DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Journal of Chemical Information and Modeling
 [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

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.

Research Organization:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, San Francisco, CA (United States); Univ. of Erlangen–Nuremberg, Erlangen (Germany)
Sponsoring Organization:
USDOE; National Inst. of Health (NIH) (United States); Deutsche Telekom Stiftung (Germany)
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1490788
Journal Information:
Journal of Chemical Information and Modeling, Journal Name: Journal of Chemical Information and Modeling Journal Issue: 10 Vol. 58; ISSN 1549-9596
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (85)

Torsional Network Model: Normal Modes in Torsion Angle Space Better Correlate with Conformation Changes in Proteins journal June 2010
An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game journal November 1997
Collective protein dynamics and nuclear spin relaxation journal February 1995
De novo design of protein homo-oligomers with modular hydrogen-bond network-mediated specificity journal May 2016
Multi-Resolution Rigidity-Based Sampling of Protein Conformational Paths
  • Luo, Dong; Haspel, Nurit
  • BCB'13: ACM-BCB2013, Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics https://doi.org/10.1145/2506583.2506710
conference September 2013
On the coupling between the dynamics of protein and water journal January 2017
Protein flexibility and dynamics using constraint theory journal February 2001
ElNemo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement journal July 2004
Generic Rigidity Percolation: The Pebble Game journal November 1995
Accurate de novo design of hyperstable constrained peptides journal September 2016
Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family journal August 2008
Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory journal February 2006
Fast, clash-free RNA conformational morphing using molecular junctions journal March 2017
Anisotropy of Fluctuation Dynamics of Proteins with an Elastic Network Model journal January 2001
Rapid simulation of protein motion: merging flexibility, rigidity and normal mode analyses journal February 2012
Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis journal August 1996
A comparison of successful and failed protein interface designs highlights the challenges of designing buried hydrogen bonds journal November 2012
Coupled Motions in β 2 AR:Gαs Conformational Ensembles journal February 2016
Frustration-guided motion planning reveals conformational transitions in proteins: BUDDAY et al. journal July 2017
iMod: multipurpose normal mode analysis in internal coordinates journal August 2011
Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models journal October 2015
Adenylate kinase motions during catalysis: an energetic counterweight balancing substrate binding journal February 1996
Functional Modes of Proteins Are among the Most Robust journal February 2006
Conventional NMA as a better standard for evaluating elastic network models: NMA as a Better Standard for Evaluating ENMs journal December 2014
Protein rigidity and thermophilic adaptation journal January 2011
Analyzing the Flexibility of RNA Structures by Constraint Counting journal June 2008
Hydrogen bonds are a primary driving force for de novo protein folding journal November 2017
Automated design of the surface positions of protein helices: Protein surface design journal June 1997
Movie of the structural changes during a catalytic cycle of nucleoside monophosphate kinases journal May 1995
A proof of the molecular conjecture conference January 2009
How soft is a single protein? The stress–strain curve of antibody pentamers with 5 pN and 50 pm resolutions journal January 2016
Generic rigidity in three-dimensional bond-bending networks journal August 1998
Nonadditivity in Conformational Entropy upon Molecular Rigidification Reveals a Universal Mechanism Affecting Folding Cooperativity journal February 2011
Protein normal-mode dynamics: Trypsin inhibitor, crambin, ribonuclease and lysozyme journal February 1985
Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces journal January 2018
Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart A Spatial Hierarchy Of Protein Motion dataset January 2018
Low-frequency modes in the Raman spectra of proteins journal July 1982
The coming of age of de novo protein design journal September 2016
Global and local indices for characterizing biomolecular flexibility and rigidity journal September 2012
Sampling large conformational transitions: adenylate kinase as a testing ground journal May 2014
Integrative, dynamic structural biology at atomic resolution—it's about time journal March 2015
Zipping and Unzipping of Adenylate Kinase: Atomistic Insights into the Ensemble of Open↔Closed Transitions journal November 2009
Efficient Approximation of Ligand Rotational and Translational Entropy Changes upon Binding for Use in MM-PBSA Calculations journal January 2017
Thermostability in rubredoxin and its relationship to mechanical rigidity journal December 2009
Accessible Surfaces of Beta Proteins Increase with Increasing Protein Molecular Mass More Rapidly than Those of Other Proteins journal December 2011
Optimized Torsion-Angle Normal Modes Reproduce Conformational Changes More Accurately Than Cartesian Modes journal December 2011
Correlation between Native-State Hydrogen Exchange and Cooperative Residue Fluctuations from a Simple Model journal January 1998
Building-block approach for determining low-frequency normal modes of macromolecules journal January 2000
Elasticity, strength and resilience: A comparative study on mechanical signatures of α-Helix, β-sheet and tropocollagen domains journal July 2008
Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential journal June 1997
A new approach for determining low-frequency normal modes in macromolecules journal June 1994
Maintaining and Enhancing Diversity of Sampled Protein Conformations in Robotics-Inspired Methods journal January 2018
Induced-fit movements in adenylate kinases journal June 1990
Algorithms for three-dimensional rigidity analysis and a first-order percolation transition journal October 2007
Intermolecular hydrogen bonding strategy to fabricate mechanically strong hydrogels with high elasticity and fatigue resistance journal January 2013
Floppy modes in network glasses journal November 1989
A unified model of protein dynamics journal February 2009
Identifying protein folding cores from the evolution of flexible regions during unfolding journal December 2002
Rigidity Theory-Based Approximation of Vibrational Entropy Changes upon Binding to Biomolecules journal March 2017
Adenylate Kinase and AMP Signaling Networks: Metabolic Monitoring, Signal Communication and Body Energy Sensing journal April 2009
Universality of vibrational spectra of globular proteins journal February 2016
Protein unfolding: Rigidity lost journal March 2002
Geometric analysis characterizes molecular rigidity in generic and non-generic protein configurations journal October 2015
Entropic Elasticity Controls Nanomechanics of Single Tropocollagen Molecules journal July 2007
Mechanical Response of Silk Crystalline Units from Force-Distribution Analysis journal May 2009
Protein flexibility predictions using graph theory journal January 2001
A Distinct Utility of the Amide III Infrared Band for Secondary Structure Estimation of Aqueous Protein Solutions Using Partial Least Squares Methods journal March 2004
Structure of the complex between adenylate kinase from Escherichia coli and the inhibitor Ap5A refined at 1.9 Å resolution journal March 1992
Constrained geometric simulation of diffusive motion in proteins journal November 2005
Application of Rigidity Theory to the Thermostabilization of Lipase A from Bacillus subtilis journal March 2016
Domain Closure in Adenylate Kinase journal January 1993
Obtaining information about protein secondary structures in aqueous solution using Fourier transform IR spectroscopy journal February 2015
KINARI-Web: a server for protein rigidity analysis journal June 2011
Sampling protein conformations and pathways journal January 2004
Simulating Protein Motions with Rigidity Analysis journal July 2007
A Method of Rapid Calculation of a Second Derivative Matrix of Conformational Energy for Large Molecules journal October 1983
Counting out to the flexibility of molecules journal November 2005
Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs journal July 2015
Direct observation of ultrafast large-scale dynamics of an enzyme under turnover conditions journal March 2018
On graphs and rigidity of plane skeletal structures journal October 1970
Geometric Confinement Governs the Rupture Strength of H-bond Assemblies at a Critical Length Scale journal February 2008
Hydration Water Dynamics Near Biological Interfaces journal December 2008
Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case journal August 2015
Detecting the native ligand orientation by interfacial rigidity: SiteInterlock: Identifying Ligand Binding Poses by Rigidity
  • Raschka, Sebastian; Bemister-Buffington, Joseph; Kuhn, Leslie A.
  • Proteins: Structure, Function, and Bioinformatics, Vol. 84, Issue 12 https://doi.org/10.1002/prot.25172
journal October 2016
Atomic torsional modal analysis for high-resolution proteins journal March 2015

Cited By (2)

Mix-and-inject XFEL crystallography reveals gated conformational dynamics during enzyme catalysis journal December 2019
Shining light on cysteine modification: connecting protein conformational dynamics to catalysis and regulation journal June 2019