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Nagahata Y, Kobayashi M, Toda M, Maeda S, Taketsugu T, Komatsuzaki T. An encompassed representation of timescale hierarchies in first-order reaction network. Proc Natl Acad Sci U S A 2024; 121:e2317781121. [PMID: 38758700 PMCID: PMC11126998 DOI: 10.1073/pnas.2317781121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 04/16/2024] [Indexed: 05/19/2024] Open
Abstract
Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.
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Affiliation(s)
- Yutaka Nagahata
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
| | - Masato Kobayashi
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Mikito Toda
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Faculty Division of Natural Sciences, Nara Women’s University, Nara630-8506, Japan
- Graduate School of Information Science, University of Hyogo, Kobe650-0047, Japan
| | - Satoshi Maeda
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Tetsuya Taketsugu
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo060-0810, Japan
| | - Tamiki Komatsuzaki
- The Institute for Chemical Reaction Design and Discovery, Hokkaido University, Sapporo001-0021, Japan
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Sapporo001-0020, Japan
- Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Suita565-0871, Japan
- The Institute of Scientific and Industrial Research, Osaka University, Ibaraki567-0047, Japan
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Woods EJ, Wales DJ. Analysis and interpretation of first passage time distributions featuring rare events. Phys Chem Chem Phys 2024; 26:1640-1657. [PMID: 38059562 DOI: 10.1039/d3cp04199a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.
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Affiliation(s)
- Esmae J Woods
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
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Woods EJ, Kannan D, Sharpe DJ, Swinburne TD, Wales DJ. Analysing ill-conditioned Markov chains. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220245. [PMID: 37211032 DOI: 10.1098/rsta.2022.0245] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 11/15/2022] [Indexed: 05/23/2023]
Abstract
Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.
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Affiliation(s)
- Esmae J Woods
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, UK
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Thomas D Swinburne
- CNRS, CINaM UMR, Aix-Marseille Université, 7325, Campus de Luminy, 13288 Marseille, France
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
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Sawato T, Yamaguchi M. Synthetic Chemical Systems Involving Self‐Catalytic Reactions of Helicene Oligomer Foldamers. Chempluschem 2020; 85:2017-2038. [DOI: 10.1002/cplu.202000489] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Revised: 08/18/2020] [Indexed: 12/15/2022]
Affiliation(s)
- Tsukasa Sawato
- Department of Organic Chemistry Graduate School of Pharmaceutical Sciences Tohoku University Aoba Sendai 980-8578 Japan
| | - Masahiko Yamaguchi
- State Key Laboratory of Fine Chemicals Dalian University of Technology Dalian 116024 China
- Department of Organic Chemistry Graduate School of Pharmaceutical Sciences Tohoku University Aoba Sendai 980-8578 Japan
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Sumiya Y, Maeda S. Rate Constant Matrix Contraction Method for Systematic Analysis of Reaction Path Networks. CHEM LETT 2020. [DOI: 10.1246/cl.200092] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Affiliation(s)
- Yosuke Sumiya
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
| | - Satoshi Maeda
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
- Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
- National Institute for Materials Science (NIMS), Research and Services Division of Materials Data and Integrated System (MaDIS), Tsukuba, Ibaraki 305-0044, Japan
- JST, ERATO Maeda Artificial Intelligence for Chemical Reaction Design and Discovery Project, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan
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Swinburne TD, Wales DJ. Defining, Calculating, and Converging Observables of a Kinetic Transition Network. J Chem Theory Comput 2020; 16:2661-2679. [PMID: 32155072 DOI: 10.1021/acs.jctc.9b01211] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Kinetic transition networks (KTNs) of local minima and transition states are able to capture the dynamics of numerous systems in chemistry, biology, and materials science. However, extracting observables is numerically challenging for large networks and generally will be sensitive to additional computational discovery. To have any measure of convergence for observables, these sensitivities must be regularly calculated. We present a matrix formulation of the discrete path sampling framework for KTNs, deriving expressions for branching probabilities, transition rates, and waiting times. Using the concept of the quasi-stationary distribution, a clear hierarchy of expressions for network observables is established, from exact results to steady-state approximations. We use these results in combination with the graph transformation method to derive the sensitivity, with respect to perturbations of the known KTN, giving explicit terms for the pairwise sensitivity and discussing the pathwise sensitivity. These results provide guidelines for converging the network, with respect to additional sampling, focusing on the estimates obtained for the overall rate coefficients between product and reactant states. We demonstrate this procedure for transitions in the double-funnel landscape of the 38-atom Lennard-Jones cluster.
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Affiliation(s)
- Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Pracht P, Bohle F, Grimme S. Automated exploration of the low-energy chemical space with fast quantum chemical methods. Phys Chem Chem Phys 2020; 22:7169-7192. [PMID: 32073075 DOI: 10.1039/c9cp06869d] [Citation(s) in RCA: 836] [Impact Index Per Article: 209.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We propose and discuss an efficient scheme for the in silico sampling for parts of the molecular chemical space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodynamic ensembles at a quantum chemical level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated minimum energy structures normally form the basis of further, mostly DFT computational work, such as the calculation of spectra or macroscopic properties. By using basic quantum chemical methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chemical methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized molecules) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chemistry and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.
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Affiliation(s)
- Philipp Pracht
- Mulliken Center for Theoretical Chemistry, Universität Bonn, Beringstr. 4, 53115 Bonn, Germany.
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Sumiya Y, Tabata Y, Maeda S. Understanding the Acetalization Reaction Based on its Reaction Path Network. CHEMSYSTEMSCHEM 2019. [DOI: 10.1002/syst.201900022] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Yosuke Sumiya
- Department of Chemistry Faculty of Science Hokkaido University Sapporo 060-0810 Japan
| | - Yotaro Tabata
- Department of Chemistry Faculty of Science Hokkaido University Sapporo 060-0810 Japan
| | - Satoshi Maeda
- Department of Chemistry Faculty of Science Hokkaido University Sapporo 060-0810 Japan
- Hokkaido University Institute for Chemical Reaction Design and Discovery (WPI-ICReDD) 001-0021 Sapporo Japan
- National Institute for Materials Science (NIMS) Research and Services Division of Materials Data and Integrated System (MaDIS) 305-0044 Tsukuba Japan
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Sawato T, Saito N, Yamaguchi M. Chemical Systems Involving Two Competitive Self-Catalytic Reactions. ACS OMEGA 2019; 4:5879-5899. [PMID: 31459737 PMCID: PMC6648109 DOI: 10.1021/acsomega.9b00133] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Accepted: 03/13/2019] [Indexed: 06/10/2023]
Abstract
Self-catalytic reactions are chemical phenomena, in which a product catalyzes the reactions of substrates further to yield products. A significant amplification of product concentration occurs during the reactions in a dilute solution, which exhibit notable properties such as sigmoidal kinetics, seeding effects, and thermal hysteresis. Chemical systems involving two competitive self-catalytic reactions can be considered, in which the competitive formation of two products occurs, which is affected by environmental changes, subtle perturbations, and fluctuations, and notable chemical phenomena appear such as formation of different structures in response to slow/fast temperature changes, chiral symmetry breaking, shortcut in reaction time, homogeneous-heterogeneous transitions, and mechanical responses. Studies on such chemical systems provide understanding on biological systems and can also be extended to the development of novel functional materials.
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Affiliation(s)
- Yosuke Sumiya
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
| | - Satoshi Maeda
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
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11
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Sugiyama K, Sumiya Y, Takagi M, Saita K, Maeda S. Understanding CO oxidation on the Pt(111) surface based on a reaction route network. Phys Chem Chem Phys 2019; 21:14366-14375. [DOI: 10.1039/c8cp06856a] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Kinetic analysis by the rate constant matrix contraction on the reaction route network of CO oxidation on the Pt(111) surface obtained by the artificial force induced reaction reveals the impact of entropic contributions arising from a variety of local minima and transition states.
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Affiliation(s)
- Kanami Sugiyama
- Graduate School of Chemical Sciences and Engineering
- Hokkaido University
- Sapporo
- Japan
| | - Yosuke Sumiya
- Department of Chemistry
- Faculty of Science
- Hokkaido University
- Sapporo
- Japan
| | - Makito Takagi
- Graduate School of Chemical Sciences and Engineering
- Hokkaido University
- Sapporo
- Japan
| | - Kenichiro Saita
- Department of Chemistry
- Faculty of Science
- Hokkaido University
- Sapporo
- Japan
| | - Satoshi Maeda
- Department of Chemistry
- Faculty of Science
- Hokkaido University
- Sapporo
- Japan
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12
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Maeda S, Sugiyama K, Sumiya Y, Takagi M, Saita K. Global Reaction Route Mapping for Surface Adsorbed Molecules: A Case Study for H2O on Cu(111) Surface. CHEM LETT 2018. [DOI: 10.1246/cl.171194] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Satoshi Maeda
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
- Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
| | - Kanami Sugiyama
- Graduate School of Chemical Sciences and Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
| | - Yosuke Sumiya
- Graduate School of Chemical Sciences and Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
| | - Makito Takagi
- Graduate School of Chemical Sciences and Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
| | - Kenichiro Saita
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
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13
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Maeda S, Harabuchi Y, Takagi M, Taketsugu T, Morokuma K. Artificial Force Induced Reaction (AFIR) Method for Exploring Quantum Chemical Potential Energy Surfaces. CHEM REC 2016; 16:2232-2248. [DOI: 10.1002/tcr.201600043] [Citation(s) in RCA: 94] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Indexed: 12/25/2022]
Affiliation(s)
- Satoshi Maeda
- Department of Chemistry, Faculty of Science; Hokkaido University; Sapporo 060-0810 Japan
| | - Yu Harabuchi
- Department of Chemistry, Faculty of Science; Hokkaido University; Sapporo 060-0810 Japan
| | - Makito Takagi
- Graduate School of Chemical Sciences and Engineering; Hokkaido University; Sapporo 060-8628 Japan
| | - Tetsuya Taketsugu
- Department of Chemistry, Faculty of Science; Hokkaido University; Sapporo 060-0810 Japan
| | - Keiji Morokuma
- Fukui Institute for Fundamental Chemistry, Kyoto University; Kyoto 606-8103 Japan
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