Improving MSA

1
Improving MSA

• Bill Zeller
• Trinity College

April 11, 2005
2
Presenting

• Improving the Practical Space and Time Efficiency
  of the Shortest-Paths Approach to Sum-of-Pairs
  Multiple Sequence Alignment
• Sandeep K. Gupta
• John D. Kececioglu
• Alejandro A. Schäffer

3
Background

• Tries
• From the word retrieval
• Allows for fast key lookup
• Requires less space than BST

4
Background (cont.)

• Dijkstras Algorithm
• Finds shortest path from source vertex to every
  other vertex in a graph

5
MSA Definitions

• S1,,SK input sequences
• S is the input alphabet
• Resulting alignment is a rectangular char array
  which satisfies the following
• There are exactly K rows
• Row I is precisely the string SI if dashes are
  ignored

6
MSA Definitions

• S1,,SK input sequences
• S is the input alphabet
• Resulting alignment is a rectangular char array
  which satisfies the following
• There are exactly K rows
• Row I is precisely the string SI if dashes are
  ignored
• --VLSPADKTNVKAAWGKVGAHAGEYGAEALE-
• -VHLTPEEKSAVTALWGKVNVD--EVGGEALGR
• --GLSDGEWQLVLNVWGKVEADIPGHGQEVLI-
• MKFFAVLALCIVGAIASPLTADEASLVQSS---

7
MSA Defintions (cont.)

• Function sub(a,b)
• sub(-,-) 0
• sub(a,b) is symmetric
• Function c(Ai,j)

8
The Problem

• Basic sum-of-pairs multiple sequence alignment
  problem is to minimize the pairwise sum
• By default, MSA multiplies each pairwise
  alignment cost by a weight, denoted

9
Boundin

• MSA searches only among alignments whose cost is
  lt U for some U
• How to get U?
• U L d

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More MSA

• For each pair of sequences Si, Sj MSA computes
  the standard two-dimensional dynamic programming
  graph Di,j
• For each vertex in the graph, the cost of an
  optimal alignment is also computed
• Accepted if admissible
• Admissible if cost at most d(Si,Sj) ei,j

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MSA Setup

• Directed acyclic graph in which source-to-sink
  paths of weight C correspond to alignments of
  cost C
• Vertices represented as integers in K
  dimensional space
• Example
• For Dijkstra, instead of array D, each vertex has
  label v.D

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MSA Setup

• Directed acyclic graph in which source-to-sink
  paths of weight C correspond to alignments of
  cost C
• Vertices represented as integers in K
  dimensional space
• Example
• lt0,0,0,0gt ? lt0,0,0,1gt ? lt0,1,0,2gt
• For Dijkstra, instead of array D, each vertex has
  label v.D

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MSA w/o Gap Penalties

• Two Stages
• Stage 1
• Find the set of points that make up a path
  between Si and Sj with cost at most d(Si,Sj)
  ei,j
• Stage 2
• Shortest source to sink path is computed

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MSA Pruning

• Two Types of pruning
• Return cost pruning
• Carrillo-Lipman

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MSA w/ Gap Penalties

• Principle of Optimality
• Allows us to do
• Principle does not apply in the same form with
  gap penalties

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MSA Improvements

• Running time mainly depends on three functions
• Cost
• Adjacent
• Edge
• Majority of space taken up by records that store
  edges

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Original Edge Storage

• Edges stored at incoming vertex
• Pros
• Easy backtracking
• Easily determine whether edge exists
• Cons
• Many list searches

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New Edge Storage

• Store outgoing edges v?w at v
• Add backtracking field to each edge
• Add reference count to each edge

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Facts Helping to Free Space

• Once an edge e is extracted from PQ, e.D will
  never decrease
• Edge can be deleted when either
• (with e v?w and w!t)
• w has no outgoing edges
• All edges in the form w?x have an edge other than
  e as backtrack edge
• If the list of outgoing edges for v becomes
  empty, after v has been visited, then all edges
  into v can be deleted.
• If vertex v has no outgoing edges or incoming
  edges after some edge outgoing from v is
  extracted, then v can never occur in an optimal
  path. V can be deleted and need not be recreated
• Deletion of vertices permits the deletion of all
  outgoing and incoming edges, which can cause
  cascading deletions.

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Improvements to Cost Function

• Inlined
• Loop invariants
• Comparison of D values
• (Given e p?q and f q?r)
• We check to see if e.D cost(e,f) lt f.D
• Experiments showed that this test very often
  fails.
• Is it possible to check this without calling the
  expensive function Cost?
• Yes. Check e.D extra lt f.D instead, where extra
  lt cost(e,f)
• Changed cost function to check extra in loop and
  exit early if value is too large

21
Results
22
Conclusions

• Made feasible many problems which were not
  previously possible
• Much of what was changed were low-level
  implementation details
• Shows that it is very useful in programs which
  allocate a lot of memory to look for
  opportunities to free memory
• Coding of inner loop that takes most of the time
  is crucial