Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Journal article
(Original article)

Publication Details

Author(s): Budday D, Leyendecker S, van den Bedem H
Journal: Journal of Chemical Information and Modeling
Publication year: 2018
Volume: 58
Journal issue: 10
Pages range: 2108-2122
ISSN: 1549-9596
Language: English


Elastic network models (ENMs) and constraint-based, topological rigidity
analysis are two distinct, coarse-grained approaches to study
conformational flexibility of macromolecules. In the two decades since
their introduction, both have contributed significantly to insights into
protein molecular mechanisms and function. However, despite a shared
purpose of these approaches, the topological nature of rigidity
analysis, and thereby the absence of motion modes, has impeded a direct
comparison. Here, we present an alternative, kinematic approach to
rigidity analysis, which circumvents these drawbacks. We introduce a
novel protein hydrogen bond network spectral decomposition, which
provides an orthonormal basis for collective motions modulated by
noncovalent interactions, analogous to the eigenspectrum of normal
modes. The zero modes decompose proteins into rigid clusters identical
to those from topological rigidity, while nonzero modes rank protein
motions by their hydrogen bond collective energy penalty. Our kinematic
flexibility analysis bridges topological rigidity theory and ENM,
enabling a detailed analysis of motion modes obtained from both
approaches. Analysis of a large, structurally diverse data set revealed
that collectivity of protein motions, reported by the Shannon entropy,
is significantly reduced for rigidity theory compared to normal mode
approaches. Strikingly, kinematic flexibility analysis suggests that the
hydrogen bonding network encodes a protein-fold specific, spatial
hierarchy of motions, which goes nearly undetected in ENM. This
hierarchy reveals distinct motion regimes that rationalize experimental
and simulated protein stiffness variations. Kinematic motion modes
highly correlate with reported crystallographic B factors and molecular
dynamics simulations of adenylate kinase. A formal expression for
changes in free energy derived from the spectral decomposition indicates
that motions across nearly 40% of modes obey enthalpy–entropy
compensation. Taken together, our results suggest that hydrogen bond
networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

FAU Authors / FAU Editors

Budday, Dominik
Chair of Applied Dynamics
Leyendecker, Sigrid Prof. Dr.-Ing.
Chair of Applied Dynamics

External institutions with authors

Stanford University

How to cite

Budday, D., Leyendecker, S., & van den Bedem, H. (2018). Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion. Journal of Chemical Information and Modeling, 58(10), 2108-2122.

Budday, Dominik, Sigrid Leyendecker, and Henry van den Bedem. "Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion." Journal of Chemical Information and Modeling 58.10 (2018): 2108-2122.


Last updated on 2019-07-01 at 05:10