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A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem

Author

Listed:
  • Forbes Burkowski

    (Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

  • Haesol Im

    (Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

  • Henry Wolkowicz

    (Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

Abstract

This paper considers the NP-hard protein side-chain positioning ( SCP ) problem, an important final task of protein structure prediction. We formulate the SCP as an integer quadratic program and derive its doubly nonnegative (DNN) (convex) relaxation. Strict feasibility fails for this DNN relaxation. We apply facial reduction to regularize the problem. This gives rise to a natural splitting of the variables. We then use a variation of the Peaceman-Rachford splitting method to solve the DNN relaxation. The resulting relaxation and rounding procedures provide strong approximate solutions. Empirical evidence shows that almost all our instances of this NP-hard SCP problem, taken from the Protein Data Bank, are solved to provable optimality . Our large problems correspond to solving a DNN relaxation with 2,883,601 binary variables to provable optimality.

Suggested Citation

  • Forbes Burkowski & Haesol Im & Henry Wolkowicz, 2025. "A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem," INFORMS Journal on Computing, INFORMS, vol. 37(4), pages 962-976, July.
    • Handle: RePEc:inm:orijoc:v:37:y:2025:i:4:p:962-976
    DOI: 10.1287/ijoc.2023.0094
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    References listed on IDEAS

    as
    1. Loren L. Looger & Mary A. Dwyer & James J. Smith & Homme W. Hellinga, 2003. "Computational design of receptor and sensor proteins with novel functions," Nature, Nature, vol. 423(6936), pages 185-190, May.
    2. Bernard Chazelle & Carl Kingsford & Mona Singh, 2004. "A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 380-392, November.
    3. Forbes Burkowski & Yuen-Lam Cheung & Henry Wolkowicz, 2014. "Efficient Use of Semidefinite Programming for Selection of Rotamers in Protein Conformations," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 748-766, November.
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