since the first modified rna ribonucleic acid was found 60 years ago , 150 known rna modifications have been reported .
emerging evidences suggest that rna modifications are critical components of the gene regulatory landscape and are involved in a variety of biological processes in the post - transcriptional level , such as protein translation and localization , mrna splicing , affecting ribosome biogenesis , mediating antibiotic resistance , and stem cell pluripotency .
however , many aspects of rna modifications remain unknown . therefore , detecting the positions of rna modifications plays an essential role for understanding their molecular mechanisms and functions .
the advent of next - generation sequencing technologies has allowed investigation of rna modifications on a genome - wide scale.9 , 10 , 11 , 12 , 13 , 14 , 15 for example , the n - methyladenosine ( ma),9 , 10 
 n - methyladenosine ( ma ) , and 5-methylcytosine ( mc ) maps are available for the human transcriptome . although these experimental methods played active roles in promoting the research progress on understanding the biological functions and the identification of rna modifications , they are still labor - intensive . as excellent complements to experimental techniques , some computational methods ( based on the high - resolution experimental data ) have been developed to identify rna modifications.7 , 16 , 17 , 18 , 19 , 20 , 21 reminiscent of the regulation of gene expression by histone modifications , it is also possible to mediate biological functions in a collective way by combining different kinds of rna modifications .
unfortunately , to the best of our knowledge , no computational tool is available for dealing with a system that simultaneously contains several different kinds of rna modifications .
actually , this kind of multi - modification systems may contain much more interesting things worthy of exploration . in view of this , the present study was initiated in an attempt to fill such a void by establishing a seamless package or platform that can be used to analyze a biological system that simultaneously contains the three well known types of rna modifications : ma , ma , and mc ( figure  1 ) .
by incorporating collective effects of nucleotides into pseknc,22 , 23 a seamless platform called  irna - psecoll  has been developed for identifying the occurrence sites of different rna modifications .
it has been observed by the most rigorous cross - validation , the jackknife test , that the success rates achieved by the new predictor are quite high for the three different types of rna modification sites , respectively ( table 1 ) . because it is the first platform predictor ever developed for simultaneously identifying three different types of rna modification sites based on its sequence information alone , it is not possible to demonstrate its power by a comparison with its counterparts because there is no such a counterpart yet for exactly the same purpose .
nevertheless , as we can see from table 1 , all the scores are quite high , particularly for the overall accuracy ( acc ) and mathew s correlation coefficient ( mcc ) .
as it is , the graphical approach is a useful vehicle for studying complicated biological systems because it can provide intuitive insights , as demonstrated by a series of previous studies.25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 therefore , it would be instructive and illuminative to give an intuitive illustration for the current study as well . to realize this , the graph of receiver operating characteristic ( roc)35 , 36 was adopted as shown in figure  2 , where the roc curves for the current method in identifying ma , ma , and mc modifications were given , respectively .
the best  possible prediction method would yield a point with the coordinate ( 0 , 1 ) representing 100% sensitivity and 0 false - positive rate or  100% specificity .
therefore , the ( 0 , 1 ) point is also called a perfect classification . a completely random guess
would give a point along a diagonal from the point ( 0 , 0 ) to ( 1 , 1 ) .
the area under the roc curve , also called auroc , is used to indicate the performance quality of the classifier : the value 0.5 of auroc is equivalent to random prediction while 1 of auroc represents a perfect one .
the auroc for the case  of ma , ma , or mc is 0.998 , 0.849 , or 0.911 , respectively , indicating that the proposed platform is quite promising , holding very high potential to become a useful high throughput tool for genome analyses .
inspired by a series of recent publications,20 , 21 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 papers published with a publicly accessible web server will significantly enhance their impacts ; this is particularly true for those papers aimed at developing novel prediction methods .
accordingly , the web server for the current platform has been established . moreover , for the convenience of the scientific community , a user guide is given in the supplemental materials and methods .
according to the chou s five - step guidelines that have been followed by many investigators in a series of recent publications,21 , 39 , 41 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 to develop a new prediction method that not only can be easily used by most experimental scientists but also can inspire theoretical scientists to develop many other relevant prediction methods , we should make the following five procedures very clear : ( 1 ) how to construct or select a valid benchmark dataset to train and test the prediction model , ( 2 ) how to represent a biological sequence sample with a mathematical formulation or vector that is really correlated with the target concerned , ( 3 ) how to introduce or develop a powerful engine ( or algorithm ) to run the prediction model , ( 4 ) how to properly perform the cross - validation tests to objectively evaluate the anticipated accuracy , and ( 5 ) how to design a user - friendly web server to make it easy for people to get their desired results .
below , we elaborate the five procedures in establishing the new predictor . owing to the fast development of high - throughput experimental techniques , the experimentally confirmed ma , ma ,
and mc modification data is available for the human genome.9 , 10 , 13 , 15 by mapping the experimental data to the human genome , the sequence samples with statistical significance were obtained for the three kinds of rna modification sites as well . for facilitating the formulation ,
let us use the following scheme to represent a potential rna modification - site - containing sample(equation  1)r()=nn(1)n2n1n+1n+2n+(1)n+,where the symbol  denotes the single nucleic acid code a ( adenine ) or c ( cytosine ) , the subscript  is an integer , n represents the  -th upstream nucleotide from the center , the n+ represents the  -th downstream nucleotide , and so forth .
the ( 2+1 ) -tuple rna sample , r( ) , can be further classified into the following two categories:(equation  2)r(){r+(),ifitscentercanbeof2-o - methylationr(),otherwise , where r+( ) denotes a true modification segment with a or c at its center , r( ) denotes a false modification segment with a or c at its center , and the symbol  means  a member of  in the set theory . in literature , the benchmark dataset usually consists of a training dataset and a testing dataset : the former is for the use of training a model , while the latter for testing the model .
however , as elucidated in a comprehensive review , there is no need to artificially separate a benchmark dataset into the aforementioned two parts if the prediction model is examined by the jackknife test or subsampling ( k - fold ) cross - validation , because the outcome thus obtained is actually from a combination of many different independent dataset tests .
thus , the benchmark datasets for the current study can be further formulated as(equation  3){s(m1a)=s+(m1a)s(m1a),when=as(m6a)=s+(m6a)s(m6a),when=as(m5c)=s+(m5c)s(m5c),when=c , where the positive subset s+(m1a ) only contains those rna samples that can have m1a modification , and the negative subset  s(m1a ) only contains those rna samples that can not have m1a modification , while u denotes the symbol of  union  in the set theory , and so forth .
the benchmark datasets were derived from the rna sequences in human genome that have the experimentally confirmed ma , ma , and mc modification sites.9 , 10 , 13 , 15 the detailed procedures to construct the benchmark dataset are as follows .
first , as done in chou , by sliding the ( 2+1 ) -tuple nucleotide window ( figure  3 ) along each of the aforementioned rna sequences , only those rna segments with = a or c at the center were collected .
second , if the upstream or downstream in a rna sequence was less than  or greater than l where l is the length of the rna sequence concerned , the lacking code was filled with the same code of its nearest neighbor .
third , the rna segment samples thus obtained were put into the positive subset s+(m1a ) , s+(m6a ) , or s+(m5c ) if their centers were experimentally annotated as the ma , ma , or mc sites ; otherwise , into the corresponding negative subset s(m1a ) , s(m6a ) , or s(m5c ) .
fourth , to reduce redundancy and bias , none of the included rna segments had pairwise sequence identity with any other in a same subset . by strictly following the above procedures
, we obtained an array of benchmark datasets with different  values and hence different lengths of rna samples ( 2+1 ) as well ( see equation  1 ) , as illustrated below(equation  4)s(){23nucleotides , when=1125nucleotides , when=1227nucleotides , when=1339nucleotides , when=1941nucleotides , when=2043nucleotides , when=21,where the symbol  means 
 it was observed via preliminary tests as well as many reports19 , 43 , 66 that when =20 ( i.e. , the rna samples formed by 41 nucleotides [ nt ] ) , the corresponding results were most promising .
by doing so , we obtained 6,366 , 1,130 and 120 sequence samples for the positive subsets s+(m1a ) , s+(m6a ) , and s+(m5c ) , respectively .
the numbers of samples thus obtained in the corresponding negative subsets are much greater , and hence the benchmark datasets would be very imbalanced .
using such highly skewed benchmark dataset to train predictors would lead to the outcome that many positive cases might be mispredicted as negative ones.42 , 44 , 56 , 67 to balance out the size between the positive subset and the negative subset , we randomly picked out 6,366 , 1,130 , and 120 from the corresponding negative samples to for the negative subsets s(m1a ) , s(m6a ) , and s(m5c ) , respectively , as done in chen et  al . and
feng et  al . finally , the detailed rna sequence samples thus obtained for the benchmark dataset s=20(m1a ) , s=20(m6a ) , and s=20(m5c ) are given in the supplemental materials and methods , which can also be directly downloaded from http://lin.uestc.edu.cn/server/irna-psecoll/dataset.htm .
one of the most challenging problems in computational biology today is how to formulate a biological sequence with a vector that can reflect its key pattern important for the function or mechanism concerned .
the importance of such a challenge is due to the fact that nearly all the existing machine - learning algorithms were developed to handle vector rather than sequence samples , as elucidated in a review article .
unfortunately , a vector defined in a discrete model may lose many important sequence pattern features . to deal with such a problem for protein / peptide sequences ,
the pseudo amino acid composition  ( pseaac)68 , 69 , 70 , 71 , 72 was developed .
ever since it was introduced , the  concept of pseaac has  penetrated into nearly all the areas of computational proteomics ( see a long list of references cited in two review papers55 , 73 ) . inspired  by the concept of pseaac and encouraged by its great successes , the pseudo nucleotide composition ( pseknc)22 , 74 , 75 , 76 was proposed and  has been increasingly used in various fields of genome analysis.20 , 21 , 23 , 37 , 39 , 40 , 42 , 43 , 51 , 52 , 53 , 58 , 59 , 60 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 with both pseaac and pseknc being increasingly and widely used , it is highly desired to design a seamless package that can generate various modes of pseaac and pseknc according to users needs for protein / peptide and dna / rna sequences , respectively .
this was exactly the driving force of establishing the web server called pse - in - one and what it is about .
the general form of pseknc for an rna sequence sample is given  by(equation  5)r=[12u]t , where t is a transpose operator , while the subscript  an integer and its value as well as the components u 
 ( u=1,2,, ) will depend on how to extract the desired features from the rna sequence sample . in order to make equation  4 able to reflect both the local feature of its individual constituent nucleotides and that of their collective effect , let us define the components in equation  4 from the following two different approaches .
rna consists of four types of nucleotides : a ( adenosine ) , c ( cytidine ) , g ( guanosine ) , and u ( uridine ) .
they can be classified into three different categories ( table 1 ) : ( 1 ) from the angle of ring number , a and g have two rings , whereas c and u only one ; ( 2 ) from the chemical functionality , a and c belong to amino group , while g and u to keto group ; and ( 3 ) from the angle of hydrogen bonding , c and g can be bonded to each other with three hydrogen bonds , but a and u with only two ( figure  4 ) .
all these properties would have different impacts to rna s low - frequency internal motion87 , 88 and its biological function89 , 90 , 91 .
to reflect the aforementioned features , let us denote the i - th nucleotide of equation  1 by92 , 93(equation  6)ni=(xi , yi , zi),where xi , yi , and zi refer to the attributes of ( 1 ) ring structure , ( 2 ) functional group , and ( 3 ) hydrogen bonding in table 2 , respectively .
accordingly , the nucleotide a can be formulated as ( 1 , 1 , 1 ) , c as ( 0 , 1 , 0 ) , g as ( 1 , 0 , 0 ) , and u as ( 0 , 0 , 1 ) ; or generally we have(equation  7)xi={1,ifni{a , g}0,ifni{c , u};yi={1,ifni{a , c}0,ifni{g , u};zi={1,ifni{a , u}0,ifni{c , g}. there are some methods to reflect the coupling of a biological sequence or the collective effect of its constituent elements , such as the conditional probability approach , degenerate kmer strategy , and g - gap dipeptide mode . in this study
, we would like to use a  different approach ; i.e. , consider the occurrence frequency of a nucleotide not only for its local site but also for its distribution along  the sequence of an rna sample , as defined by the following equation(equation  8)di=1lij=1f(nj),where di is the density of the nucleotide ni at the site i of a  rna  sequence , li the length of the sliding substring concerned ,  denotes each of the site locations counted in the substring , and(equation  9)f(nj)={1,ifnj = thenucleotideconcerned0,otherwise .
the density of  a  at the sequence position 1 , 2 , 3 , 4 , 5 , or 6 is 0=0/1 , 0.5=1/2 , 0.331/3 , 0.25=1/4 , 0.20=1/5 , or 0.16=1/6 , respectively ; that of  c  is 1=1/1 , 0=0/2 , 0.662/3 , 0.5=2/4 , 0.4=2/5 or 0.5=3/6 , respectively ; and so forth . by combing ( equation  6 ) , ( equation  9 ) ,
the i - th nucleotide of equation  1 can be uniquely defined by a set of four variables ; i.e.,(equation  10)ni=(xi , yi , zi , di ) .
for example , the rna sequence  cacguc  can be expressed by the following five sets of digital numbers : ( 0 , 1 , 0 , 1 ) , ( 1 , 1 , 1 , 0.5 ) , ( 0 , 1 , 0 , 0.66 ) , ( 1 , 0 , 0 , 0.25 ) , ( 0 , 0 , 1 , 0.2 ) , and ( 0 , 1 , 0 , 0.5 ) . submitting these numbers into equation  5 , we have(equation  11)r(cacguc)=[01011110.50100.661000.250010.20100.5]t , meaning that the 6-nt nucleotide example can be defined by a 64=24 -d ( dimensional ) pseknc vector . accordingly
, all the samples in the current benchmark datasets ( supplemental materials and methods ) can be formulated with a 414=164 -d vector .
the prediction was operated by svm ( support  vector machine ) , which has been widely used in various areas of bioinformatics and computational biology.20 , 40 , 42 , 59 , 67 , 77 , 78 , 79 , 80 , 81 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 its basic idea has been elaborated in the aforementioned the papers , and there is no need to repeat it  here . in the current study ,
the libsvm package 3.18 was used to implement svm , which can be downloaded for free from http://www.csie.ntu.edu.tw/cjlin / libsvm/. the svm algorithm contains two uncertain quantities : one is the regularization parameter c and the other is the kernel width parameter . they were optimized via an optimization procedure using the grid search approach as described by(equation  12){25c215withstepc=221525withstep=21,where c and  represent the step gaps for c and  , respectively . for those readers who are interested in knowing more about svm ,
see  chou and cai and cai et  al . or a monograph where a brief introduction or detailed description were given , respectively .
the platform predictor obtained via the aforementioned procedures is called  irna - psecoll ,  where  i  stands for  identify ,  
pse  for  pseudo component approach ,  and  coll  for  collective effects of nucleotides . 
quality control is a very important process in industries ; it is even more important for a predictor . to deal with this problem
, we need to address the following two issues : ( 1 ) what standard or metrics should we adopt to measure the predictor s quality , and ( 2 ) what test process or method we should take to calculate the metrics .
the current prediction is belonging to the category called  binary classification  widely existing in genome analyses . to measure the prediction quality of this kind , a set of four metrics
are usually used in literature : ( 1 ) sensitivity or sn , ( 2 ) specificity or sp , ( 3 ) overall accuracy or acc , and ( 4 ) mathew s correlation coefficient or mcc .
unfortunately , their formulations were directly taken from mathematical literature and difficult to be understood by most biological scientists . fortunately , using the symbols introduced by chou in studying signal peptides , xu et  al . and chen et  al .
have derived a new set of metrics that is equivalent to the old one but much more intuitive and easier to be understood by most biologists , as given below to address this , we need to consider two issues : one is what metrics should be used to reflect the predictor s success rates ; the other is what test method should be adopted to derive the metrics rates . to quantitatively evaluate the quality of a binary classification predictor ,
they are : ( 1 ) acc for the predictor s overall accuracy ; ( 2 ) mcc for its stability ; ( 3 ) sn for its sensitivity ; and ( 4 ) sp for its specificity .
unfortunately , the conventional formulations for the four metrics are not quite intuitive , and  most biologists have difficulty understanding them , particularly the stability of mcc .
fortunately , as elaborated in yu et  al . and chen et  al .
, by using the chou s symbols and derivation in studying signal peptides , the conventional metrics can be converted into a set of four intuitive equations , as formulated below:(equation  13){sn=1n+n+0sn1sp=1n+n0sp1acc==1n++n+n++n0acc1mcc=1(n+n++n+n)(1+n+n+n+)(1+n+n+n)1mcc1,where n+ represents the total number of positive samples investigated , n+ is the number of positive samples incorrectly predicted to be the negative , n is the total number of negative samples investigated , and n+ is the number of the negative samples incorrectly predicted to be the positive . with the metrics of equation  13 , the meanings of sn , sp , acc , and mcc have become crystal clear as discussed and used in a series of follow - up studies for many different areas.20 , 21 , 38 , 40 , 42 , 44 , 45 , 46 , 47 , 48 , 49 , 56 , 57 , 61 , 67 , 80 , 82 , 84 , 97 , 99 , 112 , 113 , 114 , 115 it is instructive to point out that more multi - label sequence samples have been emerging in system biology and medicine.49 , 116 , 117 , 118 , 119 to deal with this kind of multi - label system , a much more sophisticated set of metrics is needed as elaborated in chou .
these methods include : ( 1 ) an independent dataset test , ( 2 ) a subsampling ( or k - fold cross - validation ) test , and ( 3 ) the jackknife test .
however , as elucidated in chou in the above three choices , the jackknife test has been demonstrated to be the least arbitrary that can always yield a unique outcome for a given benchmark dataset .
therefore , the jackknife test has been widely recognized and increasingly adopted by researchers to analyze the quality of various predictors.83 , 103 , 121 , 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 in view of this , we also used the jackknife test to examine the quality of the current prediction method .
the jackknife test can exclude the  memory  effect because both the training dataset and testing dataset in a jackknife system are actually open , and each sample will be , in turn , moved between the two .
the arbitrariness problem intrinsic to the independent dataset and subsampling tests no longer exists , because the outcome derived via the jackknife test for a predictor is always the same on a given benchmark dataset .
w.c . , h.l . , and k .- c.c . conceived and designed the study
, h.l . , and k .- c.c . performed the analysis and wrote the paper .
 there are many different types of rna modifications , which are essential for numerous biological processes . 
 knowledge about the occurrence sites of rna modifications in its sequence is a key for in - depth understanding of their biological functions and mechanism . 
 unfortunately , it is both time - consuming and laborious to determine these sites purely by experiments alone . 
 although some computational methods were developed in this regard , each one could only be used to deal with some type of modification individually . to our knowledge , 
 no method has thus far been developed that can identify the occurrence sites for several different types of rna modifications with one seamless package or platform . 
 to address such a challenge , a novel platform called  irna - psecoll  has been developed . 
 it was formed by incorporating both the individual and collective features of the sequence elements into the general pseudo k - tuple nucleotide composition ( pseknc ) of rna via the chemicophysical properties and density distribution of its constituent nucleotides . 
 rigorous cross - validations have indicated that the anticipated success rates achieved by the proposed platform are quite high . to maximize the convenience for most experimental biologists , the platform s 
 web - server has been provided at http://lin.uestc.edu.cn/server/irna-psecoll along with a step - by - step user guide that will allow users to easily achieve their desired results without the need to go through the mathematical details involved in this paper . 
Introduction
Results and Discussion
Materials and Methods
Author Contributions
Conflicts of Interest