1. An Implementation of The Teiresias Algorithm Na Zhao Chengjun Zhan

2. Outline Introduction of Pattern Discovery Basic Definitions Teiresias Algorithm & Implementation Scan Phase Convolution Phase Results & Conclusion Q & A

3. What is Pattern Discovery? Pattern: A region or portion of a protein sequence. It may has specific structure and functionally significant. Protein family should have similar patterns so they can be characterized. Pattern Discovery: Detect patterns from known protein sequences. The result can be used to detect unknown protein sequences.

4. Why Pattern Discovery Useful? For some proteins that have similar biological properties on structural or functional features: Group together these protein sequences Discover a set of common sub-sequences Study and observe these sub-sequences The detected patterns may help to classify a protein

5. Basic Definitions ∑ (Basic alphabet set): The amino-acid with names can be abbreviated as the listed symbols in alphabetical order ∑={A,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y}  (Character/Equivalency group alphabets): a character corresponding to a subset of Σ. Ex: A-[CJ]-G. (Wild-card or don’t care): a special kind of ambiguous character that matches any character in ∑. Ex: X in protein sequences and N in nucleotide

6. Basic Definitions (Cont.) Pattern P is a (L, W) pattern iff: P is a string of characters (Σ and wild cards ‘.’). P starts and ends with a character from Σ. Characters in Σ are called residues. Any sub pattern of P (i.e subsequence starting and ending with a character from Σ) containing exactly L non-wildcard characters (residues) has length of at most W. Ex. L=3 and W=5, “CD..E” is a (3, 5) pattern.

7. TEIRESIAS Algorithm Target: Search for patterns consisting of characters of the alphabet Σ and wild cards ‘.’ Basic Idea: If a pattern P is a (L, W) pattern occurring in at least K sequences, then its sub patterns are also (L, W) patterns occurring in at least K sequences (K>=2). Ex: pattern “A.BC” is more specific than “A..C” Designed for non-aligned sequences

8. Two Phases Scan Phase: Scan the input sequences Identify all the elementary patterns which satisfy the minimum support Convolution Phase: Sort the element patterns and extract useful prefixes and suffixes Convolve the elementary patterns until find the maximal length and composition of the patterns

9. Scan Phase Input: Non-aligned sequences Parameter: K, L, W Output: a set of “Elementary Patterns” Are (L, W) patterns Occur in at least K sequences Contain exactly L non-wildcards

10. Elementary Pattern Examples SDFBASTSLP LFCASTSCP FDASTSNP TGLPACTTCPTFCP AST K=2, L=3, W=5 T.LP

11. Scan Phase (Cont.) Empty the stack of elementary patterns. (EP) For each letter in the alphabet, count how many sequences contain this letter. If less than K sequences contain this letter, ignore it. Otherwise, extend it until it is ignored or it is accepted.

12. Convolution Phase (Overall) There is a sub-phase named pre- convolution before the convolution phase. The goal of the convolution phase is to extend a elementary pattern with other elementary patterns.

13. Pre-convolution Phase Prefix of a pattern p is the unique substring containing the first L-1 residues of p. Suffix of pattern p is the unique substring containing the last L-1 residues of p. Example: for pattern a..c.e, prefix is a..c, suffix is c.e

14. Pre-convolution Phase (cont.) Given two pattern p and q, p convolve q is empty if the suffix of p is not the prefix of q, Otherwise, it is the pattern p followed by the part of q which remains when its prefix is removed.

15. Pre-convolution Phase (cont.) Left vector of a pattern q contains all the patterns p that can be left-convolved with it. Right vector of a pattern p contains all the patterns q that can be right-convolved with it. Example: Left a.c.d: ea.c b.a.c right a.c.d: fc.d

16. Pre-convolution Phase (cont.) Sort elementary patterns by prefix-wise < Construct Left and Right vector for each elementary pattern

17. Prefix-wise < Examples Example 0 abc 5 bc..f 1 bcd 6 a.cd 2 ab.d 7 b.de 3 cd.f 8 a.c.e 4 ab..e 9 a..de

18. Convolution Phase For each pattern t of the sorted EPs, firstly it is extended to the left by convolving it with every member in Left[t]. If the result r doesn’t have sufficient support or is redundant, discard it. If r has the same number of occurrences as t, t is non-maximal and is discarded.

19. Convolution Phase (cont.) If result r has adequate support and is not redundant, r is placed on the stack and becomes the new top. When the pattern at the top of the stack can not be extended to the left any more, extend it to the right. When all the extensions have been done, the current top is popped from the stack. If it is maximal, it is put into the output set.

20. An Example Scenario Suppose there are three sequences: SDFEASTS LFCASTS FDASTSNP Our goal: to find a maximal pattern, given K = 2, L = 3, W = 5

21. An Example Scenario (cont.) First, the scan phase is implemented The elementary patterns (EP) found are: AST AS.S A.TS F.AS F.A.T F..ST STS Then these EP are sorted, the result is: AST STS AS.S A.TS F.AS F.A.T F..ST

22. An Example Scenario (cont.) Then, the Left and Right vectors are constructed: Left Right AST: F.AS AST: STS STS: AST, F..ST STS: AS.S: F.AS AS.S: A.TS: F.A.T A.TS: F.AS: F.AS: AST, AS.S F.A.T: F.A.T: A.TS F..ST: F..ST: STS

23. An Example Scenario (cont.) Now the convolution phase is executed, and the result is as following: F.ASTS

24. About Our Implementation The program is written using Visual C++ 6.0 Command line arguments are provided to users for them to specify the input data file, the K, L, W value (which have default values (2, 3, 5) if users don’t specify) >Teiresias [ ] [ ] [ ]

25. Questions?