Progresses in Predicting Post-translational Modification

Abstract

Identification of the sites of post-translational modifications (PTMs) in protein, RNA, and DNA sequences is currently a very hot topic. This is because the information thus obtained is very useful for in-depth understanding the biological processes at the cellular level and for developing effective drugs against major diseases including cancers as well. Although this can be done by means of various experimental techniques, it is both time-consuming and costly to determine the PTM sites purely based on experiments. With the avalanche of biological sequences generated in the post-genomic age, it is highly desired to develop bioinformatics tools for rapidly and effectively identifying the PTM sites. In the last few years, many efforts have been made in this regard, and considerable progresses have been achieved. This review is focused on those prediction methods that have the following two features. (1) They have been developed by strictly observing the 5-steps rule so that they each have a user-friendly web-server for the majority of experimental scientists to easily get their desired data without the need to go through the detailed mathematics involved. (2) Their cornerstones have been based on Pseudo Amino Acid Composition (PseAAC) or Pseudo K-tuple Nucleotide Composition (PseKNC), and hence the prediction quality is generally higher than most of the other PTM prediction methods.

Introduction

Post-translational modification, or PTM, means the covalent and generally enzymatic modification of proteins right after they are biosynthesized. After being synthesized by ribosomes, proteins may undergo PTM to form the mature protein products. PTMs can occur on the amino acid side chains of a protein or at its C- or N- terminus. They can covalently modify the existing functional group of an amino acid and make it have other functional group. Therefore, the chemical repertoire of the 20 standard amino acids can be considerably extended via the process of PTMs.

According to their occurrence in three different type of biological sequences, PTMs can be classified into the following three different categories: (1) PTLM (post-translational modification) in proteins, (2) PTCM (post-transcriptional modification) in RNA, and (3) PTRM (post-replication modification) in DNA. PTMs play a key role in providing bio-macromolecules with structural and functional diversity, as well as in regulating cellular plasticity and dynamics. Meanwhile, PTMs are also closely associated with many major diseases including cancer, Alzheimer’s, and Parkinson’s. Therefore, identifying the PTM sites in biological sequences is very important for both basic research and drug development.

Historical Reflection

Before going on, it is illuminative to make a historical reflection. For quite a long period of time, the information derived by the computational approaches were not trusted very much by most experimental scientists due to the notorious local minimum problem (Chou and Zhang 1995). Actually, they only trusted the results determined by the experiments, and thought that computational results were not reliable unless they had been confirmed by experiments. This kind of situation has been changed during the last two decades or so owing to the rapid development of structural bioinformatics and sequential bioinformatics. For the 3D structures of proteins, what they trusted most were those determined by the X-ray crystallography. Unfortunately, it is time-consuming and expensive, and not all proteins can be successfully crystallized. Membrane proteins are difficult to crystallize and most of them will not dissolve in normal solvents. Accordingly, so far very few membrane protein structures have been determined. NMR is indeed a very powerful tool in determining the 3D structures of membrane proteins (see, e.g., Chou et al. 1998, 1999, 2001; Oxenoid et al. 2016; Dev et al. 2016; Schnell and Chou 2008; Berardi et al. 2011; OuYang et al. 2013; Wang et al. 2009a; Fu et al. 2016; Oxenoid and Chou 2005; Call et al. 2006, 2010; Gagnon et al. 2010; Bruschweiler et al. 2015; Cao et al. 2017; Piai et al. 2017; Pan et al. 2019a), but it is also time-consuming and costly. In order to acquire the structural information in a timely manner, a series of 3D protein structures have been developed by means of structural bioinformatics tools (see, e.g., Chou et al. 1997, 2000; Chou 2004a, b, c, 2005a, b, c; Chou and Howe 2002; Wang and Du 2007; Wang et al. 2009b; Li et al. 2011; Ma et al. 2012) and they have been found very useful in conducting mutagenesis studies (Chou 2004d) for rational drug design. Meanwhile, facing the explosive growth of biological sequences discovered in the post-genomic age, to timely use them for drug development, a lot of important sequence-based information have been deducted by various sequential bioinformatics tools such as PseAAC approach (Chou 2001, 2005d, e) and PseKNC approach (Chen et al. 2014a, 2015; Guo et al. 2014). Actually, the rapid development in sequential bioinformatics and structural bioinformatics have driven the medicinal chemistry undergoing an unprecedented revolution (Chou 2015), in which the computational biology has played increasingly important roles in stimulating the development of finding novel drugs (Zhong and Zhou 2014, 2016, 2017).

As it was in the last few years that many bioinformatics tools were developed for predicting the PTM sites in biological sequences (Chou 2015; Xie et al. 2013; Xu and Ding 2013; Xu et al. 2013, 2014a, b; Jia et al. 2014, 2016a, b, c, d; Qiu et al. 2014, 2015, 2016a, b, c, 2017a, b, c, 2018a; Zhang et al. 2014a; Chen et al. 2015b, 2016, 2018a, b; Ju et al. 2016; Liu et al. 2016; Xu 2016; Feng et al. 2017; Ju and He 2017a; Liu and Xu 2017; Xu and Li 2017; Akbar and Hayat 2018; Chandra et al. 2018; Ghauri et al. 2018; Ju and Wang 2018; Khan et al. 2018a, b; Sabooh et al. 2018; Hussain et al. 2019a; Li et al. 2019; Wang et al. 2019; Ning et al. 2019; Ehsan et al. 2019) in compliance with the Chou’s 5-steps rule (Chou 2011) by going through the following five procedures: (1) how to select or construct a valid benchmredict subcellular localization of mark dataset to train and test the predictor; (2) how to represent the samples with an effective formulation that can truly reflect their intrinsic correlation with the target to be predicted; (3) how to introduce or develop a powerful algorithm to conduct the prediction; (4) how to properly perform cross-validation tests to objectively evaluate the anticipated prediction accuracy; (5) how to establish a user-friendly web-server for the predictor that is accessible to the public.

Many prediction methods as reported in refs. (Xu and Ding 2013; Xu et al. 2013, 2014a, b; Qiu et al. 2014, 2015, 2016b, c, 2017a, b, c, 2018a; Chen et al. 2012, 2013, 2014b, c, 2015b, 2016a, b, c, 2017, 2018a, b, c, d; Jia et al. 2015, 2016e, 2016; Liu 2015a, 2016a, b, c, d; Feng et al. 2017; Liu and Xu 2017; Xu and Li 2017; Ghauri et al. 2018; Khan et al. 2018a, b; Hussain et al. 2019a, b; Ning et al. 2019; Ehsan et al. 2019; Min and Xiao 2013; Liu et al. 2014a, b, 2015b, c, 2016b, c, 2017, 2018a, b, c; Xiao et al. 2013a, 2015; Ding et al. 2014; Fan et al. 2014; Lin et al. 2014; Qiu and Xiao 2014; Xu et al. 2015; Liu and Long 2016; Xiao et al. 2016, 2017, 2018a, b, c; Zhang et al. 2016, 2018, 2019; Cheng and Xiao 2017a, b, 2018a, b, c, d, e; Cheng et al. 2017a, b, c; Liu and Yang 2017; Chou et al. 2018; Ehsan et al. 2018; Li et al. 2018a, b, c; Song et al. 2018a, b, c; Su et al. 2018; Wang et al. 2018a, b; Yang et al. 2018; Jia et al. 2019; Khan et al. 2019a, b; Lu et al. 2019a, b; Chou 2019; Awais et al. 2019; Niu et al. 2019) have been presented by strictly observing the Chou’s 5-steps rule (Chou 2011), sharing the following notable merits: (1) crystal clear in logic development, (2) complete transparent in operation, (3) quite easy to repeat the reported results by others, (4) holding high potential in stimulating other sequence-analyzing methods, and (5) very convenient to be used by broad experimental scientists.

Therefore, focused in the current review paper are only those PTM prediction methods that were born through the Chou’s 5-steps rule (Chou 2011). As for the importance of the 5-steps rule and how to use it in developing new predictor for proteome and genome analyses, see an insightful Wikipedia article at https://en.wikipedia.org/wiki/5-step_rules.

Besides, with the avalanche of biological sequences in the post-genomic era, one of the most important but also most difficult problems in computational biology is how to express a biological sequence with a discrete model or a vector, yet still considerably keep its sequence-order information or key pattern characteristic. This is because all the existing machine-learning algorithms [such as “Optimization” algorithm (Zhang 1992), “Covariance Discriminant” or “CD” algorithm (Chou and Elrod 2002; Chou and Cai 2003), “Nearest Neighbor” or “NN” algorithm (Hu et al. 2011), and “Support Vector Machine” or “SVM” algorithm (Hu et al. 2011; Cai et al. 2006)] can only handle vectors as elaborated in a comprehensive review (Chou 2015).

However, a vector defined in a discrete model may completely lose all the sequence-pattern information. To avoid completely losing the sequence-pattern information for proteins, the pseudo amino acid composition (Chou 2001) or PseAAC (Chou 2005d) was proposed. Ever since the concept of Chou’s PseAAC was proposed, it has been widely used in nearly all the areas of computational proteomics (see, e.g., Xie et al. 2013; Jia et al. 2014; Zhang et al. 2014a; Ju et al. 2016; Ju and He 2017a; Akbar and Hayat 2018; Ghauri et al. 2018; Ju and Wang 2018; Sabooh et al. 2018; Hussain et al. 2019a, b; Wang et al. 2019; Ning et al. 2019; Ehsan et al. 2019; Zhou et al. 2007; Ding and Zhang 2008; Fang et al. 2008; Jiang et al. 2008a, b; Li and Li 2008; Lin 2008; Lin et al. 2008; Nanni and Lumini 2008; Zhang and Fang 2008; Zhang et al. 2008; Zhang et al. 2008; Zhang et al. 2008; Chen et al. 2009, 2012; Ding et al. 2009; Georgiou et al. 2009; Li et al. 2009, 2012, 2014; Lin et al. 2009; Qiu et al. 2009, 2010, 2011, 2017d; Zeng et al. 2009; Esmaeili et al. 2010; Gu et al. 2010; Mohabatkar 2010; Sahu and Panda 2010; Yu et al. 2010; Guo et al. 2011; Lin and Wang 2011; Mohabatkar et al. 2011; Mohammad et al. 2011; Zou et al. 2011; Cao et al. 2012, 2013; Du et al. 2012; Fan and Li 2012a, b; Hayat and Khan 2012; Liao et al. 2012; Liu et al. 2012, 2013, 2015d, e; Mei 2012a, b; Nanni et al. 2012a, b, 2014; Niu et al. 2012; Qin et al. 2012; Ren et al. 2012; Sun et al. 2012; Zhao et al. 2012a, b; Zia-ur-Rehman 2012; Chang et al. 2013; Chen and Li 2013; Fan et al. 2013; Fan and Li 2013; Georgiou et al. 2013; Gupta et al. 2013; Huang and Yuan 2013a, b, c; Khosravian et al. 2013; Lin et al. 2013; Mohabatkar et al. 2013; Pacharawongsakda and Theeramunkong 2013; Qin et al. 2013; Sarangi et al. 2013; Wan et al. 2013; Wang et al. 2013; Xiaohui et al. 2013; Du et al. 2014; Hajisharifi et al. 2014; Han et al. 2014; Hayat and Iqbal 2014; Kong et al. 2014; Mondal and Pai 2014; Zhang et al. 2014b, c, 2015; Zuo et al. 2014; Ahmad et al. 2015, 2016; Ali and Hayat 2015; Dehzangi et al. 2015; Fan et al. 2015; Huang and Yuan 2015; Khan et al. 2015; Kumar et al. 2015; Mandal et al. 2015; Sanchez et al. 2015; Sharma et al. 2015; Wang et al. 2015; Zhang 2015; Behbahani et al. 2016; Fan et al. 2016; Jiao and Du 2016; Kabir and Hayat 2016; Tahir and Hayat 2016; Tang et al. 2016; Tiwari 2016; Xu et al. 2016; Zou and Xiao 2016a, b; Meher et al. 2017; Huo et al. 2017; Jiao and Du 2017; Ju and He 2017b; Khan et al. 2017; Liang and Zhang 2017, 2018; Rahimi et al. 2017; Tahir et al. 2017; Tripathi and Pandey 2017; Xu et al. 2017; Yu et al. 2017a, b; Ahmad and Hayat 2018; Al Maruf and Shatabda 2018; Arif et al. 2018; Butt et al. 2018, 2019; Contreras-Torres 2018; Cui et al. 2018; Fu et al. 2018; Javed and Hayat 2018; Krishnan 2018; Mei et al. 2018; Mei and Zhao 2018a, b; Mousavizadegan and Mohabatkar 2018; Qiu et al. 2018b; Rahman et al. 2018; Sankari and Manimegalai 2018; Srivastava et al. 2018; Tahir et al. 2019a, b; Zhang and Kong 2018, 2019; Zhang and Duan 2018; Zhang and Liang 2018; Zhang et al. 2018; Zhao et al. 2018; Adilina et al. 2019; Ahmad and Hayat 2019; Chen et al. 2019; Kabir et al. 2019; Le et al. 2019; Pan et al. 2019b; Shen et al. 2019; Tian et al. 2019) as well as a long list of references cited in Chou (2017).

Because it has been widely and increasingly used, four powerful open access soft-wares, called ‘PseAAC’ (Shen 2008), ‘PseAAC-Builder’ (Du et al. 2012), ‘propy’ (Cao et al. 2013), and ‘PseAAC-General’ (Du et al. 2014), were established: the former three are for generating various modes of Chou’s special PseAAC (Chou 2009); while the fourth one for those of Chou’s general PseAAC (Chou 2011), including not only all the special modes of feature vectors for proteins but also the higher level feature vectors such as “Functional Domain” mode (see Eqs. 9–10 of Chou 2011), “Gene Ontology” mode (see Eqs. 11–12 of Chou 2011), and “Sequential Evolution” or “PSSM” mode (see Eqs. 13–14 of Chou 2011).

Meanwhile, the idea of PseAAC was extended to generate various modes of feature vectors for DNA and RNA sequences (Chen et al. 2014a, 2015a; Guo et al. 2014; Chen and Lin 2015; Liu et al. 2015f, g, 2016d; Liu and Wu 2017), and has been proved very useful as well.

Predictors for Identifying PTM or PTLM Sites in Protein Sequences

Listed in Table 1 are 16 predictors for identifying the PTM sites in protein sequences (Xu and Ding 2013; Xu et al. 2013, 2014a, b; Qiu et al. 2014, 2015, 2016a, b, c, 2017; Jia et al. 2016a, b, c, d; Liu and Xu 2017; Xu and Li 2017). Of the 16 predictors, iPTM-mLys (Qiu et al. 2016b) has the capacity to identify multiple lysine PTM sites and their different types. Therefore, its performance or accuracy needs the following two sets of metrics to measure it (Chou 2019).

Table 1 List of 16 predictors for identifying the PTM sites in protein sequences

One is for its global accuracy, as given by

$$ \left\{ {\begin{array}{l} {{\text{Aiming}} \uparrow = \frac{1}{{N^{q} }}\mathop \sum \limits_{k = 1}^{{N^{q} }} \left( {\frac{{\left\| {{\mathbb{L}}_{k} \cap {\mathbb{L}}_{k}^{*} } \right\|}}{{\left\| {{\mathbb{L}}_{k}^{*} } \right\|}}} \right),\quad \quad [0,1]} \\ {{\text{Coverage}} \uparrow = \frac{1}{{N^{q} }}\mathop \sum \limits_{k = 1}^{{N^{q} }} \left( {\frac{{\left\| {{\mathbb{L}}_{k} \cap {\mathbb{L}}_{k}^{*} } \right\|}}{{\left\| {{\mathbb{L}}_{k} } \right\|}}} \right),\quad \quad [0,1]} \\ {{\text{Accuracy}} \uparrow = \frac{1}{{N^{q} }}\mathop \sum \limits_{k = 1}^{{N^{q} }} \left( {\frac{{\left\| {{\mathbb{L}}_{k} \cap {\mathbb{L}}_{k}^{*} } \right\|}}{{\left\| {{\mathbb{L}}_{k} \cup {\mathbb{L}}_{k}^{*} } \right\|}}} \right),\quad \quad [0,1]} \\ {{\text{Absolute true}} \uparrow = \frac{1}{{N^{q} }}\mathop \sum \limits_{k = 1}^{{N^{q} }} \Delta \left( {{\mathbb{L}}_{k} , {\mathbb{L}}_{k}^{*} } \right),\quad \quad [0,1]} \\ {{\text{Absolute false}} \downarrow = \frac{1}{{N^{q} }}\mathop \sum \limits_{k = 1}^{{N^{q} }} \left( {\frac{{\left\| {{\mathbb{L}}_{k} \cup {\mathbb{L}}_{k}^{*} } \right\| - \left\| {{\mathbb{L}}_{k} \cap {\mathbb{L}}_{k}^{*} } \right\|}}{M}} \right) ,\quad \quad [1,0]} \\ \end{array} } \right. $$
(1)

where \( {\text{N}}^{\text{q}} \) is the total number of query or tested samples, M is the total number of different labels for the investigated system, || || means the operator acting on the set therein to count the number of its elements, \( \cup \) means the symbol for the “union” in the set theory, \( \cap \) denotes the symbol for the “intersection”, \( {\mathbb{L}}_{k} \) denotes the subset that contains all the labels observed by experiments for the k-th tested sample, \( {\mathbb{L}}_{k}^{*} \) represents the subset that contains all the labels predicted for the k-th sample, and.

$$ \Delta \left( {{\mathbb{L}}_{k} , {\mathbb{L}}_{k}^{*} } \right) = \left\{ {\begin{array}{l} {1,{\text{if all the labels in}} \,{\mathbb{L}}_{k}^{*}\,{\text{are identical to those in}}\,{\mathbb{L}}_{k} } \\ {0,{\text{otherwise}} } \\ \end{array} } \right.. $$
(2)

In Eq. 1, the first four metrics with an upper arrow \( \uparrow \) are called positive metrics, meaning that the larger the rate is the better the prediction quality will be; the fifth metrics with a down arrow \( \downarrow \) is called negative metrics, implying just the opposite meaning. As we can see from Eq. 1: (1) the “Aiming” defined by the 1st sub-equation is for checking the rate or percentage of the correctly predicted labels over the practically predicted labels; (2) the “Coverage” defined in the second sub-equation is for checking the rate of the correctly predicted labels over the actual labels in the system concerned; (3) the “Accuracy” in the 3rd sub-equation is for checking the average ratio of correctly predicted labels over the total labels including correctly and incorrectly predicted labels as well as those real labels but are missed in the prediction; (4) the “Absolute true” in the 4th sub-equation is for checking the ratio of the perfectly or completely correct prediction events over the total prediction events; (5) the “Absolute false” in the 5th sub-equation is for checking the ratio of the completely wrong prediction over the total prediction events.

The five metrics in Eq. 1 reflect the quality of a multi-label predictor from five different angles at the global level. It is instructive to point out, however, among the five global metrics the most important one and also the most difficult to improve its success rate is the “Absolute true” or “perfectly correct” rate (Chou 2013). Why? This is because the score standard for the absolute true rate is very harsh. According to its definition, for a statistical sample that is actually simultaneously with the states (“A”, “B”, “C”). If the predicted result is not exactly the three states but (“A”, “B”) or (“A”, “B”, “C”, “D”), no score whatsoever will be given. In other words, when and only when the predicted outcome for the statistical sample is perfectly identical to its actual status, can we add one point for the absolute true rate; otherwise, zero. That is why many investigators even chose not to mention the metrics of absolute true rate; otherwise they would face the embarrassment of reporting a very low success rate for their prediction methods.

The set of metrics in Eq. 1 are used to evaluate the prediction quality of a multi-label predictor for all the samples in the entire system concerned (Chou 2019), and hence is called the “set of metrics for the global accuracy” or the “set of global metrics”.

The other one is for its local accuracy, as given by

$$\left\{ {\begin{array}{ll} {\text{Sn}}\left( i \right) = 1 -\frac{{N_{ - }^{ + } \left( i \right)}}{{N^{ + } \left( i \right)}}\quad 0 \le {\text{Sn}}\left( i \right) \le 1 \\ {\text{Sp}}\left( i \right) = 1 - \frac{{N_{ + }^{ - } \left( i \right)}}{{N^{ - } \left( i \right)}}\quad 0 \le {\text{Sp}}\left( i \right) \le 1 \\ {\text{Acc}}\left( i \right) = 1 - \frac{{N_{ - }^{ + } \left( i \right) + N_{ + }^{ - } \left( i \right)}}{{N^{ + } \left( i \right) + N^{ - } \left( i \right)}}\quad 0 \le {\text{Acc}}\left( i \right) \le 1 \\ {\text{MCC}}\left( i \right) = \frac{{1 - \left( {\frac{{N_{ - }^{ + } \left( i \right)}}{{N^{ + } \left( i \right)}} + \frac{{N_{ + }^{ - } \left( i \right)}}{{N^{ - } \left( i \right)}}} \right)}}{{\sqrt {\left( {1 + \frac{{N_{ + }^{ - } \left( i \right) - N_{ - }^{ + } \left( i \right)}}{{N^{ + } \left( i \right)}}} \right) \left( {1 + \frac{{N_{ - }^{ + } \left( i \right) - N_{ + }^{ - } \left( i \right)}}{{N^{ - } \left( i \right)}}} \right)} }}\quad - 1 \le {\text{MCC}}\left( i \right) \le 1\\ \qquad( i = 1, 2, \ldots , M ) \\ \end{array} } \right. $$
(3)

where Sn, Sp, Acc, and MCC represent the sensitivity, specificity, accuracy, and Mathew’s correlation coefficient, respectively (Chen et al. 2007), i denotes the i-th subset or subcellular location (Chou 2019) in the benchmark dataset, and M has exactly the same meaning as in Eq. 1. \( N^{ + } \left( i \right) \) is the total number of the samples investigated in the i-th subset, whereas \( N_{ - }^{ + } \left( i \right) \) is the number of the samples in \( N^{ + } \left( i \right) \) that are incorrectly predicted to be of other subset or locations; \( N^{ - } \left( i \right) \) is the total number of samples in any subset except for the i-th subset, whereas \( N_{ + }^{ - } \left( i \right) \) is the number of the samples in \( N^{ - } \left( i \right) \) that are incorrectly predicted to be in the i-th subset.

The set of metrics of Eq. 3 were derived (Xu and Ding 2013; Chen et al. 2013) based on the symbols originally introduced by Chou (2001b, c, d) for studying the cleavage sites of signal peptides. Owing to its merit in intuitiveness, Eq. 3 has been widely concurred and admired by many scientists (Chen et al. 2014; Guo et al. 2014; Chen et al. 2007, 2013, 2014b, c,2015a, b, 2016a, b, c, 2017, 2018a, b; Chou 2013, 2015, 2017, 2019; Xu and Ding 2013; Xu et al. 2013, 2014a; Qiu et al. 2014, 2016a, b, c, 2017a, b, c; Jia et al. 2015, 2016a, b, c, d, f, 2019; Ju et al. 2016; Liu et al. 2014a, 2015a, b, c, f, g, h, 2016a, b, c, d, 2017a, b; Xu 2016; Feng et al. 2017; Liu and Xu 2017; Xu and Li 2017; Hussain et al. 2019a, b; Li et al. 2019; Min and Xiao 2013; Xiao et al. 2013a, 2016; Ding et al. 2014; Fan et al. 2014; Lin et al. 2014; 2014; Qiu and Xiao 2014; Jia et al. 2016e; Liu and Long 2016; Cheng and Xiao 2017; Cheng et al. 2017a; Liu and Yang 2017; Ehsan et al. 2018; Li et al. 2018a, b; Song et al. 2018c; Wang et al. 2018; Khan et al. 2019a; Zhang et al. 2017, 2019; Fan and Li 2013; Ali and Hayat 2015; Meher et al. 2017; Huo et al. 2017; Khan et al. 2017; Arif et al. 2018; Krishnan 2018; Zhang and Kong 2018; Chen and Lin 2015; Ju et al. 2015; Wang 2013; Xiao and Lin 2013; Xiao et al. 2013b, c, d; Xiao and Wang 2013; Xia et al. 2014; Yu et al. 2014; Cai et al. 2015; Su et al. 2017; Cheng et al. 2019; Feng et al. 2019), and used to examine the prediction quality of most PTM predictors (Xu and Ding 2013; Xu et al. 2013; Qiu et al. 2014; Xu et al. 2014; Xu et al. 2014; Qiu et al. 2015; Jia et al. 2016a, b, c; Chandra et al. 2018; Ghauri et al. 2018; Khan et al. 2018a, b; Qiu et al. 2018a). Meanwhile, it has also been widely used in proteome and genome analyses (see, e.g., Xu et al. 2014; Chen et al. 2014, 2015b, 2016a, b, c, 2017; Jia et al. 2015, 2016b, d; Ding et al. 2014; Lin et al. 2014; Qiu and Xiao 2014; Liu et al. 2015c; Liu and Yang 2017; Li et al. 2018a; Song et al. 2018c) to evaluate the prediction quality of a multi-label predictor for the proteins in each of subcellular locations concerned (see, e.g., Cheng and Xiao 2017a, b; Cheng et al. 2017a; Xiao et al. 2017, 2018a, b; Cheng and Xiao 2018a, b, c, d, e; Chou et al. 2018; Chou 2019; Cheng et al. 2019). But it is instructive to point out that either the set of conventional metrics copied from math books or the intuitive metrics derived from the Chou’s symbols (Chou 2001b, c, d) are valid only for the single-label systems (where each sample only belongs to one and only one class). For the multi-label systems (where a sample may simultaneously belong to several classes), whose existence has become more frequent in system biology (Cheng and Xiao 2017a, b, 2018a, b; Cheng et al. 2017; Xiao et al. 2017, 2018a; Chou 2019), system medicine (Cheng et al. 2017; Cheng et al. 2017), and biomedicine (Qiu et al. 2016b, 2019; Cheng et al. 2019), a completely different set of metrics as defined in Chou (2013) is absolutely needed.

Predictors for Identifying PTM or PTCM Sites in RNA Sequences

Listed in Table 2 are 7 predictors for identifying the PTM sites in RNA sequences (Chen et al. 2016a, 2018a, b; Liu et al. 2016a; Feng et al. 2017; Qiu et al. 2017a, b).

Table 2 List of 7 predictors for identifying the PTM sites in RNA sequences

Predictors for Identifying PTM or PTRM Sites in DNA Sequences

Listed in Table 3 is only one predictor for identifying the PTM sites in DNA sequences (Liu et al. 2015c).

Table 3 List of one predictor for identifying the PTM sites in DNA sequences

Concluding Remarks and Perspectives

The PTM predictors introduced in this review paper have been all established by following the 5-steps rule (Chou 2011), and hence they each have a user-friendly web server for the majority of experimental scientists to easily get their desired data. Also, their cornerstones are based on PseAAC (Chou 2001, 2005d, e, 2009, 2011) or PseKNC (Chen et al. 2013, 2014a; Lin et al. 2014; Chen and Lin 2015; Liu et al. 2015g, 2016), and hence their prediction quality is usually higher than the other PTM prediction methods.

As we can see from the “Predictors for Identifying PTM or PTLM Sites in Protein Sequences”, “Predictors for Identifying PTM or PTCM Sites in RNA Sequences”, and “Predictors for Identifying PTM or PTRM Sites in DNA Sequences” sections, the most web-servers available are for identifying the PTM sites in protein sequences, the next are for DNA sequences, and the least for RNA sequences. It is anticipated, however, that with more experimental data available in the future, the benchmark datasets for the PTM sites in RNA and DNA sequences will be enriched as well. The existing web-servers will not only be easily extended to cover more RNA and DNA sequences, but also further improve the prediction quality in all kinds of biological sequences.

Finally, it has not escaped our notice that using graphic approaches to study biological and medical systems can provide an intuitive vision and useful insights for helping analyze complicated relations therein as shown in the systems of enzyme fast reaction (Chou and Forsen 1980; Li and Forsen 1980a, b), graphical rules in molecular biology (Chou and Forsen 1980, 1981; Forsen and Zhou 1980; Carter and Forsen 1981), and low-frequency internal motion in biomacromolecules (such as protein and DNA) (Chen and Forsen 1981). Particularly, what happened is that this kind of insightful implication has also been demonstrated in Chou et al. (1979) and many follow-up publications (Zhou and Deng 1984; Chou 1989, 1990; Althaus et al. 1993a, b, c, 1994a, b, 1996; Chou et al. 1994; Andraos 2008; Chou and Shen 2009; Shen and Song 2009; Chou 2010, 2011; Zhou 2011).

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