Spectral gap optimization of order parameters for sampling complex molecular systems
Open accessAbstract
In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.
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SGOOP singles out the linear combination of input features that correspond to the direction that is most relevant for the long-time dynamics of the system being studied.
“the spectral gap optimization of order parameters (SGOOP) method to single out the linear combination of input features that correspond to the direction that is most relevant for the long-time dynamics of the system being studied 82”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [82]
Dimensionality reduction algorithms such as TICA or SGOOP, that incorporate information on the system's dynamics, implicitly ensure that the order parameter(s) perform well as descriptors of the slowest molecular motion.
“Dimensionality reduction algorithms as TICA 80,81 or SGOOP 82 , that incorporate information on the system's dynamics, implicitly ensure that the order parameter(s) perform well as descriptors of the slowest molecular motion.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [82]
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- Authors
- Tiwary, P., & Berne, B. J.
- Affiliations
- Columbia University (US)
- ORCID
- Tiwary, Pratyush
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2016-02-29
- Volume
- 113
- Issue
- 11
- Pages
- 2839-2844
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC4801247
- OpenAlex
- W2246932694
- Cited by
- 259
- References
- 68
- Citations by year
- 2026: 14 · 2025: 20 · 2024: 27 · 2023: 29 · 2022: 32 · 2021: 27 · 2020: 24 · 2019: 28 · 2018: 29 · 2017: 19 · 2016: 8 · 2015: 1 · 2012: 1
- FWCI
- 19.11
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- HHS | NIH | National Institute of General Medical Sciences (NIH-GM4330)
- NSF | CISE | Advanced Cyberinfrastructure (TG-MCA08X002)
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Keywords
- collective variables, reaction coordinate, enhanced sampling, metadynamics, umbrella sampling, path entropy, free energy landscape, rare events, molecular dynamics
- MeSH terms
- Algorithms, Models, Molecular, Models, Theoretical, Peptides, Entropy, Molecular Dynamics Simulation
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