# The Prediction of Intrinsically Disordered Proteins Based on Feature Selection
## 2 Materials and Methods
### Feature Selection  
We start with a procedure of preprocessing features which contain structural and physicochemical properties as well as evolutionary information of the protein sequences. Without sacrificing our prediction accuracy of IDPs, through preprocessing, our scheme relies on only 70 features as its inputs for the identification of IDPs, which is far fewer features needed in comparison with the most of the other methods [16; 17]. The selection of the structural properties including the region complexity and residue location is due to the fact that the disordered region tends to have less complexity than the ordered region [14]. To further extract the complexity information of the regions, we also add the topological entropy of a protein sequence as a novel feature for our identifying IDPs. Thus, the topological and Shannon entropy together with three amino acid propensities from GlobPlot NAR paper [9; 27] are used to describe the complexity of a region around the target residue. The residue location information [28] can be obtained from computing the amino acid type, the ratio of its position in the protein sequence and the terminal position [17]. Since the IDPs and folded proteins exhibit the distinct physicochemical properties in high probability [1], we use seven physicochemical properties introduced by [PERSON] et al. [29] for our identification. They are steric parameter, polarizability, volume, hydrophobicity, isoelectric point, helix probability and sheet probability. Finally, we also compute the Position Specific Scoring Matrix (PSSM) [16; 30] through executing three iterations of PSI-BLAST (Position-Specific Iterative BasicLocal Alignment Search Tool) against NCBI (National Center for Biotechnology Information) [31] non-redundant database with default parameters. The preprocessing procedure proceeds as follows: considering a protein sequence \(w\) of length \(L\), we choose a sliding window of odd length \(N\) (\(N<L\)). For the simplicity, we first transform \(w\) into a sequence of length \(L+N-1\) through appending \((N-1)/2\) zeros to the both ends of \(w\). Using the sliding window of length \(N\), we obtain \(N\) consecutive residues \(\mathbf{w}_{j}\triangleq w(j)\,,\ldots\,,w(j+N-1)\) with \(1\leq j\leq L\). For each \(\mathbf{w}_{j}\) with \(1\leq j\leq L\), we obtain  
\[\mathbf{v}_{j}=\left[ \begin{array}{cccc}m_{1}(\mathbf{w}_{j})&m_{2}( \mathbf{w}_{j})&\ldots&m_{32}(\mathbf{w}_{j})\end{array} \right]^{\mathrm{T}}, \tag{1}\]  
where \(m_{k}(\mathbf{w}_{j})\) with \(1\leq k\leq 32\) denotes the value of \(k\)-th calculated feature of \(\mathbf{w}_{j}\). Without loss of generality, we assume that the block \(m_{k}(\mathbf{w}_{j})\) with \(1\leq k\leq 5\,,6\leq k\leq 12\) and \(13\leq k\leq 32\) corresponds to the complexity features, physicochemical features and evolutionary information, respectively. Thus, each residue in the window \(\mathbf{w}_{j}\) is associated with a vector \(\mathbf{v}_{j}\). Sliding the window to the right one residue, we can compute \(\mathbf{v}_{j+1}\) and associate it with every residue in the window \(\mathbf{w}_{j+1}\). Repeat this procedure for \(1\leq j\leq L\). Finally, every residue in the protein sequence is associated with multiple \(\mathbf{v}_{j}\) with \(1\leq j\leq L\). For each residue, we assign the average value of all the \(\mathbf{v}_{j}\) with \(1\leq j\leq L\) associated with it as the feature vector of this specific residue. Let \(\mathbf{x}_{j}^{pre}\) (\(1\leq j\leq L\)) denote the feature vector which can be computed as  
\[\mathbf{x}_{j}^{pre}=\left\{ \begin{array}{ll}\frac{1}{j+(N-1)/2}\sum_{i=1}^{ j+(N-1)/2}\mathbf{v}_{i}&,&1\leq j\leq(N-1)/2,\\ \frac{1}{N}\sum_{i=j-(N-1)/2}^{j+(N-1)/2}\mathbf{v}_{i}&,&(N-1)/2<j\leq L-(N-1) /2\\ \frac{1}{L-j+1+(N-1)/2}\sum_{i=j-(N-1)/2}^{L}\mathbf{v}_{i}&,&j>L-(N-1)/2,\end{array} \right. \tag{2}\]  
where \(\mathbf{v}_{i}\) for \(1\leq i\leq L\) is defined in Equation (1). In Equation (1), the computation of the Shannon entropy or topological entropy can be found in [27].