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nanxstats committed Jun 6, 2017
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Expand Up @@ -220,7 +220,7 @@ The area under the ROC curve (AUC) is:
## Area under the curve: 0.8697
```

<img src="figures/roc.png" width="60%" class="img-responsive" alt="ROC curve for the test set of protein subcellular localization data">
<img src="figures/roc.png" width="60%" class="img-responsive" align="center" alt="ROC curve for the test set of protein subcellular localization data">
<p align="center">Figure 1: ROC curve for the test set of protein subcellular localization data</p>

# Package Overview
Expand Down Expand Up @@ -423,7 +423,7 @@ $$
\bar{P} = \frac{\sum_{r=1}^{20} P_r}{20} \quad \textrm{and} \quad \sigma = \sqrt{\frac{1}{2} \sum_{r=1}^{20} (P_r - \bar{P})^2}
$$

<img src="figures/AAindex.png" width="80%" class="img-responsive" alt="An illustrated example in the AAIndex database">
<img src="figures/AAindex.png" width="80%" class="img-responsive" align="center" alt="An illustrated example in the AAIndex database">
<p align="center">Figure 2: An illustrated example in the AAIndex database</p>

### Normalized Moreau-Broto autocorrelation descriptors
Expand Down Expand Up @@ -568,7 +568,7 @@ head(geary, n = 36L)

These descriptors are developed and described by @dubchak1 and @dubchak2.

<img src="figures/CTD.png" width="100%" class="img-responsive" alt="CTD descriptors">
<img src="figures/CTD.png" width="100%" class="img-responsive" align="center" alt="CTD descriptors">
<p align="left">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.
Expand All @@ -587,7 +587,7 @@ references. The corresponding division is in Table 1.

<p align="center">Table 1: Amino acid attributes and the division of
the amino acids into three groups for each attribute</p>
<img src="tables/table1.png" width="80%" class="img-responsive">
<img src="tables/table1.png" width="80%" class="img-responsive" align="center">

For example, for a given sequence `MTEITAAMVKELRESTGAGA`, it will be
encoded as `32132223311311222222` according to its hydrophobicity division.
Expand Down Expand Up @@ -687,7 +687,7 @@ because of their similar characteristics.

<p align="center">Table 2: Classification of amino acids based on
dipoles and volumes of the side chains.</p>
<img src="tables/table2.png" width="60%" class="img-responsive">
<img src="tables/table2.png" width="60%" class="img-responsive" align="center">
<p align="left"><sup>1</sup> 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.</p>
Expand Down Expand Up @@ -716,7 +716,7 @@ $7 \times 7 \times 7$; thus $i = 1, 2, \ldots, 343$. The detailed
description for ($\mathbf{V}$, $\mathbf{F}$) is illustrated
in Figure 4.

<img src="figures/ctriad.png" width="100%" class="img-responsive">
<img src="figures/ctriad.png" width="100%" class="img-responsive" align="center">
<p align="left">Figure 4: Schematic diagram for constructing the
vector space ($\mathbf{V}$, $\mathbf{F}$) of protein sequence.
$\mathbf{V}$ is the vector space of the sequence features;
Expand Down Expand Up @@ -800,7 +800,7 @@ $$
X_d = \frac{w \tau_{d-20}}{\sum_{r=1}^{20} f_r + w \sum_{d=1}^{\textrm{maxlag}} \tau_d} \quad d = 21, 22, \ldots, 20 + \textrm{maxlag}
$$

<img src="figures/QSO.png" width="75%" class="img-responsive">
<img src="figures/QSO.png" width="75%" class="img-responsive" align="center">
<p align="left">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.</p>

A minimal example for `extractQSO()`:
Expand All @@ -827,7 +827,7 @@ $$

$H_2^o (i)$ and $M^o (i)$ are normalized as $H_2 (i)$ and $M (i)$ in the same way.

<img src="figures/PAAC.png" width="75%" class="img-responsive">
<img src="figures/PAAC.png" width="75%" class="img-responsive" align="center">
<p align="left">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.</p>

Then, a correlation function can be defines as
Expand Down Expand Up @@ -928,7 +928,7 @@ From these qualities, sequence order factors can be defines as:
\tau_{2 \lambda} & = \frac{1}{N-\lambda} \sum_{i=1}^{N-\lambda} H_{i, i+\lambda}^2
\end{align*}

<img src="figures/APAAC.png" width="100%" class="img-responsive">
<img src="figures/APAAC.png" width="100%" class="img-responsive" align="center">
<p align="left">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.</p>

Then a set of descriptors called _Amphiphilic Pseudo-Amino Acid Composition_ (_APAAC_) are defined as:
Expand Down Expand Up @@ -1267,7 +1267,7 @@ 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.

<img src="figures/protrweb.png" width="90%" class="img-responsive" alt="ProtrWeb">
<img src="figures/protrweb.png" width="90%" class="img-responsive" align="center" alt="ProtrWeb">
<p align="center">Figure 8: A screenshot of the web application ProtrWeb</p>

Source code repository for this Shiny web application:
Expand All @@ -1279,7 +1279,7 @@ The summary of the descriptors in the protr package are listed in
Table 3.

<p align="center">Table 3: List of commonly used descriptors in protr</p>
<img src="tables/table3.png" width="100%" class="img-responsive">
<img src="tables/table3.png" width="100%" class="img-responsive" align="center">
<p align="left"><sup>1</sup> 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
Expand All @@ -1299,7 +1299,7 @@ The scales-based PCM descriptors in the protr package are
listed in Table 4.

<p align="center">Table 4: List of PCM descriptors in protr</p>
<img src="tables/table4.png" width="100%" class="img-responsive">
<img src="tables/table4.png" width="100%" class="img-responsive" align="center">

The amino acid descriptor sets used by scales-based descriptors
provided by the protr package are listed in Table 5.
Expand All @@ -1308,6 +1308,6 @@ have only one value across all the 20 amino acids) in these
datasets have already been filtered out.

<p align="center">Table 5: List of the pre-calculated descriptor sets of the 20 amino acids in protr</p>
<img src="tables/table5.png" width="100%" class="img-responsive">
<img src="tables/table5.png" width="100%" class="img-responsive" align="center">

# References

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