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An information transmission model for transcription factor binding at regulatory DNA sites.
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MedLine Citation:
PMID:  22672438     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
BACKGROUND: Computational identification of transcription factor binding sites (TFBSs) is a rapid, cost-efficient way to locate unknown regulatory elements. With increased potential for high-throughput genome sequencing, the availability of accurate computational methods for TFBS prediction has never been as important as it currently is. To date, identifying TFBSs with high sensitivity and specificity is still an open challenge, necessitating the development of novel models for predicting transcription factor-binding regulatory DNA elements.
RESULTS: Based on the information theory, we propose a model for transcription factor binding of regulatory DNA sites. Our model incorporates position interdependencies in effective ways. The model computes the information transferred (TI) between the transcription factor and the TFBS during the binding process and uses TI as the criterion to determine whether the sequence motif is a possible TFBS. Based on this model, we developed a computational method to identify TFBSs. By theoretically proving and testing our model using both real and artificial data, we found that our model provides highly accurate predictive results.
CONCLUSIONS: In this study, we present a novel model for transcription factor binding regulatory DNA sites. The model can provide an increased ability to detect TFBSs.
Authors:
Mingfeng Tan; Dong Yu; Yuan Jin; Lei Dou; Beiping Li; Yuelan Wang; Junjie Yue; Long Liang
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Publication Detail:
Type:  Journal Article     Date:  2012-06-06
Journal Detail:
Title:  Theoretical biology & medical modelling     Volume:  9     ISSN:  1742-4682     ISO Abbreviation:  Theor Biol Med Model     Publication Date:  2012  
Date Detail:
Created Date:  2012-09-17     Completed Date:  2013-03-22     Revised Date:  2013-07-12    
Medline Journal Info:
Nlm Unique ID:  101224383     Medline TA:  Theor Biol Med Model     Country:  England    
Other Details:
Languages:  eng     Pagination:  19     Citation Subset:  IM    
Affiliation:
Beijing Institute of Biotechnology, Beijing 100071, China.
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MeSH Terms
Descriptor/Qualifier:
Base Sequence
Binding Sites / genetics
DNA / genetics*
Databases, Genetic
Models, Genetic*
Promoter Regions, Genetic / genetics
Protein Binding / genetics
Regulatory Sequences, Nucleic Acid / genetics*
Saccharomyces cerevisiae / genetics*
Transcription Factors / metabolism*
Chemical
Reg. No./Substance:
0/Transcription Factors; 9007-49-2/DNA
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Journal ID (nlm-ta): Theor Biol Med Model
Journal ID (iso-abbrev): Theor Biol Med Model
ISSN: 1742-4682
Publisher: BioMed Central
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Copyright ©2012 Tan et al.; licensee BioMed Central Ltd.
open-access:
Received Day: 8 Month: 4 Year: 2012
Accepted Day: 17 Month: 5 Year: 2012
collection publication date: Year: 2012
Electronic publication date: Day: 6 Month: 6 Year: 2012
Volume: 9First Page: 19 Last Page: 19
ID: 3442977
Publisher Id: 1742-4682-9-19
PubMed Id: 22672438
DOI: 10.1186/1742-4682-9-19

An information transmission model for transcription factor binding at regulatory DNA sites
Mingfeng Tan1 Email: anquren@126.com
Dong Yu1 Email: 438596780@qq.com
Yuan Jin1 Email: 653205194@qq.com
Lei Dou2 Email: yisusu@btamail.net.cn
Beiping Li1 Email: ping790102@sina.com
Yuelan Wang1 Email: wyl_lisa@sina.com
Junjie Yue1 Email: yue_junjie@126.com
Long Liang1 Email: ll@bmi.ac.cn
1Beijing Institute of Biotechnology, Beijing, 100071, China
2Beijing Institute of Radiation Medicine, Beijing, 100850, China

Background

The transcription of genes is controlled by transcription factors (TFs), which bind to short DNA motifs that are known as transcription factor binding sites (TFBSs). Identification of TFBSs lies not only at the very heart of expanding our knowledge of regulatory elements in the genome by helping to decode genomic data, discover regulatory patterns in gene expression, and establish transcription regulatory networks, but also of explaining the origins of organismal complexity and development [1]. Computational identification of TFBSs is a rapid, cost-efficient way to locate unknown TFBSs. With increased potential for high-throughput genome sequencing, the availability of accurate computational methods for TFBS prediction has never been as important as it currently is. However, DNA regulatory elements are frequently short and variable, making the computational identification of them a challenging problem because the real TFBSs might be easily lost in random DNA sequences, i.e., the “background noise”.

To date, many models have been developed for transcription factor binding of regulatory DNA sites, and based on those models, numerous computational algorithms have been established to identify TFBSs. Several studies have utilised the structural information of DNA and protein to build predictive models for DNA binding sites [2-5]. These algorithms are able to identify previously uncharacterised binding sites for TFs and have improved performance over simple sequence profile models [6]. However, these algorithms have not been generally used because their parameters depend on the knowledge of the solved protein-DNA complex structures, which is a limited data set.

Several methods use pattern recognition algorithms derived from computer science or other research areas. These methods include support vector machines (SVMs) [7], self-organising maps (SOMs) [8], and Bayesian networks [9]. These algorithms can automatically provide objective and non-user-defined thresholds by training the programme with known data. Nevertheless, the biggest limitation of these methods might be the lack of explicitly biochemical or biophysical explanations.

Currently, position weight matrix (PWM) is the most common model for TFBS recognition. Many methods or programmes are based on the PWM model or its expansion, such as Match [10], the expectation–maximisation (EM) algorithm [11], and the stochastic variant of EM, the Gibbs sampling method [12,13]. In PWM, an L-long sequence motif is represented by a 4*L matrix, with weights giving the frequency of the four DNA bases (or the logarithm) in each of the L positions [6,14,15]. The basic PWM model is based on the biophysical considerations of protein–DNA interactions and uses the relative entropy, which is also known as the information content, as the criterion to determine whether an input sequence is a TFBS. According to this theory, the affinity between the factor and its TFBS is related to the free energy, which correlates with the relative entropy [6,14,15]. Therefore, in order for a sequence to be a TFBS, it must have higher relative entropy. Consequently, the relative entropy can be used as the criterion to detect a TFBS.

The PWM approach assumes that the contribution of each nucleotide position within a TFBS to the free energy is independent and that the effect on the binding strength is cumulative. We call this hypothesis the “independent hypothesis” because it supposes that each base of the motif is independent of the others. Methods based on the independent hypothesis are simple and have small numbers of parameters, making them easy to implement. These methods are widely used and often considered acceptable models for binding-site predictions.

The PWM model can suffer from high false-positive (FP) rates if motifs are degenerate. In addition, in some real cases, the affinity between factors and their TFBSs is weak, causing a high false-negative (FN) rate while using these methods. More importantly, the independent hypothesis can lead to deviations in the scoring mechanism and produce inaccurate results. Experimental evidence [16-20] suggests that there is interdependence among positions in the binding sites, which has prompted the development of models that incorporate position dependencies. The related methods include Bayesian networks [21], permuted Markov models [22], Markov chain optimisation [23], hidden Markov models [24], non-parametric models [25], and generalised weight matrix models [26]. Methods based on position-dependency models usually have better binding site prediction accuracy with lower FP rates. However, these methods require more complicated mathematical tools with more parameters to estimate and more experimental data than are typically available [27].

Orthogonal information from comparative genomics and information on co-regulation at the transcriptional level have also been integrated into these methods to identify cis-regulatory sites [28-31]. Methods have also been proposed to discover the composite regulatory module (CMA) [32,33]. Because most of these methods rely on the basic algorithms proposed previously, their performances are mainly determined by these basic algorithms.

Therefore, although significant progress has been made, the accuracy of the computational identification of TFBSs can still be improved. To tackle the general problem of binding site identification in the absence of high-throughput experimental data, theoretical models of binding sites are still required.

One aim of this work is to develop a new model that incorporates position interdependencies in effective ways to improve the computational prediction of TFBSs. Based on information theory [34,35], in this study, we propose a novel computational model. By theoretically proving and testing our model using both real and artificial data, we find that our model gives highly accurate predictive results.

Information transmission model
An information transfer model for TFBS binding

In this paper, we treat the complex between a transcription factor and its binding site as a stand-alone system. During the binding process, energy exchanges occur between the TF and TFBS, and the spatial structure and physical state of the system change. We assume that the total amount of information in the system remains unchanged in this process and that information is only transferred between the factor and the site:

[Formula ID: bmcM1]
(1) 
INFO=IF1+IS1=IF2+IS2

In this equation, INFO is the total information contained by the system, IF1 and IF2 are the information carried by the transcription factor in the unbound and bound states, respectively, and IS1 and IS2 are the information possessed by the DNA site at the unbound and bound states, respectively. During the binding process, the information flows from the TFBS to the factor (Figure 1). The transferred information is

[Formula ID: bmcM2]
(2) 
TI=IF2−IF1=IS1−IS2

Taking an L-bp sequence (seq) as the input sequence to be scanned, the jth base of seq is seq(j). The background probability of A, T, C, and G is q(i). In this formula, i represents the base A, T, C, or G, and the background probability can be obtained by scanning the chromosome sequences of the species. Before binding, the occurrence probability of base seq(j) is q (seq(j)). According to information theory [25,26], the information carried by the jth base is -log2(q(seq(j))). With the independent hypothesis, the total information carried by the input sequence can be simply calculated by summing all of the information carried by each base of seq:

[Formula ID: bmcM3]
(3) 
IS1=−∑j=1Llog2qseq(j)

Suppose that a transcription factor and its known TFBSs are aligned by an appropriate algorithm. In this study, we use L to represent the length of the aligned motif, j to represent the base position and pj(i) to represent the occurrence probability that the base i (A, T, C or G) appears at the position j according to the motif.

After the TF binding to its site, the state of the DNA sequence changes. The occurrence probability of base seq(j) changes to pj (seq(j)); therefore, the information carried by the jth base becomes -log2pj (seq(j)), and with the independent hypothesis, the total information IS2 is as follows:

[Formula ID: bmcM4]
(4) 
IS2=−∑j=1Llog2pjseq(j)

The TI can be described as

[Formula ID: bmcM5]
(5) 
TI=IS1−IS2=∑j=1Llog2pjseq(j)qseq(j)

We hypothesise that a factor binds to a TFBS only if enough information is transferred from the site to the factor. We can use a basic criterion to determine whether the factor can bind to the sequence: the TI of the sequence must be larger than a threshold value. This value can be defined as the minimum transferred information (MTI), which is the natural and objective threshold used to determine whether the binding can occur. That is,

[Formula ID: bmcM6]
(6) 
threshholdfactor=MTIfactor=minTI|TI=TITFBS,TFBS∈KnownTFBSfactor

Once the TI of an input sequence is larger than MTI, then it is accepted as a possible TFBS.

Enhancement of the model to be universal

The independent model might lead to inaccurate predictive results. In this section, we discuss in detail how this can happen by example and in theory and how we enhanced our model to be independent of this hypothesis.

An example of the correlation among different bases is shown in Figure 2. The same example is used by GuhaThakurta [1] to show the basic concept of the PWM and relative entropy methods. We can see that the 1st and 11th bases are correlated: when the 1st base is C, the 11th base is strictly T. We can find that P1,11(C,T) = 0.5, and P1 (C) P11(T) = 0.5*0.75 = 0.375. As P1,11(C,T)>P1 (C)P11(T); therefore, we conclude that these bases are positively correlated. When position 1 is C, there is a high probability that position 11 is T. For these two positions, P1,11(T,T) = 0.25, P1(T)P11(T) = 0.375. So P1,11(T,T)<P1 (T)P11(T); therefore, we conclude that the positions are negatively correlated, which means that when position 1 is T, there is a high probability that position 11 is not T. Such correlations are not rare, as they can be found in most of the real TFBS data set.

Based on this observation, we propose a formal definition of positive and negative correlations of the bases in a motif: if Pseqi1,⋯,seqim>Pseqi′1,⋯,seqi′k∗Pseqi′k+1,⋯,seqi′m, then seqi′1,⋯,seqi′k and seqi′k+1,⋯,seqi′r are positively correlated. If they are equal, then seqi′1,⋯,seqi′k and seqi′k+1,⋯,seqi′rare independent; otherwise, they are negatively correlated. In this formula, seq(i) is the ith base of the sequence seq. For example, the 4th and 6th bases are positively correlated and contain no more or less information than only the individual base. Therefore, the independent hypothesis leads to an inaccurate estimation of the TI, thereby making an erroneous prediction of the TFBS. Similarly, the use of other methods that are based on the independent hypothesis also results in incorrect scores and leads to inaccurate predictive results. To avoid this inaccuracy, the model was enhanced to address the correlations such that it is capable of determining the correct TI despite the inaccuracy of the independent hypothesis.

First, we know that after binding of the TF to the TFBS, the information encoded by the TFBS seq, isIS2=IL=−log2pseq=−log2pseq1,⋯,seqL. In this equation, pseq=pseq1,⋯,seqL is the occurrence probability of seq=seq1,⋯,seqL versus all of the TFBSs of the TF. Due to unknown TFBSs and lack of statistical data of the known TFBSs, we cannot determine pseq or IL directly, but these terms can be estimated from the known TFBSs.

We use the information of r-base sub-sequences seqi1,⋯,seqiri1>i2>⋯>ir to estimate the information of the full sequence. The probability of a r-base sub-sequence,pseqi1,⋯,seqir, can be approximated as p˜seqi1,⋯,seqir by investigating the known TFBS, and in the following steps, we assume that pseqi1,⋯,seqir and p˜seqi1,⋯,seqir are the same. Therefore, −log2Pseqi1,⋯,seqir is the information of the sub-sequence.

This probability can reveal the correlation among these bases. For example, if base i1 is fully and positively correlated with base ik, as the 4th and 6th positions in Figure 2 are, then pseqi1seqik=pseqi1=pseqik>pseqi1pseqik; hence, the information of these two bases is Ii1,ik=−log2Pseqi1=12Iindependent (i.e., it is only half of the information of the independent situation). If base i1 is independent from base ik, then pseqi1seqik=pseqi1×pseqik and Ii1,ik=−log2Pseqi1×Pseqik=Iindependent.

As there are CLr such r-base sub-sequences in total, the average information for r-base sub-sequences is −1CLr∑i1>i2>⋯>irlog2Pseqi1,⋯,seqir. Because the length of these sub-sequences is r, then the average information carried by one base is −1rCLr∑i1>i2>⋯>irlog2Pseqi1,⋯,seqir. The information of the whole sequence can be estimated by simply multiplying by the length L:

[Formula ID: bmcM7]
(7) 
I=IL≈Ir≈I˜r=−LrCLr∑i1>i2>⋯>irlog2p˜seqi1,⋯,seqir

Similar to the example in Figure 2, if there is a strong tendency for the bases to be positively correlated, then it can be assumed that

[Formula ID: bmcM8]
(8) 
pseqi1,⋯,seqir>pseqi′1,⋯,seqi′kpseqi′k+1,⋯,seqi′r

Under this assumption, we can prove an important relationship, as follows:

[Formula ID: bmcM9]
(9) 
Ir+1<Ir

From (8) we know that

[Formula ID: bmcM10]
(10) 
Ir=−LrCLr∑i1>i2>⋯>irlog2pseqi1,⋯,seqir=−LrCLr∑i1>i2>⋯>ir1CrxCrxlog2pseqi1,⋯,seqir=−LrCLr∑i1>i2>⋯>ir1Crx∑iCrxlog2pseqi1,⋯,seqir<−LrCLr∑i1>i2>⋯>ir1Crx∑i′Crxlog2pseqi′1,⋯,seqi′x+log2pseqi′x+1,⋯,seqi′r=−LrCLr1CrxCrxCLrCLx∑i1>i2>⋯>ixlog2pseqi1,⋯,seqix+1CrxCrr−xCLrCLr−x∑i1>i2>⋯>ir−xlog2pseqi1,⋯,seqir−x=−Lr1CLx∑i1>i2>⋯>ixlog2pseqi1,⋯,seqir+1CLr−x∑i1>i2>⋯>ir−xlog2pseqi1,⋯,seqir−x=−LrxLLxCLx∑i1>i2>⋯>ixlog2pseqi1,⋯,seqir+r−xLLr−xCLr−x∑i1>i2>⋯>ir−xlog2pseqi1,⋯,seqir−x=xrIx+r−xrIr−x

Next, we obtain

[Formula ID: bmcM11]
(11) 
Ir<xrIx+r−xrIr−x

According to (11), we can infer that

[Formula ID: bmcM12]
(12) 
Ir+1<rr+1Ir+1r+1I1<r−1r+1Ir−1+2r+1I1<⋯<I1

If we assume that Ir+1≥Ir, then we immediately obtain Ir+1≥I1, which contradicts (11). Therefore, it must be the case that Ir+1<Ir. Hence, (10) is proved.

Immediately, we know that when the correlation is positive

[Formula ID: bmcM13]
(13) 
IL<Ir<Iindependent2≤r≤L−1

Similarly, if the correlation tends to be negative, then the following must be true:

[Formula ID: bmcM14]
(14) 
Ir+1>Ir

Therefore,

[Formula ID: bmcM15]
(15) 
IL>Ir>Iindependent2≤r≤L−1

If the TFBS seq conforms to the independent hypothesis, according to (5) and (8), its information is

[Formula ID: bmcM16]
(16) 
Iindependent≡−∑i=1Llog2Pseqi≡I1

Therefore, conversely, the tendency of Ir can be used to judge if the correlation is positive, negative, or independent. We now know that Iindependent would overestimate (when the correlation is positive) or underestimate (when the correlation is negative) the IL if the independent hypothesis is not true. Again, this finding can explain why using the independent hypothesis can lead to inaccurately predicted results. More importantly, from (13) and (15), we know that Ir is more accurate than Iindependent when r ≥ 2. So, we can use Ir (r ≥ 2) to estimate the information and obtain the predictive results with more accuracy.

The method for calculating the background probabilities must be revised accordingly to adapt to the enhanced model. Instead of counting each single base by scanning the chromosome sequences to obtain the background probability under the independent hypothesis, a window of length L slides through the chromosomes, and all of the r-base sub-sequences in this window are counted. After the scanning, 4r probabilities are calculated for all of the 4r possible r-base sub-sequences. These values are used to estimate the information carried by the TFBS before the binding event:

[Formula ID: bmcM17]
(17) 
IS1seq=IS1seqL≈IS1seqr=−LCLrr∑i1>i2>⋯>irlog2qseqi1,⋯,seqir

In this equation, qseqi1,⋯,seqir is the background correlation probability, calculated as described previously.

In addition, the formula for estimating the transferred information is changed as follows:

[Formula ID: bmcM18]
(18) 
TIr=IS1seqr−IS2seqr=LrCLr∑i1>i2>⋯>irlog2pseqi1,⋯,seqirqseqi1,⋯,seqir

Once TIr ≥ MTIr (factor), then seq is accepted as a possible TFBS.


Results
Performance in Saccharomyces cerevisiae promoter regions

We tested our model by calculating the TI for all of the known TFBSs of 10 well-characterised transcription factors in the yeast S. cerevisiae promoter database (SCPD) [36]. We found that most of the TFBSs have a TI larger than 0. This evidence strongly supports our TI hypothesis that the information is transferred from the TFBS to the factor, and binding of the TF to the TFBS only happens if enough information is transferred.

First, we use 100% of the known TFBSs as the training set to work out the MTI for each TF and test our method with r = 1, 2, 3, and 4 on this data set. We observed that the number of predicted TFBS decreases more than twofold when r changes from 1 to 2 (Figure 3), which guarantees an increase in accuracy as Figure 4 shows. From Figure 3 and Figure 4, we observe that when r ≥ 2, the performance increases with increasing r-values but not as significantly as when r changes from 1 to 2. Because the computational complexity of our method rapidly increases as r increases, r = 3 is a proper value to obtain good performance and maintain a low level of computational complexity. Therefore, the results of r = 3 were used to compare this method with the others.

Next, we examined how the average performance changes as the proportion of the training set increased from 25% to 100% with r = 3 (Figure 5). We found that as the proportion increased, 1-FN increased linearly; hence, more of the real TFBSs were identified. Moreover, this curve indicated that the method is powerful when little is known about the TFBS. For example, 49% of TFBSs were identified when the model was trained by 25% known TFBSs. Additionally, the FP rate increased little when the proportion of the training set increased, and it was always below 0.3.

In this study, we illustrate several snapshots of TI by scanning several sequences of S. cerevisiae. These sequences cover the coding regions, the regulatory regions and the “flank” regions.

In Figure 6, we illustrate a snapshot of TI by scanning a promoter region of S. cerevisiae. With 75% of the real TFBSs as the training set, we obtained the MTI for the factor. The highest peaks are precisely the real TFBSs, and there are also peaks on the opposite strand that do not reach the threshold.

A comparison of the TI model with other methods

To illustrate the performance of the information transmission model, we implemented this novel model with a programme named tfbsInfoScanner and compared it with commonly used motif identification programmes, such as SOMBRERO, MEME and AlignACE. Mahony et al. [17] proposed the TFBS prediction method SOMBRERO and compared the results derived from SOMBRERO with those from two popular motif finding programmes, MEME [37] and AlignACE [11]. These researchers used the same real data set that we used. To efficiently analyse the performance of our method and to avoid repetitive and time-consuming computation, we used the same real sequence data set and compared results derived from our method to those obtained from SOMBRERO, MEME and AlignACE.

Table 1 shows a performance comparison of our method and three other programmes. The results indicate that when the proportion of the training set is larger than or equal to 50%, our method achieves the best performance in most cases.

Performance on artificial sequences

To examine the performance of our method in discovering “unknown” TFBSs, we subsequently trained our method with all of the known TFBSs and embedded the artificial sequences with pseudo-motifs. Similar to Mahony et al. [17], we also generated three artificial test set, although using our own method. In the artificial test set used by Mahony et al., each set comprises 10 data sets, each of which comprises 10 sequences; each sequence harbours a random number of occurrences (0 ~ 3) for each of the binding motifs for gcn4gal4 and mat1 (generated from PWMs). The total lengths of these three sets of 100 sequences are 4500, 8000 and 12500 bp, respectively. The average length of one sequence is therefore 45 bp, 80 bp or 125 bp, but each sequence harbours at most 9 occurrences of the motifs. We believe this number of occurrences may be too dense, and perhaps a high occurrence of pseudo-TFBSs may be encoded by these sequences.

In our modified method, we also generated three artificial test sets with different sequence lengths (450, 800 and 1250 bp), and each test set consists of 10 sequences that were randomly generated according to the GC content of S. cerevisiae. Each sequence harbours a random number of occurrences (0 ~ 3) for each of the binding motifs for gcn4gal4 and mcb (randomly generated from PWMs). Mahony et al. [17] used mat1 as a test object, but in the new version of SCPD, the TFBS of mat1 is split into mat1_alpha and mat1_beta; therefore, we arbitrarily chose mcb as a substitute for mat1. This test set is more rigorous because these artificial sequences are 10 times longer, leading to an increase in the number of random sequences, which may result in a higher FP rate. As our method is still under development, in this test, the pseudo-TFBSs are also generated from the PWMs. Because the PWM method assumes that the independent hypothesis is true, these pseudo-TFBSs cannot correctly indicate correlation among the bases. This deficiency might lead to a lower TI, and, therefore, some pseudo-TFBSs may not be identified by our method. However, we can investigate what happens when scanning these artificial sequences.

The average performance in each test set using r = 3 is summarised in Table 2. As demonstrated, most pseudo-TFBSs of gcn4 and mcb were recognised. As for gal4, almost none of these sites was identified. Almost none of the unreal result was predicted at the same time. This result was observed mainly because the correlations of actual TFBSs are strong, while the pseudo-motifs do not have such correlations, and therefore their TI is far below the MTI. However, this finding does not mean that our method is ineffective in identifying pseudo-TFBSs. A typical snapshot of the artificial regulatory region that harbours the unrecognised pseudo-TFBSs is shown in Figure 7. Although these pseudo-TFBSs have no correlation in their sites, our method can still identify a strong TI.

The average performance for r = 1 is also summarised in Table 3. When r = 1, our method is equivalent to the assumption that the independent hypothesis is true; therefore, all of the pseudo-TFBSs were identified. Not surprisingly, the FP rate was high. According to both sets of results, the FN rate was low. The FP rate was maintained at a moderate level for r = 3, even though these artificial sequences were 10 times longer than those described previously.


Discussion

During evolution, regulatory instructions or information were encoded in the DNA sequence. Redundant coding (or correlated coding) is utilised to ensure that the important regulatory information will be inherited and transferred correctly. During the binding process, the transcription factor reads the regulatory instructions from the TFBS and subsequently guides transcription according to the regulatory information. In other words, the factor reading the special regulatory instruction from the TFBS then instructs the transcription according to the regulatory information obtained from the TFBS. Nucleic acids needed to be coded in a redundant manner to ensure that the regulatory information can be transferred correctly, and therefore these sites are not independent of the others.

With our model, for the sequences encoding motifs, such as TFBSs, the input sequences can be scanned, and the sub-sequences for which the TI is greater than the MTI of the motif can be taken as the predictive hits.

In our observations, most of the real TFBSs had a positive correlations because with the positively correlated coding, the information that they contained decreased accordingly, but the information was transferred correctly.

Interestingly, we find that if there is a real TFBS encoded by one strand, then there often are peaks on both strands, but the peaks on the opposite strand are usually lower. We think this phenomenon happens for two reasons: first, certain factors bind to their TFBS by inserting a domain into the DNA grooves. In this case, both strands of DNA could have physical contact with the transcription factor; hence, both sides could transfer the regulatory information to the factor, which is detected by our method. Second, it is not known from which strand the background noise comes. Therefore, for example, for r = 2, the occurrence probability of AG equals TC. Therefore, the complementary strand of a real TFBS can have a high TI.

Furthermore, this information transmission model has the potential to be useful in other research areas, for example, in the computational identification of other motifs.


Concluding remarks

In this work, we present a novel model for transcription factor binding regulatory DNA sites. This information transmission model is based on information theory and effectively incorporates position interdependencies. By testing the model on both real and artificial data sets, we have illustrated that our method is efficient at predicting unknown TFBSs.


Materials and methods
Data set preparation

The TFBSs of the 11 TFs and regulatory region sequences were obtained from the yeast S. cerevisiae Promoter Database (SCPD, http://rulai.cshl.edu/SCPD) [28]. This data set includes 68 regulatory regions with a total length of 30299 bp. These sequences harbour 309 experimentally mapped TFBS, including 141 real TFBSs of the 11 TFs. The chromosome sequences of S. cerevisiae were obtained from the National Center for Biotechnology Information (NCBI) reference sequence database.

The artificial sequences used in the test were randomly generated, taking into account the GC content of the S. cerevisiae genome. The pseudo-TFBSs of gcn4, gal4 and mcb were randomly generated from PWMs. We did not generate the correlated TFBSs directly because it is difficult to make the pseudo-TFBSs conform to the correlation relationships, as real TFBSs do.

Background probabilities calculation

Background probabilities are used to estimate the information carried by the TFBS before the binding event. An L-base window slides through the chromosomes, and all of the r-base sub-sequences in this window are counted. After the scanning, 4r probabilities are calculated for all the 4r possible r-base sub-sequences. This computation is time-consuming, but once the background probabilities are worked out, they can be reused in all of the TFBS predictions of this species without being recalculated.

Sequence alignment

The TFBSs of the TFs were separately aligned by the ClustalW multiple alignment programme with the default argument, and the aligned TFBSs and the background probabilities were used to calculate the MTI.

Computation environment

The novel method was implemented with a programme named tfbsInfoScaner, which was written in standard C++. This programme can be run on different computer platforms, and the full source code is available free for non-commercial use upon request by contacting the authors. Our test was run on a 64-CPU Altix 3700 server (Silicon Graphics, Mountain View, CA).


Competing interests

The authors declare that they have no competing interests.


Authors’ contributions

LL and JY formulated the study. MT, DY and YJ performed the research. LD analysed the data. YW and BL participated in analysis and discussion. MT drafted the manuscript. JY revised the manuscript. All authors read and approved the final manuscript.


References
GuhaThakurta D,Computational identification of transcriptional regulatory elements in DNA sequenceNucleic Acids ResYear: 2006343585359816855295
Kono H,Sarai A,Structure-based prediction of DNA target sites by regulatory proteinsProteinsYear: 19993511413110090291
Steffen NR,Murphy SD,Tolleri L,Hatfield GW,Lathrop RH,DNA sequence and structure: direct and indirect recognition in protein-DNA bindingBioinformaticsYear: 200218S22S3012169527
Morozov AV,Havranek JJ,Baker D,Siggia ED,Protein-DNA binding specificity predictions with structural modelsNucleic Acids ResYear: 2005335781579816246914
Siggers TW,Honig B,Structure-based prediction of C2H2 zinc-finger binding specificity: sensitivity to docking geometryNucleic Acids ResYear: 2007351085109717264128
Berg OG,von Hippel PH,Selection of DNA binding sites by regulatory proteins. Statistical-mechanical theory and application to operators and promotersJ Mol BiolYear: 19871937237503612791
Djordjevic M,Sengupta AM,Shraiman BI,A biophysical approach to transcription factor binding site discoveryGenome ResYear: 2003132381239014597652
Mahony S,Hendrix D,Golden A,Rokhsar DS,Transcription factor binding site identification using the self-organizing mapBioinformaticsYear: 2005211807181415647296
Makita Y,De Hoon MJ,Ogasawara N,Miyano S,Nakai K,Bayesian joint prediction of associated transcription factors in Bacillus subtilisPac Symp BiocomputYear: 20051050751815759655
Kel AE,Gossling E,Reuter I,Cheremushkin E,Kel-Margoulis OV,et al. MATCH: A tool for searching transcription factor binding sites in DNA sequencesNucleic Acids ResYear: 2003313576357912824369
Cardon LR,Stormo GD,et al. Expectation maximization algorithm for identifying protein-binding sites with variable lengths from unaligned DNA fragmentsJ Mol BiolYear: 19922231591701731067
Lawrence CE,Altschul SF,Boguski MS,Liu JS,Neuwald AF,et al. Detecting subtle sequence signals: a Gibbs sampling strategy for multiple alignmentScienceYear: 19932622082148211139
Hughes JD,Estep PW,Tavazoie S,Church GM,Computational identification of cis-regulatory elements associated with groups of functionally related genes in Saccharomyces cerevisiaeJ Mol BiolYear: 20002961205121410698627
Schneider TD,Stormo GD,Gold L,Ehrenfeucht A,Information content of binding sites on nucleotide sequencesJ Mol BiolYear: 19861884154313525846
Stormo GD,Fields DS,Specificity, free energy andinformation content in protein-DNA interactionsTrends Biochem SciYear: 1998231091139581503
Benos PV,et al. Probabilistic code for DNA recognition by proteins of the EGR familyJ Mol BiolYear: 200232370172712419259
Bulyk ML,Johnson PL,Church GM,Nucleotides of transcription factor binding sites exert interdependent effects on the binding affinities of transcription factorsNucleic Acids ResYear: 200231255126111861919
Man T-K,Stormo GD,Non-independence of Mnt repressor–operator interaction determined by a new quantitative multiple fluorescence relative affinity (QuMFRA) assayNucleic Acids ResYear: 2001292471247811410653
Udalova IA,et al. Quantitative prediction of NF-kappa B DNA-protein interactionsProc Natl Acad Sci USAYear: 2002998167817212048232
Wolfe SA,et al. Analysis of zinc fingers optimized via phage display: evaluating the utility of a recognition codeJ Mol BiolYear: 1999285191719349925775
Barash Y,et al. Modeling dependencies in protein-DNA binding sitesProceedings of RECOMB-03Year: 2003, 2837
Zhao X,et al. Finding short DNA motifs using permuted Markov modelsJ Comput BiolYear: 20051289490616108724
Ellrott K,et al. Identifying transcription factor binding sites through Markov chain optimizationBioinformaticsYear: 200218Suppl. 2S100S10912385991
Marinescu VD,et al. MAPPER: a search engine for the computational identification of putative transcription factor binding sites in multiple genomesBMC BioinformaYear: 2005679
King OD,Roth FP,A non-parametric model for transcription factor binding sitesNucleic Acids ResYear: 200331e11614500844
Zhou Q,Liu JS,Modeling within-motif dependence for transcription factor binding site predictionsBioinformaticsYear: 20042090991614751969
Tomovic A,Oakeley EJ,Position dependencies in transcription factor binding sitesBioinformaticsYear: 20072393394117308339
Bussemaker HJ,Li H,Siggia ED,Regulatory elementdetection using correlation with expressionNature GenetYear: 20012716717111175784
Cooper GM,Sidow A,Genomic regulatory regions:insights from comparative sequence analysisCurr Opin Genet DevYear: 20031360461014638322
Defrance M,Touzet H,Predicting transcription factor binding sites using local over-representation and comparative genomicsBMC BioinformaYear: 20067396
Blanchette M,Bataille AR,Chen X,Poitras C,Laganiere J,et al. Genome-wide computational prediction of transcriptional regulatory modules reveals new insights into human gene expressionGenome ResYear: 20061665666816606704
Aerts S,Van Loo P,Thijs G,Moreau Y,De Moor B,Computational detection of cis-regulatory modulesBioinformaticsYear: 200319II5II1414534164
Jegga AG,Gupta A,Gowrisankar S,Deshmukh MA,Connolly S,et al. CisMols analyzer: identification of compositionally similar cis-element clusters in ortholog conserved regions of coordinately expressed genesNucleic Acids ResYear: 200533W408W41115980500
Shannon CE,A mathematical theory of communication (Part 1)Bell System Technical JournalYear: 194827379423
Shannon CE,A mathematical theory of communication (Part 2)Bell System Technical JournalYear: 194827623656
Zhu J,Zhang MQ,SCPD: a promoter database of the yeast Saccharomyces cerevisiaeBioinformaticsYear: 19991560761110487868
Bailey TL,Elkan C,Fitting a mixture model by expectation maximization to discover motifs in biopolymersProc Int Conf Intell Syst Mol BiolYear: 1994228367584402

Figures

[Figure ID: F1]
Figure 1 

Information transferred from TFBS to TF during binding. In this figure, we assume the transcription factor and its binding site are a stand-alone system.



[Figure ID: F2]
Figure 2 

Example of positive correlations. The bases in the rectangles connected by the link are positively correlated. These eight known rox1 binding sites were taken from the promoter database of Saccharomyces cerevisiae.



[Figure ID: F3]
Figure 3 

The number of predicted TFBS. With 100% of the known TFBSs as the training set, the number of predicted TFBS decreases more than two times when r changes from 1 to 2, which guarantees an increase in accuracy.



[Figure ID: F4]
Figure 4 

Variety of performance as r changes from 1 to 4. In this figure, the proportion of the training set = 100%; however, the figures for proportion of training set = 25%, 75% and 100% are similar. In this figure, PERF=(k P)/(K P), where K is the set of known motif sites and P is the set of predicted motif sites. RT/ PT is defined as the ratio of the real TFBSs to the predicted TFBSs.



[Figure ID: F5]
Figure 5 

Variety of average performance as the proportion of the training set changes from 25% to 100%, where x=y. In this figure, r = 3; however, the figures for r = 1, 2, and 4 are similar. The definition of PERF is same as in SI Figure 4. The figure of our TI model is powerful when little is known about the TFBS. For example, 49% of TFBSs are identified when trained by 25% known TFBSs.



[Figure ID: F6]
Figure 6 

Snapshots 1 of TI. Factor=al4, ORF=YBR020W, r = 3, proportion of training set = 75%. The short lines on the top mark the position of the real TFBS, and the red lines are TI values from the complementary strand; the long lines in the middle denote the MTI of the specific factor. There are 4 TFBS on the strand from 5’ to 3’, and the highest peaks are almost precisely the real TFBSs.



[Figure ID: F7]
Figure 7 

A typical TI spectrum of the artificial regulatory region harbours unidentified pseudo-TFBSs. The TI spectrum is on the bottom, and the TI of the complementary side is on the right. In this figure, the horizontal axis indicates the centre of the input sub-sequence with length that equals the aligned TFBSs of the specific factor. The data shows two embedded pseudo-gal4 TFBSs in the sequence. We can see that there are two TI peaks that are distinct but do not reach the threshold.



Tables
[TableWrap ID: T1] Table 1 

Performance comparison between our TI method (r= 3) and three other programmes: SOMBRERO, MEME and AlignACE


Factor   abf1 csre gal4 gcn4 gcr1 hstf mat mcb mig1 pho2
SOMBRERO
FP
0.56
0.727
0.235
0.286
0.69
0.571
0.25
0.645
0.68
0.909
 
FN
0.45
0.25
0.071
0.6
0.222
0.111
0.308
0.083
0.2
0.5
MEME
FP
0.182
0.667
0.167
0.8
0.444
0.75
0.267
0.25
1
1
 
FN
0.55
0.5
0.286
0.92
0.444
0.333
0.154
0.25
1
1
AlignACE
FP
0.375
0.824
0.083
0.444
0.625
0.556
0
0.083
0.909
1
 
FN
0.5
0.25
0.214
0.6
0.333
0.111
0.308
0.083
0.9
1
TI model with
FP
0
0
0
0.182
0.333
0
0
0
0
0
25% known TFBS as training set
FN
0.727
0.5
0.643
0.259
0.692
0.667
0.526
0.333
0.429
0.5
TI model with
FP
0
0.333
0
0.226
0.143
0
0.294
0
0
0
50% known TFBS as training set
FN
0.455
0
0.286
0.037
0.308
0.5
0.158
0.083
0.214
0.375
TI model with
FP
0
0
0
0.25
0.615
0.783
0.25
0
0
0.25
75% known TFBS as training set
FN
0.182
0
0.143
0.037
0.077
0
0.158
0
0.143
0.125
TI model with
FP
0
0
0
0.265
0.577
0.526
0.222
0
0
0.571
100% known TFBS as training set FN 0 0 0 0 0 0.167 0.053 0 0.071 0

The best performances of the other three programmes are underlined. The performances of our method that are better than the best of the other three programmes are in bold and underlined. The performances that were close to the best of the other three programmes are in bold. The results show that when the proportion of the training set is larger than or equal to 50%, our method achieves the best performance in most cases.


[TableWrap ID: T2] Table 2 

Average performance of the artificial sequence data set (r = 3), perf = (kz∩P)/(K∪P), where K is the set of known motif sites and P is the set of predicted motif sites[30]


Length Index gcn4 gal4 mcb Average
 
FP
0.75
0
0.647
0.466
450*10
FN
0.083
1
0.143
0.409
 
perf
0.244
0
0.333
0.192
 
PT/ RT
3.667
0
2.429
2.032
 
FP
0.892
0
0.75
0.547
800*10
FN
0.2
1
0.333
0.511
 
perf
0.105
0
0.222
0.109
 
PT/ RT
7.4
0
2.667
3.356
 
FP
0.936
0
0.756
0.564
1250*10
FN
0.25
0.875
0.286
0.470
 
perf
0.063
0.143
0.222
0.143
  PT/ RT 11.75 0.143 2.929 4.941

In this table, PT/ RT is defined as the ratio of predicted TFBS versus the pseudo-TFBSs.


[TableWrap ID: T3] Table 3 

Average performance of the artificial sequence data set (r = 1)


Length Index gcn4 gal4 mcb average
 
FP
0.894
0.308
0.917
0.706
450*10
FN
0
0
0
0
 
perf
0.098
0.692
0.073
0.288
 
PT/ RT
10.25
1.444
13.714
8.469
 
FP
0.953
0.176
0.943
0.691
800*10
FN
0
0
0
0
 
perf
0.047
0.824
0.057
0.309
 
PT/ RT
21.1
1.214
17.583
13.299
 
FP
0.975
0.125
0.951
0.684
1250*10
FN
0.125
0
0
0.042
 
perf
0.024
0.875
0.049
0.316
  PT/ RT 35.625 1.143 20.286 19.018


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