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Genomics Inform > Volume 10(4); 2012 > Article
Galbadrakh, Lee, and Park: Developing JSequitur to Study the Hierarchical Structure of Biological Sequences in a Grammatical Inference Framework of String Compression Algorithms

Abstract

Grammatical inference methods are expected to find grammatical structures hidden in biological sequences. One hopes that studies of grammar serve as an appropriate tool for theory formation. Thus, we have developed JSequitur for automatically generating the grammatical structure of biological sequences in an inference framework of string compression algorithms. Our original motivation was to find any grammatical traits of several cancer genes that can be detected by string compression algorithms. Through this research, we could not find any meaningful unique traits of the cancer genes yet, but we could observe some interesting traits in regards to the relationship among gene length, similarity of sequences, the patterns of the generated grammar, and compression rate.

Introduction

In formal language theory a language is simply a set of strings of characters drawn from some alphabet, where the alphabet (terminal) is a set of symbols. When we consider biological sequences simply as a language in the context of formal language theory (treating DNA, RNA, or protein sequences just as strings of alphabets of four nucleotides or 20 amino acids), a grammatical inference method based on formal language theory can be applied [1-3].
Nevill-Manning and Witten [4] pioneered the attempt to produce the context-free grammarof biological sequences in an automatic way. This task can be formalized as the problem of finding the smallest context-free grammar by recursively replacing the repeats by a new symbol. The algorithm builds a hierarchy of phrases by forming a new rule out of existing pairs of symbols, including non-terminal symbols.
For example, if we consider the string "atattattatt," the simplest way to represent the string by context-free grammar is the following:
  • <Grammar 0>

  • S → atattattatt

The most frequently occurring sequence in the string is "at," which occurs four times. Thus, introducing a new nonterminal symbol, 'A,' and creating a new rule for this yields the following modified grammar:
  • <Grammar 1>

  • S → AAtAtAt

  • A → at,

where the grammar consists of a start symbol (i.e., S), two terminal symbols (i.e., a, t) represented by lowercase letters, two non-terminal symbols (i.e., S, A) represented by uppercase letters, and two production rules (i.e., S → AAtAtAt, A → at) with a left- and a right-hand side consisting of a sequence of these symbols.
Repeatedly replacing the frequently occurring patterns "At," again to a new nonterminal symbol, B, gives the following modified grammar:
  • <Grammar 2>

  • S → ABBB

  • A → at

  • B→ At,

where the grammar consists of a start symbol (i.e., S), two terminal symbols (i.e., a, t), three non-terminal symbols (i.e., S, A, B), and three production rules (i.e., S → ABBB, A → at, B → At).
By applying the three production rules by replacing an occurrence of the nonterminals on the left-hand side of the production rule with those that appear on the right-hand side, the string "atattattatt" can be derived from the non-terminal S by constantly applying a series of derivations: S → ABBB → atBBB → atAtBB → atattBB → atattAtB → atattattB → atattattAt → atattattatt.
Based on this concept, grammar-based compression algorithms have shown some success for various applications [4-7]. Especially, grammar can capture distant repetitions occurring far apart, which was a limitation of sliding window approaches. However, grammar-based compression algorithms at this moment do not show the best performance for compression itself [6]. Thus, our motivation of this study is not to develop a new algorithm or find the most efficient way to compress biological sequences for storage purposes. Our sole purpose of developing a new tool is to investigate any grammatical traits of biological sequences, based on formal language theory.

Implementation

We have developed a slightly modified version of Sequitur [4] called JSequitur for automatically creating hierarchical structures of sequences [8], as in Fig. 1. Our main contribution is to improve Sequitur to work better in a graphic user interface (GUI) environment, as our main interest was in studying the generated grammar, rather than enhancing the compression rate itself. JSequitur is implemented in Java and organized into six classes, as in Fig. 2: Sequitur, Symbol, Guard, Terminal, Nonterminal, and Rule. Sequitur class is called first and connects with all of the other classes. Symbol class is the connecter class, which streams sequences of input to the system. Rule class accesses Terminal and NonTerminal classes in order to create rules. Guard class, which is based on digram uniqueness, is responsible for rule confirmation.
Thus, our string compression algorithm operates by reading in a new symbol and processing it by appending it to the top-level string and then examining the last symbols of that string; it then applies zero or more of the following transformations until none applies anywhere in the grammar; it then repeats the cycle by reading in a new symbol.
The following production rules, which have been created automatically, are an exemplary output of applying JSequitur to the partial sequence of the TERT gene (175 bp, "gcccccgggtgtccctgtcacgtgcagggtgagtgaggcgcggtccccgggtgtc cctgtcacgtgcagggtgagtgaggcgcggtccccgggtgtccctgtcacgtgcag ggtgagtgaggcgcggtcccc"):
  • R0 → g R1 R2 R3 R4 R5 R6 R7 R6 R8 R5 R9 R1 R3 R4 R10 R11 g a R4 a R12 R13 R14 R7 R15 R8 R16 R10 R14 c

  • R1 → c c

  • R2 → R1 c

  • R3 → R11 R17 R2 R18

  • R4 → R17 g

  • R5 → R16 R13 R19

  • R6 → t R2

  • R7 → R19 R4

  • R8 → R18 R4

  • R9 → t R1

  • R10 → a a

  • R11 → R12 R17

  • R12 → g g

  • R13 → c g

  • R14 → R19 R15

  • R15 → R9 c

  • R16 → R10 R11 g a R4 a R12

  • R17 → g t

  • R18 → t R17 R10 c

  • R19 → R13 g,

where the grammar consists of a start symbol (i.e., R0), four terminal symbols (i.e., a, t, g, c), 20 non-terminal symbols (i.e., R0-R19), and 20 production rules for each nonterminal. In summary, the partial sequence of 175 bp of the TERT gene could be compressed to 37 symbols with 20 rules.
For testing purposes, 104 cancerous genes from 6 cancer types (bladder, breast, endometrial, leukemia, lung, and melanoma) were initially chosen, and JSequitur was applied. Table 1 shows the result of applying one of the string compression algorithms of JSequitur to these genes.
The rule column in Table 1 shows the number of generated rules from the context-free grammar, while the ratio column shows the ratios of the compressed sequences vs. the original sequences.
Fig. 3 is a sorted diagram in the order of the length of the original sequence. In this specific case, it shows that the length of the original sequence influences the compression rate of the target sequence, even though there are many other factors that influence compression rate. For example, compression rate can also be influenced by the algorithm itself, depending on whether we replace the longest pattern first or the most frequently occurring pattern first.
We also compared some mouse genes to find any homologous traits in regards to compression rate and hierarchical structure of the grammar. For example, we compared human MUC1 (Homo sapiens, 5,279 bp) with mouse MUC1 (Mus musculus, 5,614 bp), and the compression rates for these two sequences were 0.180 and 0.195, respectively. For the ARHA genes, the compression rate for human ARHA (68,833 bp) was 0.140, whereas that for mouse ARHA (41,255 bp) was 0.157. Thus, the distance on the evolutionary tree can be measured by compression algorithms, to a certain extent.

Conclusion and Future Direction

We have developed a GUI-based JSequitur, based on string compression algorithms, to examine grammatical traits of biological sequences. On top of compression capacity, a string compression algorithm is appealing for studying biological sequences, because it can give insights into the structure of these sequences. Precisely constructed models for linguistic structure can play a vital role in the process of discovery itself.
We also applied JSequitur to analyze 104 cancer genes for testing purposes only. Even though there are some interesting results in regards to the relationship among gene length, similarity of sequences, the patterns of the generated grammar, and compression rate, our test samples were too small to conclude anything. Thus, our result should be regarded as preliminary for future research. We should consider various factors other than grammatical structures and compression rates.
As our main purpose of developing the tool was to examine any grammatical traits of biological sequences, the graphical user interface was important for a semiautomatic screening process. However, we still need to implement various features to compare gene structures to summarize statistics in regards to grammatical structures and to combine evolutionary trees. Hopefully, these features will be implemented in the next version of JSequitur. We also hope to enhance the algorithm more elaborately to handle reversal, translocation, and shuffling.

References

1. Sakakibara Y. Grammatical inference in bioinformatics. IEEE Trans Pattern Anal Mach Intell 2005;27:1051–1062. PMID: 16013753.
crossref pmid
2. Coste F. Modelling biological sequences by grammatical inference. ICGI 2010 Tutorial Day. 2010. Accessed 2012 Nov 1. Valencia: International Conference on Grammatical Inference, Available from: http://www.irisa.fr/symbiose/people/fcoste/pub/biblio_tutoICGI2010_coste.pdf.

3. Park HS, Galbadrakh B, Kim YM. Recent progresses in the linguistic modeling of biological sequences based on formal language theory. Genomics Inform 2011;9:5–11.
crossref
4. Nevill-Manning CG, Witten IH. Compression and explanation using hierarchical grammars. Comput J 1997;40:103–116.
crossref
5. Lanctot JK, Li M, Yang E. Estimating DNA sequence entropy. Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms 2000. 2000 Jan 9-11; San Franciscon, CA: Philadelphia: Society for Industrial and Applied Mathematics, pp 409–418.

6. Cherniavsky N, Ladner R. Grammar-based compression of DNA sequences. UW CSE Technical Report (TR2007-05-02). DIMACS Working Group on the Burrows-Wheeler Transfrom. 2004 8 19-20 Piscataway, NJ.

7. Carrascosa R, Coste F, Gallé M, Infante-Lopez G. Searching for smallest grammars on large sequences and application to DNA. J Discrete Algorithms 2012;11:62–72.
crossref
8. Galbadrakh B. Identifying hierarchical structure in biological sequences based on context-free grammars. 2011. Seoul: Ewha Womans University, M.S. Thesis.

Fig. 1
User interface of JSequitur program.
gni-10-266-g001.jpg
Fig. 2
JSequitur class diagram.
gni-10-266-g002.jpg
Fig. 3
Compression rates in relation to gene length.
gni-10-266-g003.jpg
Table 1.
One hundred four genes and their compression rates
No. Gene Length Compressed length No. of rules Compression ratio
1 TERC 587 157 45 0.2675
2 MIF 1,099 265 79 0.2411
3 HSPB1 2,262 528 131 0.2334
4 TNFRSF6B 2,662 571 153 0.2145
5 S100A4 2,844 630 163 0.2215
6 CDKN2D 3,274 713 173 0.2178
7 GSTP1 3,977 847 200 0.2130
8 HRAS 4,301 869 206 0.2020
9 EMS1 4,741 978 235 0.2063
10 TCL1A 5,498 1,142 264 0.2077
11 TFF1 5,530 1,110 274 0.2007
12 TCTA 5,553 1,104 279 0.1988
13 MUC1 5,729 1,034 268 0.1805
14 SNCG 6,148 1,221 271 0.1986
15 IL6 6,312 1,283 287 0.2033
16 CDKN1B 6,504 1,293 301 0.1988
17 MYC 6,976 1,409 300 0.2020
18 KLK3 7,604 1,487 329 0.1956
19 GSTM1 7,734 1,525 325 0.1972
20 CYP1A1 7,793 1,527 352 0.1959
22 KISS1 7,997 1,526 342 0.1908
23 ARHC 8,159 1,587 349 0.1945
24 PLAU 8,318 1,624 346 0.1952
25 MYCN 8,381 1,655 350 0.1975
26 MYCL1 8,570 1,688 359 0.1970
27 HSPCB 8,796 1,685 380 0.1916
28 CYP2A6 8,982 1,701 395 0.1894
29 BAX 9,021 1,667 383 0.1848
30 CYP17 9,103 1,735 393 0.1906
31 GSTT1 10,590 1,941 439 0.1833
32 ING1 10,841 2,069 438 0.1909
33 CYP1B1 11,152 2,128 443 0.1908
34 NAT2 12,959 2,406 484 0.1857
35 TFAP2C 12,976 2,458 510 0.1894
36 FGF8 13,312 2,437 507 0.1831
37 CDKN1A 14,144 2,645 524 0.1870
38 RASSF1 14,497 2,621 533 0.1808
39 CTSD 14,613 2,558 532 0.1751
40 BIRC5 14,872 2,536 571 0.1705
41 MMP11 14,908 2,695 555 0.1808
42 PCNA 15,170 2,726 572 0.1797
43 CYP2E 15,280 2,750 582 0.1800
44 RCA1 15,646 2,660 611 0.1700
45 BAG1 15,979 2,967 572 0.1857
46 CCNE1 16,009 2,902 589 0.1813
47 CCND1 17,380 3,132 597 0.1802
48 BCL1 17,380 3,132 597 0.1802
49 TAL1 17,525 3,154 629 0.1800
50 NAT1 18,081 3,236 634 0.1790
51 CEACAM8 19,094 3,348 662 0.1753
52 LIBC 20,296 3,603 711 0.1775
53 VEGF 21,163 3,702 720 0.1749
54 MPL 21,659 3,807 723 0.1758
55 SLC2A3 22,189 3,853 748 0.1736
56 STIP1 23,964 4,022 825 0.1678
57 TP53 24,886 3,972 860 0.1596
58 IGF2 26,633 4,512 881 0.1694
59 CSK 27,449 4,662 875 0.1698
60 STK11 29,427 4,792 932 0.1628
61 TFAP2A 29,746 5,180 923 0.1741
62 ERBB3 30,527 5,021 961 0.1645
63 MSH6 31,034 5,038 973 0.1623
64 MLLT6 31,438 5,346 974 0.1700
65 BCL6 31,653 5,426 971 0.1714
66 SLC22A1L 33,184 5,440 1,010 0.1639
67 PSEN2 33,192 5,660 978 0.1705
68 CDKN2A 34,762 5,940 987 0.1709
69 TPMT 34,883 5,702 1,053 0.1635
70 POU2AF1 35,332 5,809 1087 0.1644
71 MMP2 35,758 6,058 1,074 0.1694
72 PI5 36,627 6,098 1,079 0.1665
73 COMT 36,706 5,860 1,131 0.1596
74 TFAP2B 37,554 6,392 1,123 0.1702
75 NOTCH4 37,993 6,191 1,123 0.1630
76 TOP2A 38,258 6,027 1,159 0.1575
77 MKI67 38,410 6,258 1,152 0.1629
78 SLC2A1 43,942 7,254 1,178 0.1651
79 MDM2 48,414 7,466 1,409 0.1542
80 CD9 49,342 7,937 1,400 0.1609
82 THBS2 49,741 7,801 1,377 0.1568
83 BCAR1 50,730 8,015 1,397 0.1580
84 PPP2R1B 51,400 8,203 1,452 0.1596
85 SH3GL1 52,262 8,222 1,465 0.1573
86 ERBB2 52,679 8,151 1,504 0.1547
87 TERT 54,445 7,781 1,531 0.1429
88 PDGFRB 54,627 8,684 1,533 0.1590
89 AXL 55,332 8,369 1,608 0.1513
90 GAS6 56,583 8,476 1,551 0.1498
91 EFNB2 58,902 9,472 1,538 0.1608
92 KRAS2 59,377 9,280 1,623 0.1563
93 TSG101 60,640 9,516 1,640 0.1569
94 EIF3S6 61,084 9,600 1,574 0.1572
95 WT1 62,089 9,980 1,718 0.1607
96 RARA 63,015 9,783 1,681 0.1552
97 TNFRSF10B 63,771 9,896 1,720 0.1552
98 NOTCH1 66,745 8,476 1,551 0.1270
99 LASP1 67,486 10,220 1,816 0.1514
100 EIF4E 67,834 10,262 1,814 0.1513
101 ARHA 68,833 9,651 1,917 0.1402
102 PML 69,091 10,636 1,826 0.1539
103 CHEK2 70,320 10,317 1,921 0.1467
104 COT 70,410 10,930 1,797 0.1552
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