Searching for transcription factor binding sites in vector spaces
 Chih Lee^{1} and
 ChunHsi Huang^{1}Email author
DOI: 10.1186/1471210513215
© Lee and Huang; licensee BioMed Central Ltd. 2012
Received: 29 January 2012
Accepted: 16 August 2012
Published: 27 August 2012
Abstract
Background
Computational approaches to transcription factor binding site identification have been actively researched in the past decade. Learning from known binding sites, new binding sites of a transcription factor in unannotated sequences can be identified. A number of search methods have been introduced over the years. However, one can rarely find one single method that performs the best on all the transcription factors. Instead, to identify the best method for a particular transcription factor, one usually has to compare a handful of methods. Hence, it is highly desirable for a method to perform automatic optimization for individual transcription factors.
Results
We proposed to search for transcription factor binding sites in vector spaces. This framework allows us to identify the best method for each individual transcription factor. We further introduced two novel methods, the negativetopositive vector (NPV) and optimal discriminating vector (ODV) methods, to construct query vectors to search for binding sites in vector spaces. Extensive crossvalidation experiments showed that the proposed methods significantly outperformed the ungapped likelihood under positional background method, a stateoftheart method, and the widelyused positionspecific scoring matrix method. We further demonstrated that motif subtypes of a TF can be readily identified in this framework and two variants called the k NPV and k ODV methods benefited significantly from motif subtype identification. Finally, independent validation on ChIPseq data showed that the ODV and NPV methods significantly outperformed the other compared methods.
Conclusions
We conclude that the proposed framework is highly flexible. It enables the two novel methods to automatically identify a TFspecific subspace to search for binding sites. Implementations are available as source code at:http://biogrid.engr.uconn.edu/tfbs_search/.
Background
Transcription of genes followed by translation of their transcripts into proteins determines the type and functions of a cell. Expression of certain genes even initiates or suppresses differentiation of stem cells. It is therefore crucial to understand the mechanisms of transcriptional regulation. Among them, transcription factor (TF) binding is the one that has been given considerable attention by computational biologists for the past decade and is still being actively researched. A TF is a protein or protein complex that regulates transcription of one or more genes by binding to the doublestranded DNA. A first step in computational identification of target genes regulated by a TF is to pinpoint its binding sites in the genome. Once the binding sites are found, the putative target genes can be searched and located in flanking regions of the binding sites.
In general, there are two approaches to computational transcription factor binding site (TFBS) identification, motif discovery and TFBS search. The former assumes that a set of sequences is given and each of the sequences may or may not contain TFBSs. An algorithm then predicts the locations and lengths of TFBSs. The term motif refers to the pattern that are shared by the discovered TFBSs. These algorithms rely on no prior knowledge of the motif and hence are known as de novo motif discovery algorithms. The latter assumes that, in addition to a set of sequences, the locations and lengths of TFBSs are known. An algorithm then learns from these examples and predicts TFBSs in new sequences. Such algorithms are also called supervised learning algorithms since they are guided by the given sequences with known TFBSs. Plenty of efforts have been devoted to the de novo motif discovery problem[1–11]. Comprehensive evaluation and comparison of the developed tools have been performed[12, 13]. In this study, we focus on the problem of TFBS search. We refer readers interested in the motif discovery problem to the evaluation and review articles[12–14] and references therein.
A typical TFBS search method searches for the binding sites of a particular transcription factor in the following manner. It scans a target DNA sequence and compare each length l subsequence (l mer) to the binding site profile of the TF, where l is the length of a binding site. Each of the l mer is scored when comparing to the profile. A cutoff score is then set by the method to select candidate TF binding sites. The positionspecific scoring matrix (PSSM)[15] is a widely used profile representation, where the binding sites of a TF are encoded as a 4 × l matrix. Column i of the matrix stores the scores of matching the i^{th} letter in an l mer to nucleotides A, C, G and T, respectively. Depending on the method of choice, the score of A at position i can be the count of A at position i in the known TFBSs, the logtransformed probability of observing A at position i , or any other reasonable number. Once computed, the scoring matrix of a TF can be stored in a database. These matrices are used by tools[16–21] to scan sequences for TFBSs.
One assumption the PSSM representation makes is that positions in a binding site are independent, which is often not the case. Osada et al.[22] exploited dependence between positions by considering nucleotide pairs in scoring methods. It was shown that incorporating nucleotide pairs significantly improved the performance of a method, meaning that most transcription factors studied demonstrated correlation between positions in a binding site. This result was reinforced in a recent study[23], in which the authors showed correlations between two nucleotides within a binding site by plotting the mutual information matrix. A novel scoring method called the ungapped likelihood under positional background (ULPB) method was proposed in this study. The ULPB method models a TFBS by two firstorder Markov chains and scores a candidate binding site by likelihood ratio produced by the two Markov chains. leaveoneout crossvalidation results on 22 TFs with 20 or more binding sites showed that ULPB is superior to the methods compared in their work.
In this work, we approach the TFBS search problem from a different perspective. We propose to search for binding sites in vector spaces. Specifically, l mers are placed in the Euclidean space such that each l mer corresponds to a vector in the space. With known binding sites of a TF, we construct a profile vector for the TF. This profile vector can then be used as a query vector to search for the unknown binding sites in the space given a similarity measure between two vectors. The vector space model has long been used in information retrieval (IR)[24, 25]. Under this model, each document in a collection is embedded in a t dimensional space. That is, each document is represented by a t element vector, where t is the number of distinct terms present in the document collection or corpus. To search for documents on a particular topic, a query composed of terms relevant to the topic is constructed. The query can be similarly embedded in the t dimensional space. Similarity between the query and a document can then be measured by measuring the similarity between the two corresponding vectors. In the TFBS search problem, the entire genome or the collection of promoter region sequences corresponds to the corpus, whereas an l mer is analogous to a document in IR. On the other hand, a TF is analogous to a topic, while a TF representation is the analog of a query for the topic.
In this framework, we propose two novel approaches to constructing a query vector for a TF of interests. We compare the proposed methods to a stateoftheart method, the ULPB method, as well as the widelyused PSSM method. Performance of a method is assessed by crossvalidation experiments on two data sets collected from RegulonDB[26] and JASPAR[27], respectively. Independent validation on human ChIPseq data gives further insights into the proposed methods. Finally, we discuss the advantages of searching for TF binding sites in the proposed framework.
The paper is organized as follows. In Methods, we present the novel negativetopositive vector and optimal discriminating vector methods, in addition to introducing the existing methods compared in this work. Crossvalidation results on prokaryotic and eukaryotic transcription factors are presented and discussed in Results and Discussion. Finally, we give the concluding remarks in Conclusions.
Methods
Data sets
Statistics of the E. coli TFs in RegulonDB
Name  Length  # TFBSs  Name  Length  # TFBSs 

MetJ  8  29  Lrp  12  62 
SoxS  18  19  HNS  15  37 
FlhDC  16  20  AraC  18  20 
Fis  15  206  ArcA  15  93 
IHF  13  101  OmpR  20  22 
PhoB  20  17  GlpR  20  23 
OxyR  17  41  CpxR  15  37 
NarL  7  90  CRP  22  249 
TyrR  18  19  NarP  7  20 
Fur  19  81  LexA  20  40 
NtrC  17  17  FNR  14  87 
MalT  10  20  PhoP  17  21 
ArgR  18  32  NsrR  11  37 
Statistics of TFs in the JASPAR database
Mus musculus  

ID  Name  Length  # TFBSs 
MA0039.2  Klf4  10  4336 
MA0047.2  Foxa2  12  809 
MA0062.2  GABPA  11  87 
MA0065.2  PPARG::RXRA  15  839 
MA0104.2  Mycn  26  85 
MA0141.1  Esrrb  12  3613 
MA0142.1  Pou5f1  15  1332 
MA0143.1  Sox2  15  666 
MA0144.1  Stat3  19  830 
MA0145.1  Tcfcp2l1  14  3931 
MA0146.1  Zfx  20  477 
MA0147.1  Myc  10  682 
MA0154.1  EBF1  10  21 
Homo sapiens  
ID  Name  Length  # TFBSs 
MA0037  GATA3  6  20 
MA0052  MEF2A  10  31 
MA0077  SOX9  9  45 
MA0080.2  SPI1  7  35 
MA0083  SRF  12  26 
MA0112.2  ESR1  20  472 
MA0115  NR1H2::RXRA  17  22 
MA0137.2  STAT1  15  2082 
MA0138  REST  19  22 
MA0138.2  REST  11  871 
MA0139.1  CTCF  11  944 
MA0148.1  FOXA1  11  896 
MA0149.1  EWSR1FLI1  17  101 
MA0159.1  RXR::RAR_DR5  17  23 
MA0258.1  ESR2  18  356 
Notation
For clarity, we list and define functions and variables used throughout this paper. Please see Additional file1 for more details.

f_{ i }(u) denotes the probability of observing letter u at position i of a TFBS, where u ∈{A, C, G, T}.

f_{i,j}(u,v) denotes the probability of observing letters u and v at positions i and j , respectively, where i <j and u,v ∈{A, C, G, T}.

f_{ i }(vu) denotes the positionspecific conditional probability of observing v at position i + 1 given u has been seen at position i , where u ,v ∈{A, C, G, T}.

f (vu) denotes the background conditional probability of observing v given u has been observed at the previous position, where u ,v ∈{A, C, G, T}.

is the indicator function given by${\mathcal{I}}_{u}(\xb7)$${\mathcal{I}}_{u}\left(v\right)=\left\{\begin{array}{cc}1& \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\text{if}v=u,\\ 0& \phantom{\rule{0.3em}{0ex}}\text{otherwise,}\end{array}\right.$(1)
where u ,v ∈{A, C, G, T}.

is similarly defined as follows:${\mathcal{I}}_{{u}_{1}{u}_{2}}(\xb7)$${\mathcal{I}}_{{u}_{1}{u}_{2}}\left({v}_{1}{v}_{2}\right)=\left\{\begin{array}{cc}1& \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\text{if}\phantom{\rule{0.3em}{0ex}}{v}_{1}={u}_{1}\phantom{\rule{0.3em}{0ex}}\text{and}\phantom{\rule{0.3em}{0ex}}{v}_{2}={u}_{2},\\ 0& \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}\text{otherwise,}\end{array}\right.$(2)
where u_{1},u_{2},v_{1},v_{2}∈{A, C, G, T}.

I C_{ i }denotes the information content at position i of a binding site. Information content is closely related to entropy, a measure of uncertainty in information theory. The entropy at position i is given by${E}_{i}=\sum _{u\in \left\{\text{A, C, G, T}\right\}}{f}_{i}\left(u\right){\text{log}}_{2}\left[{f}_{i}\left(u\right)\right]$. When${f}_{i}\left(u\right)=\frac{1}{4}$ for all u ∈{A, C, G, T}, E_{ i }attains the maximal entropy of 2 and we are most uncertain about the letter at position i . I C_{ i } is simply defined as$I{C}_{i}=2{E}_{i}=2+\sum _{u\in \left\{\text{A, C, G, T}\right\}}{f}_{i}\left(u\right){\text{log}}_{2}\left[{f}_{i}\left(u\right)\right].$(3)

I C_{i,j} denotes the information content of the position pair (i ,j ) of a binding site. Similarly,$I{C}_{i,j}=4+\sum _{u,v\in \left\{\text{A, C, G, T}\right\}}{f}_{i,j}(u,v){\text{log}}_{2}\left[{f}_{i,j}(u,v)\right],$(4)
where the maximal entropy of 4 is attained when${f}_{i,j}(u,v)=\frac{1}{16}$ for all u ,v ∈{A, C, G, T}.
Embedding short sequences in vector spaces
We further consider nucleotide pair (s_{ i },s_{ j }), where i < j . Only pairs in close proximity are considered in this study. We consider (s_{ i },s_{ j }) only if j −i = 1 or 2, i.e., a pair of nucleotides is considered only if they are adjacent or separated by one nucleotide. Nucleotide pair (s_{ i },s_{ j }) is similarly converted to 16 variables,${w}_{i,j}{\mathcal{I}}_{\mathrm{AA}}\left({s}_{i}{s}_{j}\right),{w}_{i,j}{\mathcal{I}}_{\mathrm{AC}}\left({s}_{i}{s}_{j}\right),\dots ,{w}_{i,j}{\mathcal{I}}_{\mathrm{TT}}\left({s}_{i}{s}_{j}\right)$, as there are 16 possible nucleotide pairs, {AA, AC,…,TT}. We use 32l −48 additional variables to encode the pairs since there are l −1 adjacent pairs and l −2 pairs separated by one nucleotide. Consequently, considering individual nucleotides and nucleotide pairs, each l mer is converted to a (36l −48)element vector.
In this study, we consider two choices of w_{ i }’s and w_{i,j}’s. For the first choice, all the nucleotides and nucleotide pairs are given the same weight, i.e., w_{ i }= 1 and w_{i,j}= 1 for all i and j . The second one assigns weight to the i^{th} nucleotide according to the information content at position i . Similarly, it assigns weight to pair i ,j) according to the information content at this pair of positions. Specifically,${w}_{i}=\sqrt{I{C}_{i}}$ and${w}_{i,j}=\sqrt{I{C}_{i,j}}$ for all i and j .
Searching for TFBSs in vector spaces
where s denote the corresponding vector of s . In other words, the score of s is obtained by taking the dotproduct between s and t. It can be seen that Score(s ) measures the similarity between s and t. Assuming that t corresponds to an l mer t , Score(s ) counts the number of nucleotides and nucleotide pairs shared between s and t when w_{ i }= 1 and w_{i,j}= 1 for all i and j . However, we note that t can be any vector in the space and does not necessarily correspond to an l mer.
As described above, an l mer is converted to a (36l −48)element vector. Hence, we use t to search for binding sites in${\mathbb{R}}^{(36l48)}$. Our approach offers great flexibility in that it easily allows searching for binding sites in a lower dimensional subspace. By setting all but the first 4l elements in t to zero, we are essentially searching for binding sites in${\mathbb{R}}^{4l}$. In this work, we exploit this advantage and simultaneously search for transcription factor binding sites in three subspaces. Two of them are${\mathbb{R}}^{4l}$ and${\mathbb{R}}^{(36l48)}$. The third one is${\mathbb{R}}^{(16l12)}$. This subspace is obtained from considering only the first nucleotide and the l −1 adjacent nucleotide pairs as in a first order Markov chain.
The NPV method
We can see that it computes the similarity between s and the mean binding site vector as well as the similarity between s and the mean nonbinding site vector. It then scores s by the difference of the two similarity scores. The more similar s is to the mean binding site vector, the higher the score. The less similar s is to the mean nonbinding site vector, the higher the score.
The ODV method
The constraint in (8) ensures that the projection of a TFBS s_{(i)} onto the vector β,$\frac{\mathrm{Score}\left({s}_{\left(i\right)}\right)}{\left\right\mathit{\beta}\left\right}$, exceeds the threshold$\frac{b+1}{\left\right\mathit{\beta}\left\right}$. On the other hand, the constraint in (9) ensures that the projection of a nonTFBS s_{(i)} onto β stays below the threshold$\frac{b1}{\left\right\mathit{\beta}\left\right}$. Flexibility is given to the thresholds by introducing ξ_{ i }’s with cost captured by the last two terms in (7). Finally, to clearly distinguish TFBSs from nonTFBSs, the squared difference between the two thresholds ($\frac{b+1}{\left\right\mathit{\beta}\left\right}$ and$\frac{b1}{\left\right\mathit{\beta}\left\right}$) is made as large as possible. This amounts to maximizing${\left(\frac{2}{\left\right\mathit{\beta}\left\right}\right)}^{2}$ or, equivalently, minimizing$\frac{1}{2}\left\right\mathit{\beta}{}^{2}$, which is the first term in (7). We call this approach the optimal discriminating vector (ODV) method.
The optimization problem in (7) is known as a quadratic programming problem with linear inequality constraints specified in (8), (9) and (10). There are p + n + 1 variables and 2n constraints, where p =36l −48 is the dimension of β. We can see that (8) and (9) specify n constraints whereas (10) imposes n constraints on the variables. Quadratic programming[28] is wellstudied and hence general solvers are available, e.g., the OpenOpt framework[29]. To solve this problem, the parameter C (>0) is first arbitrarily chosen. A solver then searches for values of$\mathit{\beta}={({\beta}_{1},\dots ,{\beta}_{p})}^{\mathrm{T}}$, b and$\mathit{\xi}={({\xi}_{1},\dots ,{\xi}_{n})}^{\mathrm{T}}$ such that the objective function in (7) is minimized while the constraints in (8), (9) and (10) are satisfied simultaneously. It can be seen that an optimal solution to (7) always exists since the search space of {β b ξ} is never empty. To find a feasible solution, one can arbitrarily pick$\mathit{\beta}\ne 0\in {\mathbb{R}}^{p}$ and b ∈R . For s_{(i)}∈P , one can pick ξ_{ i }∈R such that the constraint in (8) is satisfied. Similarly, for s_{(i)}∈N , one can pick ξ_{ i }∈R such that the constraint in (9) is met. We can then compute the value of the objective function as the values of all the variables are known. One way to choose the parameter C in (7) is to search for C in a range by crossvalidation. The parameter is TFdependent in general, but experiments showed that a small C =2−^{6} will usually suffice and hence we set C =2−^{6}for all the ODV experiments in this study.
The PSSM and ULPB methods
where s_{ i } denotes the i^{th} letter in s . We note that usually the ratio f_{ i }(s_{ i })/f (s_{ i }) is used in place of f_{ i }(s_{ i }), where f (s_{ i }) is the background probability of s_{ i }. The simpler form in (11) was compared in[23] and hence it serves as a baseline method in this study.
Although ULPB does not consider background probability in the first term of (12), the score is approximately the loglikelihood ratio of the two Markov chains.
The main difference between the PSSM method and the NPV, ODV and ULPB methods is that the PSSM method does not score nucleotide pairs nor does it utilize a background distribution. The NPV and ODV methods explicitly take advantage of negative binding sites, while the ULPB method does it implicitly by using a background distribution. The flexibility of the proposed framework allows the NPV and ODV methods to easily search in subspaces, further distinguishing the PSSM and ULPB methods from the proposed ones.
Results and discussion
Performance assessment and evaluation metrics
The performance of a TFBS search method is evaluated by ν fold crossvalidation (CV). Consider a TF with n_{+} TFBSs of length l with flanking regions on both sides. A set of negative examples, N_{test}, called the test negatives is constructed from the TFBSs of the other TFs with filtering as in[22]. Another set of negative examples, N_{train}, called the training negatives is collected from sequences embedding the n_{+}binding sites. It is comprised of all the l mers except for the TFBSs and two neighboring l mers of each TFBS.
The n_{+} TFBSs are first divided into ν sets, each of which contains$\lfloor \frac{{n}_{+}}{\nu}\rfloor $ or$\lfloor \frac{{n}_{+}}{\nu}\rfloor $ + 1 TFBSs. At each iteration of ν fold CV, one of the ν TFBS sets called the test TFBS set P_{test}is left out. The rest of the TFBSs are therefore called the training TFBSs . A scoring function is obtained using the training TFBSs and nonTFBSs randomly sampled from the training negatives, where the ratio of numbers of nonTFBSs to TFBSs is set to 10. The test TFBSs in P_{test} along with the nonTFBSs in N_{test}are then scored by the scoring function. To score a test sequence, both the forward and reverse strands are scored and, in case the test sequence is longer or shorter than l , the l mer producing the highest score is used. For each test TFBS t ∈P_{test}, we find its rank relative to all the nonTFBSs in N_{test}. Formally, the rank of t equals 1 + {s ∈ N_{test}Score(s ) ≥ Score(t )}.
After the ν fold CV, we end up with n_{+} ranks, each of which corresponds to a TFBS. To allow comparison of methods, we use the area under the ROC curve (AUC) to gauge the performance of a method on the TF. The ROC curve is a plot of true positive rate (TPR) against false positive rate (FPR), displaying the tradeoff between TPR and FPR. We refer readers to[30] for an introduction to this metric. In this study, ν =10 for all the CV experiments. For the NPV and ODV methods, the best weight and subspace combination is obtained at each iteration of the ν fold CV. Specifically, another (ν −1)fold CV is performed on the ν −1 sets of TFBSs to search for the best combination.
Prokaryotic transcription factor binding sites
To understand the behavior of search methods on prokaryotic TF binding sites, we conducted 10fold crossvalidation experiments on the 26TF RegulonDB data set. The proposed NPV and ODV methods were compared to the ULPB method[23]. The PSSM method, considered in[23], was also included for comparison since it served as a simple baseline method.
Eukaryotic transcription factor binding sites
Similarly, statistical tests[31] were performed on all the 6 pairs of methods. Figure5b shows that the NPV and ODV methods are significantly better than the PSSM and ULPB methods. ULPB is significantly better than PSSM, which is again consistent with the results reported in[23]. Overall, performance of the four methods remain unchanged as we shift from prokaryotic transcription factors to eukaryotic ones. This implies that a TFBS search method effective on prokaryotic transcription factors will perform equally well on eukaryotic transcription factors and vice versa.
Motif subtype identification in vector spaces
It has been shown that the binding sites of a TF can be better represented by 2 motif subtypes than by a single motif[32, 33]. In search for new binding sites, two positionspecific scoring matrices are used to score an l mer and the higher score of the two is assigned to this l mer. Searching with two PSSMs was shown to be superior to searching with a single PSSM by crossspecies conservation statistics in these studies.
where β_{+ i} is obtained using TFBSs in cluster i , i =1,2. Unlike the k NPV method, the lengths of β_{+ i}’s may be very different and hence β_{+ i}’s are scaled to unit vectors so as not to bias the scoring function. We note that the choice of k =2 came from previous studies[32, 33]. Generally, k can be greater than 2 or even automatically selected[35]. This however is beyond the scope of this study and may be investigated in the future.
Independent validation on ChIPseq data
Results of independent validation on ChIPseq data
ENCODE  JASPAR  Name  PSSM  ULPB  NPV  S  IC  ODV  S  IC 

GATA3_(SC268)  MA0037  GATA3  0.48922  0.46841  0.50963  1  Y  0.51441  1  Y 
MEF2A  MA0052  MEF2A  0.42566  0.45955  0.35283  3  Y  0.34807  3  N 
PU.1  MA0080.2  SPI1  0.50631  0.49267  0.57575  3  Y  0.58014  3  N 
SRF  MA0083  SRF  0.34299  0.38457  0.43920  2  N  0.43183  3  N 
NRSF  MA0138  REST  0.50615  0.46371  0.46603  1  N  0.47956  2  N 
MA0138.2  REST  0.48031  0.48299  0.49070  3  Y  0.49522  3  N  
ERalpha_a  MA0112.2  ESR1  0.53980  0.49058  0.52414  3  N  0.52146  1  N 
STAT1  MA0137.2  STAT1  0.55348  0.58555  0.61733  1  N  0.62338  1  Y 
CTCF  MA0139.1  CTCF  0.60370  0.60377  0.63785  2  Y  0.64769  2  Y 
CTCF_(C20)  0.44108  0.44696  0.53181  0.54306  
CTCF_(SC5916)  0.46729  0.47047  0.54097  0.55028  
FOXA1_(C20)  MA0148.1  FOXA1  0.48083  0.48698  0.48994  3  Y  0.49853  3  N 
FOXA1_(SC101058)  0.48897  0.48326  0.49945  0.50986  
EBF  MA0154.1  EBF1  0.50011  0.51202  0.56084  3  Y  0.59172  3  N 
EBF1_(C8)  0.42214  0.43705  0.52067  0.53207  
FOXA2_(SC6554)  MA0047.2  Foxa2  0.48328  0.39496  0.45500  3  Y  0.47906  3  N 
STAT3  MA0144.1  Stat3  0.39145  0.33052  0.38094  3  Y  0.43807  3  Y 
POU5F1_(SC9081)  MA0142.1  Pou5f1  0.42151  0.42793  0.40855  3  N  0.45449  3  N 
For the NPV and ODV methods, the best weight and subspace combination was found by 5fold crossvalidation on the JASPAR TFBSs, while flanking genomic sequences of the TFBSs were the sources of negative binding sites. To assess the 4 compared methods, we considered the part of a ROC curve where FPR is at most 0.01 and calculated the AUC scaled to between 0 and 1. This is nearly equivalent to allowing at most 10 false positive hits per promoter on average. As a peak spans about 200 bases, it is considered recalled when it fully contains a predicted binding site. Similarly, a predicted binding site must be fully covered by a peak to be a true positive hit.
In Table3, we observe that ODV, NPV, ULPB and PSSM produced the best AUC on 13, 1, 1 and 3 out of 18 tests, respectively. Statistical tests showed that ODV significantly outperformed the other 3 methods (p values ≤ 0.0028), NPV significantly outperformed ULPB and PSSM (p values ≤ 0.0449), and ULPB and PSSM are comparable (p value: 0.433). We notice that both NPV and ODV performed worse than the other two methods on MEF2A. As NPV and ODV both sample negative examples from flanking sequences of TFBSs, we suspect that this is one example where the flanking sequences do not represent well the entire promoters. ODV performed consistently across tests corresponding to the same JASPAR ID such as the three for CTCF. Examining the best weight and subspace, we can see that the subspace agrees on 11 out of 14 TF models, while the weight agrees on only 7 of them. The latter may be because ODV optimizes the β vector and hence is less sensitive to the weight used to embed an l mer.
Conclusions
In this work, we proposed to search for transcription factor binding sites in vector spaces. The novel NPV and ODV methods were introduced to construct a query vector to search for binding sites of a TF. We compared our methods to a stateoftheart method, the ULPB method, and the widelyused PSSM method. Crossvalidation experiments revealed that the NPV and ODV methods significantly outperformed the ULPB and PSSM methods on prokaryotic as well as eukaryotic TF binding sties. Independent validation on human ChIPseq data further verified that the NPV and ODV methods are significantly better than the other compared methods.
One of the advantages of our framework is that it allows one to easily search for binding sites in various subspaces. Hence, one can search in the best subspace for each individual TF since one can hardly find an optimal subspace for all the TFs. Another advantage is that under the proposed framework one can readily identify motif subtypes for a TF. Hence, to exploit this advantage, we introduced the k NPV and k ODV methods, immediate variants of the NPV and ODV methods. We demonstrated that, consistent with results in previous studies, k NPV (k ODV) significantly improved NPV (ODV) on the two data sets.
Our future work aims for extending our proposed methods to handling known binding sites of variable lengths. We will seek to approach this problem without resorting to multiple sequence alignment, which is notoriously timeconsuming. In the meantime, we will also seek to identify additional promising subspaces to search for TF binding sites in.
Author’s contributions
CL and CH conceived the study. CL collected the data, carried out the experiments and drafted the manuscript. CH guided the study and revised the manuscript. Both authors read and approved the final manuscript.
Declarations
Acknowledgements
This work was supported in part by National Science Foundation [grant numbers CCF0755373 and OCI1156837].
Authors’ Affiliations
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