Protein Encoding Optimization

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Protein Encoding Optimization

• Student Logan Everett
• Mentor Endre Boros
• Funded by DIMACS REU 2004

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Project Overview

• Model Biological Scoring Matrices
• Weighted Binary Hamming Space
• Optimize Using Linear Programming
• Accurate Random Generation

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Scoring Matrices
A Q M K R H A R M I F L 4 1 5 3 3
-3
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Encode To Binary Strings

• Hamming Distances
• Easy to Approximate on Binary Strings
• Statistically Proven Methods
• More Efficient
• How Do Similarity and Distance Relate?
• Inverse Relationship
• First Create Real Distance Vector D

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Precise Problem Distortion

• Dij(1e) ? lhfi,fj ? Dij(1e)
• ? unique pairs i,j (nC2)
• s.t. 0 ? e ? 1 and 0 ? l

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Encoding Scheme as Vector

• C 0110101101010101010
• S 1010110101011010101
• T 0110101010011011010
• P 1010101011010100110
• A 1011010101011011010
• G 1010101100111010101

y2 y1
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Modified Inequality

• D(1e) ? Ax ? D(1e)
• s.t. 0 ? e ? 1 and 0 ? l
• Let x ly

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Linear Programming Problem

• Need All Linear Expressions
• D(1 e) ? Ax and Ax ? D(1 e)
• -Ax De ? -D and Ax De ? D
• All xi, e ? 0
• Goal Minimize e
• Solve with CPLEX

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Problem Size

• Number of Constraints (Rows)
• 2(nC2) 380
• Number of Variables (Columns)
• 2n-1 524,288
• Total Size App. 2x108
• CPLEX App. 1 Minute

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Linear Programming Solution

• Solution Contains
• Min Value of e
• Scaled Weight Vector x
• Non-Integral Values in x
• Convert to p Vector
• X Sxi
• pi xi / X

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Random Encodings

• Randomly Select Cross Sections
• Based on Percent Weights
• Can Scale For Any N-Length Encoding
• Longer Encodings Should Approach Minimum
  Distortion

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Results
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Courtesy of DIMACS

• Mentor Endre Boros RUTCOR
• Logan Everett DIMACS REU 2004

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