Space Efficient Algorithms for Planted Motif Search

1
Space Efficient Algorithms for Planted Motif
Search

• Jaime Davila, Sudha Balla, Sanguthevar
  Rajasekaran
• CSE Department at University of Connecticut

2
Definition of (l,d) Motif Problem

• Given sequences s1, s2 , sn of length m each.
• Find a string x of size l an l-mer that
  appears as substring in all of them, with less
  than d mismatches in every occurrence. This is, x
  almost appears in si for i1,, n.

3
(l,d) Motif Problem, Example

• s1 GGCATCCGATTATTGTAGTCTGG
• s2 ATTTCTATGCTAAGCTTGCTCGA
• s3 CAGGCTGTAAGTAGTTTGTTAGC
• l5, d1

4
(l,d) Motif Problem, Solution

• s1 GGCATCCGATTATTGTAGTCTGG
• s2 ATTTCTATGCTAAGCTTGCTCGA
• s3 CAGGCTGTAAGTAGTTTGTTAGC
• x TTTTT is a (5,1) motif.

5
Motivation

• Mining of Transcription Factor Binding Sites,
  which are small sequences of DNA that mark the
  beginning of coding regions in DNA. They might
  appear slightly modified in different sequences.

6
PMS Simple Planted Motif Search Raj et al 2005

• l5 d1
• s1 GGCATCCGATTATTGTAGTCTGG
• s2 ATTTCTATGCTAAGCTTGCTCGA
• s3 CAGGCTGTAAGTAGTTTGTTAGC

7
PMS Description

• Build d-vicinities for each l-mer
• s1 GGCATCCGATTATTGTAGTCTGG
• s2 ATTTCTATGCTAAGCTTGCTCGA
• s3 CAGGCTGTAAGTAGTTTGTTAGC

B(ATCCG,1)CTCCG,TTCCG, ,ATCCT
8
PMS Description

• Let Li be the union of vicinities for each
  sequence. Sort them by using radix-sort
• GGCATCCGATTATTGTAGTCTGG
• ATTTCTATGCTAAGCTTGCTCGA
• CAGGCTGTAAGTAGTTTGTTAGC

È
L1
È
L2
È
L3
9
PMS Description

• 3) Mi is the intersection of Lk for k1, , i
• GGCATCCGATTATTGTAGTCTGG
• ATTTCTATGCTAAGCTTGCTCGA
• CAGGCTGTAAGTAGTTTGTTAGC

È
L1
Ç
È
L2
Ç
È
L3

TTTTT, M3
10
PMS Drawbacks

• As d increases the sizes of the Li increase
  considerably. For n20,m600, l15 and d4, the
  core memory requirement is over 1GB.

11
PMSi Key idea

• L1 È B(x,d) (x is an l-mer in s1)
• L2 È B(y,d) (y is an l-mer in s2)
• M2 L1 Ç L2 (È B(x,d)) Ç (È B(y,d) )
• È (B(x,d) Ç B(y,d) ) for all pairs (x, y )

12
PMSi Graphical Idea

• Generate M2 by using De Morgan
• GGCATCCGATTATTGTAGTCTGG
• ATTTCTATGCTAAGCTTGCTCGA
• CAGGCTGTAAGTAGTTTGTTAGC

È
Ç

13
PMSi Refinement

• B(x,d) Ç B(y,d) Æ if dist(x,y) gt 2d
• GGCATCCGATTATTGTAGTCTGG
• ATTTCTATGCTAAGCTTGCTCGA
• CAGGCTGTAAGTAGTTTGTTAGC

Ç

14
PMSi Intersections of vicinities

• x is fixed l-mer in s1, y is any l-mer in s2.
• È (B(x,d) Ç B(y,d) )
• z Î B(x,d) y dist(z, y) d.
• We cached the calculations of dist, to be
• more efficient.

15
PMSi Drawbacks

• We add more time depending on the number of
  l-mers whose distance is less than 2d from a
  given l-mer.
• Depending on this number, we also have a
  bigger/lesser use of memory.

16
PMSP Key idea

• We can iterate the basic principle of PMSi, i.e.
  x is fixed l-mer in s1, y is any l-mer in s2 , w
  any l-mer in s3
• È (B(x,d) Ç B(y,d) Ç B(w,d))
• z Î B(x,d)
• y dist(z, y) d, w dist(z, w) d
  .

17
PMSP Graphical Idea
B(TTATT,1)ATATT,,TTTTT,.,TTATG

• GGCATCCGATTATTGTAGTCTGG
• ATTTCTATGCTAAGCTTGCTCGA
• CAGGCTGTAAGTAGTTTGTTAGC
• All vicinities considered are at distance less
  than 2d from l-mer in first sequence.

18
PMSP Observations

• We reduce the memory usage drastically
• We add more time depending on the number of
  l-mers whose distance is less than 2d from a
  given l-mer.

19
Experimental setting

• n20, m600.
• Every letter from every sequence is generated at
  random uniformly and independently.
• A challenge instance is one where the expected
  number of (l,d) motifs is greater than 1, i.e.
  (11,3), (13,4), (15,5), (17,6)

20
Results (d3)
21
Results in Challenging Instances
22
Questions?