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Title: Layered nested Markov chain Monte Carlo

Abstract

A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.

Authors:
 [1];  [1];  [1]
+ Show Author Affiliations
  1. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1466393
Alternate Identifier(s):
OSTI ID: 1457211
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 7; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States: N. p., 2018. Web. doi:10.1063/1.5030531.
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Jackson, Nicholas E., Webb, Michael A., & de Pablo, Juan J. Layered nested Markov chain Monte Carlo. United States. https://doi.org/10.1063/1.5030531
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Jackson, Nicholas E., Webb, Michael A., and de Pablo, Juan J. Tue . "Layered nested Markov chain Monte Carlo". United States. https://doi.org/10.1063/1.5030531. https://www.osti.gov/servlets/purl/1466393.
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@article{osti_1466393,
title = {Layered nested Markov chain Monte Carlo},
author = {Jackson, Nicholas E. and Webb, Michael A. and de Pablo, Juan J.},
abstractNote = {A configurational sampling algorithm based on nested layerings of Markov chains (Layered Nested Markov Chain Monte Carlo or L-NMCMC) is presented for simulations of systems characterized by rugged free energy landscapes. The layerings are generated using a set of auxiliary potential energy surfaces. The implementation of the method is demonstrated in the context of a rugged, two-dimensional potential energy surface. The versatility of the algorithm is next demonstrated on a simple, many body system, namely, a canonical Lennard-Jones fluid in the liquid state. In that example, different layering schemes and auxiliary potentials are used, including variable cutoff distances and excluded volume tempering. In addition to calculating a variety of properties of the system, it is also shown that L-NMCMC, when combined with a free-energy perturbation formalism, provides a straightforward means to construct approximate free-energy surfaces at no additional computational cost using the sampling distributions of each auxiliary Markov chain. In conclusion, the proposed L-NMCMC scheme is general in that it could be complementary to any number of methods that rely on sampling from a target distribution or methods that exploit a hierarchy of time scales and/or length scales through decomposition of the potential energy.},
doi = {10.1063/1.5030531},
journal = {Journal of Chemical Physics},
number = 7,
volume = 149,
place = {United States},
year = {Tue Jun 26 00:00:00 EDT 2018},
month = {Tue Jun 26 00:00:00 EDT 2018}
}
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Journal Article:
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https://doi.org/10.1063/1.5030531
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Cited by: 5 works
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Figures / Tables:

FIG. 1. FIG. 1.: Schematic of a {M}=[1,3,3,2] L-NMCMC scheme using {U}=[U0,U1,U2,U3] as auxiliary potentials. Horizontal arrows denote moves in configuration space, whereas dotted vertical arrows denote interlayer checks according to the acceptance criterion of Eq. 10. For clarity, note that only the first interlayer check between each set of neighboring layersmore » is shown in the diagram.« less
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Works referenced in this record:

Computing free energies using nested sampling-based approaches
journal, November 2017

Increasing the efficiency of Monte Carlo simulation with sampling from an approximate potential
journal, January 2013

The rotation-vibration spectrum for Scarf II potential
journal, January 2010

  • Qiang, Wen-Chao; Dong, Shi-Hai
  • International Journal of Quantum Chemistry
  • DOI: 10.1002/qua.22527

Rosenbluth-sampled nonequilibrium work method for calculation of free energies in molecular simulation
journal, May 2005

  • Wu, Di; Kofke, David A.
  • The Journal of Chemical Physics, Vol. 122, Issue 20
  • DOI: 10.1063/1.1906209

Multigraining: An algorithm for simultaneous fine-grained and coarse-grained simulation of molecular systems
journal, April 2006

  • Christen, Markus; van Gunsteren, Wilfred F.
  • The Journal of Chemical Physics, Vol. 124, Issue 15
  • DOI: 10.1063/1.2187488

Configurational bias Monte Carlo: a new sampling scheme for flexible chains
journal, January 1992

Overcoming entropic barrier with coupled sampling at dual resolutions
journal, November 2005

  • Lwin, Thur Zar; Luo, Ray
  • The Journal of Chemical Physics, Vol. 123, Issue 19
  • DOI: 10.1063/1.2102871

An efficient approach to ab initio Monte Carlo simulation
journal, January 2014

  • Leiding, Jeff; Coe, Joshua D.
  • The Journal of Chemical Physics, Vol. 140, Issue 3
  • DOI: 10.1063/1.4855755

Generalized-ensemble algorithms for molecular simulations of biopolymers
journal, January 2001

Improved transition path sampling methods for simulation of rare events
journal, April 2008

  • Chopra, Manan; Malshe, Rohit; Reddy, Allam S.
  • The Journal of Chemical Physics, Vol. 128, Issue 14
  • DOI: 10.1063/1.2889943

Using a classical potential as an efficient importance function for sampling from an ab initio potential
journal, January 2000

  • Iftimie, Radu; Salahub, Dennis; Wei, Dongqing
  • The Journal of Chemical Physics, Vol. 113, Issue 12
  • DOI: 10.1063/1.1289534

Multicanonical parallel tempering
journal, April 2002

  • Faller, Roland; Yan, Qiliang; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 116, Issue 13
  • DOI: 10.1063/1.1456504

Parallel excluded volume tempering for polymer melts
journal, December 2000

Ligand-receptor interactions
journal, January 1984

Multilevel summation and Monte Carlo simulations
journal, August 2006

Chemical potential and equations of state of hard core chain molecules
journal, August 1995

  • Escobedo, Fernando A.; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 103, Issue 5
  • DOI: 10.1063/1.469719

Hyperparallel tempering Monte Carlo simulation of polymeric systems
journal, July 2000

  • Yan, Qiliang; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 113, Issue 3
  • DOI: 10.1063/1.481905

Reducing quasi‐ergodic behavior in Monte Carlo simulations by J ‐walking: Applications to atomic clusters
journal, August 1990

  • Frantz, D. D.; Freeman, D. L.; Doll, J. D.
  • The Journal of Chemical Physics, Vol. 93, Issue 4
  • DOI: 10.1063/1.458863

Optimal sampling efficiency in Monte Carlo simulation with an approximate potential
journal, April 2009

  • Coe, Joshua D.; Sewell, Thomas D.; Shaw, M. Sam
  • The Journal of Chemical Physics, Vol. 130, Issue 16
  • DOI: 10.1063/1.3116788

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles
journal, October 2007

  • Whitelam, Stephen; Geissler, Phillip L.
  • The Journal of Chemical Physics, Vol. 127, Issue 15
  • DOI: 10.1063/1.2790421

Monte Carlo methods for accelerating barrier crossing: Anti‐force‐bias and variable step algorithms
journal, February 1990

  • Cao, Jianshu; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 92, Issue 3
  • DOI: 10.1063/1.458029

Reversible multiple time scale molecular dynamics
journal, August 1992

  • Tuckerman, M.; Berne, B. J.; Martyna, G. J.
  • The Journal of Chemical Physics, Vol. 97, Issue 3
  • DOI: 10.1063/1.463137

Multiple “time step” Monte Carlo simulations: Application to charged systems with Ewald summation
journal, January 2004

  • Bernacki, Katarzyna; Hetényi, Balázs; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 121, Issue 1
  • DOI: 10.1063/1.1755195

An efficient ring polymer contraction scheme for imaginary time path integral simulations
journal, July 2008

  • Markland, Thomas E.; Manolopoulos, David E.
  • The Journal of Chemical Physics, Vol. 129, Issue 2
  • DOI: 10.1063/1.2953308

Modified Replica Exchange Simulation Methods for Local Structure Refinement
journal, April 2005

  • Cheng, Xiaolin; Cui, Guanglei; Hornak, Viktor
  • The Journal of Physical Chemistry B, Vol. 109, Issue 16
  • DOI: 10.1021/jp045437y

Stochastic potential switching algorithm for Monte Carlo simulations of complex systems
journal, June 2005

  • Mak, C. H.
  • The Journal of Chemical Physics, Vol. 122, Issue 21
  • DOI: 10.1063/1.1925273

Nested Markov chain Monte Carlo sampling of a density functional theory potential: Equilibrium thermodynamics of dense fluid nitrogen
journal, August 2009

  • Coe, Joshua D.; Sewell, Thomas D.; Shaw, M. Sam
  • The Journal of Chemical Physics, Vol. 131, Issue 7
  • DOI: 10.1063/1.3200904

Multiple Time-Step Dual-Hamiltonian Hybrid Molecular Dynamics – Monte Carlo Canonical Propagation Algorithm
journal, March 2016

  • Chen, Yunjie; Kale, Seyit; Weare, Jonathan
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 4
  • DOI: 10.1021/acs.jctc.5b00706

Extended state-space Monte Carlo methods
journal, April 2001

Replica Exchange with Solute Scaling: A More Efficient Version of Replica Exchange with Solute Tempering (REST2)
journal, August 2011

  • Wang, Lingle; Friesner, Richard A.; Berne, B. J.
  • The Journal of Physical Chemistry B, Vol. 115, Issue 30
  • DOI: 10.1021/jp204407d

Cool walking: A new Markov chain Monte Carlo sampling method
journal, December 2002

  • Brown, Scott; Head-Gordon, Teresa
  • Journal of Computational Chemistry, Vol. 24, Issue 1
  • DOI: 10.1002/jcc.10181

Efficient sampling for ab initio Monte Carlo simulation of molecular clusters using an interpolated potential energy surface
journal, January 2009

  • Nakayama, Akira; Seki, Nanami; Taketsugu, Tetsuya
  • The Journal of Chemical Physics, Vol. 130, Issue 2
  • DOI: 10.1063/1.3055910

Improving the efficiency of the configurational-bias Monte Carlo algorithm
journal, July 1998

Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations
journal, July 2010

  • Jiang, Wei; Roux, Benoît
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 9
  • DOI: 10.1021/ct1001768

Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model
journal, December 1999

  • Yan, Qiliang; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 111, Issue 21
  • DOI: 10.1063/1.480282

Multidimensional replica-exchange method for free-energy calculations
journal, October 2000

  • Sugita, Yuji; Kitao, Akio; Okamoto, Yuko
  • The Journal of Chemical Physics, Vol. 113, Issue 15
  • DOI: 10.1063/1.1308516

THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
journal, October 1992

  • Kumar, Shankar; Rosenberg, John M.; Bouzida, Djamal
  • Journal of Computational Chemistry, Vol. 13, Issue 8
  • DOI: 10.1002/jcc.540130812

Mixed time slicing in path integral simulations
journal, February 2011

  • Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip
  • The Journal of Chemical Physics, Vol. 134, Issue 7
  • DOI: 10.1063/1.3518714

A novel Monte Carlo algorithm for polarizable force fields: Application to a fluctuating charge model for water
journal, March 1998

  • Martin, Marcus G.; Chen, Bin; Siepmann, J. Ilja
  • The Journal of Chemical Physics, Vol. 108, Issue 9
  • DOI: 10.1063/1.475773

Using arbitrary trial distributions to improve intramolecular sampling in configurational-bias Monte Carlo
journal, August 2006

Smart walking: A new method for Boltzmann sampling of protein conformations
journal, December 1997

  • Zhou, Ruhong; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 107, Issue 21
  • DOI: 10.1063/1.475210

Statistically optimal analysis of samples from multiple equilibrium states
journal, September 2008

  • Shirts, Michael R.; Chodera, John D.
  • The Journal of Chemical Physics, Vol. 129, Issue 12
  • DOI: 10.1063/1.2978177

Multiple “time step” Monte Carlo
journal, November 2002

  • Hetényi, Balázs; Bernacki, Katarzyna; Berne, B. J.
  • The Journal of Chemical Physics, Vol. 117, Issue 18
  • DOI: 10.1063/1.1512645

3  Molecular structure from X-ray diffraction
journal, January 2003

  • Powell, Harold R.
  • Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., Vol. 99
  • DOI: 10.1039/b208509g

Monte Carlo Calculation of the Average Extension of Molecular Chains
journal, February 1955

  • Rosenbluth, Marshall N.; Rosenbluth, Arianna W.
  • The Journal of Chemical Physics, Vol. 23, Issue 2
  • DOI: 10.1063/1.1741967

The relative entropy is fundamental to multiscale and inverse thermodynamic problems
journal, October 2008

  • Shell, M. Scott
  • The Journal of Chemical Physics, Vol. 129, Issue 14
  • DOI: 10.1063/1.2992060

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics–Monte Carlo propagator
journal, January 2018

  • Suh, Donghyuk; Radak, Brian K.; Chipot, Christophe
  • The Journal of Chemical Physics, Vol. 148, Issue 1
  • DOI: 10.1063/1.5004154

Resolution Exchange Simulation with Incremental Coarsening
journal, May 2006

  • Lyman, Edward; Zuckerman, Daniel M.
  • Journal of Chemical Theory and Computation, Vol. 2, Issue 3
  • DOI: 10.1021/ct050337x

Monte Carlo Sampling with Hierarchical Move Sets: POSH Monte Carlo
journal, July 2009

  • Nilmeier, Jerome; Jacobson, Matthew P.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 8
  • DOI: 10.1021/ct8005166

Monte Carlo simulations using sampling from an approximate potential
journal, May 2003

  • Gelb, Lev D.
  • The Journal of Chemical Physics, Vol. 118, Issue 17
  • DOI: 10.1063/1.1563597

The gas-liquid transition of the two-dimensional Lennard-Jones fluid
journal, August 1990

Hamiltonian Switch Metropolis Monte Carlo Simulations for Improved Conformational Sampling of Intrinsically Disordered Regions Tethered to Ordered Domains of Proteins
journal, June 2014

  • Mittal, Anuradha; Lyle, Nicholas; Harmon, Tyler S.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 8
  • DOI: 10.1021/ct5002297

Optimal allocation of replicas in parallel tempering simulations
journal, January 2005

  • Rathore, Nitin; Chopra, Manan; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 122, Issue 2
  • DOI: 10.1063/1.1831273

Multiscale Monte Carlo Sampling of Protein Sidechains: Application to Binding Pocket Flexibility
journal, April 2008

  • Nilmeier, Jerome; Jacobson, Matt
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 5
  • DOI: 10.1021/ct700334a

A refined ring polymer contraction scheme for systems with electrostatic interactions
journal, October 2008

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