skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces

Abstract

The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. In this paper, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Finally, correlated protein motions identified with our algorithm agree with those from MD simulations.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Stanford Univ., CA (United States). Molecular and Cellular Physiology; SLAC National Accelerator Lab., Menlo Park, CA (United States). Bioscience Division
  2. Univ. of Erlangen-Nuremberg, Erlangen (Germany). Chair of Applied Dynamics
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Bioscience Division
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Stanford Univ., CA (United States); Univ. of Erlangen-Nuremberg, Erlangen (Germany)
Sponsoring Org.:
USDOE; Deutsche Telekom Stiftung (Germany); Novo Nordisk Foundation (Denmark)
OSTI Identifier:
1471534
Grant/Contract Number:  
AC02-76SF00515; NNF15OC0015268
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Chemistry
Additional Journal Information:
Journal Volume: 39; Journal Issue: 12; Journal ID: ISSN 0192-8651
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 97 MATHEMATICS AND COMPUTING; high dimensional motion and path planning; collision-avoidance; poisson sampling; computational biology; inverse kinematics; molecular rigidity

Citation Formats

Fonseca, Rasmus, Budday, Dominik, and van den Bedem, Henry. Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces. United States: N. p., 2018. Web. doi:10.1002/jcc.25138.
Fonseca, Rasmus, Budday, Dominik, & van den Bedem, Henry. Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces. United States. doi:10.1002/jcc.25138.
Fonseca, Rasmus, Budday, Dominik, and van den Bedem, Henry. Fri . "Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces". United States. doi:10.1002/jcc.25138. https://www.osti.gov/servlets/purl/1471534.
@article{osti_1471534,
title = {Collision-free poisson motion planning in ultra high-dimensional molecular conformation spaces},
author = {Fonseca, Rasmus and Budday, Dominik and van den Bedem, Henry},
abstractNote = {The function of protein, RNA, and DNA is modulated by fast, dynamic exchanges between three-dimensional conformations. Conformational sampling of biomolecules with exact and nullspace inverse kinematics, using rotatable bonds as revolute joints and noncovalent interactions as holonomic constraints, can accurately characterize these native ensembles. However, sampling biomolecules remains challenging owing to their ultra-high dimensional configuration spaces, and the requirement to avoid (self-) collisions, which results in low acceptance rates. In this paper, we present two novel mechanisms to overcome these limitations. First, we introduce temporary constraints between near-colliding links. The resulting constraint varieties instantaneously redirect the search for collision-free conformations, and couple motions between distant parts of the linkage. Second, we adapt a randomized Poisson-disk motion planner, which prevents local oversampling and widens the search, to ultra-high dimensions. Tests on several model systems show that the sampling acceptance rate can increase from 16% to 70%, and that the conformational coverage in loop modeling measured as average closeness to existing loop conformations doubled. Finally, correlated protein motions identified with our algorithm agree with those from MD simulations.},
doi = {10.1002/jcc.25138},
journal = {Journal of Computational Chemistry},
issn = {0192-8651},
number = 12,
volume = 39,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

Figure  1 Figure 1: Kinematic representation of molecules and constraints. a) A molecular graph with double bonds and partial double bonds highlighted. After edge-contractions these atoms become a single rigid body vertex. The remaining bonds can rotate around the bond axis and are described by dihedral angles. b) Small section of amore » protein molecule with hydrogen bonds marked as purple lines and a nitrogen-hydrogen clash marked with van der Waals spheres and the bisecting plane. c) A dynamic clash-avoiding constraint (dCC) allows individual motions of the near-clashing atoms p1 and p2 along directions tc in the plane with normal vector nc, but only a joint move along nc. This allows atoms to slide past each other, but prevents them from getting closer.« less

Save / Share:

Works referenced in this record:

Structure and Dynamics of the G121V Dihydrofolate Reductase Mutant: Lessons from a Transition-State Inhibitor Complex
journal, March 2012


Rapid Sampling of Molecular Motions with Prior Information Constraints
journal, February 2009


Random Coordinate Descent with Spinor-matrices and Geometric Filters for Efficient Loop Closure
journal, February 2013

  • Chys, Pieter; Chacón, Pablo
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 3
  • DOI: 10.1021/ct300977f

Computational Models of Protein Kinematics and Dynamics: Beyond Simulation
journal, July 2012


Transition Networks for the Comprehensive Characterization of Complex Conformational Change in Proteins
journal, May 2006

  • Noé, Frank; Krachtus, Dieter; Smith, Jeremy C.
  • Journal of Chemical Theory and Computation, Vol. 2, Issue 3
  • DOI: 10.1021/ct050162r

Correlated Motions and Interactions at the Onset of the DNA-Induced Partial Unfolding of Ets-1
journal, February 2009


Algorithm and Data Structures for Efficient Energy Maintenance during Monte Carlo Simulation of Proteins
journal, October 2004

  • Lotan, Itay; Schwarzer, Fabian; Halperin, Dan
  • Journal of Computational Biology, Vol. 11, Issue 5
  • DOI: 10.1089/cmb.2004.11.902

Stochastic sampling in computer graphics
journal, January 1986

  • Cook, Robert L.
  • ACM Transactions on Graphics, Vol. 5, Issue 1
  • DOI: 10.1145/7529.8927

Sampling-based exploration of folded state of a protein under kinematic and geometric constraints
journal, October 2011

  • Yao, Peggy; Zhang, Liangjun; Latombe, Jean-Claude
  • Proteins: Structure, Function, and Bioinformatics, Vol. 80, Issue 1
  • DOI: 10.1002/prot.23134

Probing RNA Native Conformational Ensembles with Structural Constraints
journal, May 2016

  • Fonseca, Rasmus; van den Bedem, Henry; Bernauer, Julie
  • Journal of Computational Biology, Vol. 23, Issue 5
  • DOI: 10.1089/cmb.2015.0201

Frustration-guided motion planning reveals conformational transitions in proteins: BUDDAY et al.
journal, July 2017

  • Budday, Dominik; Fonseca, Rasmus; Leyendecker, Sigrid
  • Proteins: Structure, Function, and Bioinformatics, Vol. 85, Issue 10
  • DOI: 10.1002/prot.25333

A Comparison of Methods for Generating Poisson Disk Distributions
journal, March 2008


Tracing conformational changes in proteins
journal, January 2010


An NMA-guided path planning approach for computing large-amplitude conformational changes in proteins
journal, July 2007

  • Kirillova, Svetlana; Cortés, Juan; Stefaniu, Alin
  • Proteins: Structure, Function, and Bioinformatics, Vol. 70, Issue 1
  • DOI: 10.1002/prot.21570

Integrative, dynamic structural biology at atomic resolution—it's about time
journal, March 2015

  • van den Bedem, Henry; Fraser, James S.
  • Nature Methods, Vol. 12, Issue 4
  • DOI: 10.1038/nmeth.3324

Bounding Volumes for Proteins: A Comparative Study
journal, October 2012

  • Fonseca, Rasmus; Winter, Pawel
  • Journal of Computational Biology, Vol. 19, Issue 10
  • DOI: 10.1089/cmb.2012.0104

MolProbity : all-atom structure validation for macromolecular crystallography
journal, December 2009

  • Chen, Vincent B.; Arendall, W. Bryan; Headd, Jeffrey J.
  • Acta Crystallographica Section D Biological Crystallography, Vol. 66, Issue 1
  • DOI: 10.1107/S0907444909042073

A Data-Driven Evolutionary Algorithm for Mapping Multibasin Protein Energy Landscapes
journal, September 2015

  • Clausen, Rudy; Shehu, Amarda
  • Journal of Computational Biology, Vol. 22, Issue 9
  • DOI: 10.1089/cmb.2015.0107

Coupled Motions in β 2 AR:Gαs Conformational Ensembles
journal, February 2016

  • Pachov, Dimitar V.; Fonseca, Rasmus; Arnol, Damien
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 3
  • DOI: 10.1021/acs.jctc.5b00995

A Distal Mutation Perturbs Dynamic Amino Acid Networks in Dihydrofolate Reductase
journal, June 2013

  • Boehr, David D.; Schnell, Jason R.; McElheny, Dan
  • Biochemistry, Vol. 52, Issue 27
  • DOI: 10.1021/bi400563c

A stochastic roadmap method to model protein structural transitions
journal, December 2015


A path planning approach for computing large-amplitude motions of flexible molecules
journal, June 2005


Smooth continuous transition between tasks on a kinematic control level: Obstacle avoidance as a control problem
journal, September 2013


Simulating Protein Motions with Rigidity Analysis
journal, July 2007

  • Thomas, Shawna; Tang, Xinyu; Tapia, Lydia
  • Journal of Computational Biology, Vol. 14, Issue 6
  • DOI: 10.1089/cmb.2007.R019

Motion planning algorithms for molecular simulations: A survey
journal, July 2012


The experimental survey of protein-folding energy landscapes
journal, August 2005


Automated design of the surface positions of protein helices: Protein surface design
journal, June 1997

  • Dahiyat, Bassil I.; Benjamin Gordon, D.; Mayo, Stephen L.
  • Protein Science, Vol. 6, Issue 6
  • DOI: 10.1002/pro.5560060622

Automated identification of functional dynamic contact networks from X-ray crystallography
journal, August 2013

  • van den Bedem, Henry; Bhabha, Gira; Yang, Kun
  • Nature Methods, Vol. 10, Issue 9
  • DOI: 10.1038/nmeth.2592

Resultants and loop closure
journal, January 2005

  • Coutsias, Evangelos A.; Seok, Chaok; Wester, Michael J.
  • International Journal of Quantum Chemistry, Vol. 106, Issue 1
  • DOI: 10.1002/qua.20751

Hybridizing rapidly exploring random trees and basin hopping yields an improved exploration of energy landscapes: Hybridizing RRT and BH Yields an Improved Exploration of Energy Landscapes
journal, December 2015

  • Roth, Christine-Andrea; Dreyfus, Tom; Robert, Charles H.
  • Journal of Computational Chemistry, Vol. 37, Issue 8
  • DOI: 10.1002/jcc.24256

Probabilistic roadmaps for path planning in high-dimensional configuration spaces
journal, January 1996

  • Kavraki, L. E.; Svestka, P.; Latombe, J. -C.
  • IEEE Transactions on Robotics and Automation, Vol. 12, Issue 4
  • DOI: 10.1109/70.508439

A spatial data structure for fast Poisson-disk sample generation
journal, July 2006


A Dynamic Knockout Reveals That Conformational Fluctuations Influence the Chemical Step of Enzyme Catalysis
journal, April 2011


Modeling protein conformational transitions by a combination of coarse-grained normal mode analysis and robotics-inspired methods
journal, January 2013

  • Al-Bluwi, Ibrahim; Vaisset, Marc; Siméon, Thierry
  • BMC Structural Biology, Vol. 13, Issue Suppl 1
  • DOI: 10.1186/1472-6807-13-S1-S2

Biomolecular Simulation: A Computational Microscope for Molecular Biology
journal, June 2012


Characterizing RNA ensembles from NMR data with kinematic models
journal, August 2014

  • Fonseca, Rasmus; Pachov, Dimitar V.; Bernauer, Julie
  • Nucleic Acids Research, Vol. 42, Issue 15
  • DOI: 10.1093/nar/gku707

Geometric analysis characterizes molecular rigidity in generic and non-generic protein configurations
journal, October 2015

  • Budday, Dominik; Leyendecker, Sigrid; van den Bedem, Henry
  • Journal of the Mechanics and Physics of Solids, Vol. 83
  • DOI: 10.1016/j.jmps.2015.06.006

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.