Solving the Protein Threading Problem in Parallel Nocola Yanev, Rumen Andonov

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Solving the Protein Threading Problem in
ParallelNocola Yanev, Rumen Andonov

• Indrajit Bhattacharya
• CMSC 838T Presentation

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Motivation

• Problem paper is trying to solve
• 3D structure prediction using threading
• Is a given target sequence likely to fold to a 3D
  template core?
• Find the alignment that minimizes some score
  function
• NP-complete optimal solution not possible
• MAX-SNP-hard arbitrary approximation not
  possible
• Why do we care
• 3D structure determines biological function of
  protein
• Amino acid sequence (almost) uniquely determines
  3D structure
• Threading is usually less accurate than
  comparative modeling but easier to solve

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Talk Overview

• Overview of talk
• Motivation
• Techniques
• Evaluation
• Related work
• Observations

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Techniques

• Approach
• Reduce the problem to some known theoretical
  problem of interest
• In this case, network flow
• Use existing tools for solving the theoretical
  problem efficiently
• CPLEX
• Explore possibilities for parallelizing the
  problem
• Investigate the intrinsic hardness for real
  biological examples

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Mathematical Formulation
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Reduction to Network Flow An Example
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Reduction to Network FlowVariables and
Constraints

• Standard Network Flow
• Variable xi,t for each segment to position
  assignment
• Restricted to 0, 1
• With standard flow conservation constraints
• Additional cost for non-local interactions
• Variable zi,t,i,t for each non-local
  interaction
• Restricted to 0, 1
• Constrained to sum to 1 for each non-local pair
  (i, i)
• Upper bounded by flow entering (i, t) and leaving
  (i, t)

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Drawbacks of Approach

• Integer programming is hard to solve!
• Relax to linear programming with (0, 1) variables
• Approximate to integer solution using standard
  heuristics
• Existing tools like CPLEX
• Huge number of variables
• For 36 segments and 81 positions, IP problem has
  741264 rows, 360945 columns and 54145231 non-zero
  variables!
• Need to reduce number of variables and
  constraints
• Calls for parallelization if possible

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Parallel Solution

• Utilize special flow constraints
• Split into sub-problems that may be solved
  parallely
• Split the k-th layer in the graph into r
  intervals
• Force path for a sub-problem to pass through a
  particular interval in the layer
• Pass best bound for objective function found so
  far as parameter to sub-problem
• Sub-task aborts when dual objective function
  exceeds the current best bound

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Improving Parallel Solution

• Drawback Hardest Sub-Problem Dominates!
• Parallel strategy was found to be slower than the
  sequential!
• Sub-problems can potentially become harder to
  solve
• Many more difficult sub-problems than easy ones
• Solution
• Break the atomicity of the tasks
• Each sub-task periodically checks the current
  best bound and updates its cut-off
• Extra overhead is still small compared to task
  granularity
• Now the easiest executing sub-task dominates!

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Evaluation

• Experimental environment
• Real protein sequences
• ILOG CPLEX Callable Library
• SUN Ultra-Sparc II, 450 Mhz
• Objective function coefficients generated from
  FROST
• Maximum of 7 processors and 29 sub-problems
• Evaluation results
• Sequential version much faster than previous
  branch-and-bound results for the same problem
  formulation
• Time taken comparable to PROSPECT
• Splitting and parallelization significantly
  improve turnaround
• Really tiny gap between relaxed LP and ILP
  solutions
• Mostly integer solutions even for relaxed LP!

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Result Tables
Comparison with branch and bound algorithm

• Comment Self threading results in significantly
  lower scores (as should be)

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Result Tables

• Comment Tiny relaxation gap. (significance?)

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Result Tables
Size of the LP formulation

• Comment LP problem size is still too large.

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Result Tables
Performance with parallel sub-tasks

• Comment Longer times with more sub-problems??

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Related Work

• Similar / previous approaches
• Lathrop and Smith, 1998
• Uses same cost function
• Branch and bound algorithm for searching the
  space of threadings
• Xu, Xu and Uberbacher, 1998
• Divide and conquer algorithm
• Xu, Li, Lin, Kim and Xu, 2003
• Linear programming formulation
• Solved using bb algorithm
• None of the above suggest any parallelizing scheme

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Observations

• Points of Interest
• Mapping to a known problem of interest
• Nicely utilizes particular constraints to break
  into independent subtasks
• Threading of real amino acid sequences seems
  possible
• Raises interesting questions about real-life
  protein threading being in P
• Solver tailored for this particular problem may
  yield better results

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Observations

• Criticism
• Not enough experiments with large number of
  subtasks and processors to show scaling
• Prohibitively large number of variables and
  constraints
• How accurate are the objective function
  coefficients?
• What is the resolution of the objective function?
• Threading onto multiple sequences for prediction
  still looks daunting
• Not clear how to extend the idea for 3-way and
  more complex interactions
• Improvements
• Seems possible to break up the sub-tasks
  recursively

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Thank you!