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Paragraph: Text: With the ability to directly bind to DNA ( Figure 1 ) and regulate the expression of adjacent genes, nuclear receptors (NRs) are a class of ligand-inducible transcription factors . They regulate various biological processes, such as homeostasis, differentiation, embryonic development, and organ physiology [1] [2] [3] . The NR superfamily has been classified into seven families: NR0 (knirps or DAX like) [4, 5] ; NR1 (thyroid hormone like), NR2 (HNF4-like), NR3 (estrogen like), NR4 (nerve growth factor IB-like), NR5 (fushi tarazu-F1 like), and NR6 (germ cell nuclear factor like). Since they are involved in almost all aspects of human physiology and are implicated in many major diseases such as cancer, diabetes and osteoporosis, nuclear receptors have become major drug targets [6, 7] , along with G protein-coupled receptors (GPCRs) [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] , ion channels [18] [19] [20] , and kinase proteins [21] [22] [23] [24] . Identification of drug-target interactions is one of the most important steps for the new medicine development [25, 26] . The method usually adopted in this step is molecular docking simulation [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] . However, to make molecular docking study feasible, a reliable 3D (three dimensional) structure of the target protein is the prerequisite condition. Although X-ray crystallography is a powerful tool in determining protein 3D structures, it is time-consuming and expensive. Particularly, not all proteins can be successfully crystallized. For example, membrane proteins are very difficult to crystallize and most of them will not dissolve in normal solvents. Therefore, so far very few membrane protein 3D structures have been determined. Although NMR (Nuclear Magnetic Resonance) is indeed a very powerful tool in determining the 3D structures of membrane proteins as indicated by a series of recent publications (see, e.g., [44] [45] [46] [47] [48] [49] [50] [51] and a review article [20] ), it is also time-consuming and costly. To acquire the 3D structural information in a timely manner, one has to resort to various structural bioinformatics tools (see, e.g., [37] ), particularly the homologous modeling approach as utilized for a series of protein receptors urgently needed during the process of drug development [19, [52] [53] [54] [55] [56] [57] . Unfortunately, the number of dependable templates for developing high quality 3D structures by means of homology modeling is very limited [37] . To overcome the aforementioned problems, it would be of help to develop a computational method for predicting the interactions of drugs with nuclear receptors in cellular networking based on the sequences information of the latter. The results thus obtained can be used to pre-exclude the compounds identified not in interaction with the nuclear receptors, so as to timely stop wasting time and money on those unpromising compounds [58] . Actually, based on the functional groups and biological features, a powerful method was developed recently [59] for this purpose. However, further development in this regard is definitely needed due to the following reasons. (a) He et al. [59] did not provide a publicly accessible web-server for their method, and hence its practical application value is quite limited, particularly for the broad experimental scientists; (b) The prediction quality can be further enhanced by incorporating some key features into the formulation of NR-drug (nuclear receptor and drug) samples via the general form of pseudo amino acid composition [60] . The present study was initiated with an attempt to develop a new method for predicting the interaction of drugs with nuclear receptors by addressing the two points. As demonstrated by a series of recent publications [10, 18, [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] and summarized in a comprehensive review [60] , to establish a really effective statistical predictor for a biomedical system, we need to consider the following steps: (a) select or construct a valid benchmark dataset to train and test the predictor; (b) represent the statistical samples with an effective formulation that can truly reflect their intrinsic correlation with the object to be predicted; (c) introduce or develop a powerful algorithm or engine to operate the prediction; (d) properly perform cross-validation tests to objectively evaluate the anticipated accuracy of the predictor; (e) establish a user-friendly web-server for the predictor that is accessible to the public. Below, let us elaborate how to deal with these steps. The data used in the current study were collected from KEGG (Kyoto Encyclopedia of Genes and Genomes) [71] at http://www.kegg.jp/kegg/. KEGG is a database resource for understanding high-level functions and utilities of the biological system, such as the cell, the organism and the ecosystem, from molecular-level information, especially large-scale molecular datasets generated by genome sequencing and other high-throughput experimental technologies. Here, the benchmark dataset can be formulated as

where is the positive subset that consists of the interactive drug-NR pairs only, while the negative subset that contains of the non-interactive drug-NR pairs only, and the symbol represents the union in the set theory. The so-called "interactive" pair here means the pair whose two counterparts are interacting with each other in the drug-target networks as defined in the KEGG database [71] ; while the "non-interactive" pair means that its two counterparts are not interacting with each other in the drug-target networks. The positive dataset contains 86 drug-NR pairs, which were taken from He et al. [59] . The negative dataset contains 172 non-interactive drug-NR pairs, which were derived according to the following procedures: (a) separating each of the pairs in into single drug and NR; (b) re-coupling each of the single drugs with each of the single NRs into pairs in a way that none of them occurred in ; (c) randomly picking the pairs thus formed until reaching the number two times as many as the pairs in . The 86 interactive drug-NR pairs and 172 non-interactive drug-NR pairs are given in Supplementary Information S1, from which we can see that the 86 + 172 = 258 pairs in the current benchmark dataset are actually formed by 25 different NRs and 53 different compounds. Since each of the samples in the current network system contains a drug (compound) and a NR (protein), the following procedures were taken to represent the drug-NR pair sample. First, for the drug part in the current benchmark dataset, we can use a 256-D vector to formulate it as given by

where D represents the vector for a drug compound, and d i its i-th (i = 1,2, ,256) component that can be derived by following the "2D molecular fingerprint procedure" as elaborated in [10] . The 53 molecular fingerprint vectors thus obtained for the 53 drugs in are, respectively, given in Supplementary Information S2. The protein sequences of the 25 different NRs in are listed in Supplementary Information S3. Suppose the sequence of a nuclear receptor protein P with L residues is generally expressed by

where 1 R represents the 1st residue of the protein sequence P , 2 R the 2nd residue, and so forth. Now the problem is how to effectively represent the sequence of Equation (3) with a non-sequential or discrete model [72] . This is because all the existing operation engines, such as covariance discriminant (CD) [17, 65, [73] [74] [75] [76] [77] [78] [79] , neural network [80] [81] [82] , support vector machine (SVM) [62] [63] [64] 83] , random forest [84, 85] , conditional random field [66] , nearest neighbor (NN) [86, 87] ; K-nearest neighbor (KNN) [88] [89] [90] , OET-KNN [91] [92] [93] [94] , and Fuzzy K-nearest neighbor [10, 12, 18, 69, 95] , can only handle vector but not sequence samples. However, a vector defined in a discrete model may completely lose all the sequence-order information and hence limit the quality of prediction. Facing such a dilemma, can we find an approach to partially incorporate the sequence-order effects? Actually, one of the most challenging problems in computational biology is how to formulate a biological sequence with a discrete model or a vector, yet still keep considerable sequence order information. To avoid completely losing the sequence-order information for proteins, the pseudo amino acid composition [96, 97] or Chou's PseAAC [98] was proposed. Ever since the concept of PseAAC was proposed in 2001 [96] , it has penetrated into almost all the areas of computational proteomics, such as predicting anticancer peptides [99] , predicting protein subcellular location [100] [101] [102] [103] [104] [105] [106] , predicting membrane protein types [107, 108] , predicting protein submitochondria locations [109] [110] [111] [112] , predicting GABA(A) receptor proteins [113] , predicting enzyme subfamily classes [114] , predicting antibacterial peptides [115] , predicting supersecondary structure [116] , predicting bacterial virulent proteins [117] , predicting protein structural class [118] , predicting the cofactors of oxidoreductases [119] , predicting metalloproteinase family [120] , identifying cysteine S-nitrosylation sites in proteins [66] , identifying bacterial secreted proteins [121] , identifying antibacterial peptides [115] , identifying allergenic proteins [122] , identifying protein quaternary structural attributes [123, 124] , identifying risk type of human papillomaviruses [125] , identifying cyclin proteins [126] , identifying GPCRs and their types [15, 16] , discriminating outer membrane proteins [127] , classifying amino acids [128] , detecting remote homologous proteins [129] , among many others (see a long list of papers cited in the References section of [60] ). Moreover, the concept of PseAAC was further extended to represent the feature vectors of nucleotides [65] , as well as other biological samples (see, e.g., [130] [131] [132] ). Because it has been widely and increasingly used, recently two powerful soft-wares, called "PseAAC-Builder" [133] and "propy" [134] , were established for generating various special Chou's pseudo-amino acid compositions, in addition to the web-server "PseAAC" [135] built in 2008. According to a comprehensive review [60] , the general form of PseAAC for a protein sequence P is formulated by

where the subscript  is an integer, and its value as well as the components ( 1, 2, , ) u u   will depend on how to extract the desired information from the amino acid sequence of P (cf. Equation (3)). Below, let us describe how to extract useful information to define the components of PseAAC for the NR samples concerned. First, many earlier studies (see, e.g., [136] [137] [138] [139] [140] [141] ) have indicated that the amino acid composition (AAC) of a protein plays an important role in determining its attributes. The AAC contains 20 components with each representing the occurrence frequency of one of the 20 native amino acids in the protein concerned. Thus, such 20 AAC components were used here to define the first 20 elements in Equation (4); i.e., (1) ( 1, 2, , 20) ii fi   (5) where f i (1) is the normalized occurrence frequency of the i-th type native amino acid in the nuclear receptor concerned. Since AAC did not contain any sequence order information, the following steps were taken to make up this shortcoming. To avoid completely losing the local or short-range sequence order information, we considered the approach of dipeptide composition. It contained 20 × 20 = 400 components [142] . Such 400 components were used to define the next 400 elements in Equation (4); i.e., (2) 20 ( 1, 2, , 400) jj fj

where (2) j f is the normalized occurrence frequency of the j-th dipeptides in the nuclear receptor concerned. To incorporate the global or long-range sequence order information, let us consider the following approach. According to molecular evolution, all biological sequences have developed starting out from a very limited number of ancestral samples. Driven by various evolutionary forces such as mutation, recombination, gene conversion, genetic drift, and selection, they have undergone many changes including changes of single residues, insertions and deletions of several residues [143] , gene doubling, and gene fusion. With the accumulation of these changes over a long period of time, many original similarities between initial and resultant amino acid sequences are gradually faded out, but the corresponding proteins may still share many common attributes [37] , such as having basically the same biological function and residing at a same subcellular location [144, 145] . To extract the sequential evolution information and use it to define the components of Equation (4), the PSSM (Position Specific Scoring Matrix) was used as described below. According to Schaffer [146] , the sequence evolution information of a nuclear receptor protein P with L amino acid residues can be expressed by a 20 L matrix, as given by

where (7) were generated by using PSI-BLAST [147] to search the UniProtKB/Swiss-Prot database (The Universal Protein Resource (UniProt); http://www.uniprot.org/) through three iterations with 0.001 as the E-value cutoff for multiple sequence alignment against the sequence of the nuclear receptor concerned.

Question: What are nuclear receptors (NRs)?
class of ligand-inducible transcription factors