# Identification of Intrinsically Disordered Protein Regions Based on Deep Neural Network-VGG16
## 2 Materials and Methods
### Pre-Processing the Features of Proteins for the Input of Our Model  
The input features of our deep neural network can be classified into three types, i.e., the physicochemical properties, evolutionary information, and amino acid propensities. The physicochemical parameters [32] we use are steric parameter, polarizability, volume, hydrophobicity, isoelectric point, helix, and sheet probability. The evolutionary information is a 20-dimensional position-specific substitution matrix (PSSM) [33] derived from the Position-Specific Iterative Basic Local Alignment Search Tool (PSI-BLAST) [34]. Three propensities of amino-acids are from GlobPlot NAR paper.  
The procedure of pre-processing proceeds, as follows:  
1. Given an amino-acid sequence of a protein of size \(L\), we use a sliding window of size 21 and, for each amino-acid in the sliding window, compute the physicochemical properties, evolutionary information, and amino-acid propensities that are defined in the above paragraph. These computed feature values of amino-acids are then averaged over our sliding window and used to represent the feature value of the amino-acid in the center of our sliding window. For two terminal amino-acids of a protein, we append 10 zeros on the left and right side of the amino-acid sequence of a protein, respectively. Thus, for each amino-acid sequence of a protein, we can associate it with a \(30\times L\) feature matrix \[\mathbf{F}=[\mathbf{x}_{1}\ \ \mathbf{x}_{2}\ \ \cdots\ \ \mathbf{x}_{L}],\] (1) where the entries of vector \(\mathbf{x}_{j}(1\leq j\leq L)\) represents the feature values (seven physicochemical properties, twenty entries of a column in the PSSM matrix, and 3 amino-acid propensities) associated with the \(j\)-th amino-acid. Assume that a \(30\times 1\) vector \(\mathbf{x}_{j}(1\leq j\leq L)\) can be denoted by \[\mathbf{x}_{j}=[m_{1,j}\ \ m_{2,j}\ \ \cdots\ \ m_{30,j}]^{\mathrm{T}},\] (2) where \(m_{k,j}\) is the \(k\)-th feature value \((1\leq k\leq 30)\) that is associated with the \(j\)-th amino-acid \((1\leq j\leq L)\) averaged over the sliding window of size 21.
2. Because the minimum input size of the VGG16 is required to be \(32\times 32\times 3\), we transfer the \(30\times L\) feature matrix to three matrices of size \(32\times 32\), as Figure 2 depicts. That is, for each feature vector \(m_{k,j}\ 1\leq k\leq 30\) and \(1\leq j\leq L\) defined in (2), we introduce an associated \(32\times 32\) matrix \(\mathbf{w}_{k,j}\), which is \[\mathbf{w}_{k,j}=\left[\begin{array}{cccc}\mathbf{F}(k,j-31:j)\\ \mathbf{F}(k,j-30:j+1)\\ \vdots\\ \mathbf{F}(k,j:j+31)\end{array}\right]=\left[\begin{array}{cccc}m_{k,(j-31 )}&m_{k,(j-30)}&\cdots&m_{k,j}\\ m_{k,(j-30)}&m_{k,(j-29)}&\cdots&m_{k,(j+1)}\\ \vdots&\vdots&\ddots&\vdots\\ m_{k,j}&m_{k,(j+1)}&\cdots&m_{k,(j+31)}\end{array}\right],\] (3) where \(m_{k,j}=0\) with \(j<1\) or \(j>L\).
3. Thus, for the \(j\)-th amino-acid, its thirty input features yield a sequence of \(32\times 32\) matrices \(\mathbf{w}_{1,j},\mathbf{w}_{2,j}\cdots\mathbf{w}_{30,j}\). Therefore, at each step, we choose three consecutive from the sequence of matrices \(\mathbf{w}_{1,j},\mathbf{w}_{2,j}\cdots\mathbf{w}_{30,j}\) as the input of VGG16 network.