Solving the Protein Threading
Problem in Parallel
Nocola Yanev, Rumen Andonov
Indrajit Bhattacharya
CMSC 838T Presentation
Motivation
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Problem paper is trying to solve
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3D structure prediction using threading
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Is a given target sequence likely to fold to a 3D template core?
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Find the alignment that minimizes some score function
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NP-complete; optimal solution not possible
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MAX-SNP-hard; arbitrary approximation not possible
Why do we care
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3D structure determines biological function of protein
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Amino acid sequence (almost) uniquely determines 3D
structure
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Threading is usually less accurate than comparative modeling
but easier to solve
CMSC 838T – Presentation
Talk Overview
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Overview of talk
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Motivation
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Techniques
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Evaluation
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Related work
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Observations
CMSC 838T – Presentation
Techniques
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Approach
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Reduce the problem to some known theoretical problem of
interest
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In this case, network flow
Use existing tools for solving the theoretical problem efficiently
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CPLEX
Explore possibilities for parallelizing the problem
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Investigate the intrinsic hardness for real biological examples
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Mathematical Formulation
Two structurally
similar proteins
Spatial adjacencies
(interactions)
Possible threading
with a sequence
Objective function
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Reduction to Network Flow: An Example
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Reduction to Network Flow:
Variables and Constraints
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Standard Network Flow
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Variable xi,t for each segment to position assignment
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Restricted to [0, 1]
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With standard flow conservation constraints
Additional cost for non-local interactions
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Variable zi,t,i’,t’ for each non-local interaction
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Restricted to {0, 1}
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Constrained to sum to 1 for each non-local pair (i, i’)
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Upper bounded by flow entering (i, t) and leaving (i’, t’)
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Drawbacks of Approach
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Integer programming is hard to solve!
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Relax to linear programming with (0, 1) variables
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Approximate to integer solution using standard heuristics
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Existing tools like CPLEX
Huge number of variables
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For 36 segments and 81 positions, IP problem has 741264
rows, 360945 columns and 54145231 non-zero variables!
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Need to reduce number of variables and constraints
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Calls for parallelization if possible
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Parallel Solution
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Utilize special flow constraints
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Split into sub-problems that may be solved parallely
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Split the k-th layer in the graph into r intervals
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Force path for a sub-problem to pass through a particular
interval in the layer
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Pass best bound for objective function found so far as
parameter to sub-problem
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Sub-task aborts when dual objective function exceeds the
current best bound
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Improving Parallel Solution
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Drawback: Hardest Sub-Problem Dominates!
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Parallel strategy was found to be slower than the sequential!
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Sub-problems can potentially become harder to solve
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Many more difficult sub-problems than easy ones
Solution:
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Break the atomicity of the tasks
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Each sub-task periodically checks the current best bound and
updates its cut-off
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Extra overhead is still small compared to task granularity
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Now the easiest executing sub-task dominates!
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Evaluation
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Experimental environment
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Real protein sequences
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ILOG CPLEX Callable Library
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SUN Ultra-Sparc II, 450 Mhz
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Objective function coefficients generated from FROST
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Maximum of 7 processors and 29 sub-problems
Evaluation results
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Sequential version much faster than previous branch-andbound results for the same problem formulation
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Time taken comparable to PROSPECT
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Splitting and parallelization significantly improve turnaround
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Really tiny gap between relaxed LP and ILP solutions
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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
Gap between relaxed LP and ILP
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
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Similar / previous approaches
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Lathrop and Smith, 1998
 Uses same cost function
 Branch and bound algorithm for searching the space of
threadings
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Xu, Xu and Uberbacher, 1998
 Divide and conquer algorithm
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Xu, Li, Lin, Kim and Xu, 2003
 Linear programming formulation
 Solved using b&b algorithm
None of the above suggest any parallelizing scheme
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Observations
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Points of Interest
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Mapping to a known problem of interest
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Nicely utilizes particular constraints to break into independent
subtasks
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Threading of real amino acid sequences seems possible
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Raises interesting questions about real-life protein threading
being in P
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Solver tailored for this particular problem may yield better
results
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Observations
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Criticism
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Not enough experiments with large number of subtasks and
processors to show scaling
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Prohibitively large number of variables and constraints
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How accurate are the objective function coefficients?
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What is the resolution of the objective function?
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Threading onto multiple sequences for prediction still looks
daunting
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Not clear how to extend the idea for 3-way and more complex
interactions
Improvements
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Seems possible to break up the sub-tasks recursively
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Thank you!
CMSC 838T – Presentation