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

  • Xiao-Bo Li
  • Forbes J. Burkowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8492)

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.

Keywords

cliques rigid clusters elastic network interpolation Euclidean distance matrix Gram matrix positive semidefinite facial reduction geodesic Riemannian manifold principal geodesic analysis 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xiao-Bo Li
    • 1
  • Forbes J. Burkowski
    • 1
  1. 1.University of WaterlooCanada

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