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

Abstract

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. 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, spatialmore » 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.« less

Authors:
 [1];  [1]; ORCiD logo [2]
  1. Univ. of Erlangen–Nuremberg, Erlangen (Germany). Chair of Applied Dynamics
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States). Biosciences Division; Univ. of California, San Francisco, CA (United States). Dept. of Bioengineering and Therapeutic Sciences
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, San Francisco, CA (United States); Univ. of Erlangen–Nuremberg, Erlangen (Germany)
Sponsoring Org.:
USDOE; National Inst. of Health (NIH) (United States); Deutsche Telekom Stiftung (Germany)
OSTI Identifier:
1490788
Grant/Contract Number:  
AC02-76SF00515; GM123159
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Information and Modeling
Additional Journal Information:
Journal Volume: 58; Journal Issue: 10; Journal ID: ISSN 1549-9596
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Budday, Dominik, Leyendecker, Sigrid, and van den Bedem, Henry. Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion. United States: N. p., 2018. Web. doi:10.1021/acs.jcim.8b00267.
Budday, Dominik, Leyendecker, Sigrid, & van den Bedem, Henry. Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion. United States. https://doi.org/10.1021/acs.jcim.8b00267
Budday, Dominik, Leyendecker, Sigrid, and van den Bedem, Henry. Fri . "Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion". United States. https://doi.org/10.1021/acs.jcim.8b00267. https://www.osti.gov/servlets/purl/1490788.
@article{osti_1490788,
title = {Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion},
author = {Budday, Dominik and Leyendecker, Sigrid and van den Bedem, Henry},
abstractNote = {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. 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.},
doi = {10.1021/acs.jcim.8b00267},
journal = {Journal of Chemical Information and Modeling},
number = 10,
volume = 58,
place = {United States},
year = {2018},
month = {9}
}

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Figures / Tables:

Figure 1 Figure 1: Coarse-grained protein modeling via topological rigidity analysis (left) and elastic network models (ENM, right). The pebble game represents proteins as constraint graphs (top left), with pebble DoF (small dots) and bar constraints (thin lines are single constraints, thick lines are rigid links with six constraints), connecting atomic verticesmore » (spheres). It decomposes a protein into rigid clusters of atoms (lower left, individually colored), quantifying the number of internal ’floppy modes’ (circular arrow), without an explicit motion basis. By contrast, ENM obtains an explicit motion basis (arrows lower right) corresponding to eigenmodes of a spring-mass network (top right), with covalent (black) and non-covalent (blue) one-dimensional spring restraints. Our kinematic flexibility approach (center) models proteins as kinematic spanning trees, with a root vertex (yellow), dihedral DoF (arrows between vertices) and non-covalent constraints (red dashed lines), for example, hydrogen bonds. It combines features from topological rigidity and ENM, providing explicit motion modes from a spectral decomposition of the constraint Jacobian matrix.« less

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