Research Article

Protein flexibility predictions using graph theory

  1. Donald J. Jacobs1,†,
  2. A.J. Rader1,
  3. Leslie A. Kuhn2,‡,*,
  4. M.F. Thorpe1,‡

Article first published online: 29 MAY 2001

DOI: 10.1002/prot.1081

Issue

Proteins: Structure, Function, and Bioinformatics

Proteins: Structure, Function, and Bioinformatics

Volume 44, Issue 2, pages 150–165, 1 August 2001

Additional Information

How to Cite

Jacobs, D. J., Rader, A.J., Kuhn, L. A. and Thorpe, M.F. (2001), Protein flexibility predictions using graph theory. Proteins, 44: 150–165. doi: 10.1002/prot.1081

Author Information

  1. 1

    Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan

  2. 2

    Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan

  1. †

    Department of Physics and Astronomy, California State University Northridge, Northridge, CA 91330.

  1. ‡

    Leslie A. Kuhn and M.F. Thorpe are contributing authors.

*Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI

Publication History

  1. Issue published online: 29 MAY 2001
  2. Article first published online: 29 MAY 2001
  3. Manuscript Accepted: 15 MAR 2001
  4. Manuscript Received: 23 SEP 2000

Funded by

  • National Science Foundation. Grant Numbers: DMR-96 32182, DBI-96 00831
  • National Institutes of Health. Grant Number: R43 GM58337-01
  • Michigan State University
  • American Heart Association. Grant Number: 9940091N

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Keywords:

  • conformational change;
  • mobility and dynamics;
  • coupled/collective motions;
  • hydrogen-bond networks;
  • distance constraints;
  • dihedral angle constraints and rotations;
  • structural stability;
  • dihydrofolate reductase;
  • adenylate kinase

Abstract

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase. Proteins 2001;44:150–165. © 2001 Wiley-Liss, Inc.

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