DHU-Pred: accurate prediction of dihydrouridine sites using position and composition variant features on diverse classifiers

Positive and negative samples

Each data set sample was composed of 41 nucleotides with U at its center, i.e., at position 21. The experimental results revealed the optimal accuracy scores were achieved using a sequence length of 41 nucleotides. In addition, an RNA sample containing the D site was expressed as mentioned in Eq. (1). (1)${\displaystyle P\left(U\right)=P_{-ϵ}{P}_{-\left(ϵ-1\right)}....P_{-2}{P}_{-1}U{P}_{+1}{P}_{+2}....P_{+\left(ϵ-1\right)}{P}_{+ϵ}.}$

In Eq. (1), the symbol U represents uridine (U), the center of nucleotide sequences, and the subscript value ϵ is set as 20. Thus, the total length of the nucleotide sequence is (2 ϵ+1). P_−ϵ represents the ϵ-th upstream nucleotide from the central uridine and P_+ϵ represents the ϵ-th downstream nucleotide. The positive samples signify the sequence with D modification, whereas the negative samples express the sequences without D modification. The total positive and negative sites of all three previously mentioned species were 1,155 and 1,669, respectively. However, removing redundant samples with CD-HIT (16) at 0.80 reduced the sample size to 1,035 positive and 1,396 negative samples.

Sequence logo

The distribution of nucleotide bases in the obtained sequences can be illustrated with the help of the sequence logo. An online Two Sample Logo tool (Vacic, Iakoucheva & Radivojac, 2006) was used for the said purpose. The sequence logo shown in Fig. 3 expressed the distribution of cytosine (C), guanine (G), adenine (A), and uracil (U) in the dataset.

The nucleotide base distribution from the centre nucleotide base (i.e., uracil) is different between positive sites (from position 22 to 41) and negative sites (from position 1 to 20). It can be observed from Fig. 3 that G and C are enriched in the region located from position 19 (negative site) to position 31 (positive site). However, the base A is symmetrically distributed along the whole region within all nucleotides. The nucleotide base U is mostly concentrated in and around the centre of all RNA samples.

Statistical moment calculation

The quantification of the collected nucleotide sequences is based on their composition and position. Moments have been applied to various data distributions by statisticians and data analysts (Malebary & Khan, 2021). For this purpose, central, raw, and Hahn moments were used in the feature extraction process. Raw and Hahn moments are scale and location variant, whereas central moments are scale and vicinity variant. Therefore, the dataset’s mean, asymmetry, and variance were calculated using raw and central moments. On the contrary, Hahn moments were calculated by the reference of Hahn polynomials to maintain the sequence order information (Khan et al., 2020). Butt et al. (2016) used these moments as a means for feature extraction, which was used to identify membrane proteins. A matrix K′ in Eq. (4) is a m*n two-dimensional matrix in which a single element, k_mn, represents the nth nucleotide base in mth sequence. (4)${\displaystyle K^{\prime }=\left[\begin{array}{cccc}\hfill k_{11}\hfill & \hfill k_{12}\hfill & \hfill \dots \hfill & \hfill k_{1n}\hfill \\ \hfill k_{21}\hfill & \hfill k_{22}\hfill & \hfill \dots \hfill & \hfill k_{2n}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill k_{m1}\hfill & \hfill k_{m2}\hfill & \hfill \dots \hfill & \hfill k_{mn}\hfill \end{array}\right].}$

Raw moments were used to extract location variant features by calculating the dataset’s mean, variance, and unequal probability distribution. Raw moments expressed in Eq. (5) where, u + v is the sum of raw moments and R₀₀, R₀₁, R₁₀, R₁₁, R₁₂, R₂₁, R₃₀, R₀₃, were calculated up to 3rd-degree polynomial. (5)${\displaystyle R_{uv}=\sum _{a=1}^m\sum _{b=1}^m{a}^u{b}^v{\beta }_{ab}.}$

Central moments do not depend upon the location. Instead, these are related to the composition and shape of the distribution (TLo & Don, 1989). The central moments were calculated based on the deviations of the random variable from the mean. For this study, the central moments were computed as expressed in Eq. (6). (6)${\displaystyle n_{ij}=\sum _{b=1}^n\sum _{q=1}^n{\left(b-x\right)}^i{\left(q-y\right)}^j{\beta }_{bq}.}$

Hahn moments were computed using Hahn polynomials. Hahn moments calculation mentioned in the Eq. (7). (7)${\displaystyle h_n^{u,v}\left(r,N\right)={\left(N+V-1\right)}_n{\left(N-1\right)}_n\times \sum _{k=0}^n{\left(-1\right)}^k\frac{{\left(-n\right)}_k{\left(-r\right)}_k{\left(2N+u+v-n-1\right)}_k}{{\left(N+v-1\right)}_k{\left(N-1\right)}_k}\frac{1}{k!}.}$

The following expression Eq. (8) was used to determine the orthogonal normalized Hahn of the two-dimensional data. (8)${\displaystyle H_{ij}=\sum _{q=0}^{N-1}\sum _{p=0}^{N-1}{\beta }_{ij}{h}_j^{\widetilde{u,v}}\left(q,N\right)h_j^{\widetilde{u,v}}\left(p,N\right),m,n=0,1,\dots ,N-1.}$

Construction of Position Relative Incidence Matrix (PRIM)

The current study focused on improving the model’s prediction abilities. Therefore, a complete feature generation model was required for the said purpose. The relative positions of nucleotides within an RNA sequence are helpful and become the basis for mathematical formulation. For this purpose, three types of position relative incidence matrix (PRIM) were constructed by considering single nucleotide composition (SNC), di-nucleotide composition (DNC), and tri-nucleotide composition (TNC). These matrices were created to reveal the relative positions of nucleotide bases, which helped in comprehensively quantizing the relative positions of nucleotides. The matrix, A_Prim, is a 4*4 matrix Eq. (9) that produced a total of 16 coefficients. (9)${\displaystyle A_{prim}=\left[\begin{array}{cccc}\hfill {Ԏ}_{A\to A}\hfill & \hfill {Ԏ}_{A\to G}\hfill & \hfill {Ԏ}_{A\to U}\hfill & \hfill {Ԏ}_{A\to C}\hfill \\ \hfill {Ԏ}_{G\to A}\hfill & \hfill {Ԏ}_{G\to G}\hfill & \hfill {Ԏ}_{G\to U}\hfill & \hfill {Ԏ}_{G\to C}\hfill \\ \hfill {Ԏ}_{U\to A}\hfill & \hfill {Ԏ}_{U\to G}\hfill & \hfill {Ԏ}_{U\to U}\hfill & \hfill {Ԏ}_{U\to C}\hfill \\ \hfill {Ԏ}_{C\to A}\hfill & \hfill {Ԏ}_{C\to G}\hfill & \hfill {Ԏ}_{C\to U}\hfill & \hfill {Ԏ}_{C\to C}\hfill \end{array}\right].}$

Where, Ԏ _i→j, represents the relative position of any nucleotide (i.e., A, C, U, or G) to other nucleotides. The matrix, B_Prim, is a 16*16 matrix Eq. (10) that denotes the DNC producing 16 unique combinations of nucleotides (i.e., AA, AG, AU, …, CG, CU, CC). This matrix yielded a total of 256 coefficients. However, with the fusion of statistical moments, only 30 coefficients were derived. (10)${\displaystyle B_{prim}=\left[\begin{array}{ccccccc}\hfill {ժ}_{AA\to AA}\hfill & \hfill {ժ}_{AA\to AG}\hfill & \hfill {ժ}_{AA\to AU}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AA\to j}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AA\to CC}\hfill \\ \hfill {ժ}_{AG\to AA}\hfill & \hfill {ժ}_{AG\to AG}\hfill & \hfill {ժ}_{AG\to AU}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AG\to j}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AG\to CC}\hfill \\ \hfill {ժ}_{AU\to AA}\hfill & \hfill {ժ}_{AU\to AG}\hfill & \hfill {ժ}_{AU\to AU}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AU\to j}\hfill & \hfill \dots \hfill & \hfill {ժ}_{AU\to CC}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill \\ \hfill {ժ}_{GA\to AA}\hfill & \hfill {ժ}_{GA\to AG}\hfill & \hfill {ժ}_{GA\to AU}\hfill & \hfill \dots \hfill & \hfill {ժ}_{GA\to j}\hfill & \hfill \dots \hfill & \hfill {ժ}_{GA\to CC}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill \\ \hfill {ժ}_{N\to AA}\hfill & \hfill {ժ}_{N\to AG}\hfill & \hfill {ժ}_{N\to AU}\hfill & \hfill \dots \hfill & \hfill {ժ}_{N\to j}\hfill & \hfill \dots \hfill & \hfill {ժ}_{N\to CC}\hfill \end{array}\right].}$

The matrix, C_Prim, is a 64*64 matrix Eq. (11) representing 64 unique tri-nucleotide combinations (i.e., AAA, AAG, AAU, …., CCG, CCU, CCC). C_Prim yielded 4,096 coefficients. However, with the incorporation of central, raw, and Hahn moments, 30 coefficients were computed. (11)${\displaystyle C_{prim}=\left[\begin{array}{ccccccc}\hfill {\Psi }_{AAA\to AAA}\hfill & \hfill {\Psi }_{AAA\to AAG}\hfill & \hfill {\Psi }_{AAA\to AAU}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAA\to j}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAA\to CCC}\hfill \\ \hfill {\Psi }_{AAG\to AAA}\hfill & \hfill {\Psi }_{AAG\to AAG}\hfill & \hfill {\Psi }_{AAG\to AAU}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAG\to j}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAG\to CCC}\hfill \\ \hfill {\Psi }_{AAU\to AAA}\hfill & \hfill {\Psi }_{AAU\to AAG}\hfill & \hfill {\Psi }_{AAU\to AAU}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAU\to j}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAU\to CCC}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill \\ \hfill {\Psi }_{AAC\to AAA}\hfill & \hfill {\Psi }_{AAC\to AAG}\hfill & \hfill {\Psi }_{AAC\to AAU}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAC\to j}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{AAC\to CCC}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill \\ \hfill {\Psi }_{N\to AAA}\hfill & \hfill {\Psi }_{N\to AAG}\hfill & \hfill {\Psi }_{N\to AAU}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{N\to j}\hfill & \hfill \dots \hfill & \hfill {\Psi }_{N\to CCC}\hfill \end{array}\right].}$

Reverse Position Relative Indices Matrix (RPRIM)

The main objective in feature vector determination is to extract as much information as possible to develop a reliable predictive model. Reversing the sequence order to get more embedded information within the sequences yielded a reverse position relative indices matrix (RPRIM). Eq. (12) states, V_RPRIM, in which any arbitrary element, R_i→j, represents the relative position value of the i th nucleotide base to the j th nucleotide. The calculation of RPRIM was carried out using mononucleotide, di-nucleotide, and tri-nucleotide combinations like PRIM matrices. (12)${\displaystyle V_{RPRIM}=\left[\begin{array}{ccccccc}\hfill V_{1\to 1}\hfill & \hfill V_{1\to 2}\hfill & \hfill V_{1\to 3}\hfill & \hfill \dots \hfill & \hfill V_{1\to y}\hfill & \hfill \dots \hfill & \hfill V_{1\to j}\hfill \\ \hfill V_{2\to 1}\hfill & \hfill V_{2\to 2}\hfill & \hfill V_{2\to 3}\hfill & \hfill \dots \hfill & \hfill V_{2\to y}\hfill & \hfill \dots \hfill & \hfill V_{2\to j}\hfill \\ \hfill V_{3\to 1}\hfill & \hfill V_{3\to 2}\hfill & \hfill V_{3\to 3}\hfill & \hfill \dots \hfill & \hfill V_{3\to y}\hfill & \hfill \dots \hfill & \hfill V_{3\to j}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill \\ \hfill V_{x\to 1}\hfill & \hfill V_{x\to 2}\hfill & \hfill V_{x\to 3}\hfill & \hfill \dots \hfill & \hfill V_{x\to y}\hfill & \hfill \dots \hfill & \hfill V_{4\to j}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill & \hfill \hfill & \hfill ⋮\hfill \\ \hfill V_{N\to 1}\hfill & \hfill V_{N\to 2}\hfill & \hfill V_{N\to 3}\hfill & \hfill \dots \hfill & \hfill V_{N\to y}\hfill & \hfill \dots \hfill & \hfill V_{N\to j}\hfill \end{array}\right].}$

Frequency Matrices (FMs) generation

It is necessary to extract information about the location as well as the composition of the sequence for generating attributes. The frequency vector Ġ in Eq. (13), on the other hand, provided the count for each nucleotide in the sequence. (13)${\displaystyle \text{Ġ}=\left\{{\delta }_1,{\delta }_2,\dots ..,{\delta }_n\right\}.}$

Where δ_i represents the count of each ith nucleotide within a sequence. The frequency vector Ġ was computed for single as well as paired nucleotides.

Generation of Accumulative Absolute Position Incidence Vector (AAPIV)

The extraction of compositional information did not provide enough information regarding the position-specific calculation of each nucleotide. For this purpose, accumulative absolute position incidence vectors (AAPIVs) of lengths 4, 16, and 64 were computed, which are represented as K_AAPIV4, K_AAPIV16, and K_AAPIV64 in Eqs. (14), (15) and (16) respectively.

(14)${\displaystyle K_{AAPIV4}=\left\{{\rho }_1,{\rho }_2,{\rho }_3,{\rho }_4,\right\}}$ (15)${\displaystyle K_{AAPIV16}=\left\{{\rho }_1,{\rho }_2,{\rho }_3,...,{\rho }_{15},{\rho }_{16},\right\}}$ (16)${\displaystyle K_{AAPIV64}=\left\{{\rho }_1,{\rho }_2,{\rho }_3,...,{\rho }_{63},{\rho }_{64}\right\}.}$

Any element ρ_i is computed as follows: (17)${\displaystyle {\rho }_i={\sum }_{k=1}^n{p}_k.}$

Reverse Accumulative Absolute Position Incidence Vector (RAAPIV) generation

The reverse accumulative absolute position incidence vector (RAAPIV) helped explore hidden information related to the relative positions of nucleotides in the sequence. The length of RAAPIV was 4, 16, and 64, expressed as K_RAAPIV4 Eq. (18), K_RAAPIV16 Eq. (19), and K_RAAPIV64 Eq. (20), respectively, but with reverse sequence order.

(18)${\displaystyle K_{RAAPIV4}=\left\{{\tau }_1,{\tau }_2,{\tau }_3,{\tau }_4\right\}}$ (19)${\displaystyle K_{RAAPIV16}=\left\{{\tau }_1,{\tau }_2,{\tau }_3,...,{\tau }_{16}\right\}}$ (20)${\displaystyle K_{RAAPIV64}=\left\{{\tau }_1,{\tau }_2,{\tau }_3,...,{\tau }_{64}\right\}.}$

Feature vector formulation

In the concluding step of extracting features, a single feature vector was created and fed into the prediction model. Therefore, the following steps were taken in developing the final feature set: (1) Statistical moments were computed initially for PRIM and RPRIM for feature dimensionality reduction. (2) The resultant features were then assimilated into FV, AAPIV, and RAAPIV. Ultimately, a feature vector with 522 attributes was obtained. Each feature vector represents a single sample within the dataset. For binary classification, the positive samples were designated as “1”, and the negative samples were designated as “0”.

Feature scaling technique

A standard scalar technique (https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html) within the Python framework was used in this research study to standardise feature values obtained through the methods mentioned above. It is a common method to preprocess data before putting it into a computational model.

Random forest (RF)

A RF is an ensemble technique that combines various decision trees to get a more appropriate and accurate prediction result. Many decision trees participated in the classification, but, the majority voting by these decision trees won. The margin function $mg\left(X,Y\right)$ in Eq. (21) describes the ensemble of classifiers with the training set drawn at random from the distribution of the random vector Y, X. (21)${\displaystyle mg\left(X,Y\right)=a{v}_{k}I\left(h_k\left(X\right)=Y\right)-ma{x}_{j\ne y}a{v}_{k}I\left(h_k\left(X\right)=j\right).}$

Wenric & Shemirani (2018) utilised RF classifiers to rank genes by their expression values with the RNA-sequence sample set. This research implemented the algorithm using scikit-learn (version 0.24.2; https://scikit-learn.org/stable/). Optimal results were achieved by tuning hyperparameters such as maximum depth, maximum features, minimum samples, and the number of estimators. Nevertheless, tuning hyperparameters had a profound effect on the performance of the RF-based model (Probst, Wright & Boulesteix, 2019). In the current study, the max_depth was set to 100. Similarly, max_features was configured to Auto and min_sample_leaf, defining the number of samples required to be a leaf node, was set to 6. Following numerous experiments, the subsequent parameters for model training were determined, as shown in Table 1.

Support Vector Machine (SVM)

In supervised machine learning approaches, SVM is used for classification, regression, and outlier identification. In bioinformatics, SVM is well applied to the prediction problems of proteins and DNA/RNA sequences as well (Han, Wang & Zhou, 2019; Manavalan et al., 2019; Meng et al., 2019). Researchers (Feng et al., 2019; Xu et al., 2019) utilised SVM for the classification of D sites and non-D sites. The SVM-based model was deployed in the current study using the Python Scikit-learn library. Considering the hyper-parameters optimization through experiments, the following parameters were tuned to get the best results, as shown in Table 2.

K Nearest Neighbor (KNN)

KNN is a supervised machine learning method that uses training data to perform classification. It forecasts the values of new outcomes based on the closely matched training data points. Dongardive and Abraham (Dongardive & Abraham) conducted experiments using KNN with different neighbour values. They achieved the highest accuracy of 84%, with a neighbour value of 15 on the dataset containing 717 protein sequences. For experimental purposes, the research also employed the KNN model with the neighbour value (K) set to 3.

Artificial Neural Network (ANN)

A network of artificial neurons, often referred to as nodes, is what constitutes an ANN. These nodes are brought together to form a network that performs functions analogous to those of a biological neuron found in the brain. These nodes form different layers. There can be various hidden layers, with input and output layers. Each input signal is routed into a single input layer neuron before being passed on to the hidden layer. The final level of processing is completed by the output layer, which sends out output signals. ANN models have been extensively used in many research areas especially computational biology (Hussain et al., 2019a; Hussain et al., 2019b). In the present study, the ANN model was trained by modifying parameters such as hidden layer sizes, activation, solver, alpha, and learning rate, as indicated in Table 3.