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

Budday D, Leyendecker S, van den Bedem H (2018)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2018

Journal

Journal of Chemical Information and Modeling American Chemical Society

Book Volume: 58

Pages Range: 2108-2122

Journal Issue: 10

URI: https://pubs.acs.org/doi/abs/10.1021/acs.jcim.8b00267?journalCode=jcisd8

DOI: 10.1021/acs.jcim.8b00267

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. 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.

Authors with CRIS profile

Dominik Budday Institute of Applied Dynamics Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

Protein flexibility and conformational ensembles from kino-geometric modeling and sampling to motion planning June 1, 2014 - March 31, 2019

Involved external institutions

Stanford University

United States (USA) (US)

How to cite

APA:

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. https://dx.doi.org/10.1021/acs.jcim.8b00267

MLA:

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.

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