iMethylK_pseAAC: Improving Accuracy of Lysine Methylation Sites Identification by Incorporating Statistical Moments and Position Relative Features into General PseAAC via Chou's 5-steps Rule.

BACKGROUND: Methylation is one of the most important post-translational modifications in the human body which usually arises on lysine among the most intensely modified residues. It performs a dynamic role in numerous biological procedures, such as regulation of gene expression, regulation of protein function and RNA processing. Therefore, to identify lysine methylation sites is an important challenge as some experimental procedures are time-consuming.
OBJECTIVE: Herein, we propose a computational predictor named iMethylK_pseAAC to identify lysine methylation sites.
METHODS: Firstly, we constructed feature vectors based on PseAAC using position and composition rel-ative features and statistical moments. A neural network is trained based on the extracted features. The performance of the proposed method is then validated using cross-validation and jackknife testing.
RESULTS: The objective evaluation of the predictor showed accuracy of 96.7% for self-consistency, 91.61% for 10-fold cross-validation and 93.42% for jackknife testing.
CONCLUSION: It is concluded that iMethylK_pseAAC outperforms the counterparts to identify lysine methylation sites such as iMethyl_pseACC, BPB_pPMS and PMeS.

INTRODUCTION

The overall process of generating new proteins is called protein synthesis, which is governed by the loss of cellular proteins with the help of dissemination. The process of synthesizing a protein from an mRNA is known as translation. Post-translational modification is one of the most significant modifications in biology that highlights the covalent and most commonly enzymatic modification of proteins throughout the process of protein biosynthesis [1]. Covalent post-translational modifications (PTMs) of proteins produce a complicated layer of the proteome. High-throughput proteomics with focused investigation on site-specific PTM and protein adjusting enzymes have revealed insight into the extent of these alterations over a diverse range of organisms.

Among the 20 amino acids, lysine is a standout amongst the most intensely modified residues. Nowadays, lysine residues are identified to be covalently altered by acetyl, hydroxyl, glycosyl, propionyl, butyryl, crotonyl, malonyl, succinyl, and methyl. Among all these modifications, lysine methylation is the most complex and difficult PTM that has, in any case, the possibility to transform the capacity of the altered protein [2]. A well-known PTM, which includes the modification of up to three methyl groups to the e-amine of a lysine residue, has attracted remarkable attention in recent years. Lysine methylation has been observed in both atomic and cytoplasmic proteins and is currently viewed as a common modification in eukaryotes, prokaryotes and archaea.

Protein methylation is a form of post-translational modification which arises on lysine residues and is basically catalysed by enzymes [3]. The methyltransferases transform amino acids by adding a methyl group as shown in Fig. . Methylation has been mostly observed in the histones, where the transferal of methyl groups is catalysed by histone methyltransferases. Histones which are methylated on solid residues can perform epigenetically to suppress or activate gene expression [4]. It takes place on nitrogen side-chains in arginine and lysine residues and also on the carboxyl-terminus of different proteins. Protein methylation which occurs on nitrogen atoms at the N-terminus cannot be inverted and reduces the protein activity, whereas methylation on the C-terminus residues can increase the activity of a protein which is regularly performed in a body [5]. The process of protein methylation is basically the accumulation of a methyl group in proteins that usually takes place on the lysine residues in the protein sequence. Protein methylation is involved in the modification of substantial metals, regulation of gene expression, regulation of protein function, and RNA processing. De-methylation is the event in contrast to methylation. Lysine can be methylated once, twice, or thrice through lysine methyltransferases. Lysine methylation acts as an essential part in how histones work together with proteins [6].

Proper methylation is essential for dangerous reactions in the body. It can cause a number of serious health issues including heart diseases [7], brain diseases such as depression and migraines [8], cancer [9, 10], and many more. It can occur on the nitrogen atoms of either back or sidechain of lysine (K), Arginine (R), histidine (H), alanine (A), proline (P), and glutamine (Q) residues, oxygen atoms of aspartate (D) and glutamate (E) residues as well as on the sulphur atom of cysteine (C) residue [11]. Among all of them, lysine (K) is the most frequently observed amino acid of methylation. Lysine residues accept up to three methyl groups forming mono-, di-and tri-methylated proteins, which are the main types of lysine methylation and are severe in several biological procedures [12].

It is an important challenge to identify lysine methylation sites experimentally without disturbing the overall sequence of the protein structure. Such type of modifications can be performed experimentally which is a time-consuming and expensive technique. In this regard, various researchers have used computational methodologies to identify lysine methylation by using the primary structure of the protein. In recent decades, researchers have made various contributions to improve numerous computational models in order to predict an element of a protein [13-22]. A number of computational models have been proposed for the prediction of PTM sites [23-29]. In the last few years, many studies have been conducted by previous researchers in the field of bioinformatics and computational biology, which help in identifying the function and characteristics of proteins [2, 14-16, 19-21, 23-27, 30-60]. Besides these, various papers have been reported targeting the prediction of PTM [2, 17, 20, 21, 23-28, 30-35, 37-51, 53-58, 61-68]. Struggles have been made for the prediction of protein domains. A novel method was introduced by merging the methods of RF, mRMR and IFS including the features of physicochemical and biological properties, sequence conservation, residual disorder, and solvent accessibility [69]. Sun and others noticed that the methylation position of CpG sites is another essential problem while studying gene regulation and indicates a robust relationship with the transcription factor binding sites (TFBS) involved. They established the models that are used to compare the modifications among regions and tissues [70]. Shao et al. established a predictor named BPB_pPMS, to identify methylation sites via Bi_profile Bayes feature extraction approach. It was only designed to predict the methylation position for lysine and arginine residues [71]. In this regard, another method was proposed using feature selection technique and nearest neighbour algorithm by Hu et al. [72]. This method works as a useful tool for biologists to find the possible methylated sites of proteins. A method called PMeS was developed by Shi et al. to increase the prediction of methylation sites depending upon an enhanced feature encoding scheme and SVM. When PMeS is used with other existing approaches, it provides enhanced predictive performance and greater strength [73]. Valavanis et al. studied the computational structure for the logarithmic ratio of methylated as well as un-methylated sites, quoted as M-value. The consequences presented here are linked to those derived by applying typical pre_processing and statistical selection procedures [74]. Li and co-workers in 2014 proposed a novel predictor called Methyl-SVMIACO, depending upon the Support Vector Machine and enhanced IACO Algorithm, to discover methylation sites. This algorithm is basically used to find the best feature subgroup and a parameter of SVM, whereas SVM is active in finding the methylation sites [75]. Qiu et al. determined a new predictor called iMethyl_pseAAC. In this prediction scheme, a sample of the peptide was framed via 346-dimensional vector designed as a result of combining physicochemical, biochemical and physical disorder data with overall pseudo amino acid composition [48]. Karagod and Sinha discovered a machine learning structure that produces greater accuracy than the previous MS-SPCA and EVORA methods for predicting the phases of different diseases like cancer using CpG data [76].

Although various efforts have been made for the prediction of methylation sites which have its own merit but problems still exist; they all need perfection to develop improved methods for the following characteristics: (i) the standard dataset, which was considered by previous researchers, needs to be restructured or updated by combining some novel and computational-based data, (ii) can be boosted by eliminating redundancy and duplicate sequences as compared to the existing ones, (iii) constructing statistical samples that are totally dependent on the sequence data, (iv) accuracy of the current models should be enhanced as some earlier models, (v) further enhancing the prediction quality as compared to others by using the computational method. For efficient prediction of methylation, it would be suitable to propose more exact models after considering these inefficiencies.

In the present study, a computational method is proposed using a broad feature extraction procedure for the prediction of Lysine (K) methylation. The dataset for this prediction is collected from two well-known sources namely, dbPTM and UniProt. Features which are relevant to the post-translational modification sites are extracted. A Neural Network (NN) is trained based on the extracted features using backpropagation technique [18, 77-79]. Consequently, the validation of the proposed model is achieved with various methods consisting of accuracy metrics, Mathew’s correlation coefficient (MCC), Sensitivity (Sn), Specificity (Sp) and Cross-validation testing. The first aim of this study is to make it easier for experimental researchers to acquire their expected data while the second is to simulate previous studies related to some extent. To understand these two aims, we follow the 5-step rule [80]. The whole process is carried out with the aid of Chou’s 5-step rule [81] which is followed in current studies [16, 20, 21, 31, 82-88]. As demonstrated by a series of recent publications [17, 19, 22, 23, 31, 33, 36, 38, 41, 65, 84, 89-104] and summarized in two comprehensive review papers [80, 105], to develop a really useful predictor for a biological system, one needs to follow Chou’s 5-step rule: (1) select or construct a valid benchmark dataset to train and test the predictor; (2) represent the samples with an effective formulation that can truly reflect their intrinsic correlation with the target to be predicted; (3) introduce or develop a powerful algorithm to conduct the prediction; (4) properly perform cross-validation tests to objectively evaluate the anticipated prediction accuracy; (5) establish a user-friendly web-server for the predictor that is accessible to the public. Papers presented for developing a new sequence-analyzing method or statistical predictor by observing the guidelines of Chou’s 5-step rules have the following notable merits: (1) crystal clear in logic development, (2) completely transparent in operation, (3) easy to repeat the reported results by other investigators, (4) high potential in stimulating other sequence-analyzing methods, and (5) very convenient to be used by the majority of experimental scientists.

MATERIALS AND METHODS

In this section, the overall process adopted for the prediction of lysine methylation is described in detail, as shown in Fig. . It involves three basic steps i.e. data collection, feature extraction, training neural network. In the first step, the benchmark datasets are collected from a renowned online database of proteins called UniProt [106] as well as dbPTM [107]. Sub-sequences which were most relevant to lysine methylation were extracted. After the extraction of the most relevant sequences, duplication in them was removed and carefully selected sequence data was used for training purpose. In the second step, feature extraction technique was applied to get a range of feature vectors (FV). In the end, the input matrix containing feature vectors (FVs) and an output matrix containing expected output were used to train the Neural Network (NN) via backpropagation technique. Furthermore, the trained model was used for the prediction of methylation sites. Afterwards, the trained model was validated on test dataset that will be explained under the validation part.

The Benchmark Datasets

The benchmark dataset collection is the first step according to the 5-step rule. To develop a statistical model, it is significant to initiate a consistent and standard dataset to train and test that model. The accuracy of the trained model would be fully unpredictable and meaningless if the standard dataset comprises of errors. The dataset was gathered from UniProt and dbPTM to predict lysine methylation sites. Universal Protein Resource (UniProt) is a broad, high-quality and freely available resource of protein sequence and annotation data whereas dbPTM is a unified resource for protein post-translational modifications (PTMs) data. DbPTM is a comprehensive database that combines experimentally verified PTMs from various databases and interprets potential PTMs for all UniProtKB protein entries. To collect positive samples, the database was downloaded from dbPTM in which a total of 226 positive samples were accumulated. From UniProt, 569 samples were collected, thus a total of 795 sequences were gathered.

Moreover, for the negative dataset, a converse query (same query as for the positive dataset but initiating with a NOT) was produced. The sequences observed were those that had clear experimental annotations with field PTM/Processing about their Lysine Methylation sites. Furthermore, the sequences that we found were only those proteins which contained the term, modified residues (FT). To further find out the reliability of the dataset, only those proteins were acquired where the observation was dependent on experimental assertion. Accordingly, the sequences for negative methylation sites against raw data involved 135826 instances. After obtaining these sites, 2000 negative sites were randomly selected. The composed dataset was filtered by eliminating the redundant sequences using CD-HIT [108], with a threshold of 0.6 (60% similarity). After that, 670 positive instances and 984 negative sites of lysine methylation were left in the dataset. Taking into account Chou’s scheme [81], a protein containing lysine site can be expressed as:

1

Amino acid code K is denoted by I_I in this equation, the character ρ is an integer, M- represents ρ -th upstream amino acid residue from the centre, M+ represents ρ +th downstream amino acid residue from the centre.(2ρ+1) a tuple can be illustrated in 2 types:

2

In the following condition, holds if the centre is methyllysine site, if it is not then holds. Set theory represents symbol ‘Ԑ’ as “a member of”.

Testing and training dataset is developed for the statistical prediction model. The model is trained using training dataset and then tested using testing dataset. The model is extensively illustrated [22], explaining that there is no compelling reason to isolate a benchmark dataset into two subsets if jackknife and cross-validation tests are used for testing the prediction model because the result acquired in this way is from a combination of many different independent dataset results. In this research paper, the ideal value of ρ for the test is 20, while the dataset has (2ρ+1)=41 residues. Considering all this, the dataset was minimized to

3

In the equation, T+ holds 670 positive samples, T- holds 984 negative samples and ∪ represents “union of two sets”. In total, 670+984 = 1654 samples are included in the benchmark dataset (Supplementary information S1). Frequency plots for positive and negative sequences are presented in Figs. and ), respectively [109]. The significance of the length of neighbouring residues was based on examining and testing in order to get the best peak result.

Feature Extraction

For assistance in feature vector construction, Chou’s computational model sample formation was implemented [110]. A feature is a numerical and computable property of protein represented as n-dimension by the vector. A feature vector represents multiple properties relevant to the protein sequence. To study the properties of the protein, the construction of the feature vector holds the primary position. An array of amino acids is utilized to develop a feature vector that increases the probability of site prediction in protein. Protein’s performance is determined by the location of amino acid; a slight change in the location modifies protein qualities [111]. Feature vector sequences represented by the feature vector are broadly utilized in predicting different structural characteristics.

Site Vicinity Vector

Site vicinity vector is determined in terms of a sub-group of the protein sequence. αq shows probable post-translational modification and its neighbouring amino acids are represented as:

4

It also comprises possible PTM sites with its neighbouring residues represented as:

5

In this equation, & is known as a smaller integer number and is ideally chosen via examining and experimentation. The site vicinity vector frames a segment of the comprehensive feature vector which is allocated remarkable numerical qualities replacing all residue positions. Only twenty amino acids are important for the extraction of feature vectors where each amino acid is allotted an exclusive integer.

Statistical Moments

Statistical moments are the quantitative measures that are essentially used to represent an accumulation of data. A moment is a specific quantitative measure of the shape of a set of points. Researchers proved that statistical moments are suitable to make features from a known pattern. Various researchers have used these moments to capture the main features and describe the functionalities of a particular pattern [18, 77, 79]. The resolution to the proposed problem is pursued with the help of several moments such as raw moments, central moments, and Hahn moments along with the origin and centroid of the data as used in several studies [18, 77, 79]. In a recent study, it has been observed that discrete orthogonal moments produced better results than continuous orthogonal moments for discrete and quantized data. These orthogonal moments have the ability to transform the object illustrations with the lowest amount of loss of data.

A protein sequence is denoted as:

6

With a specific end goal to calculate two-dimensional moments, the one-dimensional design is reformed into a two-dimensional design by using a row-major scheme. The length of the two-dimensional matrix is calculated by taking the square root of the length of the protein.

7

Where n is the measurement of the two-dimensional matrix and k is the length of the protein.

Furthermore, to adjust all the components of the protein sequence 𝑃, a new matrix 𝑃' is designed along with n * n dimensions.

8

A function is used to convert the matrix into .

9

Where is populated in a sequence substantial way.

The substance of two-dimensional matrix 𝑃' is considered to calculate the moments till order 3; the raw/crude moments are calculated from the given expression.

10

Where, i+j is the direction of the moment. The calculated moments are listed as:

up to direction/order 3.

The central moments use the centroid of the data as the reference point. These points can be represented as , where,

11

It can be calculated after the calculation of raw moments by using the given equation,

12

Hahn moments can be computed after the transformation of 1D representation 𝑃 into a 2D square matrix 𝑃'. 2D Hahn moments require a square matrix as 2D input data. Hahn polynomial of direction/order 𝑛 is known as:

13

The above equation utilizes the pochhammer representation summed up as,

14

And can also be simplified via the Gamma Operator

15

Therefore, raw/crude values of orthogonal Hahn moments are generally mounted by utilizing a weight function and also a square root as given below:

16

While,

17

Standardized Hahn moments for 2D discrete matrix are calculated by the given expression,

18

2D discrete orthogonal moments such as raw moments, central moments and Hahn moments are calculated up to direction/order 3. The whole procedure is carried out by following the method defined in various studies [13, 17, 19-23, 61, 97].

Position Relative and Reverse Position Relative Incidence Matrix

The initial phase in feature extraction is to calculate the matrix form of the input protein probe. For this reason, the length of the protein sequence is utilized to produce PRIM and RPRIM. These matrices are then utilized for the figuring of moments through which included vectors are shaped. A protein sequence 𝑆 with the addition of 𝑁 amino acid residues is characterised through PRIM as shown below:

19

RPRIM can also be represented as:

20

In the given protein sequence, the indication of the gain of 𝑖th position residue is determined by B→𝑗 for PRIM and Z→ for RPRIM. In the genetic evolutionary procedure, this gain is replaced by amino acid form. The values of j = 1, 2. . . 20 are the presentation of the sequential order of 20 native amino acid residues. The method is further defined in other studies [13, 17, 20-22].

Frequency Matrix

Another matrix called a frequency matrix is designed which covers the information about the composition of protein structure. The main purpose of using this matrix is that it basically extracts the information of the sequence which has previously been mined into position relative incidence matrix (PRIM). The matrix is shown as:

(21)

Where shows the frequency of occurrence of ith native amino acid.

Accumulative Absolute Position Incidence Vector (AAPIV)

The frequency matrix was computed for extracting the compositional information but it did not provide the relative positions of residues. Therefore, a new matrix is formed named Accumulative Absolute Position Incidence matrix (AAPIV). AAPIV has a length of 20 elements where each element grasps the sum of all the ordinal values occurring in the primary sequence at their respective locations.

Consider AAPIV to be represented as:

(22)

Therefore, ith element of AAPIV is calculated as given below:

(23)

Where represents the position of the occurrence of amino acid residues in the sequence. Further information regarding this protocol can be found in other studies [13, 17, 20-22].

Reverse Accumulative Absolute Position Incidence Vector (RAAPIV)

In order to extract deep and obscure information about the relative positioning of each amino acid residue, a reverse accumulative absolute position incidence vector (RAAPIV) is used. RAAPIV is developed by reversing the primary sequence and then producing AAPIV by using that reversed sequence.

Hence, RAAPIV having 20 elements is represented as:

(24)

RAAPIV is calculated on the same protocol as AAPIV.

Training of Operational Algorithm

The neural network is the most prevailing technique which is used to resolve decision problems. This network is composed of an enormous number of interrelated processing elements called neurons, which works correspondingly to solve a precise decision problem. Neural networks process the information in a similar manner as the human brain. As it takes the information from the environment and obtains experience, the neural network also embraces the same method. It takes many inputs as well as produce one output depending on the knowledge gained after each input throughout the training procedure. When the training procedure is over, the neural network apparently performs in a manner that categorises each known input with a suitable accuracy measure.

Throughout the overall learning procedure of the neural network, the basic goal is to decrease an error. This network modifies its weights during each iteration, in a way that the error is reduced between the preferred output and the real output which results in enhanced learning and improved accuracy. The neural network starts its training based on two values including the input values along with the initial weights that are given to the network as shown in Fig. .

Neural networks are mostly referred to in terms of their depth, including the number of layers they have between input and output, called the hidden layers. They can also be labelled by the number of hidden nodes the model has or in terms of how many inputs and outputs each node has. Variations in the Neural Network (NN) model allow various forms of forward and backward propagation of information among iterations. In this study, a Multi-layered Back Propagation Neural Network (MBPNN) model has been used to tackle the research problem as used in a study [22]. The model is presented as given below in Fig. .

The data sets were constructed containing positive and negative samples, and a feature vector (FV) is then constructed using the datasets for the prediction of Lysine Methylation sites consisting of a large number of coefficients. These two FVs are then merged to form an input matrix whereas each input vector is considered as both positive and negative samples in an additional output matrix. These two matrices are employed to train the Multi-Layer Neural Network. The input matrix iterates the input to the neural network while the output matrix is used to compute the errors through backpropagation methodology. To increase the prediction accuracy and reduce an error rate, gradient descent algorithm and adaptive learning rate were used.

Gradient Descent and Adaptive Learning

Backpropagation neural network uses the gradient descent algorithm. It makes several attempts to reduce its error along its gradient to increase the overall performance of the network. Gradient descent is a simple optimization technique that can be used to solve machine learning problems. It is an algorithm used to find the parameter values of the training function that minimizes the cost of that function. Gradient descent starts its working with an initial set of parameter values and iteratively transfers a set of parameter values which minimizes the objective function. Therefore, minimization is achieved by moving toward the opposite direction of the gradient function. To achieve successive results,

gradient function is computed via calculating the rate of change. As gradient descent is a way to minimize an objective function, objective function parameterized by model’s variable is assessed by updating the parameters in the opposite direction of the gradient of the opposite function with respect to the parameters. On the basis of the above concept, these parameters are recomputed for each phase through the relation given below.

(25)

Where Gamma is known as the learning rate, generally kept constant, and the performance of the algorithm is significantly determined by the learning rate. It usually concludes how quick the function is reduced. An appropriate learning rate may be hard to choose. It can be based on two conditions; if the learning rate is excessively small then it takes more time to achieve concurrence while if the learning rate is excessively large then the capacity of the function may get affected and never achieve the optimal point. In adaptive learning, the algorithm is permitted to make decisions and acclimate the learning process depending upon the information it already has from the existing data sets.

This algorithm differs from the estimation of the learning rate that is dependent on the execution of the calculation. Learning rate is different from the end goal as the size is limited in each rotation. and are considered as the two progressively assumed parameters. The assigned weights are re-calculated by applying the above two parameters and the concerning results, thus the errors are similarly calculated.

Subsequently, if the errors are more significant when linked with earlier epoch, at that point the learning rate is expanded, weights are disposed off and more recent estimation of is enumerated. Furthermore, with the enumeration being smaller, the learning rate is expanded. Hypothetically, the learning rate can change on every epoch, appropriately if are the main parameters calculated for every epoch, and afterwards, they are calculated via the following condition.

(26)

Where, Gamma is the learning rate which is utilized for mth epoch. The algorithm confirms that the learning rate is difficult to achieve as the gradient function is minimized at every epoch. The following condition consistently fulfils at the time of the determination of the learning rate.

RESULTS AND DISCUSSION

The proposed model is employed for the prediction of lysine-methylated sites in protein molecules depending upon the specific amino acid representation of proteins. It plays a vital role in the reformation of protein molecules or protein folding. The prediction is based on the position variant feature extraction techniques. The overall process of validation tests and the results acquired from that validation are described in detail in the current section.

Estimated Accuracy

The objective evaluation of a newly developed predictor is a very important aspect, which helps to assess the success rate of that model [80]. However, for such objective evaluation, one needs to consider two important factors which are: (i) selection of accuracy metrics and (ii) the testing method employed to validate the model. Herein, firstly we formulate the metrics for objective evaluation and then employ various validation methods.

Formulation of Metrics

For objective evaluation, one needs to consider the metrics and method of evaluation. The most observed practice for the objective evaluation of the predictor is the use of accuracy metrics which are (1) Accuracy (Acc), which is used for the estimation of the overall accuracy of that prediction model, (2) Sensitivity (Sn), which is used for the estimation of positive sample prediction capability, (3) Specificity (Sp), which is used for the estimation of negative sample prediction capability, and (4) Mathews Correlation Coefficient (MCC), which is used for the estimation of prediction model stability. Initially, these measures have been introduced in a study [112], and a set of four intuitive equations has been derived in various studies [113, 114] for all these measures, which are:

Where represents the total number of non-methyllysine sites, correctly predicted as non-methyllysine sites by iMethylK_pseAAC. represents the total number of non-methyllysine sites which are predicted incorrectly as methyl-lysine sites by iMethylK_pseAAC. Moreover, is the total number of methyllysine sites which are correctly predicted as methyllysine sites by iMethylK_pseAAC and is the total number of methyllysine sites which are predicted incorrectly as the non_protease by iMethylK_pseAAC. Thus, Eq. (28) explains the specificity, sensitivity, overall-accuracy, and stability in a more easy to understand and intuitive manner, particularly when we talk about MCC [115-117].

This set of perceptive metrics has been used by a number of modern publications [33-35, 38-41, 43, 91, 99, 113, 118-138] but only for binary labelled data. Multi-label prediction is a completely different problem, which has been more popular in computational biology [139-141] and biomedicine [142]. Thus, it requires a different kind of metrics [143]. For the multi-label systems (where a sample may simultaneously belong to several classes), the existence of which has become more frequent in system biology [84, 144-150], system medicine [151, 152] and biomedicine [47], a completely different set of metrics as defined in a study [153] is absolutely needed.

Self-consistency Testing

Self-consistency test is basically used to obtain the confusion matrix. It is one of the important tests used to substantiate the efficiency of the predictive model in which the training datasets were used for testing the model. The reason for conducting the self-consistency test is that we already know the actual true positive of benchmark dataset. The results of self-consistency are shown in Table ; it can be observed that iMethylK_pseAAC has 98.32% Acc, 98.76% Sp, 97.51% Sp, and 0.98 MCC.

The Receiver Operating Characteristics (ROC) is an additional essential tool used to explain the distribution of the experimental results [154]. It allows creating a curve and a complete sensitivity and specificity report. The curve is made by plotting the true positive rate (TPR) against the false positive rate (FPR) for a specific decision threshold. The TPR (sensitivity) depicts how many correct positive outcomes arise between all the positive sequences while FPR (specificity) expresses how many incorrect positive outcomes arise between all of the negative sequences accessible during the prediction. Moreover, Area under the Curve (AUC) is an extent of how well a parameter can differentiate between TPR and FPR. It represents the overall accuracy of the proposed system. In short, each prediction result or instance of a confusion matrix signifies one point in the ROC space. A graphical representation of ROC for the proposed model is shown in Fig. .

10-fold Cross-validation

Cross-validation is a procedure to estimate the predictive model by dividing the original sample into a training set to train the model, and a test set to evaluate it. It is useful in the situation when the accurate estimation of the predictive model is required. In a prediction problem, a model is typically a dataset of known data in which training is performed (training dataset), and a dataset of unknown data against which the model is tested (testing dataset).

Cross-validation is a technique to develop a possibility that the suggested method is smooth while an observable validation test set is not accessible. In k- fold cross-validation, the original sample is randomly split into equal size subsamples. A single subsample obtained from subsamples is used as the validation data for testing the model, and the remaining subsamples are used as training data. The procedure is repeated times where, with each of the subsamples used exactly once as the validation data as shown in Fig. . The mean for all the values of is used to produce a single estimation which is the result of the cross-validation.

Therefore, let be considered as the population of samples that contains equall positive and negative samples denoted as;

Where is any random positive and negative sequence. Data set is split into equivalent size subgroups essentially given as:

And

Similarly, the subsets are nominated arbitrarily such that the previous dimensions are parallel. i.e.

Where and are some random sets, therefore in a distinct iteration the components of the set are excluded and the model is trained on the remaining dataset. After training, the trained model is used to test the excluded data and then the accuracy rate is calculated. The whole cross-validation result is calculated by just taking the average of the results of all the k iterations.

The effects of cross-validation prove that the proposed model sufficiently performed well than the other predictors. The average of the cross-validation testing results is depicted in Table .

Jackknife Testing

The effectiveness of cross-validation can be remarkable in the case of diversified and biased data. Jackknife testing is also executed by various researchers for validation [17, 19-23, 29-31, 33, 36, 42, 51, 59, 68, 82-88, 92, 96, 135, 148, 155-164]. Out of the frequently used methods, jackknife is the most common. There are few other techniques to test the predictor through randomly selected or portioned dataset. There are a lot of ways for partition, therefore, results can either be good or else through each partition. Due to the use of very small selection in this subsampling technique, it is inevitable for different selections to yield different results.

The jackknife can be utilized to evaluate the real predictive power of such models by anticipating the dependent variable estimations of every insight considering the insight as another observation. Keeping in mind the end goal, the predicted values of every new insight are acquired from the model based on the sample of insights minus the insights to be predicted. The jackknife, in this perspective, is a technique which is utilized to get a fair prediction, to assess the ability to produce unique results, (i.e., an arbitrary effect) and to limit the hazard of over-fitting.

The main objective of jackknife is to evaluate a parameter of a population of interest from a random sample of data from this population. The parameter is indicated as θ, its measurement from a sample is denoted by T, and its jackknife measure is denoted by Ai for the ith iteration. The sample of N observations is a set represented as:

The sample measure of the parameter is a factor of the observation in the sample. The dataset used to compute leaves out the ith element in the population using the dataset given as:

The trained NN is simulated through the feature vector of all the samples in . The accuracy of this permutation is calculated by using the number of false positives and false negatives as well as the number of true positives and true negatives. The average of all the values of is calculated .

Where signifies the whole accuracy of the predictors and signifies the total amount of observations. The results for jackknife testing are shown in Table .

Comparison with Existing Methodologies

In this section, we compare the proposed model with some existing methodologies as shown in Table . These existing predictors have used the same classifier named SVM. The datasets used by previous researchers were imbalanced, outdated and the feature construction techniques did not extract important information which resulted in a low accuracy rate. In the proposed prediction system, the Neural Network is used to get high accuracy as some existing methods. Table shows the existing methods i.e. iMethyl_pseACC [48], BPB_pPMS [71] and PMeS [73]. iMethyl_pseACC achieved an accuracy of 75% through independent testing and 70.74% using jackknife testing and BPB_pPMS achieved an accuracy of 91.19% through independent testing and 75.51% with 5-fold cross-validation. Similarly, PMeS achieved an accuracy rate of 89.16% by using 10-fold cross-validation and 85.87% through independent testing but the proposed model achieved an accuracy of 96.7% through self-consistency testing, 91.61% through 10-fold cross-validation and 93.42% with jackknife testing which means it is highly accurate by using the backpropagation methodology.

Similarly, comparative results of ROC for the proposed model and the existing models are shown in Fig. . It is clearly shown in the figure that the Area under cure line in blue colour has almost 0.967 true positive rate which means that the accuracy of the proposed model is 96.7% and it is observed that the proposed predictor is highly accurate than the existing ones.

Using graphic approaches to study biological and medical systems can provide an intuitive vision and useful insights for analyzing complicated relations therein, as indicated by many previous studies on a series of important biological topics [165-178], particularly in enzyme kinetics, protein folding rates [172, 179-181], and low-frequency internal motion [179-184].

The importance of methylation has been highlighted in several existing research. Analysts have suggested different computational methodologies to recognize lysine methylation sites. Researchers have put their greatest determination towards the improvement of prediction accuracy and to distinguish lysine methylation sites. In this research, we focus on attaining greatest accuracy by overwhelming disadvantages within the existing ones. A few key highlights make the studied methodology more predictable as well as precise from the existing methodologies. The collected benchmark dataset is latest and balanced as experimental observations have been incorporated. Also, it is non-repetitive and has a defined length. Moreover, it is different in nature as it creates essential sequences from various entities. In particular, the feature extraction method is position and scale variant which is able to carefully extract profound ambiguous patterns. Furthermore, to gauge the performance of the prognostic model, complete 10-fold cross-validation and jackknife testing are implemented [36, 185]. Some existing approaches depicted previously have distinctive requisites in their methodologies. The datasets used by the previous researchers were imbalanced and outdated and the feature construction techniques do not mine the important information [48, 71, 73]. In this research, non-repetitive and up-to-date datasets of massive size have been employed and comprehensive features have been mined. After the mining of most relevant features, early experiments were directed with lesser feature vectors. These features were then extended by constant testing and experimentation to the point that most exact outcomes were accomplished. The feature which has been used for the proposed model helps in revealing profound ambiguous patterns, about position and composition having the most extreme significance. Moreover, different performance metrics have been processed and compared with some previous models. Finally, 10-fold cross-validation, as well as jackknife testing, have been used in order to verify and validate the accuracy of the proposed model.

Webserver

The final step of Chou’s 5-steps rule is the development of user-friendly publicly available web-server for the ease of users and biologists as explained in recent publications by various authors [45, 116, 123, 126, 145, 146, 149, 151]. As pointed out in a study [183] and demonstrated in a series of recent publications [23, 44, 45, 65, 82-85, 89, 92, 93, 97, 98, 103, 133, 138, 144-150, 186], user-friendly and publicly accessible web-servers represent the future direction for developing practically more useful prediction methods and computational tools. Actually, many practically useful web-servers have significantly increased the impacts of bioinformatics on medical science [63], driving medicinal chemistry into an unprecedented revolution [187]. Accordingly, in our future work, we shall strive to establish a web-server for the new method presented in this paper. However, the source code for iMethylK_pseAAC is available at: https://github.com/umtwaqar/iMethylK_pseAAC.

CONCLUSION

Methylation is one of the most significant Post-Translational Modification occuring on lysine residues which can cause dangerous reactions in the body. To appropriately obtain the information of lysine methylation sites is significant for studying and examining various human diseases. In this research, feature vectors are formed by using several feature extraction techniques including scale and position variant features and raw, central and Hahn moments. The proposed model could effectively identify the lysine methylation sites by using backpropagation methodology. The neural network is an effectual method for supervised and unsupervised learning problems. The prediction algorithm developed for lysine methylation also employs supervised learning. The results obtained from the trained neural network are authenticated by 10 fold cross-validation and jackknife testing. It proves that the model beats the existing methods such as iMethyl_pseACC, BPB_pPMS and PMeS. Also, the accuracy of the proposed model is proved with the help of accuracy metrics including sensitivity, specificity, Accuracy and Mathew’s correlation coefficient which demonstrates that the accuracy of the model provides an effective and exact rate and time in comparison with the previous ones like iMethyl_pseACC, BPB_pPMS, PMeS.

Sn=1-N-+N^+  ≤Sn≤1 Sp=1-N+-N^- ≤Sp≤1  Acc=1-N-++N+-N^++N^- ≤Acc≤1  MCC= 1-N-+N^++N+-N^-1+N+--N-+N^+ 1+N-+-N+-N^- -1≤MCC≤1

(28)

Table 1

Results for self-consistency testing for iMethylK_pseAAC.

Predictor	Accuracy Metrics
	Acc (%)	Sp (%)	Sn (%)	MCC
iMethylK_pseAAC	96.7	97.7	95.8	0.934

Table 2

Results for 10-fold cross-validation of iMethylK_pseAAC.

Folds	Sn (%)	Sp (%)	MCC	Acc (%)
K1	79.5	94.6	0.71	92.1
K2	81.3	92.7	0.67	91.2
K3	68.4	92.5	0.59	88.7
K4	83.3	94.6	0.74	92.9
K5	86.5	95.5	0.79	94.1
K6	85.7	91.9	0.66	91.2
K7	82.4	93.6	0.70	92.0
K8	73.8	94.9	0.69	91.2
K9	84.8	97.3	0.72	92.4
K10	73.7	93.5	0.65	90.3
Average	79.88	94.11	0.692	91.61

Table 3

Jackknife validation results for iMethylK_pseAAC (Average of n-iterations).

Predictor	Accuracy Metrics
	Sn (%)	Sp (%)	Acc (%)	MCC
iMethylK_pseAAC	92.34	97.80	93.42	0.82

Table 4

Comparison between existing methodologies.

Predictors	Classifiers	Validation Methods	Sn%	Sp%	Acc%	MCC
iMethylK_pseAAC	Neural Network	Self-consistency testing	95.8	97.7	96.7	0.9345
		10-fold cross validation	79.88	94.11	91.61	0.692
		Jackknife testing	92.34	97.80	93.42	0.82
iMethyl_pseACC [ 48 ]	SVM	Independent testing	100.00	61.54	75.00	0.60
		Jackknife testing	68.58	72.99	70.74	0.42
BPB_pPMS [ 71 ]	SVM	Independent testing	71.43	91.51	91.19	-
		5-fold cross validation	70.05	77.08	75.51	0.3400
PMeS [ 73 ]	SVM	10-fold cross validation	84.38	93.94	89.16	0.786
		Independent testing	76.09	95.65	85.87	0.7315