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MISCORE: a new scoring function for characterizing DNA regulatory motifs in promoter sequences
BMC Systems Biologyvolume 6, Article number: S4 (2012)
Abstract
Background
Computational approaches for finding DNA regulatory motifs in promoter sequences are useful to biologists in terms of reducing the experimental costs and speeding up the discovery process of de novo binding sites. It is important for rulebased or clusteringbased motif searching schemes to effectively and efficiently evaluate the similarity between a kmer (a klength subsequence) and a motif model, without assuming the independence of nucleotides in motif models or without employing computationally expensive Markov chain models to estimate the background probabilities of kmers. Also, it is interesting and beneficial to use a priori knowledge in developing advanced searching tools.
Results
This paper presents a new scoring function, termed as MISCORE, for functional motif characterization and evaluation. Our MISCORE is free from: (i) any assumption on model dependency; and (ii) the use of Markov chain model for background modeling. It integrates the compositional complexity of motif instances into the function. Performance evaluations with comparison to the wellknown Maximum a Posteriori (MAP) score and Information Content (IC) have shown that MISCORE has promising capabilities to separate and recognize functional DNA motifs and its instances from nonfunctional ones.
Conclusions
MISCORE is a fast computational tool for candidate motif characterization, evaluation and selection. It enables to embed priori known motif models for computing motiftomotif similarity, which is more advantageous than IC and MAP score. In addition to these merits mentioned above, MISCORE can automatically filter out some repetitive kmers from a motif model due to the introduction of the compositional complexity in the function. Consequently, the merits of our proposed MISCORE in terms of both motif signal modeling power and computational efficiency will make it more applicable in the development of computational motif discovery tools.
Background
Gene transcription is controlled by the essential interactions between Transcription Factor Binding Sites (TFBSs, or simply Binding Sites) and Transcription Proteins known as Transcription Factors (TFs) [1]. Understanding these interactions requires a knowledge on all binding sites associated with their TFs and cisregulatory modules. Hence, discovering unknown motifs (i.e., a collection of binding sites) in coexpressed genes or finding de novo binding sites associated with a known TF is crucial to understand the gene regulatory mechanisms [2–4]. Experimental approaches for finding DNA motifs are laborious and expensive [5, 6]. Additionally, experimental techniques such as ChIPchip [7], ChIPseq [8] and microarray technology are mostly incapable of predicting specific locations of the binding sites.
It was the biological significance of the costeffective identification of the DNA motifs that computational motif discovery has received considerable attention in the last two decades. In addition to being costeffective and timeefficient, the nature of computational techniques offers the fastest and usually the easiest means of adopting rapidly emerging new and revised understandings on the biological process to produce more sensible motif discovery results. Despite being enormously attempted, an effective motif discovery performance by the computational approaches still remains challenging [9–11]. This is partly due to the lack of effective characterization on regulatory motifs which helps in distinguishing the functional motifs from the nonfunctional ones.
Due to the functional significance in gene regulation, motifs are evolutionarily conserved. Hence, motif instances appear to be rather similar to each other despite having variability in their nucleotide compositions [12]. Motif instances are rarely found in the background sequences, which is often termed as the background rareness. Also, functional motifs are often overrepresented in the regulatory regions (foreground) compared to the backgrounds [13–16]. Thus, a motif's backgroundtoforeground appearance ratio should be smaller than the random ones. Overrepresentation can be similarly interpreted with the rareness characteristic. However, they are typically expressed with different statistical representations. Another useful characteristic of functional motifs is related to the compositional complexity of the nucleotides, which is termed as motif complexity [17].
Information Content (IC) [18] and Maximum a Posteriori (MAP) [19] score are two conventional motif scoring schemes that are widely adopted in evaluating and ranking candidate motifs. They are capable of characterizing the model conservation and the background rareness properties of the functional motifs. However, they suffer from the following shortcomings:

1.
IC evaluates a motif by quantifying the relative entropy of the motif PFM (Positional Frequency Matrix) under assumption of model independence. This assumption on model independence is fundamentally weak as shown in [20–23].

2.
MAP, on the other hand, requires a higher order Markov chain model to estimate the background probabilities [24] prior to motif evaluation. Its computational time and cost increases along with the increment of the order of the used Markov chain model. Also, MAP score can not be used to evaluate the similarity between a kmer and a motif model, which is essential in computational motif discovery exercises.

3.
Both IC and MAP score ignore the motifcomplexity feature in the evaluation of the candidate motifs. Hence, a complexity scorebased filtering [17] has to be used in candidate motif evaluation. The complexity threshold is empirically set in the filtering process that needs human intervention and careful attempts.

4.
Computational motif discovery can be guided by some known motif models as useful a priori knowledge (pk). Motif evaluation in terms of ranking then becomes a motiftomotif similarity task. Unfortunately, IC and MAP score are not able to embed the pk models in scoring.
Motivated by the above issues, this paper introduces a new motif scoring function, termed as MISCORE (mismatchbased matrix similarity scores), to quantify similarity between a kmer and a motif PFM using a mismatch computation on the nucleotides. By evaluating each instance kmer (a candidate binding site) of a motif, MISCORE can quantify the likeliness of the candidate motif to be functional by a combined characterization on the model conservation, the background rareness and the compositional complexity. Our proposed MISCORE share the following three remarkable features: (i) computational efficiency due to its simplicity; (ii) free from any assumption on model dependency; and (iii) an embedability of a priori knowledge in motif scoring. An extension of MISCORE, that adopts a biologically inclined pattern localization approach for an improved recognition of the functional motifs, is also reported in this paper.
Experiments on 33 benchmark DNA datasets have been carried out for evaluating the performance of MISCORE with comparison to IC and MAP score. Firstly, we examine how well these metrics can separate the functional motifs from the random ones. Secondly, we are interested in learning how well they can recognize the functional motifs from a set of putative motif models in terms of candidate ranking. Lastly, we evaluate the effectiveness of MISCORE in recognizing the functional motifs using pk models. The experimental results are found promisingly supportive to MISCORE.
Overrepresentation is a widely recognized numerical feature for characterizing functional motifs [13–15], that typically differs from the statistical quantification of the background rareness property. Due to their common objective of motif characterization, correlating them through a single framework is fundamentally meaningful and it has not been addressed sufficiently in the literature. MISCORE can be utilized as a similarity metric to perform this correlation as detailed in the latter portion of this paper.
Methods
This section describes MISCORE and its localized version in details. For the sake of completeness, some preliminaries are given, including the notations and the kmer encoding scheme used throughout this paper, followed by a preliminary introduction on the motif complexity score [17], Information Content [18] and the Maximum a Posteriori score [19].
Preliminaries
Model representation
In this paper, Positional Frequency Matrix (PFM) is employed as the motif model [18]. The PFMbased motif model, denoted by M, is a matrix, i.e., M = [f(b_{ i } , i)]_{4×k}, where b_{ i } ∈ χ = {A, C, G, T} and i = 1, . . ., k, and each entry f(b_{ i } , i) represents the probability of nucleotide b_{ i } at position i. Similarly, a kmer K_{ s } = q_{1}q_{2} . . . q_{ k } is encoded as a binary matrix K = [k(b_{ i } , i)]_{4×k}with k(q_{ i } , i) = 1 and k(b_{ i } , i) = 0 for b_{ i } ≠ q_{ i } . For example, a kmer K_{ s } = AGCGTGT can be encoded as,
For a given binary encoded set of kmers, S = {K_{1}, K_{2}, ..., K_{ P } }, the motif PFM model M_{ S } can be computed by ${M}_{S}=\frac{1}{P}{\sum}_{i=1}^{P}{K}_{i}$.
Model complexity
Motif discovery tools often return models with low complexity, that show a repetitive occurrence of nucleotides. Hence, a motifcomplexity score was proposed in [17] to filter out models with lower complexities, that is,
where k is the length of kmers and f(b_{ i } , i) is the observed frequency of the base b_{ i } at position i in the model M. Here, the complexity score lies in [(1/4) ^{k} , 1], where 1 refers to a fully complex motif PFM.
Maximum a posteriori (MAP) score
MAP score [19] is a powerful quantifier that evaluates the merit of a candidate motif (a set of kmers, S) by considering its model conservation and the background rareness. The background rareness of S is computed using a higher order Markov chain model [24]. For each K ∈ S, this model can produce an estimation of background probability, namely p(KB), for a given background model B:
where m is the Markov chain order; k is the length of kmers; p(b_{1}, b_{2}, . . ., b_{ m } ) is the estimated probability of subsequence b_{1}, b_{2}, . . ., b_{ m } and p(b_{ i } b_{im}, b_{im+1}, . . ., b_{i1}) is the conditional probability of the subsequence b_{ i } under b_{im}, b_{im+1}, . . ., b_{i1}occurrence constraint. Then, for the candidate motif S, MAP score can be expressed as,
where S is the cardinality of the set S and E(S) is the entropy [25] of the PFM (M), expressed as,
A higher MAP score indicates a better likeliness of the motif S to be functional.
Information content (IC)
IC [18], measuring the average binding energy of the kmers set S, can be given by,
where f(b_{ i } , i) is frequency of the base b_{ i } at position i in the model M, and p(b_{ i } ) is the precomputed background frequency of the nucleotide base b_{ i } . A higher IC score of a candidate motif indicates a better potential of being a functional one.
MISCORE for motif characterization
MISCORE is a new scoring function for modeling motif signals that uses a combined characterization on the model conservation, the background rareness and the compositional complexity of functional motifs. It quantifies a similarity between a kmer K and a putative model M with respect to the background reference model M_{ ref } , that is,
where d(K, M) is defined as a generalized Hamming distance, expressed as,
where f(b_{ i } , i) and k(b_{ i } , i) are the observed frequencies of base b_{ i } at position i in M and K, respectively.
Motivated by the wellknown Gini index to quantify impurity of data clusters, we define c(K) in Eq (6) to compute the compositional complexity of K as follows:
where the complexity is scored according to the distribution of bases (A, C, G, T) in the K. An equal distribution gives the maximum score of 1 and a dominant distribution, i.e., a nucleotide appears at all positions of the K, gives the minimum complexity of 0. In Eq (6), the score range for both d(K, M_{ ref } ) and c(K) is 0[1]. The complexity measure given in Eq (6) helps in automatically eliminating the lowcomplex motifs from the top rank. In this way, an empirical thresholdbased filtering [17] for filtering the lowcomplex candidate motifs can be avoided.
While no pk model associated with the target motifs is available, then we need to employ some searching tools to generate a model that is qualified to be an approximation M of the target motifs. Then, this putative model is essentially derived from the information embedded in the input sequences by the employed search algorithms. For instance, in the clustering type of motif finding algorithms [17, 26, 27], the putative models can be obtained by grouping kmers based on a similarity metric.
Binding sites are evolutionarily constrained with limited mutations, hence a K can be a putative motif instance if d(K, M) <d(K, M_{ ref } ) holds, which implies a smaller mismatch to the putative model M than the background reference model M_{ ref } . Note that the M_{ ref } is a PFM that can be constructed by all kmers from the background sequences. For a large sized background, each column of the M_{ ref } approximates the nucleotides background frequency. Thus, the M_{ ref } can be conveniently composed of the nucleotides precomputable background frequency in each column. Large sequenceportions that have a minimal chance of having the true binding sites can be taken as the backgrounds, e.g., random chunks of large genomic portions or a large collection of upstream regions from the relevant species. Note that a smaller r(K, M) score characterizes a higher similarity of that K to M in respect to its dissimilarity to M_{ ref } and a better nucleotide complexity in K, which implies a combined characterization on the model conservation, the background rareness and the compositional complexity.
A mathematical expectation of the MISCORE values of a set of kmers can be viewed as a metric to characterize the candidate motifs. Given a set of kmers S and its PFM model M_{ S } , a MISCOREbased Motif Score (MMS), denoted as R(S), can be evaluated by,
where  *  is the set cardinality and r(*, *) is the MISCORE given in Eq (6). A smaller MMS score indicates a better potential for a candidate motif to be functional.
Remark
Initially, MISCORE was introduced in [28] to quantify a mismatchbased similarity between a K and a model M_{ S } , i.e., $d\left(K,\phantom{\rule{2.77695pt}{0ex}}{M}_{S}\right)=k{\sum}_{i=1}^{k}{\sum}_{\forall {b}_{i}\in \chi}f\left({b}_{i},\phantom{\rule{2.77695pt}{0ex}}i\right)k\left({b}_{i},\phantom{\rule{2.77695pt}{0ex}}i\right)$. A corresponding MMS was defined by $MMS\left(S\right)=\frac{1}{\leftS\right}{\sum}_{\forall K\in S}d\left(K,\phantom{\rule{2.77695pt}{0ex}}{M}_{S}\right)$, and utilized as a motif scoring function to quantify the conservation property of a motif S. In [29], an improved version of MISCORE, termed as relativeMISCORE, was introduced to characterize a motif's conservation and the rareness properties by introducing a background reference model M_{ ref } in the MISCORE computation. Let r(K, M_{ S } ) denote a relative similarity between a K and a model M_{ S } . Then, it can be computed by r(K, M_{ S } ) = d(K, M_{ S } )/d(K, M_{ ref } ) that results in a relativeMMS: $RMMS\left(S\right)=\frac{1}{\leftS\right}{\sum}_{\forall K\in S}r\left(K,\phantom{\rule{2.77695pt}{0ex}}{M}_{S}\right)$. As a new scoring function, it was employed as a fitness function in our GAPK framework for motif discovery. In this paper, we introduce a compositional complexity term in the relativeMISCORE as shown in Eq (6), which improves our previous work by preventing kmers with repetitive nucleotides from motif models. This new characterization simultaneously addresses the model conservation, backgroundrareness and the compositional complexity properties of the regulatory motifs, which makes the present MISCORE functionally advantageous than IC, MAP score and the previous MISCORE versions. It should be pointed out that other forms of characterization on regulatory motifs exist, provided that they can model the motif signals effectively and efficiently.
Observation: Experiments on real DNA datasets demonstrated that R scores of the functional motifs are with statistically significant pvalues and zscores, that can be computed using large collections of (i) random and (ii) conserved models, generated from the respective promoter sequences. Results obtained on 12 real DNA datasets are presented in Table 1, showing that R scores of the true models M_{ t } (functional motif) are mostly rare with comparison to the conservedmodels M_{ c } , indicated by close to zero pvalues. Each M_{ c } is generated by a random selection of a seed K from a random sequence and by collecting the most similar Ks to the seed, only one was picked from each sequence. It shows that, despite being conserved, M_{ c } models are rarely putative to be functional in MMS scoring as anticipated. In regard to this, R(M_{ t } ) scores are found to be the rarest with comparison to the random models M_{ r } , which is indicated clearly by the 0.000 pvalues and reasonably high zscores. Each random model M_{ r } was composed of one randomly selected K from each sequence.
LocalizedMISCORE
Transcription proteins rarely contact a single nucleotide without interacting with the adjacent bases in the binding process. Hence, the positions with a higher binding energy given by IC (and also a lower binding energy) are usually clustered as local information blocks in the PFM model of functional motifs [30]. Positionspecific similarity metrics assign an equal weight to every position in the model and ignore the variability among the local blocks appearing in the motif PFMs. Since, a motif PFM can be regarded as a descriptor of its binding preferences, the underlaying nucleotide blocks are believed to carry useful information that constitutes the overall characterization of the motif. Based on this understanding, we aim to decompose a motif PFM into a set of local blocks and assign a weight to each block according to its potential of being functional.
MISCORE is then extended to a localizedMISCORE, denoted by r_{ l } (K, M_{ S } ), that can be written as,
where β_{ j } (K), β_{ j } (M_{ S } ) and β_{ j } (M_{ ref } ) are the j^{th} local block in the K, the M_{ S } and the background model M_{ ref } , respectively. A wlength local block β_{ j } (.) can be produced by shifting a small matrix window β_{[4×w]}such that (2 ≤ w <k) in the K, the M_{ S } and the M_{ ref } so that, k  w + 1 number of blocks can be produced.
The weight g_{ j } for the j^{th} block in M_{ S } (i.e., β_{ j } (M_{ S } )) can be assigned as,
where G(β_{ j } (M_{ S } )) is a modified Gini purity index (a complement of the Gini impurity index) that can be evaluated by,
where p(b_{ i } ) is a background frequency of the base b_{ i } . Inspired by IC, G(β_{ j } (M_{ S } )) can characterize the conservation and the rareness properties of a block. Then, a localizedMMS with notation R_{ l } (S), for evaluating the merit of a set of kmers S as a potential motif, can be given by,
where r_{ l } (K, M_{ S } ) is the localizedMISCORE given by Eq (10).
Note that the localizedMMS aims to improve the discrimination power for weak motifs, while it performs closely to the MMS for the strong motifs.
Results and discussion
In this section, we evaluate the separability and the recognizability performances of MISCORE with comparison to IC and MAP score. The latter portion of the recognizability analysis describes how our MISCORE can perform motiftomotif similarity computation and incorporate pk models in recognizing functional motifs.
Separability
It is interesting to observe the performance of MISCORE, IC and MAP score in terms of separating functional motifs from the random ones. Hence, a separability performance evaluation on these modeling metrics are conducted, where the separability is considered as a metric to measure the discriminative scoregaps (normalized) between a functional motif model and a large collection of random nonfunctional ones.
Separability metric
Sep(*, *) score compares two metrics to learn which one has stronger discriminative power to distinguish a true motif from the random models. Given two metrics A and B, a true motif S_{ t } and a large collection of random models $\left({S}_{{r}_{q}},\phantom{\rule{0.3em}{0ex}}for\phantom{\rule{0.3em}{0ex}}q=1,2,3,\dots ,N\right)$, Sep(A, B) can be defined by
where E{*} represents the mathematical expectation, γ_{ A } = [A_{ max }  A_{ min } ]^{1}, γ_{ B } = [B_{ max }  B_{ min } ]^{1}, and $\left[A\left({S}_{t}\right)A\left({S}_{{r}_{q}}\right)\right]$ is the scoregap produced by metric A for S_{ t } and ${S}_{{r}_{q}}$, $\left[B\left({S}_{t}\right)B\left({S}_{{r}_{q}}\right)\right]$ reads similarly for the metric B. A_{ max } (A_{ min } ) and B_{ max } (B_{ min } ) are the metricspecific maximum (minimum), i.e., the best (worst) possible scores, that perform a normalization. Sep(A, B) > 0 score interprets that the metric B outperforms the metric A, and Sep(A, B) < 0 score indicates the opposite case, while Sep(A, B) = 0 score indicates an equal separability performance by the two metrics.
For each dataset, firstly a true motif S_{ t } is generated by carefully aligning all known binding sites using CLUSTAL W [31]. Then, N = 5000 random models are generated by collecting random kmers from the dataset and by carefully avoiding overlap with the true binding sites subject to $\left{S}_{{r}_{q}}\right\phantom{\rule{0.3em}{0ex}}=\phantom{\rule{0.3em}{0ex}}\left{S}_{t}\right$. The metric bounds, i.e., the best and the worst possible scores, for score normalization is required in Eq (14). The bestpossible score (upper bound) of a metric can be obtained by ensuring the maximum quantification of the motif characteristics. To find the upper bound of a metric, we assume that there exist a hypothetical set of kmers S^{*} that can ensure the bestpossible score of a metric. With an assumption of a perfect conservation between the motif instances, i.e., $\delta \left({K}_{a}^{*},\phantom{\rule{2.77695pt}{0ex}}{K}_{b}^{*}\right)=0$, $\forall {K}_{a,b}^{*}\in {S}^{*}$, where δ(*, *) is a similarity quantification, the upper bound for the metrics can be deduced using their respective equation. However, the lower bound (i.e., the worstpossible score) of the metrics are difficult to be computed since the conservation characteristic of a given motif can not be completely eliminated in any situation. Having no viable solution to compute this, the lowerbound of these metrics are practically approximated by the worst score produced by the metrics over a large collection of random models.
Separability results
The datasets used in this paper are split into three groups based on their origins. The first data group (denoted as dg_{1}) contains 8 datasets that are composed of 200bp promoters that contain the known binding sites (functional motifs) associated with the following TFs: ERE, MEF2, SRF, CREB, E2F, MYOD, TBP and CRP. The whole datasets were collected from [32], and each dataset contains a varying number of sequences and a verified motif with known location of the binding sites. The second group (dg_{2}) contains 20 mixed datasets (real and artificial) with 500bp ~ 2000bp sequences that were collected from [10]. The third group (dg_{3}) contains 5 datasets that are composed of 500bp promoters with known binding sites associated with the following TFs: CREB, SRF, TBP, MEF2 and MYOD. The 500bp promoters were collected from the Annotated regulatory Binding Sites (ABS, v1.0) database [33]. Details on these 33 datasets are presented in Table 2.
First of all, Sep(R, R_{ l } ) scores are computed to evaluate the improvement of the localized version. Several criteria for the local blocklength (w) selection have been examined; and the Sep(R, R_{ l } ) scores are presented in Table 3, showing that the localized version is likely to perform favorably with a smaller w, e.g., w = round(k/3), since Sep(R, R_{ l } ) > 0 holds for most of the datasets. As w becomes larger and gets closer to k, the Sep(R, R_{ l } ) scores tend to be zero, which makes sense in logic.
A separability comparison among R, R_{ l } , IC and MAP score is then conducted on the 33 datasets. The results are presented in Table 4, showing that MISCORE can achieve a comparable separability performance to IC and a remarkably improved performance than MAP score, which is indicated by the average Sep(*, *) scores on the three data groups, that is, [Sep(IC, R), Sep(IC, R_{ l } ), Sep(MAP, R), Sep(MAP, R_{ l } )]= [0.144, 0.016, 0.273, 0.374]. In our experiments, MAP score is computed using a 3rdorder Markov chain model. A higher order Markov chain model may improve the separability performance for MAP score, however, the computational cost would be much higher in such a case.
Recognizability
It is often observed that after evaluating a set of candidate motifs returned by a discovery tool, the top ranked candidates are not necessarily functional. The ineffectiveness of the motif evaluation metric used can be one of the reasons behind this. Therefore, we have conducted a recognizability performance comparison among these metrics.
Recognizability refers to how well a metric can recognize the best candidate motif from a set of putative candidates in terms of ranking, where the best candidate motif is expected to be top ranked. To conduct this evaluation, we need to have a set of putative candidate motifs generated by some motif discovery tools on each dataset. In this study, we employed MEME [34] to generate a set of putative motifs for each dataset. Then, the best candidate motif is identified by the Fmeasure [35]: F = 2PR/(P + R), where P = TP/(TP + FP), R = TP/(TP + FN), where TP, FP and FN are the number of true positive, false positive and the false negative predictions, respectively. TP refers to the number of the true binding sites overlapped by at least one predicted site. In this study, we considered a true positive count if a true binding site is overlapped by a predicted site with at least 25% of the length of the true site. FP is the number of the predicted sites that do not have more than 25% overlap with any true binding sites; and FN is the number of the true binding sites that are not overlapped by any predicted sites with at least 25% of the length of the binding site.
These candidate motifs for each dataset are then scored by IC, MAP score, R, and R_{ l } respectively, and ranked according to their scores. The assigned rank of the best motif is recorded for each dataset in order to find that which metric can assign a comparatively higher rank to the best motif. In order to evaluate the ranking order, the following criterion is adopted to compute a mean rank (μ) score [36]:
where Q is the number of the relevant items whose rank orders are to be considered. In our case, only the best motif's rank is considered, hence Q = 1 and Eq (15) becomes μ = 1/rank(best motif).
An average μ score over 10 runs with each metric on each dataset is recorded using a set of candidate motifs produced by MEME during each run. The results are presented in Table 5, which also includes a data groupwise E{μ} score as result summary showing that both R and R_{ l } offer a considerably better recognizability than MAP score, while IC is likely to perform the best recognizability performance. However, we observed that a 10run average μ score computed using dg_{1} and dg_{2} (i.e., 28/33 datasets) indicates that both R and R_{ l } can outperform IC and MAP score.
Recognizability on degenerated motifs
Weak motif characterization and recognition is challenging to all evaluation metrics. Therefore, in order to observe how the considered metrics perform in recognizing degenerated motifs, we first split the 33 datasets into two categories, i.e., strong and weak motif classes, based on the average positional conservation of the motif PFMs, which is defined as $apc\left({S}_{t}\right)=\frac{1}{k}{\sum}_{i=1}^{k}{\displaystyle \underset{{b}_{i}}{\text{max}}}\left\{f\left({b}_{i},\phantom{\rule{2.77695pt}{0ex}}i\right)\right\}$, b_{ i } ∈ {A, C, G, T}.
Table 6 reports the average recognizability scores of these metrics on the datasets. The results show that MISCORE can noticeably outperform MAP score and perform comparably to IC in recognizing weak motifs. However, IC outperforms our MISCORE and MAP score in recognizing strong motifs.
Motif recognition using prioriknown models
If there exists priori known (pk) estimation of the target motif profile during the search in the query sequences, then the motif discovery algorithms can greatly benefit by utilizing such a priori knowledge in finding motifs that have similar characteristics to the pk model. Often a priori estimation of a target motif model can be obtained from the public databases e.g., [37–39], or by collecting a set of binding sites from the sequences that are known to be coregulated by the target TF [29]. These pk models can only be the estimation of the target motifs in the search, since: (i) the known binding sites in the public databases are usually incomplete, which may cause the pk profiles to have an incomplete representation that may not be able to reliably discriminate a true motif from a false one [40], and (ii) due to the sequence dissimilarity between the query sequences and the sequences that are known to be coregulated by the target TF.
One plausible use of the pk models is their involvement in the process of motif evaluation, where the putative motifs will be recognized by referring to the pk models. The ranking of the candidate motifs then becomes a motiftomotif similarity quantification between the putative and the pk models.
MAP score is unable to evaluate the motiftomotif similarity. IC, on the other hand, is not originally meant for motiftomotif similarity computation. However, it has been extended as the average log likelihood ratio (ALLR) [41] for this task. Several other metrics can perform motiftomotif similarity quantification, e.g., Pearson correlation coefficient (PCC) [42], KullbackLeibler divergence (KLD) [43–45], Euclidean distance (ED) [46] and SandelinWasserman (SW) metric [47]. But, these metrics can only compute a motiftomotif similarity without considering motif characteristics.
Motivated by the above facts, MISCORE framework is examined to perform the motiftomotif similarity while taking account of the motif characterization. Let a candidate motif S be ranked by using a pk model M_{ pk } . Then, MISCORE becomes
The MMS score (R) given in Eq (9) then can be written as,
Note that R_{ pk } and r_{ pk } , characterizing motif signals with assistance of pk models, can be regarded as the supervised counterparts of R and r, respectively. localizedMISOCRE can be expressed to accommodate the pk models in a similar manner. Similarly, MISCORE can be employed to compute the motiftomotif similarity in order to group similar candidate motifs in the relevant applications.
For simplicity, we demonstrate that MISCORE with the use of pk models can help in recognizing putative motifs, and performs favorably against other metrics. To do this, we first generated a pk model for each dataset by extracting the nonredundant known binding sites associated with CREB, E2F, MEF2 and SRF transcription factors from JASPAR [37]; ERE, MYOD and TBP from TRANSFAC (public v7.0) [38]; and CRP from RegulonDB [39] databases. After alignment, the pk models are generated for the datasets in dg_{1} and dg_{3} since they share common transcription factors. For the 20 datasets in dg_{2}, we applied a multiple sequence alignment tool GLAM [48] to align the binding sites of each dataset. Then, the longest conserved block from the alignment is extracted to form a pk model for each dataset.
The data groupwise average recognizability scores obtained by the metrics over 10 runs are presented in Table 7, showing that MISCORE others a promising performance with comparison to other metrics in terms of recognizing the best candidate motifs using the pk models.
Background rareness and overrepresentation
Another key concept in computational motif discovery is overrepresentation [13–15, 49]. It looks for motifs that have significant occurrences in the query sequences (input promoters) than the background sequences through some statistical quantification [13, 16]. The functionality of this site multiplicity, i.e., 'the shadow appearances of the binding sites', in the regulatory regions could constitute a mechanism for lateral diffusion of the transcription factors along the sequences, and/or the shadow sites might be the fossils from the process of binding site turnover [16, 50]. Even though the biological reasons behind this site multiplicity are yet to be fully understood [16], it is often considered as a useful motif characteristic and well recognized in the working field.
It is interesting to analyze the correlation between a functional motif's background rareness and overrepresentation, although both can partially characterize the functional motifs. This section tries to make a sensible link between these two key concepts.
Correlation between background rareness and overrepresentation
Our aim is to show how MISCORE can be used to characterize a motif's background rareness through its overrepresentation feature using foreground (i.e., promoters) and background information. We first define a constrained frequency (cf) measure in order to compute an occurrence score of a given motif using MISCORE. Given a set S_{ all } to contain all possible kmers from a set of sequences (either foreground or background) and a motif S with a PFM model M_{ S } , cf is defined as:
where  *  represents the set cardinality, r(K, M_{ S } ) is the MISCORE given in Eq (6) and θ is a cutoff threshold that can be defined as θ = R(S) + std(S)λ, where std represents the standard deviation operator, λ is a threshold regulator and R(*) is the MMS given in Eq (9).
Regulatory regions often contain more frequent occurrences of a functional motif compare to the sequencebackgrounds, due to the mutational constraints in the foreground compared to the backgrounds. Hence, a true motif is expected to produce a larger cf in the promoter regions (foreground) than the backgrounds for a given similarity threshold. Therefore, the MISCOREbased overrepresentation score ORS_{ r } for a motif S can be given using Eq (18) as,
where S_{ bg } and S_{ fg } are the sets of all kmers produced by window shifting in the background and in the foreground regions, respectively.
The condition ORS_{ r } (M_{ S } ) < 1 indicates that M_{ S } has a higher frequency in the foreground than the background for a given threshold, which implies that there are comparatively less occurrences of that motif in the background (i.e., background rareness) than the foreground. Hence, the background rareness of a motif can be characterized through its overrepresentation feature, that can be statistically quantified.
Demonstration
We collected the background sequences for CREB, SRF, TBP, MEF2 and MYOD datasets from public databases (e.g., http://www.ncbi.nlm.nih.gov and http://www.ebi.ac.uk) as the respective sequence backgrounds. The respective 200bp and 500bp promoter regions are then taken as the sequenceforegrounds for each TF. The ORS_{ r } (M_{ t } ) scores for different thresholds are computed for each TF and presented in Table 8, showing that the background rareness can be characterized through the overrepresentation of the functional motifs since ORS_{ r } (M_{ t } ) < 1 holds for all cases. It also shows that, as the promoter region grows in length from 200bp to 500bp, the ORS_{ r } scores tend to increase for the functional motifs, as anticipated.
In order to conduct a statistical evaluation, the ORS_{ r } (M_{ t } ) score of the true motif of each dataset is evaluated using two large sets of (i) conserved (M_{ c } ) and (ii) random models (M_{ r } ). Each random model M_{ r } and conserved model M_{ c } is generated according to the criteria that have been described earlier. It has been observed that the following holds for all cases with a given similarity threshold, that is,
This implies that ORS_{ r } (M_{ t } ) scores are relatively rare in respect to E{ORS_{ r } (M_{ c } )} with a given similarity threshold. Since the M_{ c } models, despite being conserved, have less chance of being overrepresented than a true model M_{ t } . In addition to this, ORS_{ r } (M_{ t } ) scores are found to be the rarest with comparison to the random models M_{ r } . In other words, E{ORS_{ r } (M_{ r } )} >ORS_{ r } (M_{ t } ) implies that, the random models have a comparatively larger backgroundtoforeground occurrence ratio (see Eq (19)) than the functional motifs. This characterizes the background rareness property of a functional motif through its overrepresentation property. Figure 1 demonstrates the correlation between the background rareness and the overrepresentation for 10 datasets.
Conclusions
This paper contributes a mismatchbased fast computational tool for modeling DNA regulatory motifs. It is free from any assumption on the model dependency, and it escapes from the use of background modeling using Markov chain models. Simultaneously, it embeds the compositional complexity in modeling the motif signals. Our proposed MISCORE can be used as a metric to measure the similarity between kmers and a motif model, also it can be employed to compute the motiftomotif similarity.
The experimental results on 33 datasets indicate that MISCORE performs favorably with comparison to the wellknown IC and MAP score in terms of the separability and the recognizability. These results also show that MISOCRE is functionally effective in recognizing degenerated motifs, and it can embed the pk models to perform candidate motif ranking.
MISCORE has good potential to be employed as a similarity metric in rulebased or clusteringbased motif discovery algorithms, it can also be employed as a numerical feature in machine learning approaches for finding motifs. Furthermore, MISCOREbased Motif Score (MMS) can be employed as a fitness function in evolutionary computation approaches for motif discovery, and for candidate motif ranking in computational motif discovery tools.
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Acknowledgements
The authors are grateful to Dr Nung Kion Lee (UNIMAS, Malaysia) and Dr Xi Li (CSIRO, Australia) for their contributions to the development of MISCORE during their PhD studies at La Trobe University.
This article has been published as part of BMC Systems Biology Volume 6 Supplement 2, 2012: Proceedings of the 23rd International Conference on Genome Informatics (GIW 2012). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/6/S2.
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Authors' contributions
DW proposed and developed the MISCORE framework with original ideas and the mathematical formulas. He also directed the experimental design and performance analysis. ST mainly contributed to the development of the localized version of MISCORE and the implementation of experiments. Both authors contributed to the writing of the paper, and read and approved the final manuscript.
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Keywords
 Markov Chain Model
 Random Model
 Motif Discovery
 Motif Model
 Functional Motif