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Li W. Potential Energy Weighted Reactive Flux and Total Rate of Change of Potential Energy: Theory and Illustrative Applications. J Phys Chem A 2022; 126:7774-7786. [PMID: 36251005 DOI: 10.1021/acs.jpca.2c04886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Reactive flux can be largely nonzero in a nonequilibrium ensemble of trajectories and provide insightful information for reactive transitions from the reactant state to the product state. Based on the reactive flux, a theoretical framework is proposed here for two quantities, the potential energy weighted reactive flux and the total rate of change of potential energy, which are useful for the identification of the mechanism from a nonequilibrium ensemble. From such quantities, two multidimensional free-energy analogues can be derived in the subspace of collective variables and they are equivalent in the regions where the reactive flux is divergence-free. These free-energy analogues are assumed to be closely related to the free energy in the subspace of collective variables, and they are reduced in the one-dimensional case to be the ensemble average of the potential energy weighted with reactive flux intensity, which was proposed recently [Li, W. J. Phys. Chem. A 2022, DOI: 10.1021/acs.jpca.2c04130] and could be decomposed into energy components at the per-coordinate level. In the subspace of collective variables, the decomposition of the multidimensional free-energy analogues at the per-coordinate level is theoretically possible and is numerically difficult to be calculated. Interestingly, the total rate of change of potential energy is able to identify the location of the transition state ensemble or the stochastic separatrix, in addition to the locations of the reactant and product states. The total rate of change of potential energy can be decomposed at the per-coordinate level, and its components can quantify the contribution of a coordinate to the reactive transition in the subspace of collective variables. We then illustrated the main insights and objects that can be provided by the approach in the applications to a two-dimensional system with various diffusion anisotropies and the alanine peptide in vacuum in various nonequilibrium ensembles of short trajectories, from which the results were found to be consistent.
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Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, China
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Li W. Energy Decomposition along the Reaction Coordinate: Theory and Applications to Nonequilibrium Ensembles of Trajectories. J Phys Chem A 2022; 126:7763-7773. [PMID: 36214522 DOI: 10.1021/acs.jpca.2c04130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A theoretical framework is proposed for an energy decomposition scheme along the reaction coordinate, in which the ensemble average of the potential energy weighted with reactive flux intensity is decomposed into energy components at the per-coordinate level. The decomposed energy quantity is demonstrated to be closely related to the free energy along the reaction coordinate, and its connection to the emergent potential energy is provided. In the application to alanine dipeptide under vacuum, illustrative calculations were performed in three nonequilibrium ensembles of trajectories: (1) transition path ensemble sampled with transition path sampling; (2) ensemble of short trajectories initiated from configurations around the transition-state region; and (3) ensemble of short trajectories shooting from configurations in several transition paths. The energy components on each coordinate were found to be consistent among the three ensembles of trajectories, indicating a broad applicability of the approach in biomolecular studies. In addition, the free energies along an optimized reaction coordinate obtained with these nonequilibrium ensembles were largely overlapped with a reference free energy calculated from a long equilibrium trajectory.
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Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen518060, China
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Li W. Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory. J Phys Chem A 2022; 126:3797-3810. [PMID: 35670470 DOI: 10.1021/acs.jpca.2c02221] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The transition path ensemble is of special interest in reaction coordinate identification as it consists of reactive trajectories that start from the reactant state and end in the product one. As a theoretical framework for describing the transition path ensemble, the transition path theory has been introduced more than 10 years ago, and so far, its applications have only been illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curves are derived here in the space of collective variables from the transition path theory, and they are applicable to time series obtained from molecular dynamics simulations of high-dimensional systems, i.e., the position coordinates as a function of time in the transition path ensemble. The connection of the transition path theory is made to a density-weighted average flux, a quantity proposed in a previous work to appraise the relevance of a coordinate to the reaction coordinate [Li, W. J. Chem. Phys. 2022, 156, 054117]. Most importantly, as an extension of the existing quantities, time-lagged quantities such as flux and current are also proposed. The main insights and objects provided by these time-lagged quantities are illustrated in the application to the alanine peptide in vacuum.
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Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
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Li W. Optimizing reaction coordinate by flux maximization in the transition path ensemble. J Chem Phys 2022; 156:054117. [DOI: 10.1063/5.0079390] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen, China
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de Medeiros AF, de Souza BBP, Coutinho LP, Murad AM, dos Santos PIM, Monteiro NDKV, dos Santos EA, Maciel BLL, de Araújo Morais AH. Structural insights and molecular dynamics into the inhibitory mechanism of a Kunitz-type trypsin inhibitor from Tamarindus indica L. J Enzyme Inhib Med Chem 2021; 36:480-490. [PMID: 33491503 PMCID: PMC7875565 DOI: 10.1080/14756366.2021.1876686] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Revised: 12/23/2020] [Accepted: 01/11/2021] [Indexed: 11/08/2022] Open
Abstract
Trypsin inhibitors from tamarind seed have been studied in vitro and in preclinical studies for the treatment of obesity, its complications and associated comorbidities. It is still necessary to fully understand the structure and behaviour of these molecules. We purifed this inhibitor, sequenced de novo by MALDI-TOF/TOF, performed its homology modelling, and assessed the interaction with the trypsin enzyme through molecular dynamics (MD) simulation under physiological conditions. We identified additional 75 amino acid residues, reaching approximately 72% of total coverage. The four best conformations of the best homology modelling were submitted to the MD. The conformation n°287 was selected considering the RMSD analysis and interaction energy (-301.0128 kcal.mol-1). Residues Ile (54), Pro (57), Arg (59), Arg (63), and Glu (78) of pTTI presented the highest interactions with trypsin, and arginine residues were mainly involved in its binding mechanism. The results favour bioprospecting of this protein for pharmaceutical health applications.
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Affiliation(s)
| | - Beatriz Blenda Pinheiro de Souza
- Postgraduate Biological Molecular, Institute of Biological Sciences, University of Brasília, Brasília, Brazil
- Laboratory of Mass Spectometry-LEM, Embrapa Genetic Resources and Biotechnology, Brasília, Brazil
| | | | - Aline Melro Murad
- Laboratory of Mass Spectometry-LEM, Embrapa Genetic Resources and Biotechnology, Brasília, Brazil
| | | | | | - Elizeu Antunes dos Santos
- Postgraduate Biochemistry Program, Biosciences Center, Federal University of Rio Grande do Norte, Natal, Brazil
- Department of Biochemistry, Biosciences Center, Federal University of Rio Grande, Natal, Brazil
- Tropical Medicine Institute, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Bruna Leal Lima Maciel
- Postgraduate Nutrition Program, Center for Health Sciences, Federal University of Rio Grande do Norte, Natal, Brazil
- Department of Nutrition, Center for Health Sciences, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Ana Heloneida de Araújo Morais
- Postgraduate Biochemistry Program, Biosciences Center, Federal University of Rio Grande do Norte, Natal, Brazil
- Postgraduate Nutrition Program, Center for Health Sciences, Federal University of Rio Grande do Norte, Natal, Brazil
- Department of Nutrition, Center for Health Sciences, Federal University of Rio Grande do Norte, Natal, Brazil
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Zhong H, Chen Z, Lin J, Xu Y, Liu D, Yin X. The inhibition mechanism of carp (
Cyprinus carpio
) stefin to cathepsin B and their tertiary structures. Int J Food Sci Technol 2021. [DOI: 10.1111/ijfs.15265] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Haixia Zhong
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
| | - Zhiguang Chen
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
| | - Jianhe Lin
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
| | - Yi Xu
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
| | - Dan Liu
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
| | - Xianfeng Yin
- Department of Agricultural Technology Neijiang Vocational and Technical College Neijiang 641100 China
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