A statistical thin-tail test of predicting regulatory regions in the Drosophila genome
- Jian-Jun Shu^{1}Email author and
- Yajing LI^{1}
DOI: 10.1186/1742-4682-10-11
© Shu and Li; licensee BioMed Central Ltd. 2013
Received: 11 September 2012
Accepted: 7 February 2013
Published: 14 February 2013
Abstract
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.
Keywords
Statistical approach Transcription factor binding sites (TFBSs) Cis-regulatory modules (CRMs)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 non-coding 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 over-represented 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.
Methods
Training datasets
To estimate the statistical properties of distinguishing CRMs from NCNRs, two (positive and negative) training datasets are employed in this paper. The positive training dataset is a collection of 60 experimentally-verified functional Drosophila melanogaster regulatory regions [14]. The positive training dataset consists of CRMs located far from gene coding sequences and transcription start sites. It contains many binding sites and site clusters, including abdominal-b, bicoid, caudal, deformed, distal-less, engrailed, even-skipped, fushi tarazu, giant, hairy, huckebein, hunchback, knirps, krüppel, odd-paired, pleiohomeotic, runt, tailless, tramtrack, twist, wingless and zeste. The total size of the positive training dataset comprises about 99 kilobase (kb) sequences. The negative training dataset is 60 randomly-picked Drosophila melanogaster NCNRs: The NCNRs of length 1 kb upstream and downstream of genes are excluded by using the Ensembl genome browser. The negative training dataset contains 90 kb sequences in total.
Formulation of the thin-tail test
Step 1: Search for all different seed-words (Wm)
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 m = 5, all 5-letter segments W_{5} 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 Wm, all m-letter words with no more than j substitution comprise a corresponding similar-word set Nj(Wm). In this example, the first seed-word W_{5}, ACGAC, has 3 similar-words with no more than 1 mismatch: ACGAC, ACGCC, CCGAC. n is the cardinality, n = |N_{ j }(W_{ m })| = |N_{1}(ACGAC)| = 3.
Step 3: Z-score with the same seed-word (Z)
Step 4: Number of seed-words with the same Z-score (f)
Step 5: Kurtosis (k)
where i is the i th seed-word, M is the total number of seed-words, μ and σ are the mean and standard deviation of Z-score distribution f(Z) respectively.
Step 6: Two thinness coefficients (E and T_{r})
E is used to measure how strongly Z-score distribution deviates from the normal distribution. The 95% confidence interval is set between -2ε and 2ε.
Here T_{ r } 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.
where L_{ r } is the number of the seed-words with the maximal similar-words for the r-times randomly-shuffled sequences and s_{r} is the standard deviation of the similar-word set distribution between the number g(n) 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 T_{ r } based on Z-score distribution should be a more reasonable index than the fluffiness coefficient F_{ r } based on similar-word set distribution in order to distinguish CRMs from NCNRs.
Results
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 positive/negative Z-score (Z > 3 or Z < -3). This means that some similar-word sets are overrepresented or underrepresented.
To obtain a random distribution, the original sequence is randomly shuffled r = 50 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. similar-word set with extreme Z-score, Z > 3 or Z < -3).
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
Classification of 120 sequences
(a) Thin-tail test with E | ||||
Functional type | E < 0.6 | E > 0.6 | Positive rate | Negative rate |
CRMs | 43 | 17 | 71.7% | 28.3% |
NCNRs | 25 | 35 | 41.7% | 58.3% |
(b) Thin-tail test with T _{ 50 } | ||||
Functional type | T_{50} < 0 | T_{50} > 0 | Positive rate | Negative rate |
CRMs | 44 | 16 | 73.3% | 26.7% |
NCNRs | 24 | 36 | 40% | 60% |
(c) Fluffy-tail test | ||||
Functional type | F_{50} > 2 | F_{50} < 2 | Positive rate | Negative rate |
CRMs | 49 | 11 | 81.7% | 18.3% |
NCNRs | 31 | 29 | 51.7% | 48.3% |
Discussion
Some statistical properties of Z-score distribution in these two training datasets have been explored. Results show that CRMs have a thin-tail distribution, i.e., tend to have low thinness coefficients (E < 0.6, T_{ r } < 0), while NCNRs lack a thin-tail distribution, i.e., tend to have high fatness coefficients. Thus, E and T_{ r } can be used to distinguish CRMs from NCNRs effectively. CRMs are predominant if (E < 0.6, T_{ r } < 0), while NCNRs are prevailing if (E > 0.6, T_{ r } > 0). Thus, the regions with (E < 0.6, T_{ r } < 0) are CRMs and those with (E > 0.6, T_{ r } > 0) are NCNRs.
Comparison with fluffy-tail test
The thin-tail test is evaluated by comparison with the fluffy-tail test [9]. The performance of three parameters is assessed: 1) the first thinness coefficient E, 2) the second thinness coefficient T_{ r } and 3) the fluffiness coefficient F_{ r } based on the separation between CRMs and NCNRs.
Evaluation of E , T _{ 50 } and F _{ 50 }
(a) Distinguish CRMs from NCNRs | |||
The thin-tail test | The fluffy-tail test | ||
E | T_{50} | F_{50} | |
SN | 71.7% | 73.3% | 81.7% |
SP | 58.3% | 60% | 48.3% |
Accuracy | 65% | 66.7% | 65% |
(b) CPU time for a sequence length of 1000 | |||
The thin-tail test | The fluffy-tail test | ||
E | T_{50} | F_{50} | |
CPU time | 54 second | 2700 second | 310 second |
The thin-tail test with T_{50} has the best accuracy (66.7%), as compared with the other two parameters (E: 65%; F_{50}: 65%). Thus, the thin-tail test with T_{50} can effectively distinguish CRMs from NCNRs. Moreover, the thin-tail test (SP = 60% for T_{50} and SP = 58.3% for E) can more efficiently identify NCNRs than the fluffy-tail test (SP = 48.3% for F_{50}). 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 T_{50} and 6 times faster than that of calculating F_{ 50 } for the same original input sequence due to no sequence shuffle. Thus, the thin-tail test with E is very suitable for long sequences and large database.
Time complexity
The second thinness coefficient T_{ r } is gotten by bootstrapping procedure, the value is affected by the number of realization r. In order to get the more reliable estimation of T_{ r }, 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 T_{ r }.
In Table 2(c), 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 T_{ 50 } and 6 times faster than that of calculating F_{ 50 } for the same original input sequence due to no sequence shuffle. All computations are run on a 3.2 GHz Pentium IV processor with 1 G physical memory.
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 E < 0.6 and 70.8% CRMs has T_{ 50 } < 0 passing the thin-tail 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 Z-score 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 T_{ r } are introduced here. By using E and T_{ r }, 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 T_{ r } and F_{ r }. For the example as r = 50, the thin-tail test with E is 50 times faster than the thin-tail test with T_{50}, and is 6 times faster than the fluffy-tail test with F_{50}. 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 [19–23].
Declarations
Authors’ Affiliations
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