in the
protr package. This dataset include each amino acid's name, one-letter
representation, three-letter representation, SMILE representation, PubChem
CID and PubChem link. See data(AAMetaInfo) for details.
ProtrWeb
The web service built on protr, namely ProtrWeb, is located at http://protr.org.
ProtrWeb (Figure 8) does not require any knowledge of programming
for the user. It is a user-friendly web application for computing
the protein sequence descriptors presented in the protr package.
Figure 8: A screenshot of the web application ProtrWeb
Source code repository for this Shiny web application:
https://github.com/nanxstats/protrweb.
Summary
The summary of the descriptors in the protr package are listed in
Table 3.
Descriptor Group Descriptor Name Descriptor Dimension Function Name
Amino Acid Composition Amino Acid Composition 20 extractAAC()
Dipeptide Composition 400 extractDC()
Tripeptide Composition 8000 extractTC()
Autocorrelation Normalized Moreau-Broto Autocorrelation 240$^1$ extractMoreauBroto()
Moran Autocorrelation 240$^1$ extractMoran()
Geary Autocorrelation 240$^1$ extractGeary()
CTD Composition 21 extractCTDC(), extractCTDCClass()
Transition 21 extractCTDT(), extractCTDTClass()
Distribution 105 extractCTDD(), extractCTDDClass()
Conjoint Triad Conjoint Triad 343 extractCTriad(), extractCTriadClass()
Quasi-Sequence-Order Sequence-Order-Coupling Number 60$^2$ extractSOCN()
Quasi-Sequence-Order Descriptors 100$^2$ extractQSO()
Pseudo-Amino Acid Composition Pseudo-Amino Acid Composition 50$^3$ extractPAAC()
Amphiphilic Pseudo-Amino Acid Composition 80$^4$ extractAPAAC()
: Table 3: List of commonly used descriptors in protr
1 The number depends on the choice of the
number of properties of amino acids and the choice of the maximum
values of the `lag`. The default is use 8 types of properties and
`lag = 30`.
2 The number depends on the maximum value
of `lag`. By default, `lag = 30`. Two distance matrices are used,
so the descriptor dimension is $30 \times 2 = 60$ and
$(20 + 30) \times 2 = 100$.
3 The number depends on the choice of
the number of the set of amino acid properties and the choice of
the $\lambda$ value. The default is use 3 types of properties
proposed by Kuo-Chen Chou and $\lambda = 30$.
4 The number depends on the choice of
the $\lambda$ vlaue. The default is $\lambda = 30$.
The scales-based PCM descriptors in the protr package are
listed in Table 4.
Derived by Descriptor Class Function Name
Principal Components Analysis Scales-based descriptors derived by Principal Components Analysis extractScales(), extractScalesGap()
Scales-based descriptors derived by amino acid properties from AAindex (a.k.a. Protein Fingerprint) extractProtFP(), extractProtFPGap()
Scales-based descriptors derived by 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.) extractDescScales()
Factor Analysis Scales-based descriptors derived by Factor Analysis extractFAScales()
Multidimensional Scaling Scales-based descriptors derived by Multidimensional Scaling extractMDSScales()
Substitution Matrix BLOSUM and PAM matrix-derived descriptors extractBLOSUM()
: Table 4: List of PCM descriptors in protr
The amino acid descriptor sets used by scales-based descriptors
provided by the protr package are listed in Table 5.
Note that the non-informative descriptors (like the descriptors
have only one value across all the 20 amino acids) in these
datasets have already been filtered out.
Dataset Name Descriptor Set Name Dimensionality Calculated by
AA2DACOR 2D Autocorrelations Descriptors 92 Dragon
AA3DMoRSE 3D-MoRSE Descriptors 160 Dragon
AAACF Atom-Centred Fragments Descriptors 6 Dragon
AABurden Burden Eigenvalues Descriptors 62 Dragon
AAConn Connectivity Indices Descriptors 33 Dragon
AAConst Constitutional Descriptors 23 Dragon
AAEdgeAdj Edge Adjacency Indices Descriptors 97 Dragon
AAEigIdx Eigenvalue-Based Indices Descriptors 44 Dragon
AAFGC Functional Group Counts Descriptors 5 Dragon
AAGeom Geometrical Descriptors 41 Dragon
AAGETAWAY GETAWAY Descriptors 194 Dragon
AAInfo Information Indices Descriptors 47 Dragon
AAMolProp Molecular Properties Descriptors 12 Dragon
AARandic Randic Molecular Profiles Descriptors 41 Dragon
AARDF RDF Descriptors 82 Dragon
AATopo Topological Descriptors 78 Dragon
AATopoChg Topological Charge Indices Descriptors 15 Dragon
AAWalk Walk and Path Counts Descriptors 40 Dragon
AAWHIM WHIM Descriptors 99 Dragon
AACPSA CPSA Descriptors 41 Accelrys Discovery Studio
AADescAll All the 2D Descriptors Calculated by Dragon 1171 Dragon
AAMOE2D All the 2D Descriptors Calculated by MOE 148 MOE
AAMOE3D All the 3D Descriptors Calculated by MOE 143 MOE
: Table 5: List of the pre-calculated descriptor sets of the 20 amino acids in
protr
References
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Introduction
The protr package offers a unique and comprehensive toolkit for generating various numerical representation schemes of protein sequences. The descriptors included are extensively utilized in bioinformatics and chemogenomics research.
The commonly used descriptors listed in protr include amino acid composition, autocorrelation, CTD, conjoint traid, quasi-sequence order, pseudo amino acid composition, and profile-based descriptors derived by Position-Specific Scoring Matrix (PSSM).
The descriptors for proteochemometric (PCM) modeling, includes the scales-based descriptors derived by principal components analysis, factor analysis, multidimensional scaling, amino acid properties (AAindex), 20+ classes of 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.), and BLOSUM/PAM matrix-derived descriptors.
The protr package also implemented parallelized similarity computation derived by pairwise protein sequence alignment and Gene Ontology (GO) semantic similarity measures. ProtrWeb, the web application built on protr, can be accessed from http://protr.org.
If you find protr useful in your research, please feel free to cite our paper:
Nan Xiao, Dong-Sheng Cao, Min-Feng Zhu, and Qing-Song Xu. (2015). protr/ProtrWeb: R package and web server for generating various numerical representation schemes of protein sequences. _Bioinformatics_ 31 (11), 1857-1859.
BibTeX entry:
@article{Xiao2015, author = {Xiao, Nan and Cao, Dong-Sheng and Zhu, Min-Feng and Xu, Qing-Song.}, title = {protr/{ProtrWeb}: {R} package and web server for generating various numerical representation schemes of protein sequences}, journal = {Bioinformatics}, year = {2015}, volume = {31}, number = {11}, pages = {1857--1859}, doi = {10.1093/bioinformatics/btv042} }
An example predictive modeling workflow
Here we use the subcellular localization dataset of human proteins presented in @chou2008cell to demonstrate the basic usage of protr.
The complete dataset includes 3,134 protein sequences (2,750 different proteins), classified into 14 human subcellular locations. We selected two classes of proteins as our benchmark dataset. Class 1 contains 325 extracell proteins, and class 2 includes 307 mitochondrion proteins. Here we aim to build a random forest classification model to classify these two types of proteins.
First, we load the protr package, then read the protein sequences
stored in two separated FASTA files with readFASTA():
library("protr") # load FASTA files # (system.file is for accessing example file in protr package, # replace it with your path) extracell <- readFASTA(system.file( "protseq/extracell.fasta", package = "protr" )) mitonchon <- readFASTA(system.file( "protseq/mitochondrion.fasta", package = "protr" ))
To read protein sequences stored in PDB format files, use readPDB() instead.
The loaded sequences will be stored as two lists in R, and each
component in the list is a character string representing one protein sequence.
In this case, there are 325 extracell protein sequences and
306 mitonchon protein sequences:
length(extracell)
## [1] 325
length(mitonchon)
## [1] 306
To ensure that the protein sequences only have the 20 standard amino acid
types which is usually required for the descriptor computation, we use the
protcheck() function to do the amino acid type sanity check and
remove the non-standard sequences:
extracell <- extracell[(sapply(extracell, protcheck))] mitonchon <- mitonchon[(sapply(mitonchon, protcheck))]
length(extracell)
## [1] 323
length(mitonchon)
## [1] 304
Two protein sequences were removed from each class. For the remaining sequences, we calculate the Type II PseAAC descriptor, i.e., the amphiphilic pseudo amino acid composition (APseAAC) descriptor [@chouapaac] and make class labels for classification modeling.
# calculate APseAAC descriptors x1 <- t(sapply(extracell, extractAPAAC)) x2 <- t(sapply(mitonchon, extractAPAAC)) x <- rbind(x1, x2) # make class labels labels <- as.factor(c(rep(0, length(extracell)), rep(1, length(mitonchon))))
In protr, the functions of commonly used descriptors for protein
sequences and proteochemometric (PCM) modeling descriptors are named
after extract...().
Next, we will split the data into a 75% training set and a 25% test set.
set.seed(1001) # split training and test set tr.idx <- c( sample(1:nrow(x1), round(nrow(x1) * 0.75)), sample(nrow(x1) + 1:nrow(x2), round(nrow(x2) * 0.75)) ) te.idx <- setdiff(1:nrow(x), tr.idx) x.tr <- x[tr.idx, ] x.te <- x[te.idx, ] y.tr <- labels[tr.idx] y.te <- labels[te.idx]
We will train a random forest classification model on the training set
with 5-fold cross-validation, using the randomForest package.
library("randomForest") rf.fit <- randomForest(x.tr, y.tr, cv.fold = 5) rf.fit
The training result is:
## Call: ## randomForest(x = x.tr, y = y.tr, cv.fold = 5) ## Type of random forest: classification ## Number of trees: 500 ## No. of variables tried at each split: 8 ## ## OOB estimate of error rate: 25.11% ## Confusion matrix: ## 0 1 class.error ## 0 196 46 0.1900826 ## 1 72 156 0.3157895
With the model trained on the training set, we predict on the test set
and plot the ROC curve with the pROC package, as is shown
in Figure 1.
# predict on test set rf.pred <- predict(rf.fit, newdata = x.te, type = "prob")[, 1] # plot ROC curve library("pROC") plot.roc(y.te, rf.pred, grid = TRUE, print.auc = TRUE)
The area under the ROC curve (AUC) is:
## Call: ## plot.roc.default(x = y.te, predictor = rf.pred, col = "#0080ff", ## grid = TRUE, print.auc = TRUE) ## ## Data: rf.pred in 81 controls (y.te 0) > 76 cases (y.te 1). ## Area under the curve: 0.8697
Figure 1: ROC curve for the test set of protein subcellular localization data
Package overview
The protr package [@Xiao2015] implemented most of the
state-of-the-art protein sequence descriptors with R.
Generally, each type of the descriptors (features) can be calculated
with a function named extractX() in the protr package,
where X stands for the abbrevation of the descriptor name.
The descriptors are:
- Amino acid composition
extractAAC()- Amino acid compositionextractDC()- Dipeptide compositionextractTC()- Tripeptide composition
- Autocorrelation
extractMoreauBroto()- Normalized Moreau-Broto autocorrelationextractMoran()- Moran autocorrelationextractGeary()- Geary autocorrelation
- CTD descriptors
extractCTDC()- CompositionextractCTDT()- TransitionextractCTDD()- Distribution
- Conjoint triad descriptors
extractCTriad()- Conjoint triad descriptors
- Quasi-sequence-order descriptors
extractSOCN()- Sequence-order-coupling numberextractQSO()- Quasi-sequence-order descriptors
- Pseudo-amino acid composition
extractPAAC()- Pseudo-amino acid composition (PseAAC)extractAPAAC()- Amphiphilic pseudo-amino acid composition (APseAAC)
- Profile-based descriptors
extractPSSM()extractPSSMAcc()extractPSSMFeature()
The descriptors commonly used in Proteochemometric Modeling (PCM) implemented in protr include:
extractScales(),extractScalesGap()- Scales-based descriptors derived by Principal Components AnalysisextractProtFP(),extractProtFPGap()- Scales-based descriptors derived by amino acid properties from AAindex (a.k.a. Protein Fingerprint)extractDescScales()- Scales-based descriptors derived by 20+ classes of 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.)
extractFAScales()- Scales-based descriptors derived by Factor AnalysisextractMDSScales()- Scales-based descriptors derived by Multidimensional ScalingextractBLOSUM()- BLOSUM and PAM matrix-derived descriptors
The protr package integrates the function of parallelized similarity score
computation derived by local or global protein sequence alignment between
a list of protein sequences, the sequence alignment computation is
provided by Biostrings, the corresponding functions listed in the
protr package include:
twoSeqSim()- Similarity calculation derived by sequence alignment between two protein sequencesparSeqSim()- Parallelized pairwise similarity calculation with a list of protein sequences (in-memory version)parSeqSimDisk()- Parallelized pairwise similarity calculation with a list of protein sequences (disk-based version)crossSetSim()- Parallelized pairwise similarity calculation between two sets of protein sequences (in-memory version)
The protr package also integrates the function of parallelized similarity
score computation derived by Gene Ontology (GO) semantic similarity measures
between a list of GO terms / Entrez Gene IDs, the GO similarity computation
is provided by GOSemSim, the corresponding functions listed
in the protr package include:
twoGOSim()- Similarity calculation derived by GO-terms semantic similarity measures between two GO terms / Entrez Gene IDs;parGOSim()- Pairwise similarity calculation with a list of GO terms / Entrez Gene IDs.
To use the parSeqSim() function, we suggest the users to install
the packages foreach and doParallel first, in order to make
the parallelized pairwise similarity computation available.
In the following sections, we will introduce the descriptors and function usage in this order.
Commonly used descriptors
Note: Users need to intelligently evaluate the underlying details of the descriptors provided, instead of using protr with their data blindly, especially for the descriptor types with more flexibility. It would be wise for the users to use some negative and positive control comparisons where relevant to help guide interpretation of the results.
A protein or peptide sequence with $N$ amino acid residues can be generally represented as ${\,R_1, R_2, \ldots, R_n\,}$, where $R_i$ represents the residue at the $i$-th position in the sequence. The labels $i$ and $j$ are used to index amino acid position in a sequence, and $r$, $s$, $t$ are used to represent the amino acid type. The computed descriptors are roughly categorized into 4 groups according to their major applications.
A protein sequence can be partitioned equally into segments. The descriptors designed for the complete sequence, can be often applied to each individual segment.
Amino acid composition descriptor
The amino acid composition describes the fraction of each amino acid type within a protein sequence. The fractions of all 20 natural amino acids are calculated as:
$$ f(r) = \frac{N_r}{N} \quad r = 1, 2, \ldots, 20. $$ where $N_r$ is the number of the amino acid type $r$ and $N$ is the length of the sequence.
As was described above, we can use the function extractAAC() to
extract the descriptors (features) from protein sequences:
library("protr") x <- readFASTA(system.file( "protseq/P00750.fasta", package = "protr" ))[[1]] extractAAC(x)
Here, with the function readFASTA() we loaded a single protein sequence
(P00750, Tissue-type plasminogen activator) from a FASTA format file.
Then extracted the AAC descriptors with extractAAC().
The result returned is a named vector, whose elements are tagged
with the name of each amino acid.
Dipeptide composition descriptor
Dipeptide composition gives a 400-dimensional descriptor, defined as:
$$ f(r, s) = \frac{N_{rs}}{N - 1} \quad r, s = 1, 2, \ldots, 20. $$
where $N_{rs}$ is the number of dipeptide represented by amino acid
type $r$ and type $s$. Similar to extractAAC(),
here we use extractDC() to compute the descriptors:
dc <- extractDC(x) head(dc, n = 30L)
Here we only showed the first 30 elements of the result vector and omitted the rest of the result. The element names of the returned vector are self-explanatory as before.
Tripeptide composition descriptor
Tripeptide composition gives a 8000-dimensional descriptor, defined as:
$$ f(r, s, t) = \frac{N_{rst}}{N - 2} \quad r, s, t = 1, 2, \ldots, 20 $$
where $N_{rst}$ is the number of tripeptides represented by amino acid type
$r$, $s$, and $t$. With function extractTC(), we can easily obtain
the length-8000 descriptor, to save some space, here we also omitted
the long outputs:
tc <- extractTC(x) head(tc, n = 36L)
Autocorrelation descriptors
Autocorrelation descriptors are defined based on the distribution of amino acid properties along the sequence. The amino acid properties used here are various types of amino acids index (Retrieved from the AAindex database, see @aaindex1999, @aaindex2000, and @aaindex2008; see Figure 2 for an illustrated example). Three types of autocorrelation descriptors are defined here and described below.
All the amino acid indices are centralized and standardized before the calculation, i.e.
$$ P_r = \frac{P_r - \bar{P}}{\sigma} $$
where $\bar{P}$ is the average of the property of the 20 amino acids:
$$ \bar{P} = \frac{\sum_{r=1}^{20} P_r}{20} \quad \textrm{and} \quad \sigma = \sqrt{\frac{1}{2} \sum_{r=1}^{20} (P_r - \bar{P})^2} $$
Figure 2: An illustrated example in the AAIndex database
Normalized Moreau-Broto autocorrelation descriptors
For protein sequences, the Moreau-Broto autocorrelation descriptors can be defined as:
$$ AC(d) = \sum_{i=1}^{N-d} P_i P_{i + d} \quad d = 1, 2, \ldots, \textrm{nlag} $$
where $d$ is called the lag of the autocorrelation; $P_i$ and $P_{i+d}$ are the properties of the amino acids at position $i$ and $i+d$; $\textrm{nlag}$ is the maximum value of the lag.
The normalized Moreau-Broto autocorrelation descriptors are defined as:
$$ ATS(d) = \frac{AC(d)}{N-d} \quad d = 1, 2, \ldots, \textrm{nlag} $$
The corresponding function for this descriptor is extractMoreauBroto().
A typical call would be:
moreau <- extractMoreauBroto(x) head(moreau, n = 36L)
The eight default properties used here are:
- AccNo. CIDH920105 - Normalized Average Hydrophobicity Scales
- AccNo. BHAR880101 - Average Flexibility Indices
- AccNo. CHAM820101 - Polarizability Parameter
- AccNo. CHAM820102 - Free Energy of Solution in Water, kcal/mole
- AccNo. CHOC760101 - Residue Accessible Surface Area in Tripeptide
- AccNo. BIGC670101 - Residue Volume
- AccNo. CHAM810101 - Steric Parameter
- AccNo. DAYM780201 - Relative Mutability
Users can change the property names of AAindex database with the argument
props. The AAindex data shipped with protr can be loaded by
data(AAindex), which has the detailed information of each property.
With the argument customprops and nlag, users can specify
their own properties and lag value to calculate with. For example:
# Define 3 custom properties myprops <- data.frame( AccNo = c("MyProp1", "MyProp2", "MyProp3"), A = c(0.62, -0.5, 15), R = c(-2.53, 3, 101), N = c(-0.78, 0.2, 58), D = c(-0.9, 3, 59), C = c(0.29, -1, 47), E = c(-0.74, 3, 73), Q = c(-0.85, 0.2, 72), G = c(0.48, 0, 1), H = c(-0.4, -0.5, 82), I = c(1.38, -1.8, 57), L = c(1.06, -1.8, 57), K = c(-1.5, 3, 73), M = c(0.64, -1.3, 75), F = c(1.19, -2.5, 91), P = c(0.12, 0, 42), S = c(-0.18, 0.3, 31), T = c(-0.05, -0.4, 45), W = c(0.81, -3.4, 130), Y = c(0.26, -2.3, 107), V = c(1.08, -1.5, 43) ) # Use 4 properties in the AAindex database, and 3 cutomized properties moreau2 <- extractMoreauBroto( x, customprops = myprops, props = c( "CIDH920105", "BHAR880101", "CHAM820101", "CHAM820102", "MyProp1", "MyProp2", "MyProp3" ) ) head(moreau2, n = 36L)
About the standard input format of props and customprops,
see ?extractMoreauBroto for details.
Moran autocorrelation descriptors
For protein sequences, the Moran autocorrelation descriptors can be defined as:
$$ I(d) = \frac{\frac{1}{N-d} \sum_{i=1}^{N-d} (P_i - \bar{P}') (P_{i+d} - \bar{P}')}{\frac{1}{N} \sum_{i=1}^{N} (P_i - \bar{P}')^2} \quad d = 1, 2, \ldots, 30 $$
where $d$, $P_i$, and $P_{i+d}$ are defined in the same way as in the first place; $\bar{P}'$ is the considered property $P$ along the sequence, i.e.,
$$ \bar{P}' = \frac{\sum_{i=1}^N P_i}{N} $$
$d$, $P$, $P_i$ and $P_{i+d}$, $\textrm{nlag}$ have the same meaning as above.
With extractMoran() (which has the identical parameters as
extractMoreauBroto()), we can compute the Moran autocorrelation
descriptors (only print out the first 36 elements):
# Use the 3 custom properties defined before # and 4 properties in the AAindex database moran <- extractMoran( x, customprops = myprops, props = c( "CIDH920105", "BHAR880101", "CHAM820101", "CHAM820102", "MyProp1", "MyProp2", "MyProp3" ) ) head(moran, n = 36L)
Geary autocorrelation descriptors
Geary autocorrelation descriptors for protein sequences can be defined as:
$$ C(d) = \frac{\frac{1}{2(N-d)} \sum_{i=1}^{N-d} (P_i - P_{i+d})^2}{\frac{1}{N-1} \sum_{i=1}^{N} (P_i - \bar{P}')^2} \quad d = 1, 2, \ldots, 30 $$
where $d$, $P$, $P_i$, $P_{i+d}$, and $\textrm{nlag}$ have the same meaning as above.
For each amino acid index, there will be $3 \times \textrm{nlag}$
autocorrelation descriptors. The usage of extractGeary() is
exactly the same as extractMoreauBroto() and extractMoran():
# Use the 3 custom properties defined before # and 4 properties in the AAindex database geary <- extractGeary( x, customprops = myprops, props = c( "CIDH920105", "BHAR880101", "CHAM820101", "CHAM820102", "MyProp1", "MyProp2", "MyProp3" ) ) head(geary, n = 36L)
Composition/Transition/Distribution
The CTD descriptors are developed by @dubchak1 and @dubchak2.
Figure 3: The sequence of a hypothetic protein indicating
the construction of composition, transition, and distribution descriptors
of a protein. Sequence index indicates the position of an amino acid in
the sequence. The index for each type of amino acids in the sequence
(1, 2 or 3) indicates the position of the first, second, third,
... of that type of amino acid. 1/2 transition indicates the position
of 12 or 21 pairs in the sequence (1/3 and 2/3 are defined
in the same way).
Step 1: Sequence Encoding
The amino acids are categorized into three classes according to its attribute, and each amino acid is encoded by one of the indices 1, 2, 3 according to which class it belongs. The attributes used here include hydrophobicity, normalized van der Waals volume, polarity, and polarizability. The corresponding classification for each attribute is listed in Table 1.
**Group 1** **Group 2** **Group 3**
Hydrophobicity Polar Neutral Hydrophobicity R, K, E, D, Q, N G, A, S, T, P, H, Y C, L, V, I, M, F, W Normalized van der Waals Volume 0-2.78 2.95-4.0 4.03-8.08 G, A, S, T, P, D, C N, V, E, Q, I, L M, H, K, F, R, Y, W Polarity 4.9-6.2 8.0-9.2 10.4-13.0 L, I, F, W, C, M, V, Y P, A, T, G, S H, Q, R, K, N, E, D Polarizability 0-1.08 0.128-0.186 0.219-0.409 G, A, S, D, T C, P, N, V, E, Q, I, L K, M, H, F, R, Y, W Charge Positive Neutral Negative K, R A, N, C, Q, G, H, I, L, M, F, P, S, T, W, Y, V D, E Secondary Structure Helix Strand Coil E, A, L, M, Q, K, R, H V, I, Y, C, W, F, T G, N, P, S, D Solvent Accessibility Buried Exposed Intermediate A, L, F, C, G, I, V, W R, K, Q, E, N, D M, S, P, T, H, Y
: Table 1: Amino acid attributes, and the three-group classification of the 20 amino acids by each attribute
For example, for a given sequence MTEITAAMVKELRESTGAGA, it will be
encoded as 32132223311311222222 according to its hydrophobicity.
Step 2: Compute Composition, Transition, and Distribution Descriptors
Three types of descriptors, Composition (C), Transition (T), and Distribution (D) can be calculated for a given attribute as follows.
Composition
Composition is defined as the global percentage for each encoded class
in the protein sequence. In the above example using the hydrophobicity
classification, the numbers for encoded classes 1, 2, 3 are 5, 10, and 5,
so that the compositions for them will be $5/20=25\%$, $10/20=10\%$,
and $5/20=25\%$, where 20 is the length of the protein sequence.
The composition descriptor can be expressed as
$$ C_r = \frac{n_r}{n} \quad r = 1, 2, 3 $$
where $n_r$ is the number of amino acid type $r$ in the encoded
sequence; $N$ is the length of the sequence.
An example for extractCTDC():
extractCTDC(x)
The result shows the elements who are named as PropertyNumber.GroupNumber
in the returned vector.
Transition
A transition from class 1 to 2 is the percent frequency with which 1 is followed by 2 or 2 is followed by 1 in the encoded sequences. The transition descriptor can be computed as
$$ T_{rs} = \frac{n_{rs} + n_{sr}}{N - 1} \quad rs = \text{12}, \text{13}, \text{23} $$
where $n_{rs}$, $n_{sr}$ are the numbers of dipeptide encoded as rs and
sr in the sequence; $N$ is the length of the sequence.
An example for extractCTDT():
extractCTDT(x)
Distribution
The distribution descriptor describes the distribution of each attribute in the sequence.
There are five "distribution" descriptors for each attribute and they are
the position percents in the whole sequence for the first residue, 25%
residues, 50% residues, 75% residues, and 100% residues for a certain
encoded class. For example, there are 10 residues encoded
as 2 in the above example, the positions for the first residue 2,
the 2nd residue 2 (25% * 10 = 2), the 5th 2 residue (50% * 10 = 5),
the 7th 2 (75% * 10 = 7) and the 10th residue 2 (100% * 10)
in the encoded sequence are 2, 5, 15, 17, 20, so that
the distribution descriptors for 2 are: 10.0 (2/20 * 100),
25.0 (5/20 * 100), 75.0 (15/20 * 100), 85.0 (17/20 * 100),
100.0 (20/20 * 100).
To compute the distribution descriptor, use extractCTDD():
extractCTDD(x)
Conjoint triad descriptors
Conjoint triad descriptors are proposed by @shenjw. The conjoint triad descriptors were used to model protein-protein interactions based on the classification of amino acids. In this approach, each protein sequence is represented by a vector space consisting of descriptors of amino acids. To reduce the dimensions of vector space, the 20 amino acids were clustered into several classes according to their dipoles and volumes of the side chains. The conjoint triad descriptors are calculated as follows:
Step 1: Classification of Amino Acids
Electrostatic and hydrophobic interactions dominate protein-protein interactions. These two kinds of interactions may be reflected by the dipoles and volumes of the side chains of amino acids, respectively. Accordingly, these two parameters were calculated by using the density-functional theory method B3LYP/6-31G and molecular modeling approach. Based on the dipoles and volumes of the side chains, the 20 amino acids can be clustered into seven classes (See Table 2). Amino acids within the same class likely involve synonymous mutations because of their similar characteristics.
No. Dipole Scale$^1$ Volume Scale$^2$ Class
1 $-$ $-$ Ala, Gly, Val 2 $-$ $+$ Ile, Leu, Phe, Pro 3 $+$ $+$ Tyr, Met, Thr, Ser 4 $++$ $+$ His, Asn, Gln, Tpr 5 $+++$ $+$ Arg, Lys 6 $+'+'+'$ $+$ Asp, Glu 7 $+^3$ $+$ Cys
: Table 2: Classification of amino acids based on dipoles and volumes of the side chains
1 Dipole Scale (Debye): $-$, Dipole < 1.0; $+$, 1.0 < Dipole < 2.0; $++$, 2.0 < Dipole < 3.0; $+++$, Dipole > 3.0; $+'+'+'$, Dipole > 3.0 with opposite orientation.
2 Volume Scale ($\overset{\lower.5em\circ}{\mathrm{A}}\lower.01em^3$): $-$, Volume < 50; $+$, Volume > 50.
3 Cys is separated from class 3 because of its ability to form disulfide bonds.
Step 2: Conjoint Triad Calculation
The conjoint triad descriptors considered the properties of one amino acid and its vicinal amino acids and regarded any three continuous amino acids as a unit. Thus, the triads can be differentiated according to the classes of amino acids, i.e., triads composed by three amino acids belonging to the same classes, such as ART and VKS, can be treated identically. To conveniently represent a protein, we first use a binary space $(\mathbf{V}, \mathbf{F})$ to represent a protein sequence. Here, $\mathbf{V}$ is the vector space of the sequence features, and each feature $v_i$ represents a sort of triad type; $\mathbf{F}$ is the frequency vector corresponding to $\mathbf{V}$, and the value of the $i$-th dimension of $\mathbf{F} (f_i)$ is the frequency of type $v_i$ appearing in the protein sequence. For the amino acids that have been catogorized into seven classes, the size of $\mathbf{V}$ should be $7 \times 7 \times 7$; thus $i = 1, 2, \ldots, 343$. The detailed description for ($\mathbf{V}$, $\mathbf{F}$) is illustrated in Figure 4.
Figure 4: Schematic diagram for constructing the vector space ($\mathbf{V}$, $\mathbf{F}$) of protein sequences. $\mathbf{V}$ is the vector space of the sequence features; each feature ($v_i$) represents a triad composed of three consecutive amino acids; $\mathbf{F}$ is the frequency vector corresponding to $\mathbf{V}$, and the value of the $i$-th dimension of $\mathbf{F} (f_i)$ is the frequency that $v_i$ triad appeared in the protein sequence.
Clearly, each protein correlates to the length (number of amino acids) of protein. In general, a long protein would have a large value of $f_i$, which complicates the comparison between two heterogeneous proteins. Thus, we defined a new parameter, $d_i$, by normalizing $f_i$ with the following equation:
$$ d_i = \frac{f_i - \min{\,f_1, f_2 , \ldots, f_{343}\,}}{\max{\,f_1, f_2, \ldots, f_{343}\,}} $$
The numerical value of $d_i$ of each protein ranges from 0 to 1, which thereby enables the comparison between proteins. Accordingly, we obtain another vector space (designated $\mathbf{D}$) consisting of $d_i$ to represent protein.
To compute conjoint triads of protein sequences, we can simply use:
ctriad <- extractCTriad(x) head(ctriad, n = 65L)
by which we only outputted the first 65 of total 343 dimension to save space.
Quasi-sequence-order descriptors
The quasi-sequence-order descriptors are proposed by @chouqsoe. They are derived from the distance matrix between the 20 amino acids.
Sequence-order-coupling number
The $d$-th rank sequence-order-coupling number is defined as:
$$ \tau_d = \sum_{i=1}^{N-d} (d_{i, i+d})^2 \quad d = 1, 2, \ldots, \textrm{maxlag} $$
where $d_{i, i+d}$ is the distance between the two amino acids at position $i$ and $i+d$.
Note: maxlag is the maximum lag and the length of the protein must be not less than $\textrm{maxlag}$.
The function extractSOCN() is used for computing the
sequence-order-coupling numbers:
extractSOCN(x)
Users can also specify the maximum lag value with the nlag argument.
Note: In addition to Schneider-Wrede physicochemical distance
matrix [@wrede] used by Kuo-Chen Chou, another chemical distance
matrix by @grantham is also used here. So the descriptors dimension
will be nlag * 2. The quasi-sequence-order descriptors described
next also utilized the two matrices.
Quasi-sequence-order descriptors
For each amino acid type, a quasi-sequence-order descriptor can be defined as:
$$ X_r = \frac{f_r}{\sum_{r=1}^{20} f_r + w \sum_{d=1}^{\textrm{maxlag}} \tau_d} \quad r = 1, 2, \ldots, 20 $$
where $f_r$ is the normalized occurrence for amino acid type $i$ and $w$ is a weighting factor ($w=0.1$). These are the first 20 quasi-sequence-order descriptors. The other 30 quasi-sequence-order are defined as:
$$ X_d = \frac{w \tau_{d-20}}{\sum_{r=1}^{20} f_r + w \sum_{d=1}^{\textrm{maxlag}} \tau_d} \quad d = 21, 22, \ldots, 20 + \textrm{maxlag} $$
Figure 5: A schematic drawing to show (a) the 1st-rank, (b) the 2nd-rank, and (3) the 3rd-rank sequence-order-coupling mode along a protein sequence. (a) Reflects the coupling mode between all the most contiguous residues, (b) that between all the 2nd most contiguous residues, and (c) that between all the 3rd most contiguous residues. This figure is from @chouqsoe.
A minimal example for extractQSO():
extractQSO(x)
where users can also specify the maximum lag with the argument nlag
and the weighting factor with the argument w.
Pseudo-amino acid composition (PseAAC)
This group of descriptors are proposed by @choupaac. PseAAC descriptors are also named as the type 1 pseudo-amino acid composition. Let $H_1^o (i)$, $H_2^o (i)$, $M^o (i)$ ($i=1, 2, 3, \ldots, 20$) be the original hydrophobicity values, the original hydrophilicity values and the original side chain masses of the 20 natural amino acids, respectively. They are converted to following qualities by a standard conversion:
$$ H_1 (i) = \frac{H_1^o (i) - \frac{1}{20} \sum_{i=1}^{20} H_1^o (i)}{\sqrt{\frac{\sum_{i=1}^{20} [H_1^o (i) - \frac{1}{20} \sum_{i=1}^{20} H_1^o (i) ]^2}{20}}} $$
$H_2^o (i)$ and $M^o (i)$ are normalized as $H_2 (i)$ and $M (i)$ in the same way.
Figure 6: A schematic drawing to show (a) the first-tier, (b) the second-tier, and (3) the third-tiersequence order correlation mode along a protein sequence. Panel (a) reflects the correlation mode between all the most contiguous residues, panel (b) that between all the second-most contiguous residues, and panel (c) that between all the third-most contiguous residues. This figure is from @choupaac.
Then, a correlation function can be defines as
$$ \Theta (R_i, R_j) = \frac{1}{3} \bigg{ [ H_1 (R_i) - H_1 (R_j) ]^2 + [ H_2 (R_i) - H_2 (R_j) ]^2 + [ M (R_i) - M (R_j) ]^2 \bigg} $$
This correlation function is actually an average value for the three amino acid properties: hydrophobicity value, hydrophilicity value and side chain mass. Therefore, we can extend this definition of correlation functions for one amino acid property or for a set of $n$ amino acid properties.
For one amino acid property, the correlation can be defined as:
$$ \Theta (R_i, R_j) = [H_1 (R_i) - H_1(R_j)]^2 $$
where $H (R_i)$ is the amino acid property of amino acid $R_i$ after standardization.
For a set of n amino acid properties, it can be defined as: where $H_k (R_i)$ is the $k$-th property in the amino acid property set for amino acid $R_i$.
$$ \Theta (R_i, R_j) = \frac{1}{n} \sum_{k=1}^{n} [H_k (R_i) - H_k (R_j)]^2 $$
where $H_k(R_i)$ is the $k$-th property in the amino acid property set for amino acid $R_i$.
A set of descriptors named sequence order-correlated factors are defined as:
\begin{align} \theta_1 & = \frac{1}{N-1} \sum_{i=1}^{N-1} \Theta (R_i, R_{i+1})\ \theta_2 & = \frac{1}{N-2} \sum_{i=1}^{N-2} \Theta (R_i, R_{i+2})\ \theta_3 & = \frac{1}{N-3} \sum_{i=1}^{N-3} \Theta (R_i, R_{i+3})\ & \ldots \ \theta_\lambda & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} \Theta (R_i, R_{i+\lambda}) \end{align}
$\lambda$ ($\lambda < L$) is a parameter to be specified. Let $f_i$ be the normalized occurrence frequency of the 20 amino acids in the protein sequence, a set of $20 + \lambda$ descriptors called the pseudo-amino acid composition for a protein sequence can be defines as:
$$ X_c = \frac{f_c}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{\lambda} \theta_j} \quad (1 < c < 20) $$
$$ X_c = \frac{w \theta_{c-20}}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{\lambda} \theta_j} \quad (21 < c < 20 + \lambda) $$
where $w$ is the weighting factor for the sequence-order effect and is set to $w = 0.05$ in protr as suggested by Kuo-Chen Chou.
With extractPAAC(), we can compute the PseAAC descriptors directly:
extractPAAC(x)
The extractPAAC() fucntion also provides the additional arguments
props and customprops, which are similar to those arguments for
Moreau-Broto/Moran/Geary autocorrelation descriptors. For their minor
differences, please see ?extracPAAC. Users can specify the lambda
parameter and the weighting factor with arguments lambda and w.
Note: In the work of Kuo-Chen Chou, the definition for "normalized occurrence frequency" was not given. In this work, we define it as the occurrence frequency of amino acid in the sequence normalized to 100% and hence our calculated values are not the same as values by them.
Amphiphilic pseudo-amino acid composition (APseAAC)
Amphiphilic Pseudo-Amino Acid Composition (APseAAC) was proposed in @choupaac. APseAAC is also recognized as the type 2 pseudo-amino acid composition. The definitions of these qualities are similar to the PAAC descriptors. From $H_1 (i)$ and $H_2 (j)$ defined before, the hydrophobicity and hydrophilicity correlation functions are defined as:
\begin{align} H_{i, j}^1 & = H_1 (i) H_1 (j)\ H_{i, j}^2 & = H_2 (i) H_2 (j) \end{align}
From these qualities, sequence order factors can be defines as:
\begin{align} \tau_1 & = \frac{1}{N-1} \sum_{i=1}^{N-1} H_{i, i+1}^1\ \tau_2 & = \frac{1}{N-1} \sum_{i=1}^{N-1} H_{i, i+1}^2\ \tau_3 & = \frac{1}{N-2} \sum_{i=1}^{N-2} H_{i, i+2}^1\ \tau_4 & = \frac{1}{N-2} \sum_{i=1}^{N-2} H_{i, i+2}^2\ & \ldots \ \tau_{2 \lambda - 1} & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} H_{i, i+\lambda}^1\ \tau_{2 \lambda} & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} H_{i, i+\lambda}^2 \end{align}
Figure 7: A schematic diagram to show (a1/a2) the first-rank, (b1/b2) the second-rank and (c1/c2) the third-rank sequence-order-coupling mode along a protein sequence through a hydrophobicity/hydrophilicity correlation function, where $H_{i, j}^1$ and $H_{i, j}^2$ are given by Equation (3). Panel (a1/a2) reflects the coupling mode between all the most contiguous residues, panel (b1/b2) that between all the second-most contiguous residues and panel (c1/c2) that between all the third-most contiguous residues. This figure is from @chouapaac.
Then a set of descriptors called Amphiphilic Pseudo-Amino Acid Composition (APseAAC) are defined as:
$$ P_c = \frac{f_c}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{2 \lambda} \tau_j} \quad (1 < c < 20) $$
$$ P_c = \frac{w \tau_u}{\sum_{r=1}^{20} f_r + w \sum_{j=1}^{2 \lambda} \tau_j} \quad (21 < u < 20 + 2 \lambda) $$
where $w$ is the weighting factor. Its default value is set to $w = 0.5$ in protr.
A minimal example for extracAPAAC() is:
extractAPAAC(x)
This function has the same arguments as extractPAAC().
Profile-based descriptors
The profile-based descriptors for protein sequences are available in
the protr package. The feature vectors of profile-based methods
were based on the PSSM by running PSI-BLAST, and often show good performance.
See @ye2011assessment and @rangwala2005profile for details.
The functions extractPSSM(), extractPSSMAcc() and
extractPSSMFeature() are used to generate these descriptors.
Users need to install the NCBI-BLAST+ software package first to make
the functions fully functional.
Proteochemometric modeling descriptors
Proteochemometric (PCM) modeling utilizes statistical modeling techniques to model ligand-target interaction space. The below descriptors implemented in protr are extensively used in Proteochemometric modeling.
-
Scales-based descriptors derived by Principal Components Analysis
- Scales-based descriptors derived by Amino Acid Properties from AAindex (Protein Fingerprint)
- Scales-based descriptors derived by 20+ classes of 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.)
-
Scales-based descriptors derived by Factor Analysis
- Scales-based descriptors derived by Multidimensional Scaling
- BLOSUM and PAM matrix-derived descriptors
Note that each of the scales-based descriptor functions are freely to combine with the more than 20 classes of 2D and 3D molecular descriptors to construct highly customized scales-based descriptors. Of course, these functions are designed to be flexible enough that users can provide totally self-defined property matrices to construct scales-based descriptors.
For example, to compute the "topological scales" derived by PCA
(using the first 5 principal components),
one can use extractDescScales():
x <- readFASTA(system.file( "protseq/P00750.fasta", package = "protr" ))[[1]] descscales <- extractDescScales( x, propmat = "AATopo", index = c(37:41, 43:47), pc = 5, lag = 7, silent = FALSE )
the argument propmat involkes the AATopo dataset shipped with the
protr package, and the argument index selects the 37 to 41 and the
43 to 47 columns (molecular descriptors) in the AATopo dataset to use,
the parameter lag was set for the Auto Cross Covariance (ACC) for
generating scales-based descriptors of the same length. At last,
we printed the summary of the first 5 principal components (standard
deviation, proportion of variance, cumulative proportion of variance).
The result is a length 175 named vector, which is consistent with the descriptors before:
length(descscales) head(descscales, 15)
For another example, to compute the descriptors derived by the BLOSUM62 matrix and use the first 5 scales, one can use:
x <- readFASTA(system.file( "protseq/P00750.fasta", package = "protr" ))[[1]] blosum <- extractBLOSUM( x, submat = "AABLOSUM62", k = 5, lag = 7, scale = TRUE, silent = FALSE )
The result is a length 175 named vector:
length(blosum) head(blosum, 15)
Dealing with gaps. In proteochemometrics, (sequence alignment)
gaps can be very useful, since a gap in a certain position contains information.
The protr package has built-in support for such gaps. We deal with
the gaps by using a dummy descriptor to code for the 21st type
of amino acid. The function extractScalesGap() and extractProtFPGap()
can be used to deal with such gaps. See ?extractScalesGap and
?extractProtFPGap for details.
Similarity calculation by sequence alignment
Similarity computation derived by local or global protein sequence alignment between a list of protein sequences is of great need in protein research. However, this type of pairwise similarity computation often computationally intensive, especially when there exists many protein sequences. Luckily, this process is also highly parallelizable, the protr package integrates the function of parallelized similarity computation derived by local or global protein sequence alignment between a list of protein sequences.
The function twoSeqSim() calculates the alignment result between
two protein sequences. The function parSeqSim() calculates
the pairwise similarity with a list of protein sequences in parallel:
s1 <- readFASTA(system.file("protseq/P00750.fasta", package = "protr"))[[1]] s2 <- readFASTA(system.file("protseq/P08218.fasta", package = "protr"))[[1]] s3 <- readFASTA(system.file("protseq/P10323.fasta", package = "protr"))[[1]] s4 <- readFASTA(system.file("protseq/P20160.fasta", package = "protr"))[[1]] s5 <- readFASTA(system.file("protseq/Q9NZP8.fasta", package = "protr"))[[1]] plist <- list(s1, s2, s3, s4, s5) psimmat <- parSeqSim(plist, cores = 4, type = "local", submat = "BLOSUM62") psimmat
## [,1] [,2] [,3] [,4] [,5] ## [1,] 1.00000000 0.11825938 0.10236985 0.04921696 0.03943488 ## [2,] 0.11825938 1.00000000 0.18858241 0.12124217 0.06391103 ## [3,] 0.10236985 0.18858241 1.00000000 0.05819984 0.06175942 ## [4,] 0.04921696 0.12124217 0.05819984 1.00000000 0.05714638 ## [5,] 0.03943488 0.06391103 0.06175942 0.05714638 1.00000000
Similarly, the function crossSetSim() calculates the pairwise
similarity between two sets of protein sequences in parallel.
Note that for a small number of proteins, calculating their pairwise similarity scores derived by sequence alignment in parallel may not significantly reduce the overall computation time, since each of the task only requires a relatively small time to finish, thus, computational overheads may exist and affect the performance. In our benchmarks, we used about 1,000 protein sequences on 64 CPU cores, and observed significant performance improvement comparing to the sequential computation.
Scaling up for a large number of sequences
batches.
A useful argument for reducing the memory usage is batches.
It splits the similarity computations into smaller batches.
A larger batch number reduces the memory need for each parallel process,
but also adds the overhead of forking new processes. This is a trade-off
between time (CPU) and space (memory). Also, use verbose = TRUE
to print the computation progress.
parSeqSimDisk().
For similarity computations over an even larger number of protein sequences,
please try parSeqSimDisk() and set batches to a large number.
Unlike the in-memory version, this disk-based function caches the
partial results in each batch to the hard drive and merges all the
results together in the end, which further reduces the memory usage.
Example.
Let's assume we have 20,000 sequences. By setting cores = 64 and
batches = 10000 in parSeqSimDisk(), the workload will be
around 20000^2/2/64/10000 = 312.5 alignments per batch per core.
This could give you a relatively quick feedback about if the memory
size is going to be sufficient, and how long the computation will
take in total, after the first few batches.
Similarity calculation by GO semantic similarity measures
The protr package also integrates the function of similarity score computation derived by Gene Ontology (GO) semantic similarity measures between a list of GO terms or Entrez Gene IDs.
The function twoGOSim() calculates the similarity derived by GO-terms
semantic similarity measures between two GO terms / Entrez Gene IDs, and the
function parGOSim() calculates the pairwise similarity with a list
of GO terms / Entrez Gene IDs:
# By GO Terms go1 <- c( "GO:0005215", "GO:0005488", "GO:0005515", "GO:0005625", "GO:0005802", "GO:0005905" ) # AP4B1 go2 <- c( "GO:0005515", "GO:0005634", "GO:0005681", "GO:0008380", "GO:0031202" ) # BCAS2 go3 <- c( "GO:0003735", "GO:0005622", "GO:0005840", "GO:0006412" ) # PDE4DIP golist <- list(go1, go2, go3) parGOSim(golist, type = "go", ont = "CC", measure = "Wang")
## [,1] [,2] [,3] ## [1,] 1.000 0.344 0.17 ## [2,] 0.344 1.000 0.24 ## [3,] 0.170 0.240 1.00
# By Entrez gene id genelist <- list(c("150", "151", "152", "1814", "1815", "1816")) parGOSim(genelist, type = "gene", ont = "BP", measure = "Wang")
## 150 151 152 1814 1815 1816 ## 150 1.000 0.702 0.725 0.496 0.570 0.455 ## 151 0.702 1.000 0.980 0.456 0.507 0.551 ## 152 0.725 0.980 1.000 0.460 0.511 0.538 ## 1814 0.496 0.456 0.460 1.000 0.687 0.473 ## 1815 0.570 0.507 0.511 0.687 1.000 0.505 ## 1816 0.455 0.551 0.538 0.473 0.505 1.000
Miscellaneous tools
In this section, we will briefly introduce some useful tools provided by the protr package.
Retrieve protein sequences from UniProt
This function getUniProt() gets protein sequences from uniprot.org
by protein ID(s). The input ID is a character vector specifying
the protein ID(s). The returned sequences are stored in a list:
ids <- c("P00750", "P00751", "P00752") prots <- getUniProt(ids) prots
## [[1]] ## [1] "MDAMKRGLCCVLLLCGAVFVSPSQEIHARFRRGARSYQVICRDEKTQMIYQQHQSWLRPVLRSNRVEYCWCN ## SGRAQCHSVPVKSCSEPRCFNGGTCQQALYFSDFVCQCPEGFAGKCCEIDTRATCYEDQGISYRGTWSTAESGAECT ## NWNSSALAQKPYSGRRPDAIRLGLGNHNYCRNPDRDSKPWCYVFKAGKYSSEFCSTPACSEGNSDCYFGNGSAYRGT ## HSLTESGASCLPWNSMILIGKVYTAQNPSAQALGLGKHNYCRNPDGDAKPWCHVLKNRRLTWEYCDVPSCSTCGLRQ ## YSQPQFRIKGGLFADIASHPWQAAIFAKHRRSPGERFLCGGILISSCWILSAAHCFQERFPPHHLTVILGRTYRVVP ## GEEEQKFEVEKYIVHKEFDDDTYDNDIALLQLKSDSSRCAQESSVVRTVCLPPADLQLPDWTECELSGYGKHEALSP ## FYSERLKEAHVRLYPSSRCTSQHLLNRTVTDNMLCAGDTRSGGPQANLHDACQGDSGGPLVCLNDGRMTLVGIISWG ## LGCGQKDVPGVYTKVTNYLDWIRDNMRP" ## ## [[2]] ## [1] "MGSNLSPQLCLMPFILGLLSGGVTTTPWSLARPQGSCSLEGVEIKGGSFRLLQEGQALEYVCPSGFYPYPVQ ## TRTCRSTGSWSTLKTQDQKTVRKAECRAIHCPRPHDFENGEYWPRSPYYNVSDEISFHCYDGYTLRGSANRTCQVNG ## RWSGQTAICDNGAGYCSNPGIPIGTRKVGSQYRLEDSVTYHCSRGLTLRGSQRRTCQEGGSWSGTEPSCQDSFMYDT ## PQEVAEAFLSSLTETIEGVDAEDGHGPGEQQKRKIVLDPSGSMNIYLVLDGSDSIGASNFTGAKKCLVNLIEKVASY ## GVKPRYGLVTYATYPKIWVKVSEADSSNADWVTKQLNEINYEDHKLKSGTNTKKALQAVYSMMSWPDDVPPEGWNRT ## RHVIILMTDGLHNMGGDPITVIDEIRDLLYIGKDRKNPREDYLDVYVFGVGPLVNQVNINALASKKDNEQHVFKVKD ## MENLEDVFYQMIDESQSLSLCGMVWEHRKGTDYHKQPWQAKISVIRPSKGHESCMGAVVSEYFVLTAAHCFTVDDKE ## HSIKVSVGGEKRDLEIEVVLFHPNYNINGKKEAGIPEFYDYDVALIKLKNKLKYGQTIRPICLPCTEGTTRALRLPP ## TTTCQQQKEELLPAQDIKALFVSEEEKKLTRKEVYIKNGDKKGSCERDAQYAPGYDKVKDISEVVTPRFLCTGGVSP ## YADPNTCRGDSGGPLIVHKRSRFIQVGVISWGVVDVCKNQKRQKQVPAHARDFHINLFQVLPWLKEKLQDEDLGFL" ## ## [[3]] ## [1] "APPIQSRIIGGRECEKNSHPWQVAIYHYSSFQCGGVLVNPKWVLTAAHCKNDNYEVWLGRHNLFENENTAQF ## FGVTADFPHPGFNLSLLKXHTKADGKDYSHDLMLLRLQSPAKITDAVKVLELPTQEPELGSTCEASGWGSIEPGPDB ## FEFPDEIQCVQLTLLQNTFCABAHPBKVTESMLCAGYLPGGKDTCMGDSGGPLICNGMWQGITSWGHTPCGSANKPS ## IYTKLIFYLDWINDTITENP"
Read FASTA files
The function readFASTA() provides a convenient way to read protein
sequences stored in FASTA format files. See ?readFASTA for details.
The returned sequences are stored in a named list, whose components are
named with the protein sequences' names.
Read PDB files
The Protein Data Bank (PDB) file format is a text file
format describing the three dimensional structures of protein.
The function readPDB() provides the function to read
protein sequences stored in PDB format files.
See ?readPDB for details.
Sanity check for amino acid types
The protcheck() function checks if the protein sequence's amino acid
types are in the 20 default types, which returns a TRUE if all the
amino acids in the sequence belongs to the 20 default types:
x <- readFASTA(system.file("protseq/P00750.fasta", package = "protr"))[[1]] # a real sequence protcheck(x) # an artificial sequence protcheck(paste(x, "Z", sep = ""))
Remove gaps from sequences
The removeGaps() function allows us to remove/replace gaps (-) or any
"irregular" characters from amino acid sequences, to prepare them for
feature extraction or sequence alignment based similarity computation.
Protein sequence partition
The protseg() function partitions the protein sequences to create
sliding windows. This is usually required when creating feature vectors
for machine learning tasks. Users can specify a sequence x, and
a character aa, one of the 20 amino acid types, and a positive
integer k, which controls the window size (half of the window).
This function returns a named list, each component contains one of the segmentations (a character string), names of the list components are the positions of the specified amino acid in the sequence. See the example below:
protseg(x, aa = "M", k = 5)
Auto cross covariance computation
Auto Cross Covariance (ACC) is extensively used in the scales-based
descriptors computation, this approach calculates the auto covariance
and auto cross covariance for generating scale-based descriptors of
the same length. Users can write their own scales-based descriptor
functions with the help of acc() function in the protr package.
Pre-computed 2D and 3D descriptor sets for the 20 amino acids
The protr package ships with more than 20 pre-computed 2D and 3D
descriptor sets for the 20 amino acids to use with the scales-based
descriptors. Please use data(package = "protr") to list all
the datasets included in the protr package.
BLOSUM and PAM matrices for the 20 amino acids
The BLOSUM and PAM matrices for the 20 amino acids can be used to calculate
BLOSUM and PAM matrix-derived descriptors with function extractBLOSUM(),
the datasets are named in AABLOSUM45, AABLOSUM50,
AABLOSUM62, AABLOSUM80, AABLOSUM100, AAPAM30,
AAPAM40, AAPAM70, AAPAM120, and AAPAM250.
Metadata of the 20 amino acids
As the reference, the AAMetaInfo dataset includes the meta information
of the 20 amino acids used for the 2D and 3D descriptor calculation in the
protr package. This dataset include each amino acid's name, one-letter
representation, three-letter representation, SMILE representation, PubChem
CID and PubChem link. See data(AAMetaInfo) for details.
ProtrWeb
The web service built on protr, namely ProtrWeb, is located at http://protr.org.
ProtrWeb (Figure 8) does not require any knowledge of programming for the user. It is a user-friendly web application for computing the protein sequence descriptors presented in the protr package.
Figure 8: A screenshot of the web application ProtrWeb
Source code repository for this Shiny web application: https://github.com/nanxstats/protrweb.
Summary
The summary of the descriptors in the protr package are listed in Table 3.
Descriptor Group Descriptor Name Descriptor Dimension Function Name
Amino Acid Composition Amino Acid Composition 20 extractAAC() Dipeptide Composition 400 extractDC() Tripeptide Composition 8000 extractTC() Autocorrelation Normalized Moreau-Broto Autocorrelation 240$^1$ extractMoreauBroto() Moran Autocorrelation 240$^1$ extractMoran() Geary Autocorrelation 240$^1$ extractGeary() CTD Composition 21 extractCTDC(), extractCTDCClass() Transition 21 extractCTDT(), extractCTDTClass() Distribution 105 extractCTDD(), extractCTDDClass() Conjoint Triad Conjoint Triad 343 extractCTriad(), extractCTriadClass() Quasi-Sequence-Order Sequence-Order-Coupling Number 60$^2$ extractSOCN() Quasi-Sequence-Order Descriptors 100$^2$ extractQSO() Pseudo-Amino Acid Composition Pseudo-Amino Acid Composition 50$^3$ extractPAAC() Amphiphilic Pseudo-Amino Acid Composition 80$^4$ extractAPAAC()
: Table 3: List of commonly used descriptors in protr
1 The number depends on the choice of the number of properties of amino acids and the choice of the maximum values of the `lag`. The default is use 8 types of properties and `lag = 30`.
2 The number depends on the maximum value of `lag`. By default, `lag = 30`. Two distance matrices are used, so the descriptor dimension is $30 \times 2 = 60$ and $(20 + 30) \times 2 = 100$.
3 The number depends on the choice of the number of the set of amino acid properties and the choice of the $\lambda$ value. The default is use 3 types of properties proposed by Kuo-Chen Chou and $\lambda = 30$.
4 The number depends on the choice of the $\lambda$ vlaue. The default is $\lambda = 30$.
The scales-based PCM descriptors in the protr package are listed in Table 4.
Derived by Descriptor Class Function Name
Principal Components Analysis Scales-based descriptors derived by Principal Components Analysis extractScales(), extractScalesGap() Scales-based descriptors derived by amino acid properties from AAindex (a.k.a. Protein Fingerprint) extractProtFP(), extractProtFPGap() Scales-based descriptors derived by 2D and 3D molecular descriptors (Topological, WHIM, VHSE, etc.) extractDescScales() Factor Analysis Scales-based descriptors derived by Factor Analysis extractFAScales() Multidimensional Scaling Scales-based descriptors derived by Multidimensional Scaling extractMDSScales() Substitution Matrix BLOSUM and PAM matrix-derived descriptors extractBLOSUM()
: Table 4: List of PCM descriptors in protr
The amino acid descriptor sets used by scales-based descriptors provided by the protr package are listed in Table 5. Note that the non-informative descriptors (like the descriptors have only one value across all the 20 amino acids) in these datasets have already been filtered out.
Dataset Name Descriptor Set Name Dimensionality Calculated by
AA2DACOR 2D Autocorrelations Descriptors 92 Dragon AA3DMoRSE 3D-MoRSE Descriptors 160 Dragon AAACF Atom-Centred Fragments Descriptors 6 Dragon AABurden Burden Eigenvalues Descriptors 62 Dragon AAConn Connectivity Indices Descriptors 33 Dragon AAConst Constitutional Descriptors 23 Dragon AAEdgeAdj Edge Adjacency Indices Descriptors 97 Dragon AAEigIdx Eigenvalue-Based Indices Descriptors 44 Dragon AAFGC Functional Group Counts Descriptors 5 Dragon AAGeom Geometrical Descriptors 41 Dragon AAGETAWAY GETAWAY Descriptors 194 Dragon AAInfo Information Indices Descriptors 47 Dragon AAMolProp Molecular Properties Descriptors 12 Dragon AARandic Randic Molecular Profiles Descriptors 41 Dragon AARDF RDF Descriptors 82 Dragon AATopo Topological Descriptors 78 Dragon AATopoChg Topological Charge Indices Descriptors 15 Dragon AAWalk Walk and Path Counts Descriptors 40 Dragon AAWHIM WHIM Descriptors 99 Dragon AACPSA CPSA Descriptors 41 Accelrys Discovery Studio AADescAll All the 2D Descriptors Calculated by Dragon 1171 Dragon AAMOE2D All the 2D Descriptors Calculated by MOE 148 MOE AAMOE3D All the 3D Descriptors Calculated by MOE 143 MOE
: Table 5: List of the pre-calculated descriptor sets of the 20 amino acids in protr
References
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