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Conformational Transitions and Principal Geodesic Analysis on the Positive Semidefinite Matrix Manifold

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Bioinformatics Research and Applications (ISBRA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 8492))

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Abstract

Given an initial and final protein conformation, generating the intermediate conformations provides important insight into the protein’s dynamics. We represent a protein conformation by its Gram matrix, which is a point on the rank 3 positive semidefinite matrix manifold, and show matrices along the geodesic linking an initial and final Gram matrix can be used to generate a feasible pathway for the protein’s structural change. This geodesic is based on a particular quotient geometry. If a protein is known to contain domains or groups of atoms that act as rigid clusters, facial reduction can be used to decrease the size of the Gram matrices before calculating the geodesic. The geodesic between two conformations is only one path a protein’s Gram matrix can follow; principal geodesic analysis (PGA) is one possible strategy to find other geodesics.

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Author information

Authors and Affiliations

  1. University of Waterloo, Canada

    Xiao-Bo Li & Forbes J. Burkowski

Authors
  1. Xiao-Bo Li
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  2. Forbes J. Burkowski
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Editor information

Editors and Affiliations

  1. Johns Hopkins University, Computer Science Department, Baltimore, MD 21218, USA and National Science Foundation, 1115, CCF, USA

    Mitra Basu

  2. Department of Computer Science, Georgia State University, 30303, Atlanta, GA, USA

    Yi Pan

  3. School of Information Science and Engineering, Central South University, 410083, Changsha, China

    Jianxin Wang

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Li, XB., Burkowski, F.J. (2014). Conformational Transitions and Principal Geodesic Analysis on the Positive Semidefinite Matrix Manifold. In: Basu, M., Pan, Y., Wang, J. (eds) Bioinformatics Research and Applications. ISBRA 2014. Lecture Notes in Computer Science(), vol 8492. Springer, Cham. https://doi.org/10.1007/978-3-319-08171-7_30

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  • DOI: https://doi.org/10.1007/978-3-319-08171-7_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08170-0

  • Online ISBN: 978-3-319-08171-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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