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

Title: Quantifying Energetic and Entropic Pathways in Molecular Systems

Abstract

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Lastly, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Univ. of Maryland, College Park, MD (United States)
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1991216
Grant/Contract Number:  
SC0021009
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Physical Chemistry. B
Additional Journal Information:
Journal Volume: 126; Journal Issue: 21; Journal ID: ISSN 1520-6106
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemical reactions; Computer simulations; Entropy; Free energy; Vesicles

Citation Formats

Beyerle, Eric R., Mehdi, Shams, and Tiwary, Pratyush. Quantifying Energetic and Entropic Pathways in Molecular Systems. United States: N. p., 2022. Web. doi:10.1021/acs.jpcb.2c01782.
Beyerle, Eric R., Mehdi, Shams, & Tiwary, Pratyush. Quantifying Energetic and Entropic Pathways in Molecular Systems. United States. https://doi.org/10.1021/acs.jpcb.2c01782
Beyerle, Eric R., Mehdi, Shams, and Tiwary, Pratyush. Mon . "Quantifying Energetic and Entropic Pathways in Molecular Systems". United States. https://doi.org/10.1021/acs.jpcb.2c01782. https://www.osti.gov/servlets/purl/1991216.
@article{osti_1991216,
title = {Quantifying Energetic and Entropic Pathways in Molecular Systems},
author = {Beyerle, Eric R. and Mehdi, Shams and Tiwary, Pratyush},
abstractNote = {When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Lastly, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.},
doi = {10.1021/acs.jpcb.2c01782},
journal = {Journal of Physical Chemistry. B},
number = 21,
volume = 126,
place = {United States},
year = {Mon May 23 00:00:00 EDT 2022},
month = {Mon May 23 00:00:00 EDT 2022}
}

Works referenced in this record:

Building maps in collective variable space
journal, September 2018

  • Gimondi, Ilaria; Tribello, Gareth A.; Salvalaglio, Matteo
  • The Journal of Chemical Physics, Vol. 149, Issue 10
  • DOI: 10.1063/1.5027528

Ensemble of transition states for two-state protein folding from the eigenvectors of rate matrices
journal, November 2004

  • Berezhkovskii, Alexander; Szabo, Attila
  • The Journal of Chemical Physics, Vol. 121, Issue 18
  • DOI: 10.1063/1.1802674

Forward flux sampling for rare event simulations
journal, October 2009

  • Allen, Rosalind J.; Valeriani, Chantal; Rein ten Wolde, Pieter
  • Journal of Physics: Condensed Matter, Vol. 21, Issue 46
  • DOI: 10.1088/0953-8984/21/46/463102

Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory
journal, October 2019

  • Tsai, Sun-Ting; Smith, Zachary; Tiwary, Pratyush
  • The Journal of Chemical Physics, Vol. 151, Issue 15
  • DOI: 10.1063/1.5124385

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977


Perspective: Identification of collective variables and metastable states of protein dynamics
journal, October 2018

  • Sittel, Florian; Stock, Gerhard
  • The Journal of Chemical Physics, Vol. 149, Issue 15
  • DOI: 10.1063/1.5049637

Auto-Encoding Variational Bayes
preprint, January 2013


Understanding the role of predictive time delay and biased propagator in RAVE
journal, April 2020

  • Wang, Yihang; Tiwary, Pratyush
  • The Journal of Chemical Physics, Vol. 152, Issue 14
  • DOI: 10.1063/5.0004838

The information bottleneck method
preprint, January 2000


Simulation-Based Approaches for Determining Membrane Permeability of Small Compounds
journal, March 2016

  • Lee, Christopher T.; Comer, Jeffrey; Herndon, Conner
  • Journal of Chemical Information and Modeling, Vol. 56, Issue 4
  • DOI: 10.1021/acs.jcim.6b00022

Nucleation in aqueous NaCl solutions shifts from 1-step to 2-step mechanism on crossing the spinodal
journal, March 2019

  • Jiang, Hao; Debenedetti, Pablo G.; Panagiotopoulos, Athanassios Z.
  • The Journal of Chemical Physics, Vol. 150, Issue 12
  • DOI: 10.1063/1.5084248

Computational study of peptide permeation through membrane: searching for hidden slow variables
journal, December 2013


Using metadynamics to explore complex free-energy landscapes
journal, March 2020


On the Role of Enthalpic and Entropic Contributions to the Conformational Free Energy Landscape of MIL‐101(Cr) Secondary Building Units
journal, September 2020

  • Kollias, Loukas; Cantu, David C.; Glezakou, Vassiliki‐Alexandra
  • Advanced Theory and Simulations, Vol. 3, Issue 12
  • DOI: 10.1002/adts.202000092

Robust Perron cluster analysis in conformation dynamics
journal, March 2005


Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states
journal, April 2007

  • Noé, Frank; Horenko, Illia; Schütte, Christof
  • The Journal of Chemical Physics, Vol. 126, Issue 15
  • DOI: 10.1063/1.2714539

Nonclassical Nucleation Pathways in Stacking-Disordered Crystals
journal, July 2021


Optimized Markov state models for metastable systems
journal, July 2016

  • Guarnera, Enrico; Vanden-Eijnden, Eric
  • The Journal of Chemical Physics, Vol. 145, Issue 2
  • DOI: 10.1063/1.4954769

Simple few-state models reveal hidden complexity in protein folding
journal, July 2012

  • Beauchamp, K. A.; McGibbon, R.; Lin, Y. -S.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 44
  • DOI: 10.1073/pnas.1201810109

GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
journal, September 2015


Permeability across lipid membranes
journal, October 2016


XSEDE: Accelerating Scientific Discovery
journal, September 2014

  • Towns, John; Cockerill, Timothy; Dahan, Maytal
  • Computing in Science & Engineering, Vol. 16, Issue 5
  • DOI: 10.1109/MCSE.2014.80

Nucleation of Hexagonal Ice ( I h ) in Liquid Water
journal, June 2003

  • Radhakrishnan, Ravi; Trout, Bernhardt L.
  • Journal of the American Chemical Society, Vol. 125, Issue 25
  • DOI: 10.1021/ja0211252

Free Energy Barriers to Evaporation of Water in Hydrophobic Confinement
journal, October 2012

  • Sharma, Sumit; Debenedetti, Pablo G.
  • The Journal of Physical Chemistry B, Vol. 116, Issue 44
  • DOI: 10.1021/jp308362h

Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation
journal, March 2020


Adding calorimetric data to decision making in lead discovery: a hot tip
journal, December 2009

  • Ladbury, John E.; Klebe, Gerhard; Freire, Ernesto
  • Nature Reviews Drug Discovery, Vol. 9, Issue 1
  • DOI: 10.1038/nrd3054

A theory of entropic bonding
journal, January 2022

  • Vo, Thi; Glotzer, Sharon C.
  • Proceedings of the National Academy of Sciences, Vol. 119, Issue 4
  • DOI: 10.1073/pnas.2116414119

PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models
journal, October 2015

  • Scherer, Martin K.; Trendelkamp-Schroer, Benjamin; Paul, Fabian
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 11
  • DOI: 10.1021/acs.jctc.5b00743

Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions
journal, January 2018

  • Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G.
  • The Journal of Chemical Physics, Vol. 148, Issue 4
  • DOI: 10.1063/1.5016554

Machine learning approaches for analyzing and enhancing molecular dynamics simulations
journal, April 2020

  • Wang, Yihang; Lamim Ribeiro, João Marcelo; Tiwary, Pratyush
  • Current Opinion in Structural Biology, Vol. 61
  • DOI: 10.1016/j.sbi.2019.12.016

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics
journal, December 2020

  • Pant, Shashank; Smith, Zachary; Wang, Yihang
  • The Journal of Chemical Physics, Vol. 153, Issue 23
  • DOI: 10.1063/5.0030931

Cholesterol Flip-Flop: Insights from Free Energy Simulation Studies
journal, October 2010

  • Jo, Sunhwan; Rui, Huan; Lim, Joseph B.
  • The Journal of Physical Chemistry B, Vol. 114, Issue 42
  • DOI: 10.1021/jp108166k

Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9
journal, March 2013

  • Schwantes, Christian R.; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 4
  • DOI: 10.1021/ct300878a

Do enthalpy and entropy distinguish first in class from best in class?
journal, October 2008


Markov models of molecular kinetics: Generation and validation
journal, May 2011

  • Prinz, Jan-Hendrik; Wu, Hao; Sarich, Marco
  • The Journal of Chemical Physics, Vol. 134, Issue 17
  • DOI: 10.1063/1.3565032

Identifying the leading dynamics of ubiquitin: A comparison between the tICA and the LE4PD slow fluctuations in amino acids’ position
journal, December 2021

  • Beyerle, E. R.; Guenza, M. G.
  • The Journal of Chemical Physics, Vol. 155, Issue 24
  • DOI: 10.1063/5.0059688

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability
journal, November 2018

  • Fathizadeh, Arman; Elber, Ron
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b00882

Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)
journal, August 2018

  • Ribeiro, João Marcelo Lamim; Bravo, Pablo; Wang, Yihang
  • The Journal of Chemical Physics, Vol. 149, Issue 7
  • DOI: 10.1063/1.5025487

Diffusion maps tailored to arbitrary non-degenerate Itô processes
journal, January 2020

  • Banisch, Ralf; Trstanova, Zofia; Bittracher, Andreas
  • Applied and Computational Harmonic Analysis, Vol. 48, Issue 1
  • DOI: 10.1016/j.acha.2018.05.001

Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
journal, January 2008


Computing time scales from reaction coordinates by milestoning
journal, June 2004

  • Faradjian, Anton K.; Elber, Ron
  • The Journal of Chemical Physics, Vol. 120, Issue 23
  • DOI: 10.1063/1.1738640

Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: The case of domain motions
journal, February 2011

  • Naritomi, Yusuke; Fuchigami, Sotaro
  • The Journal of Chemical Physics, Vol. 134, Issue 6
  • DOI: 10.1063/1.3554380

Computer Simulation of the Distribution of Hexane in a Lipid Bilayer:  Spatially Resolved Free Energy, Entropy, and Enthalpy Profiles
journal, December 2005

  • MacCallum, Justin L.; Tieleman, D. Peter
  • Journal of the American Chemical Society, Vol. 128, Issue 1
  • DOI: 10.1021/ja0535099

Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
journal, May 2016


Driving Force for the Association of Amphiphilic Molecules
journal, September 2011

  • Mondal, Jagannath; Yethiraj, Arun
  • The Journal of Physical Chemistry Letters, Vol. 2, Issue 19
  • DOI: 10.1021/jz201046x

Entropy–enthalpy compensation as a fundamental concept and analysis tool for systematical experimental data
journal, June 2012


Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
journal, June 2018

  • Wehmeyer, Christoph; Noé, Frank
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5011399

Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
journal, May 2013

  • Röblitz, Susanna; Weber, Marcus
  • Advances in Data Analysis and Classification, Vol. 7, Issue 2
  • DOI: 10.1007/s11634-013-0134-6

Optimized parameter selection reveals trends in Markov state models for protein folding
journal, November 2016

  • Husic, Brooke E.; McGibbon, Robert T.; Sultan, Mohammad M.
  • The Journal of Chemical Physics, Vol. 145, Issue 19
  • DOI: 10.1063/1.4967809

A simple molecular thermodynamic theory of hydrophobic hydration
journal, February 2002

  • Ashbaugh, Henry S.; Truskett, Thomas M.; Debenedetti, Pablo G.
  • The Journal of Chemical Physics, Vol. 116, Issue 7
  • DOI: 10.1063/1.1436479

Order through entropy
journal, December 2014


On two possible definitions of the free energy for collective variables
journal, November 2011

  • Hartmann, C.; Latorre, J. C.; Ciccotti, G.
  • The European Physical Journal Special Topics, Vol. 200, Issue 1
  • DOI: 10.1140/epjst/e2011-01519-7

Entropic colloidal crystallization pathways via fluid–fluid transitions and multidimensional prenucleation motifs
journal, July 2019

  • Lee, Sangmin; Teich, Erin G.; Engel, Michael
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 30
  • DOI: 10.1073/pnas.1905929116

RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics
journal, January 2022

  • Gu, Hanlin; Wang, Wei; Cao, Siqin
  • Physical Chemistry Chemical Physics, Vol. 24, Issue 3
  • DOI: 10.1039/D1CP03622J

Reaction-rate theory: fifty years after Kramers
journal, April 1990

  • Hänggi, Peter; Talkner, Peter; Borkovec, Michal
  • Reviews of Modern Physics, Vol. 62, Issue 2
  • DOI: 10.1103/RevModPhys.62.251

Multiple pathways in NaCl homogeneous crystal nucleation
journal, January 2022

  • Finney, Aaron R.; Salvalaglio, Matteo
  • Faraday Discussions, Vol. 235
  • DOI: 10.1039/D1FD00089F

Towards a Theory of Transition Paths
journal, May 2006


Enthalpy−Entropy Contributions to the Potential of Mean Force of Nanoscopic Hydrophobic Solutes
journal, April 2006

  • Choudhury, Niharendu; Pettitt, B. Montgomery
  • The Journal of Physical Chemistry B, Vol. 110, Issue 16
  • DOI: 10.1021/jp056909r

Simulating nucleation of molecular solids
journal, August 2007

  • Black, Simon
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2087
  • DOI: 10.1098/rspa.2007.0008

Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework
journal, August 2010


Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations
journal, November 2009

  • Noé, Frank; Schütte, Christof; Vanden-Eijnden, Eric
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 45
  • DOI: 10.1073/pnas.0905466106

Accelerating All-Atom Simulations and Gaining Mechanistic Understanding of Biophysical Systems through State Predictive Information Bottleneck
journal, April 2022

  • Mehdi, Shams; Wang, Dedi; Pant, Shashank
  • Journal of Chemical Theory and Computation, Vol. 18, Issue 5
  • DOI: 10.1021/acs.jctc.2c00058

Funnels, pathways, and the energy landscape of protein folding: A synthesis
journal, March 1995

  • Bryngelson, Joseph D.; Onuchic, José Nelson; Socci, Nicholas D.
  • Proteins: Structure, Function, and Genetics, Vol. 21, Issue 3
  • DOI: 10.1002/prot.340210302

Coarse Master Equations for Peptide Folding Dynamics
journal, May 2008

  • Buchete, Nicolae-Viorel; Hummer, Gerhard
  • The Journal of Physical Chemistry B, Vol. 112, Issue 19
  • DOI: 10.1021/jp0761665

State predictive information bottleneck
journal, April 2021

  • Wang, Dedi; Tiwary, Pratyush
  • The Journal of Chemical Physics, Vol. 154, Issue 13
  • DOI: 10.1063/5.0038198

SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations
journal, October 2021

  • Tsai, Sun-Ting; Smith, Zachary; Tiwary, Pratyush
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 11
  • DOI: 10.1021/acs.jctc.1c00431

Deep Variational Information Bottleneck
text, January 2016


Temperature Dependence of Peptide Conformational Equilibria from Simulations at a Single Temperature
journal, March 2021

  • Katiyar, Ankita; Thompson, Ward H.
  • The Journal of Physical Chemistry A, Vol. 125, Issue 11
  • DOI: 10.1021/acs.jpca.1c00150

Simulation of water transport through a lipid membrane
journal, April 1994

  • Marrink, Siewert-Jan; Berendsen, Herman J. C.
  • The Journal of Physical Chemistry, Vol. 98, Issue 15
  • DOI: 10.1021/j100066a040

THEORY OF PROTEIN FOLDING: The Energy Landscape Perspective
journal, October 1997


Escaping free-energy minima
journal, September 2002

  • Laio, A.; Parrinello, M.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue 20
  • DOI: 10.1073/pnas.202427399

Structural and Thermodynamic Strategies for Site-Specific DNA Binding Proteins
journal, October 2000


Accelerated molecular dynamics through stochastic iterations and collective variable based basin identification
journal, March 2013


Identification of slow molecular order parameters for Markov model construction
journal, July 2013

  • Pérez-Hernández, Guillermo; Paul, Fabian; Giorgino, Toni
  • The Journal of Chemical Physics, Vol. 139, Issue 1
  • DOI: 10.1063/1.4811489