A new sequence distance measure for phylogenetic tree construction

1
A new sequence distance measure for phylogenetic
tree construction

• Bioinformatics Vol19 Nov 2003
• Hasan H. Otu and Khalid Sayood
• HMS, Beth Israel Deaconess Med.

2
Abstract

• Most existing approaches for phylogenetic
  inference use multiple sequence alignment of
  sequences and assume some sort of an evolutionary
  model.
• The MSA does not work for all types of data, e.g.
  whole genome phylogeny and the evolutionary model
  may not always be correct.
• A new distance measure based on relative
  information between sequence using Lempel-Ziv
  complexity.

3
Outline

• Retrospect to phylogeny
• Introduction
• LZ 77
• LZ 78
• LZW
• Proposed algorithm and distance measure
• Result
• Discussion

4
Types of data used in phylogenetic
inference Character-based methods Use the
aligned characters, such as DNA or protein
sequences, directly during tree inference.
Taxa Characters Species
A ATGGCTATTCTTATAGTACG Species
B ATCGCTAGTCTTATATTACA Species
C TTCACTAGACCTGTGGTCCA Species
D TTGACCAGACCTGTGGTCCG Species
E TTGACCAGTTCTCTAGTTCG Distance-based methods
Transform the sequence data into pair-wise
distances (dissimilarities), and then use the
matrix during tree building. A
B C D E Species A ---- 0.20
0.50 0.45 0.40 Species B 0.23 ---- 0.40
0.55 0.50 Species C 0.87 0.59 ----
0.15 0.40 Species D 0.73 1.12 0.17 ----
0.25 Species E 0.59 0.89 0.61 0.31 ----
5
Introduction

• Some of the approaches in the first category
  utilize various distance measures (Jukes and
  Cantor, 1969 Kimura, 1980Barry and Hartigan,
  1987 Kishino and Hasegawa, 1989 Lake, 1994)
  which use different models of nucleotide
  substitutions or amino acid replacement.
• The second category can further be divided into
  two groups based on the optimality criterion used
  in tree evaluation parsimony and maximum
  likelihood methods.

6
(No Transcript)
7
Introduction (Cont)

• All of these methods require a multiple sequence
  alignment of sequences and some sort of an
  evolutionary model, these methods become
  insufficient for phylogenies using complete
  genomes.
• Due to gene rearrangements, inversion,
  transposition and translocation, unequal length
  of sequences.

8
LZ 77
9
The encoding algorithm

• Set the coding position to the beginning of the
  input stream
• find the longest match in the window for the
  lookahead buffer
• output the pair (P,C) with the following meaning
  
• This gives the following instruction to the
  decoder "Go back P characters in the window and
  copy C characters to the output"

10
LZ78
11
The encoding algorithm

• At the start, the dictionary and P are empty
• C next character in the charstream
• Is the string PC present in the dictionary?
• if it is, P PC (extend P with C)
• if not,
• output these two objects to the codestream
• the code word corresponding to P (if P is empty,
  output a zero)
• C, in the same form as input from the charstream
  
• add the string PC to the dictionary
• P empty
• are there more characters in the charstream?
• if yes, return to step 2
• if not
• if P is not empty, output the code word
  corresponding to P
• END.

12
LZW
13
Proposed distance

• Given two sequence Q and S, consider the sequence
  SQ and its exhaustive history.
• The number of the components needed to build Q
  when appended to S is c(SQ)-c(S), this number
  will be less than or equal to c(Q).
• How much c(SQ)-c(S) is less than c(Q) will depend
  on the degree of similarity of S and Q.

14
Example

• SAACGTACCATTG
• HE(S)A,AC,G,T,ACC,AT,TG
• c(S)7
• RCTAGGGACTTAT
• HE(R)C,T,A,G,GG,AC,TT,AT
• c(R)8
• QACGGTCACCAA
• HE(Q)A,C,G,GT,CA,CC,AA
• c(Q)7

15
Example (Cont)

• SQAACGTACCATTGACGGTCACCAA
• HE(SQ)A,AC,G,T,ACC,AT,TG,ACG,GT,C,ACCA
• c(SQ)11, Q took 4 steps
• RQCTAGGGACTTATACGGTCACCAA
• HE(RS)C,T,A,G,GG,AC,TT,AT,ACG,GT,CA,CC,AA
• c(RQ)13, Q took 5 steps
• The reason RQ took more steps then SQ is because
  Q is closer to S than Q.

16
Proposed distance (Cont)

• Formulate the numbers of steps it takes to
  generate a sequence Q form a sequence S by
  c(SQ)-c(S).
• If S is closer to Q than R then we would expect
  c(SQ)-c(Q)ltc(RQ)-c(R).
• 11-7 lt 13-8 , TRUE!

17
Distance Measure

• Sequence S and Q given, defined the function as
• 
  
  
• dm1
• Normalize form (eliminate the effect of length)
• dm2

18
Distance Measure (Cont)

• The idea of building sequence Q using S is the
  sum distance.
• Similarity, normalize version of d1 as follows

19
Satisfaction conditions

• D(S,Q) ?0 where the equality is satisfied iff SQ
  (identity).
• D(S,Q)D(Q,S) (symmetry).
• D(S,Q)?D(S,T)D(T,Q) (triangle inequality).
• D(Q,R)D(S,T)?
• maxD(Q,S)D(R,T),D(Q,T)D(S,R)
• (additivity).

20
Results and Discussion

• Neighbor joining by PHYLIP package and parsimony
  and maximum likelihood methods are using
  ClustalW.
• 1000bp sequence and evolved it into two sequence
  A and B using point mutations(10) and
  segment-based modifications(10).
• Evolved A into A1 and A2, B into B1 and B2, A to
  A and B to B.

21
Results (Cont)
22
(No Transcript)
23
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
24
2
1
3
19
20
25
Conclusion

• Proposed a new distance measure and its
  variations.
• The proposed does not require multiple sequence
  alignment and is fully automatic.
• Perform comparisons at the whole genome level.
• Unequal sequence length or the relatively
  different positioning are not problem.
• Distance measures do not use any evolutionary
  model.