A statistical thin-tail test of predicting regulatory regions in the Drosophila genome

Background The identification of transcription factor binding sites (TFBSs) and cis-regulatory modules (CRMs) is a crucial step in studying gene expression, but the computational method attempting to distinguish CRMs from NCNRs still remains a challenging problem due to the limited knowledge of specific interactions involved. Methods The statistical properties of cis-regulatory modules (CRMs) are explored by estimating the similar-word set distribution with overrepresentation (Z-score). It is observed that CRMs tend to have a thin-tail Z-score distribution. A new statistical thin-tail test with two thinness coefficients is proposed to distinguish CRMs from non-coding non-regulatory regions (NCNRs). Results As compared with the existing fluffy-tail test, the first thinness coefficient is designed to reduce computational time, making the novel thin-tail test very suitable for long sequences and large database analysis in the post-genome time and the second one to improve the separation accuracy between CRMs and NCNRs. These two thinness coefficients may serve as valuable filtering indexes to predict CRMs experimentally. Conclusions The novel thin-tail test provides an efficient and effective means for distinguishing CRMs from NCNRs based on the specific statistical properties of CRMs and can guide future experiments aimed at finding new CRMs in the post-genome time.


Background
The identification of transcription factor binding sites (TFBSs) and cis-regulatory modules (CRMs) is a crucial step in studying gene expression.The computational methods of predicting CRMs from non-coding non-regulatory regions (NCNRs) can be classified into three types: 1) TFBS-based methods, 2) homology-based methods and 3) content-based methods.TFBS-based methods, such as ClusterBuster [1] and MCAST [2], use information about known TFBSs to identify potential CRMs.The methods of this type are limited to the recognition of similarly regulated CRMs, and generally unable to be applied to genes for which TFBSs have not yet been studied experimentally.Homology-based methods use information contained in the pattern of conservation among related sequences.The related sequences can come from single species [3], two species [4] and multiple species [5].The methods of this type using the pattern of conservation alone are limited in their performance because TFBS conservation necessary to maintain regulatory function in binding sequences may not be significantly higher than in non-binding sequences [6,7].In addition, it still remains an open question that how many genomes are sufficient to the reliable extraction of regulatory regions.Content-based methods assume that different genome regions (CRMs and NCNRs) have the different rates of evolutionary micro changes; therefore, they exhibit different statistical properties in nucleotide composition.TFBSs often occur together in clusters as CRMs.The binding site cluster causes a biased word distribution within CRMs, and this bias leaves a distinct "signature" in nucleotide composition.Content-based methods detect this signature by statistical [8,9] or machine-learning [10,11] techniques, in order to distinguish CRMs from non-CRMs.The methods of this type may be used to predict the CRMs which have not yet been observed experimentally, but the poor performance on noncoding sequences limits their applications [12].A large number of CRM search tools have been reported in the literature, but the computational method attempting to distinguish CRMs from NCNRs still remains a challenging problem due to the limited knowledge of specific interactions involved [13].
The fluffy-tail test [9] is one of content-based methods.It is a bootstrapping procedure to recognize statistically significant abundant similar-words in CRMs.
There are two problems with the fluffy-tail test: 1) Due to its bootstrapping procedure, the computational time of calculating the fluffiness coefficient is determined by the number of realization.In order to get reliable results statistically, the number of realization is usually set as very large in the fluffy-tail test, so the computational time is expensive, especially for long sequences.This limits the use of the fluffy-tail test under the situation when more and more DNA sequences need to be analyzed in the post-genome time.2) The separation performance between CRMs and NCNRs is far from satisfactory [12].The reason of poor performance is that both CRMs and NCNRs contain repetitive elements such as poly(N) tracts (… TTT…) or long simple repeats (…CACACA…).These strings are less interesting than the overrepresented strings with more balanced AT/GC ratio.It is an interest to address these two issues of the fluffy-tail test and to develop a more efficient and effective CRM prediction method.
In this paper, the statistical properties of CRMs are explored by evaluating the overrepresentation value of similar-word sets (motifs).Z-score is used as the measure of overrepresentation of similar-word sets.Then, Z-score distribution is estimated to distinguish CRMs from NCNRs.

Training datasets
To

Formulation of the thin-tail test
The thin-tail test is based on the assumption that each word (binding site) recognized by a given transcription factor belongs to its own family of similar-word sets (binding site motifs) found in the same enhancer sequence and the redundancy of the binding sites within CRMs leaves distinct "signatures" in similar-word set distribution.For a given m -letter segment m W as a seed-word, all m -letter words that differ from m W by no more than j substitution comprise a corresponding similar-word set Because the core of TFBSs is relatively short [15], a 5-letter seed-word is considered, allowing for 1 mismatch, i.e., 5 m  and 1 j  .In order to distinguish CRMs from NCNRs, the thin-tail test is adopted to study the Z-score distribution shape and to predict the probable function of the original input sequence.The test features special statistics accounting for word overlaps in the same DNA strand.A flow chart of the thin-tail test is shown in Figure 1.
Step 1: Search for all different seed-words ( m W ) The input sequence is scanned to find all the different m -letter words, allowing overlaps.As an example, consider a stretch of DNA: ACGACGCCGACT.For 5 m  , all 5-letter segments 5 W are selected as seed-words, i.e., ACGAC, CGACG, …, CGACT.
Step 2: Number of similar-words with the same seed-word ( n ) For each seed-word m W , all m -letter words with no more than j substitution comprise a corresponding similar-word set   m j N W .In this example, the first seedword 5 W , ACGAC, has 3 similar-words with no more than 1 mismatch: ACGAC , ACGCC , CCGAC.n is the cardinality, Step 3: Z-score with the same seed-word ( Z ) A similar-word set that occurs significantly more often than chance expectation is said to be overrepresentation.A reasonable overrepresentation measure would reflect whether the actual occurrence number of similar-word set is significantly greater than the number counted in a random sequence with the same composition of input sequence.For any seed-word m W , a statistical overrepresentation measure Z-score can be defined by where   m E W and   m V W are, respectively, the occurrence expectation and variance of similar-word set   m j N W , these being calculated for a random sequence with the same composition of input sequence [16].In a random Bernoulli type sequence, both occurrence expectation and variance can be derived analytically by using a generating function technique [17].The Z-score with more overlaps is smaller than one with less overlaps.For example, the Z-score corresponding to simple repeat strings, TTTTT or AAAAA, is smaller than one corresponding to the seed-word with more balanced composition.Z (Z-score) forms X axis in Figures 2-5.
Step 4: Number of seed-words with the same Z-score is the number of the seed-words with Z-score and forms Y axis in Figures 2-7.
Step 5: Kurtosis ( k ) The kurtosis where i is the i th seed-word, M is the total number of seed-words,  and  are the mean and standard deviation of Z-score distribution   Z f respectively.
Step 6: Two thinness coefficients ( E and r T ) The first thinness coefficient E is defined as: Here 0 k denotes the kurtosis k of the original input sequence without random shuffle and  is the standard error calculated by: E is used to measure how strongly Z-score distribution deviates from the normal distribution.The 95% confidence interval is set between A sequence is called "random" if it is obtained by randomly shuffling the original input sequence r times, preserving its single nucleotide composition.To measure how strongly the Z-score distribution deviates from randomness, the second thinness coefficient r T is computed by comparing with all r -times randomly-shuffled sequence versions of the original input sequence: Here r T can be regarded as measuring the degree of the difference between signal and noise, where the signal is regarded as the original input sequence, and the noise is regarded as randomized sequences.
In the fluffy-tail test [9], the fluffiness coefficient r F is defined as:

Distribution for CRMs
Figure 2 shows the Z-score distribution for all Drosophila melanogaster CRMs in the positive training dataset.It can be seen that some similar-word sets have extreme . This means that some similar-word sets are overrepresented or underrepresented.
To obtain a random distribution, the original sequence is randomly shuffled 50 r  times.Figure 3 shows a typical example of Z-score distribution after random shuffle.
As compared with the original input sequence in Figure 2, the randomized sequence in Figure 3 lacks the overrepresented/underrepresented similar-word set (i.e.similarword set with extreme Z-score, 3 Z  or 3 Z   ).

Distribution for NCNRs
Figure 4 shows the Z-score distribution for all randomly-picked Drosophila melanogaster NCNRs in the negative training dataset.The presence of short right tail is noted in Figure 4. Figure 5 shows a typical example of Z-score distribution after random shuffle.The distribution for the original input sequence notably differs from that for the randomized version.The difference degree of the distribution between the original and randomly-shuffled sequences for NCNRs is greater than that for CRMs.

Thin-tail test
In order to distinguish CRMs from NCNRs, E and r T are calculated for 120 sequences in these two training datasets.Figure 6 shows that CRMs tend to have a smaller E than NCNRs.

Comparison with fluffy-tail test
The thin-tail test is evaluated by comparison with the fluffy-tail test [9].The  T respectively (see Table 1).For each parameter, sensitivity (SN) (number of true positive/number of positive), specificity (SP) (number of true negative/number of negative) and accuracy (number of true positive+number of true negative)/(number of positive+number of negative) are calculated to distinguish CRMs from NCNRs (Table 2).
The thin-tail test with 50 T has the best accuracy (66.7%), as compared with the other two parameters ( E : 65%; ).The thin-tail test with E has the same accuracy as the fluffy-tail test.
However, the computational time (CPU time) of calculating E for an original input DNA sequence length of 1000 is 50 times faster than that of calculating 50 T and 6 times faster than that of calculating sequence shuffle.Thus, the thin-tail test with E is very suitable for long sequences and large database.

Time complexity
The second thinness coefficient r T is gotten by bootstrapping procedure, the value is affected by the number of realization r .In order to get the more reliable estimation of r T , a large r is needed, so that high computational time is expected.For the reliable result within reasonable computational time, the original input sequence is randomly shuffled 50 times to calculate r T . In

Large CRM datasets
The thin-tail algorithm has been tested on the current version 3 of the REDfly database [18], which contains 894 experimentally-verified CRMs from Drosophila.Results show that 72.5% CRMs has 6 .0 E  and 70.8% CRMs has 0 T 50  passing the thintail test.It is worth to mention to the point that the fluffy-tail algorithm has never been tested on the large CRM datasets.

Conclusions
In the thin-tail test, the statistical properties of CRMs are investigated by examining Z-score distribution pattern.The special statistical method used for calculating Zscore can reduce the effect of poly N and other simple strings on the distribution pattern of similar-word sets.Results show that the Z-score distribution of CRMs tends to be a thin-tail distribution as compared with that of NCNRs.Based on this observation, two thinness coefficients E and r T are introduced here.By using E and r T , the thin-tail test has the better separation accuracy of distinguishing CRMs from NCNRs than the fluffy-tail test [9].Especially by using the first thinness coefficient E , the computational time is significantly decreased, in view of a bootstrapping procedure to be required for calculating r T and r F .For the example as 50 r  , the thin-tail test with E is 50 times faster than the thin-tail test with 50 T , and is 6 times faster than the fluffy-tail test with 50 F .Thus, the novel thin-tail test greatly simplifies the function prediction of an original input DNA sequence and can guide future experiments aimed at finding new CRMs in the post-genome time [19][20][21][22][23].

LF
is the number of the seed-words with the maximal similar-words for the rtimes randomly-shuffled sequences and r s is the standard deviation of the similar- word set distribution between the number   n g of seed-words and the number n of similar-words.Here it is worth to mention to this end that both CRMs and NCNRs contain repetitive elements such as poly(N) tracts (… TTT…) or long simple repeats (…CACACA…), which are less interesting than the over-represented strings with more balanced AT/GC ratio.Since Z-score measures the overrepresentation of similar-word sets, the second thinness coefficient r T based on Z-score distribution should be a more reasonable index than the fluffiness coefficient r based on similar- word set distribution in order to distinguish CRMs from NCNRs.

F
performance of three parameters is assessed: 1) the first thinness coefficient E , 2) the second thinness coefficient r T and 3) the fluffiness coefficient r based on the separation between CRMs and NCNRs.

50F
: 65%).Thus, the thin-tail test with 50 T can effectively distinguish CRMs from NCNRs.Moreover, the thin-tail test (SP = 60% for 50 T and SP = 58.3%for E ) can more efficiently identify NCNRs than the fluffy-tail test (SP = 48.3%for 50 F

Table 1
These two training datasets are employed to evaluate the above three parameters.For comparison, the original input sequence is randomly shuffled 50 times to calculate

Table Captions Table 1 :
Classification of 120 sequences

Table 2 :
Evaluation of E , 50 T and