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Singh D, Punia B, Chaudhury S. Theoretical Tools to Quantify Stochastic Fluctuations in Single-Molecule Catalysis by Enzymes and Nanoparticles. ACS OMEGA 2022; 7:47587-47600. [PMID: 36591158 PMCID: PMC9798497 DOI: 10.1021/acsomega.2c06316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/02/2022] [Indexed: 06/11/2023]
Abstract
Single-molecule microscopic techniques allow the counting of successive turnover events and the study of the time-dependent fluctuations of the catalytic activities of individual enzymes and different sites on a single heterogeneous nanocatalyst. It is important to establish theoretical methods to obtain the statistical measurements of such stochastic fluctuations that provide insight into the catalytic mechanism. In this review, we discuss a few theoretical frameworks for evaluating the first passage time distribution functions using a self-consistent pathway approach and chemical master equations, to establish a connection with experimental observables. The measurable probability distribution functions and their moments depend on the molecular details of the reaction and provide a way to quantify the molecular mechanisms of the reaction process. The statistical measurements of these fluctuations should provide insight into the enzymatic mechanism.
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Affiliation(s)
- Divya Singh
- School
of Chemistry, Tel Aviv University, Tel Aviv6997801, Israel
| | - Bhawakshi Punia
- Department
of Chemistry, Indian Institute of Science
Education and Research, Dr. Homi Bhabha Road, Pune411008, Maharashtra, India
| | - Srabanti Chaudhury
- Department
of Chemistry, Indian Institute of Science
Education and Research, Dr. Homi Bhabha Road, Pune411008, Maharashtra, India
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Bogojeski M, Vogt-Maranto L, Tuckerman ME, Müller KR, Burke K. Quantum chemical accuracy from density functional approximations via machine learning. Nat Commun 2020; 11:5223. [PMID: 33067479 PMCID: PMC7567867 DOI: 10.1038/s41467-020-19093-1] [Citation(s) in RCA: 127] [Impact Index Per Article: 31.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 09/24/2020] [Indexed: 12/21/2022] Open
Abstract
Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol-1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol-1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT is highlighted by correcting "on the fly" DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.
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Affiliation(s)
- Mihail Bogojeski
- Machine Learning Group, Technische Universität Berlin, Marchstr. 23, 10587, Berlin, Germany
| | | | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, NY, 10003, USA.
- Courant Institute of Mathematical Science, New York University, New York, NY, 10012, USA.
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China.
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, Marchstr. 23, 10587, Berlin, Germany.
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Korea.
- Max-Planck-Institut für Informatik, Stuhlsatzenhausweg, 66123, Saarbrücken, Germany.
| | - Kieron Burke
- Department of Physics and Astronomy, University of California, Irvine, CA, 92697, USA.
- Department of Chemistry, University of California, Irvine, CA, 92697, USA.
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Kundu P, Saha S, Gangopadhyay G. Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder. ACS OMEGA 2020; 5:9104-9113. [PMID: 32363262 PMCID: PMC7191566 DOI: 10.1021/acsomega.9b03701] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/01/2019] [Accepted: 03/09/2020] [Indexed: 06/11/2023]
Abstract
Mechanical unfolding of single polyubiquitin molecules subjected to a constant stretching force showed nonexponentiality in the measured probability density of unfolding (waiting time distribution) and the survival probability of the folded state during the course of the measurements. These observations explored the relevance of disorder present in the system under study with implications for a static disorder approach to rationalize the experimental results. Here, an approach for dynamic disorder is presented based on Zwanzig's fluctuating bottleneck (FB) model, in which the rate of the reaction is controlled by the passage through the cross-sectional area of the bottleneck. The radius of the latter undergoes stochastic fluctuations that in turn is described in terms of the end-to-end distance fluctuations of the Rouse-like dynamics using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our results are comprised of analytical expressions for the survival probability and waiting time distribution, which show excellent agreement with the experimental data throughout the range of the applied forces. In addition, by fitting the survival probabilities at different stretching forces, we quantify two system parameters, namely, the average free energy ΔG av and the average distance to the transition state Δx av, both perfectly recovered the experimental estimates. These agreements validate the present model of polymer dynamics, which captures the very essence of dynamic disorder in single-molecule pulling experiments.
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Affiliation(s)
- Prasanta Kundu
- S.
N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Soma Saha
- Department
of Chemistry, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Gautam Gangopadhyay
- S.
N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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