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Protein Structure by Semidefinite Facial Reduction

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Research in Computational Molecular Biology (RECOMB 2012)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 7262))

Abstract

All practical contemporary protein NMR structure determination methods use molecular dynamics coupled with a simulated annealing schedule. The objective of these methods is to minimize the error of deviating from the NOE distance constraints. However, this objective function is highly nonconvex and, consequently, difficult to optimize. Euclidean distance geometry methods based on semidefinite programming (SDP) provide a natural formulation for this problem. However, complexity of SDP solvers and ambiguous distance constraints are major challenges to this approach. The contribution of this paper is to provide a new SDP formulation of this problem that overcomes these two issues for the first time. We model the protein as a set of intersecting two- and three-dimensional cliques, then we adapt and extend a technique called semidefinite facial reduction to reduce the SDP problem size to approximately one quarter of the size of the original problem. The reduced SDP problem can not only be solved approximately 100 times faster, but is also resistant to numerical problems from having erroneous and inexact distance bounds.

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Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Babak Alipanahi & Ming Li

  2. INRIA Grenoble Rhône-Alpes, France

    Nathan Krislock

  3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada

    Ali Ghodsi

  4. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    Henry Wolkowicz

  5. Department of Biology, York University, Toronto, Ontario, Canada

    Logan Donaldson

Authors
  1. Babak Alipanahi
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  2. Nathan Krislock
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  3. Ali Ghodsi
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  4. Henry Wolkowicz
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  5. Logan Donaldson
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  6. Ming Li
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Editor information

Editors and Affiliations

  1. Computer Science Department, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Benny Chor

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Alipanahi, B., Krislock, N., Ghodsi, A., Wolkowicz, H., Donaldson, L., Li, M. (2012). Protein Structure by Semidefinite Facial Reduction. In: Chor, B. (eds) Research in Computational Molecular Biology. RECOMB 2012. Lecture Notes in Computer Science(), vol 7262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29627-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-29627-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29626-0

  • Online ISBN: 978-3-642-29627-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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