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De DS, Krummenacher M, Schaefer B, Goedecker S. Finding Reaction Pathways with Optimal Atomic Index Mappings. PHYSICAL REVIEW LETTERS 2019; 123:206102. [PMID: 31809087 DOI: 10.1103/physrevlett.123.206102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.
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Affiliation(s)
- Deb Sankar De
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Marco Krummenacher
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Bastian Schaefer
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Stefan Goedecker
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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Elenewski JE, Velizhanin KA, Zwolak M. A spin-1 representation for dual-funnel energy landscapes. J Chem Phys 2018; 149:035101. [PMID: 30037251 PMCID: PMC7723752 DOI: 10.1063/1.5036677] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The interconversion between the left- and right-handed helical folds of a polypeptide defines a dual-funneled free energy landscape. In this context, the funnel minima are connected through a continuum of unfolded conformations, evocative of the classical helix-coil transition. Physical intuition and recent conjectures suggest that this landscape can be mapped by assigning a left- or right-handed helical state to each residue. We explore this possibility using all-atom replica exchange molecular dynamics and an Ising-like model, demonstrating that the energy landscape architecture is at odds with a two-state picture. A three-state model-left, right, and unstructured-can account for most key intermediates during chiral interconversion. Competing folds and excited conformational states still impose limitations on the scope of this approach. However, the improvement is stark: Moving from a two-state to a three-state model decreases the fit error from 1.6 kBT to 0.3 kBT along the left-to-right interconversion pathway.
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Affiliation(s)
- Justin E. Elenewski
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Maryland Nanocenter, University of Maryland, College Park, MD 20742, USA
| | | | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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Abstract
Recent advances in the potential energy landscapes approach are highlighted, including both theoretical and computational contributions. Treating the high dimensionality of molecular and condensed matter systems of contemporary interest is important for understanding how emergent properties are encoded in the landscape and for calculating these properties while faithfully representing barriers between different morphologies. The pathways characterized in full dimensionality, which are used to construct kinetic transition networks, may prove useful in guiding such calculations. The energy landscape perspective has also produced new procedures for structure prediction and analysis of thermodynamic properties. Basin-hopping global optimization, with alternative acceptance criteria and generalizations to multiple metric spaces, has been used to treat systems ranging from biomolecules to nanoalloy clusters and condensed matter. This review also illustrates how all this methodology, developed in the context of chemical physics, can be transferred to landscapes defined by cost functions associated with machine learning.
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Affiliation(s)
- David J Wales
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom;
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Ballard AJ, Das R, Martiniani S, Mehta D, Sagun L, Stevenson JD, Wales DJ. Energy landscapes for machine learning. Phys Chem Chem Phys 2018; 19:12585-12603. [PMID: 28367548 DOI: 10.1039/c7cp01108c] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.
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Affiliation(s)
- Andrew J Ballard
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Ritankar Das
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Stefano Martiniani
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Dhagash Mehta
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, IN, USA
| | - Levent Sagun
- Mathematics Department, Courant Institute, New York University, NY, USA
| | | | - David J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
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Chakraborty D, Wales DJ. Energy Landscape and Pathways for Transitions between Watson-Crick and Hoogsteen Base Pairing in DNA. J Phys Chem Lett 2018; 9:229-241. [PMID: 29240425 DOI: 10.1021/acs.jpclett.7b01933] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The recent discovery that Hoogsteen (HG) base pairs are widespread in DNA across diverse sequences and positional contexts could have important implications for understanding DNA replication and DNA-protein recognition. While evidence is emerging that the Hoogsteen conformation could be a thermodynamically accessible conformation of the DNA duplex and provide a means to expand its functionality, relatively little is known about the molecular mechanism underlying the Watson-Crick (WC) to HG transition. In this Perspective, we describe pathways and kinetics for this transition at an atomic level of detail, using the energy landscape perspective. We show that competition between the duplex conformations results in a double funnel landscape, which explains some recent experimental observations. The interconversion pathways feature a number of intermediates, with a variable number of WC and HG base pairs. The relatively slow kinetics, with possible deviations from two-state behavior, suggest that this conformational switch is likely to be a challenging target for both simulation and experiment.
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Affiliation(s)
- Debayan Chakraborty
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Chemistry, The University of Texas at Austin , 24th Street Stop A5300, Austin, Texas 78712, United States
| | - David J Wales
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Mallory JD, Mandelshtam VA. Quantum Melting and Isotope Effects from Diffusion Monte Carlo Studies of p-H2 Clusters. J Phys Chem A 2017; 121:6341-6348. [DOI: 10.1021/acs.jpca.7b06649] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Joel D. Mallory
- Department of Chemistry, University of California, Irvine, California 92697, United States
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Cezar HM, Rondina GG, Da Silva JLF. Parallel tempering Monte Carlo combined with clustering Euclidean metric analysis to study the thermodynamic stability of Lennard-Jones nanoclusters. J Chem Phys 2017; 146:064114. [DOI: 10.1063/1.4975601] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Henrique M. Cezar
- Institute of Physics, University of São Paulo, P.O. Box 66318, 05314-970 São Paulo, SP, Brazil
| | - Gustavo G. Rondina
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany
| | - Juarez L. F. Da Silva
- São Carlos Institute of Chemistry, University of São Paulo, P.O. Box 780, 13560-970 São Carlos, SP, Brazil
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Ballard AJ, Stevenson JD, Das R, Wales DJ. Energy landscapes for a machine learning application to series data. J Chem Phys 2016; 144:124119. [DOI: 10.1063/1.4944672] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew J. Ballard
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jacob D. Stevenson
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Ritankar Das
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Wales DJ. Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape. J Chem Phys 2015; 142:130901. [DOI: 10.1063/1.4916307] [Citation(s) in RCA: 73] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Stevenson JD, Wales DJ. Communication: Analysing kinetic transition networks for rare events. J Chem Phys 2014; 141:041104. [DOI: 10.1063/1.4891356] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jacob D. Stevenson
- University Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- University Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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