1
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Midha T, Kolomeisky AB, Igoshin OA. Linear-Decoupling Enables Accurate Speed and Accuracy Predictions for Copolymerization Processes. J Phys Chem Lett 2024; 15:9361-9368. [PMID: 39240239 DOI: 10.1021/acs.jpclett.4c02132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/07/2024]
Abstract
Biological processes exhibit remarkable accuracy and speed and can be theoretically explored through various approaches. The Markov-chain copolymerization theory, describing polymer growth kinetics as a Markov chain, provides an exact set of equations to solve for error and speed. Still, due to nonlinearity, these equations are hard to solve. Alternatively, the enzyme-kinetics approach, which formulates a set of linear equations, simplifies the biological processes as transitions between discrete chemical states, but generally, it might not be accurate. Here, we show that the enzyme-kinetic approach can lead to inaccurate fluxes, even for first-order polymerization processes. To address the problem, we propose a simplified linear-decoupling approximation for steady-state probabilities of higher-order copolymer chains under biologically relevant conditions. Our findings demonstrate that the stationary speed and error rate obtained from the linear-decoupling method align closely with exact values from the Markov-chain (nonlinear) approximation. Extending the technique to higher-order processes with proofreading and internal states shows that it works equally well to describe trade-offs between speed and accuracy for DNA replication and transcription elongation. Our work underscores the proposed linear-decoupling approximation's efficacy in addressing the nonlinear behavior of the Markov-chain approach and the enzyme-kinetic approach's limitations, ensuring accurate predictions for high-fidelity biological processes.
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Affiliation(s)
- Tripti Midha
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Oleg A Igoshin
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Bioengineering, Rice University, Houston, Texas 77005, United States
- Department of Biosciences, Rice University, Houston, Texas 77005, United States
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2
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Midha T, Kolomeisky AB, Igoshin OA. Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited. J Phys Chem B 2024; 128:5612-5622. [PMID: 38814670 DOI: 10.1021/acs.jpcb.4c02173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
The high fidelity observed in biological information processing ranging from replication to translation has stimulated significant research efforts to clarify the underlying microscopic picture. Theoretically, several approaches to analyze the error rates have been proposed. The copolymerization theory describes the addition and removal of monomers at the growing tip of a copolymer, leading to a closed set of nonlinear equations. On the other hand, enzyme-kinetics approaches formulate linear equations of biochemical networks, describing transitions between discrete chemical states. However, it is still unclear whether the error values computed by the two approaches agree. Moreover, there are conflicting interpretations on whether the error is under thermodynamic or kinetic discrimination control. In this work, we examine the error rate in persistent copying biochemical processes by specifically analyzing both theoretical approaches. The initial disagreement of the results between the two theories motivated us to rederive the formula for the error rate in the kinetic model. The error computed with the new method resulted in excellent agreement between both theoretical approaches and with Monte Carlo simulations. Furthermore, our theoretical analysis shows that the kinetic discrimination controls the error, even when the energy difference between adding the right and wrong products is very small. Our theoretical investigation gives important insights into the physical-chemical properties of complex biological processes by providing the quantitative framework to evaluate them.
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Affiliation(s)
- Tripti Midha
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Oleg A Igoshin
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Bioengineering, Rice University, Houston, Texas 77005, United States
- Department of Biosciences, Rice University, Houston, Texas 77005, United States
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3
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Nam KM, Gunawardena J. The linear framework II: using graph theory to analyse the transient regime of Markov processes. Front Cell Dev Biol 2023; 11:1233808. [PMID: 38020901 PMCID: PMC10656611 DOI: 10.3389/fcell.2023.1233808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 10/02/2023] [Indexed: 12/01/2023] Open
Abstract
The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent chemical species or molecular states, edges represent reactions or transitions and edge labels represent rates that also describe how the system is interacting with its environment. The present paper is a sequel to a recent review of the framework that focussed on how graph-theoretic methods give insight into steady states as rational algebraic functions of the edge labels. Here, we focus on the transient regime for systems that correspond to continuous-time Markov processes. In this case, the graph specifies the infinitesimal generator of the process. We show how the moments of the first-passage time distribution, and related quantities, such as splitting probabilities and conditional first-passage times, can also be expressed as rational algebraic functions of the labels. This capability is timely, as new experimental methods are finally giving access to the transient dynamic regime and revealing the computations and information processing that occur before a steady state is reached. We illustrate the concepts, methods and formulas through examples and show how the results may be used to illuminate previous findings in the literature.
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Affiliation(s)
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, MA, United States
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4
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Huang L, Liu Q, Wu W, Gao G, Zheng X, Wang J, Dong S. Identifying the active sites in unequal iron-nitrogen single-atom catalysts. Nat Commun 2023; 14:5594. [PMID: 37696805 PMCID: PMC10495408 DOI: 10.1038/s41467-023-41311-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 08/28/2023] [Indexed: 09/13/2023] Open
Abstract
Single-atom catalysts (SACs) have become one of the most attractive frontier research fields in catalysis and energy conversion. However, due to the atomic heterogeneity of SACs and limitations of ensemble-averaged measurements, the essential active sites responsible for governing specific catalytic properties and mechanisms remain largely concealed. In this study, we develop a quantitative method of single-atom catalysis-fluorescence correlation spectroscopy (SAC-FCS), leveraging the atomic structure-dependent catalysis kinetics and single-turnover resolution of single-molecule fluorescence microscopy. This method enables us to investigate the oxidase-like single-molecule catalysis on unidentical iron-nitrogen (Fe-N) coordinated SACs, quantifying the active sites and their kinetic parameters. The findings reveal the significant differences of single sites from the average behaviors and corroborate the oxidase-like catalytic mechanism of the Fe-N active sites. We anticipate that the method will give essential insights into the rational design and application of SACs.
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Affiliation(s)
- Liang Huang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei, 230026, China
| | - Qiong Liu
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China
| | - Weiwei Wu
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei, 230026, China
| | - Ge Gao
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China
| | - Xiliang Zheng
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China
| | - Jin Wang
- Center for Theoretical Interdisciplinary Sciences Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, 325001, China.
- Department of Chemistry and Physics, State University of New York at Stony Brook, Stony Brook, NY, 11794-3400, USA.
| | - Shaojun Dong
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China.
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei, 230026, China.
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5
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Bose A, Walters PL. Impact of Solvent on State-to-State Population Transport in Multistate Systems Using Coherences. J Chem Theory Comput 2023. [PMID: 37466459 DOI: 10.1021/acs.jctc.3c00200] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2023]
Abstract
Understanding the pathways taken by a quantum particle during a transport process is an enormous challenge. There are broadly two different aspects of the problem that affect the route taken. First is obviously the couplings between the various sites, which translates into the intrinsic "strength" of a state-to-state channel. Apart from these inter-state couplings, the relative coupling strengths and timescales of the solvent modes form the second factor. This impact of the dissipative environment is significantly more difficult to analyze. Building on the recently derived relations between coherences and population derivatives, we present an analysis of the transport that allows us to account for both the effects in a rigorous manner. We demonstrate the richness hidden behind the transport even for a relatively simple system, a 4-site coarse-grained model of the Fenna-Matthews-Olson complex. The effect of the local dissipative media is highly nontrivial. We show that while the impact on the total site population may be small, there are noticeable changes to the pathway taken by the transport process. We also demonstrate how an analysis in a similar spirit can be done using the Förster approximation. The ability to untangle the dynamics at a greater granularity opens up possibilities in terms of design of novel systems with an eye toward quantum control.
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Affiliation(s)
- Amartya Bose
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai 400005, India
| | - Peter L Walters
- Department of Chemistry and Biochemistry, George Mason University, Fairfax, Virginia 22030, United States
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6
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Analytical Decomposition of Transition Flux to Cycle Durations via Integration of Transition Times. Symmetry (Basel) 2022. [DOI: 10.3390/sym14091857] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Rigorous methods of decomposing kinetic networks to cycles are available, but the solutions usually contain entangled transition rates, which are difficult to analyze. This study proposes a new method of decomposing net transition flux to cycle durations, and the duration of each cycle is an integration of the transition times along the cycle. The method provides a series of neat dependences from the basic kinetic variables to the final flux, which support direct analysis based on the formulas. An assisting transformation diagram from symmetric conductivity to asymmetric conductivity is provided, which largely simplifies the application of the method. The method is likely a useful analytical tool for many studies relevant to kinetics and networks. Applications of the method shall provide new kinetic and thermodynamic information for the studied system.
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7
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An S, Patel P, Liu C, Skodje RT. Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis. J Phys Chem A 2022; 126:3783-3796. [PMID: 35658508 DOI: 10.1021/acs.jpca.2c02153] [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
Catalysis from single active sites is analyzed using methods developed from single-molecule kinetics. Using a stochastic Markov-state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated for model problems and for a physically realistic mechanism for an alkene hydrogenation reaction on a single-atom catalyst. The spectral analysis permits a hierarchy of timescales to be identified from the single-molecule signal, which correspond to specific relaxation modes in the network.
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Affiliation(s)
- Suming An
- Department of Chemistry, University of Colorado, Boulder, Colorado 80309, United States
| | - Prajay Patel
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60639, United States
| | - Cong Liu
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60639, United States
| | - Rex T Skodje
- Department of Chemistry, University of Colorado, Boulder, Colorado 80309, United States
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8
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Martsenyuk V, Klos-Witkowska A, Dzyadevych S, Sverstiuk A. Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action. SENSORS 2022; 22:s22030980. [PMID: 35161724 PMCID: PMC8839366 DOI: 10.3390/s22030980] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 01/15/2022] [Accepted: 01/25/2022] [Indexed: 02/01/2023]
Abstract
The paper is devoted to the extension of Brown’s model of enzyme kinetics to the case with distributed delays. Firstly, we construct a multi-substrate multi-inhibitor model using discrete and distributed delays. Furthermore, we consider simplified models including one substrate and one inhibitor, for which an experimental study has been performed. The algorithm of parameter identifications was developed which was tested on the experimental data of solution conductivity. Both the model and Kohlrausch’s law parameters are obtained as a result of the optimization procedure. Comparison of plots constructed with the help of the estimated parameters has shown that in such case the model with distributed delays is more chemically adequate in comparison with the discrete one. The methods of generalization of the results to the multi-substrate multi-inhibitor cases are discussed.
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Affiliation(s)
- Vasyl Martsenyuk
- Department of Computer Science and Automation, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland;
- Correspondence: ; Tel.: +48-3382-792-64
| | - Aleksandra Klos-Witkowska
- Department of Computer Science and Automation, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland;
| | - Sergei Dzyadevych
- Institute of Molecular Biology and Genetics, National Academy of Sciences of Ukraine, 150 Zabolotnogo St., 03143 Kiev, Ukraine;
| | - Andriy Sverstiuk
- Medical Informatics Department, Ternopil National Medical University, 46001 Ternopil, Ukraine;
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9
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Mu W, Kong J, Cao J. Understanding the Optimal Cooperativity of Human Glucokinase: Kinetic Resonance in Nonequilibrium Conformational Fluctuations. J Phys Chem Lett 2021; 12:2900-2904. [PMID: 33724849 DOI: 10.1021/acs.jpclett.1c00438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The cooperativity of a monomeric enzyme arises from dynamic correlation instead of spatial correlation and is a consequence of nonequilibrium conformation fluctuations. We investigate the conformation-modulated kinetics of human glucokinase, a monomeric enzyme with important physiological functions, using a five-state kinetic model. We derive the non-Michealis-Menten (MM) correction term of the activity (i.e., turnover rate), predict its relationship to cooperativity, and reveal the violation of conformational detailed balance. Most importantly, we reproduce and explain the observed resonance effect in human glucokinase (i.e., maximal cooperativity when the conformational fluctuation rate is comparable to the catalytic rate). With the realistic parameters, our theoretical results are in quantitative agreement with the reported measurement by Miller and co-workers. The analysis can be extended to a general chemical network beyond the five-state model, suggesting the generality of kinetic cooperativity and resonance.
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Affiliation(s)
- Weihua Mu
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325001, China
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge 02139, U.K
| | - Jing Kong
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge 02139, U.K
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge 02139, U.K
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10
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Dhatt S, Nandi M, Chaudhury P. Substrate inhibition versus product feedback inhibition: In the perspective of single molecule enzyme kinetics. INT J CHEM KINET 2021. [DOI: 10.1002/kin.21480] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Mintu Nandi
- Department of Chemistry University of Calcutta Kolkata India
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11
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Kumar A, Adhikari R, Dua A. Transients generate memory and break hyperbolicity in stochastic enzymatic networks. J Chem Phys 2021; 154:035101. [DOI: 10.1063/5.0031368] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Ashutosh Kumar
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
| | - R. Adhikari
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Arti Dua
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
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12
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Kundu P, Saha S, Gangopadhyay G. Kinetics of Allosteric Inhibition of Single Enzyme by Product Molecules. J Phys Chem B 2020; 124:11793-11801. [DOI: 10.1021/acs.jpcb.0c08392] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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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13
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Fang X, Wang J. Nonequilibrium Thermodynamics in Cell Biology: Extending Equilibrium Formalism to Cover Living Systems. Annu Rev Biophys 2020; 49:227-246. [DOI: 10.1146/annurev-biophys-121219-081656] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We discuss new developments in the nonequilibrium dynamics and thermodynamics of living systems, giving a few examples to demonstrate the importance of nonequilibrium thermodynamics for understanding biological dynamics and functions. We study single-molecule enzyme dynamics, in which the nonequilibrium thermodynamic and dynamic driving forces of chemical potential and flux are crucial for the emergence of non-Michaelis-Menten kinetics. We explore single-gene expression dynamics, in which nonequilibrium dissipation can suppress fluctuations. We investigate the cell cycle and identify the nutrition supply as the energy input that sustains the stability, speed, and coherence of cell cycle oscillation, from which the different vital phases of the cell cycle emerge. We examine neural decision-making processes and find the trade-offs among speed, accuracy, and thermodynamic costs that are important for neural function. Lastly, we consider the thermodynamic cost for specificity in cellular signaling and adaptation.
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Affiliation(s)
- Xiaona Fang
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA
| | - Jin Wang
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
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14
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Hosaka Y, Komura S, Andelman D. Shear viscosity of two-state enzyme solutions. Phys Rev E 2020; 101:012610. [PMID: 32069562 DOI: 10.1103/physreve.101.012610] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2019] [Indexed: 01/17/2023]
Abstract
We discuss the shear viscosity of a Newtonian solution of catalytic enzymes and substrate molecules. The enzyme is modeled as a two-state dimer consisting of two spherical domains connected with an elastic spring. The enzymatic conformational dynamics is induced by the substrate binding and such a process is represented by an additional elastic spring. Employing the Boltzmann distribution weighted by the waiting times of enzymatic species in each catalytic cycle, we obtain the shear viscosity of dilute enzyme solutions as a function of substrate concentration and its physical properties. The substrate affinity distinguishes between fast and slow enzymes, and the corresponding viscosity expressions are obtained. Furthermore, we connect the obtained viscosity with the diffusion coefficient of a tracer particle in enzyme solutions.
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Affiliation(s)
- Yuto Hosaka
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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15
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Liu Q, Wang J. Quantifying the flux as the driving force for nonequilibrium dynamics and thermodynamics in non-Michaelis-Menten enzyme kinetics. Proc Natl Acad Sci U S A 2020; 117:923-930. [PMID: 31879351 PMCID: PMC6969527 DOI: 10.1073/pnas.1819572117] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The driving force for active physical and biological systems is determined by both the underlying landscape and nonequilibrium curl flux. While landscape can be experimentally quantified from the histograms of the collected real-time trajectories of the observables, quantifying the experimental flux remains challenging. In this work, we studied the single-molecule enzyme dynamics of horseradish peroxidase with dihydrorhodamine 123 and hydrogen peroxide (H2O2) as substrates. Surprisingly, significant deviations in the kinetics from the conventional Michaelis-Menten reaction rate were observed. Instead of a linear relationship between the inverse of the enzyme kinetic rate and the inverse of substrate concentration, a nonlinear relationship between the two emerged. We identified nonequilibrium flux as the origin of such non-Michaelis-Menten enzyme rate behavior. Furthermore, we quantified the nonequilibrium flux from experimentally obtained fluorescence correlation spectroscopy data and showed this flux to led to the deviations from the Michaelis-Menten kinetics. We also identified and quantified the nonequilibrium thermodynamic driving forces as the chemical potential and entropy production for such non-Michaelis-Menten kinetics. Moreover, through isothermal titration calorimetry measurements, we identified and quantified the origin of both nonequilibrium dynamic and thermodynamic driving forces as the heat absorbed (energy input) into the enzyme reaction system. Furthermore, we showed that the nonequilibrium driving forces led to time irreversibility through the difference between the forward and backward directions in time and high-order correlations were associated with the deviations from Michaelis-Menten kinetics. This study provided a general framework for experimentally quantifying the dynamic and thermodynamic driving forces for nonequilibrium systems.
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Affiliation(s)
- Qiong Liu
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022 Jilin, China
| | - Jin Wang
- Department of Chemistry, Physics and Applied Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794-3400
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16
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Muñoz-Cobo JL, Berna C. Chemical Kinetics Roots and Methods to Obtain the Probability Distribution Function Evolution of Reactants and Products in Chemical Networks Governed by a Master Equation. ENTROPY 2019; 21:e21020181. [PMID: 33266897 PMCID: PMC7514663 DOI: 10.3390/e21020181] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Accepted: 02/11/2019] [Indexed: 11/16/2022]
Abstract
In this paper first, we review the physical root bases of chemical reaction networks as a Markov process in multidimensional vector space. Then we study the chemical reactions from a microscopic point of view, to obtain the expression for the propensities for the different reactions that can happen in the network. These chemical propensities, at a given time, depend on the system state at that time, and do not depend on the state at an earlier time indicating that we are dealing with Markov processes. Then the Chemical Master Equation (CME) is deduced for an arbitrary chemical network from a probability balance and it is expressed in terms of the reaction propensities. This CME governs the dynamics of the chemical system. Due to the difficulty to solve this equation two methods are studied, the first one is the probability generating function method or z-transform, which permits to obtain the evolution of the factorial moment of the system with time in an easiest way or after some manipulation the evolution of the polynomial moments. The second method studied is the expansion of the CME in terms of an order parameter (system volume). In this case we study first the expansion of the CME using the propensities obtained previously and splitting the molecular concentration into a deterministic part and a random part. An expression in terms of multinomial coefficients is obtained for the evolution of the probability of the random part. Then we study how to reconstruct the probability distribution from the moments using the maximum entropy principle. Finally, the previous methods are applied to simple chemical networks and the consistency of these methods is studied.
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Affiliation(s)
- José-Luis Muñoz-Cobo
- Department of Chemical and Nuclear Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
- Instituto Universitario de Ingeniería Energética, Universitat Politècnica de València, 46022 Valencia, Spain
- Correspondence: ; Tel.: +34-96-387-7631
| | - Cesar Berna
- Instituto Universitario de Ingeniería Energética, Universitat Politècnica de València, 46022 Valencia, Spain
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17
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Charge Transfer between [4Fe4S] Proteins and DNA Is Unidirectional: Implications for Biomolecular Signaling. Chem 2018; 5:122-137. [PMID: 30714018 DOI: 10.1016/j.chempr.2018.09.026] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Recent experiments suggest that DNA-mediated charge transport might enable signaling between the [4Fe4S] clusters in the C-terminal domains of human DNA primase and polymerase α, as well as the signaling between other replication and repair high-potential [4Fe4S] proteins. Our theoretical study demonstrates that the redox signaling cannot be accomplished exclusively by DNA-mediated charge transport because part of the charge transfer chain has an unfavorable free energy profile. We show that hole or excess electron transfer between a [4Fe4S] cluster and a nucleic acid duplex through a protein medium can occur within microseconds in one direction, while it is kinetically hindered in the opposite direction. We present a set of signaling mechanisms that may occur with the assistance of oxidants or reductants, using the allowed charge transfer processes. These mechanisms would enable the coordinated action of [4Fe4S] proteins on DNA, engaging the [4Fe4S] oxidation state dependence of the protein-DNA binding affinity.
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18
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Structural conditions on complex networks for the Michaelis-Menten input-output response. Proc Natl Acad Sci U S A 2018; 115:9738-9743. [PMID: 30194237 DOI: 10.1073/pnas.1808053115] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.
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19
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Singh D, Chaudhury S. Effect of Substrate Number Fluctuations in Stochastic Enzyme Kinetics. ACS OMEGA 2018; 3:5574-5583. [PMID: 31458761 PMCID: PMC6641702 DOI: 10.1021/acsomega.8b00611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/30/2018] [Accepted: 05/10/2018] [Indexed: 06/10/2023]
Abstract
Conventional studies on enzyme kinetics assume that the substrate concentration remains constant. However, for catalytic reactions taking place in intracellular compartments, the substrate molecules are fed in and out of the compartment and are catalyzed into product molecules within the compartment. In this work, we use a chemical master equation approach to study the stochastic kinetics of a single enzyme for different reaction pathways with one or more intermediate states. We obtain velocity expressions that deviate from the Michaelis-Menten expression. We study the coefficient of variation, which is a measure of the noise strength as a function of the mean substrate concentration for systems where there is influx or/and outflux of substrate molecules. Our results show that the noise strength decreases with the increase in the substrate concentration and finally remains the same when the substrate is present in abundance.
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20
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Singh D, Chaudhury S. Single-Molecule Kinetics of an Enzyme in the Presence of Multiple Substrates. Chembiochem 2018; 19:842-850. [PMID: 29393555 DOI: 10.1002/cbic.201700695] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2017] [Indexed: 11/07/2022]
Abstract
Herein, the catalytic activity of a single enzyme in the presence of multiple substrates is studied. Three different mechanisms of bisubstrate binding, namely, ordered sequential, random sequential and ping-pong nonsequential pathway, are broadly discussed. By means of the chemical master equation approach, exact expressions for the waiting-time distributions, the mean turnover time and the randomness parameter as a function of the substrate concentration, such that both concentrations are fixed, but one of them is changed quasi-statically are obtained. The randomness parameter is not equal to unity at intermediate to high substrate concentrations, which indicates the presence of multiple rate-limiting steps in the reaction pathway in all three modes of bisubstrate binding. This arises due to transitions between the free enzyme and the enzyme-substrate complexes that occur on comparable timescales. Such turnover statistics of the single enzyme can also distinguish between the different types of bisubstrate binding mechanisms.
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Affiliation(s)
- Divya Singh
- Department of Chemistry, Indian Institutes of Science Education and Research, Dr. Homi Bhabha Road, Pune, 411008, Maharashtra, India
| | - Srabanti Chaudhury
- Department of Chemistry, Indian Institutes of Science Education and Research, Dr. Homi Bhabha Road, Pune, 411008, Maharashtra, India
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21
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Ptaszyński K. First-passage times in renewal and nonrenewal systems. Phys Rev E 2018; 97:012127. [PMID: 29448475 DOI: 10.1103/physreve.97.012127] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Indexed: 11/07/2022]
Abstract
Fluctuations in stochastic systems are usually characterized by full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of the first-passage times, i.e., the time delays after which the counting variable reaches a certain threshold value, is studied. This paper presents the approach to calculate the first-passage time distribution in systems in which the analyzed current is associated with an arbitrary set of transitions within the Markovian network. Using this approach, it is shown that when the subsequent first-passage times are uncorrelated, there exist strict relations between the cumulants of the full counting statistics and the first-passage time distribution. On the other hand, when the correlations of the first-passage times are present, their distribution may provide additional information about the internal dynamics of the system in comparison to the full counting statistics; for example, it may reveal the switching between different dynamical states of the system. Additionally, I show that breaking of the fluctuation theorem for first-passage times may reveal the multicyclic nature of the Markovian network.
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Affiliation(s)
- Krzysztof Ptaszyński
- Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Poznań, Poland
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22
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Taylor AB, Zijlstra P. Single-Molecule Plasmon Sensing: Current Status and Future Prospects. ACS Sens 2017; 2:1103-1122. [PMID: 28762723 PMCID: PMC5573902 DOI: 10.1021/acssensors.7b00382] [Citation(s) in RCA: 152] [Impact Index Per Article: 21.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2017] [Accepted: 08/01/2017] [Indexed: 12/14/2022]
Abstract
Single-molecule detection has long relied on fluorescent labeling with high quantum-yield fluorophores. Plasmon-enhanced detection circumvents the need for labeling by allowing direct optical detection of weakly emitting and completely nonfluorescent species. This review focuses on recent advances in single molecule detection using plasmonic metal nanostructures as a sensing platform, particularly using a single particle-single molecule approach. In the past decade two mechanisms for plasmon-enhanced single-molecule detection have been demonstrated: (1) by plasmonically enhancing the emission of weakly fluorescent biomolecules, or (2) by monitoring shifts of the plasmon resonance induced by single-molecule interactions. We begin with a motivation regarding the importance of single molecule detection, and advantages plasmonic detection offers. We describe both detection mechanisms and discuss challenges and potential solutions. We finalize by highlighting the exciting possibilities in analytical chemistry and medical diagnostics.
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Affiliation(s)
- Adam B. Taylor
- Molecular Biosensing for
Medical Diagnostics, Faculty of Applied Physics, & Institute for
Complex Molecular Systems, Eindhoven University
of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Peter Zijlstra
- Molecular Biosensing for
Medical Diagnostics, Faculty of Applied Physics, & Institute for
Complex Molecular Systems, Eindhoven University
of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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23
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Avila TR, Piephoff DE, Cao J. Generic Schemes for Single-Molecule Kinetics. 2: Information Content of the Poisson Indicator. J Phys Chem B 2017; 121:7750-7760. [DOI: 10.1021/acs.jpcb.7b01516] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Thomas R. Avila
- Department
of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - D. Evan Piephoff
- Department
of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Jianshu Cao
- Department
of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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24
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Piephoff DE, Wu J, Cao J. Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation. J Phys Chem Lett 2017; 8:3619-3623. [PMID: 28737397 DOI: 10.1021/acs.jpclett.7b01210] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
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Affiliation(s)
- D Evan Piephoff
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Jianlan Wu
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, United States
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25
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Park SJ, Song S, Jeong IC, Koh HR, Kim JH, Sung J. Nonclassical Kinetics of Clonal yet Heterogeneous Enzymes. J Phys Chem Lett 2017; 8:3152-3158. [PMID: 28609615 DOI: 10.1021/acs.jpclett.7b01218] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Enzyme-to-enzyme variation in the catalytic rate is ubiquitous among single enzymes created from the same genetic information, which persists over the lifetimes of living cells. Despite advances in single-enzyme technologies, the lack of an enzyme reaction model accounting for the heterogeneous activity of single enzymes has hindered a quantitative understanding of the nonclassical stochastic outcome of single enzyme systems. Here we present a new statistical kinetics and exactly solvable models for clonal yet heterogeneous enzymes with possibly nonergodic state dynamics and state-dependent reactivity, which enable a quantitative understanding of modern single-enzyme experimental results for the mean and fluctuation in the number of product molecules created by single enzymes. We also propose a new experimental measure of the heterogeneity and nonergodicity for a system of enzymes.
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Affiliation(s)
- Seong Jun Park
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
- National Institute of Innovative Functional Imaging, Chung-Ang University , Seoul 06974, Korea
| | - Sanggeun Song
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
- Department of Chemistry, Chung-Ang University , Seoul 06974, Korea
- National Institute of Innovative Functional Imaging, Chung-Ang University , Seoul 06974, Korea
| | - In-Chun Jeong
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
- Department of Chemistry, Chung-Ang University , Seoul 06974, Korea
- National Institute of Innovative Functional Imaging, Chung-Ang University , Seoul 06974, Korea
| | - Hye Ran Koh
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
- Department of Chemistry, Chung-Ang University , Seoul 06974, Korea
| | - Ji-Hyun Kim
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
| | - Jaeyoung Sung
- National Creative Research Initiative Center for Chemical Dynamics in Living Cells, Chung-Ang University , Seoul 06974, Korea
- Department of Chemistry, Chung-Ang University , Seoul 06974, Korea
- National Institute of Innovative Functional Imaging, Chung-Ang University , Seoul 06974, Korea
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26
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Ding B, Li L, Yang H. An artificial neural network approach to estimating the enzymatic hydrolysis of Chinese yam (Dioscorea opposita
Thunb.) starch. J FOOD PROCESS PRES 2017. [DOI: 10.1111/jfpp.13176] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Baomiao Ding
- College of Life Science; Yangtze University, Jingmi Road 266; Jingzhou Hubei 434025 China
| | - Li Li
- College of Life Science; Yangtze University, Jingmi Road 266; Jingzhou Hubei 434025 China
| | - Hualin Yang
- College of Life Science; Yangtze University, Jingmi Road 266; Jingzhou Hubei 434025 China
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27
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Abstract
The reversible Michaelis-Menten equation is shown to follow from a very broad class of steady-state kinetic models involving enzymes that adopt a unique free (i.e., not complexed to substrate/product) state in solution. In the case of enzymes with multiple free states/conformations (e.g., fluctuating, hysteretic, or co-operative monomeric enzymes), Michaelian behavior is still assured if the relative steady-state populations of free enzyme states are independent of substrate and product concentration. Prior models for Michaelian behavior in multiple conformer enzymes are shown to be special cases of this single condition.
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Affiliation(s)
- Itay Barel
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA and Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Frank L H Brown
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA and Department of Physics, University of California, Santa Barbara, California 93106, USA
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28
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Affiliation(s)
- Ramon Grima
- School
of Biological Sciences, University of Edinburgh, Edinburgh EH8 9YL, U.K
| | - André Leier
- Okinawa Institute of Science and Technology, Okinawa 904-0412, Japan
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29
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Probing conformational dynamics of an enzymatic active site by an in situ single fluorogenic probe under piconewton force manipulation. Proc Natl Acad Sci U S A 2016; 113:15006-15011. [PMID: 27940917 DOI: 10.1073/pnas.1613404114] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Unraveling the conformational details of an enzyme during the essential steps of a catalytic reaction (i.e., enzyme-substrate interaction, enzyme-substrate active complex formation, nascent product formation, and product release) is challenging due to the transient nature of intermediate conformational states, conformational fluctuations, and the associated complex dynamics. Here we report our study on the conformational dynamics of horseradish peroxidase using single-molecule multiparameter photon time-stamping spectroscopy with mechanical force manipulation, a newly developed single-molecule fluorescence imaging magnetic tweezers nanoscopic approach. A nascent-formed fluorogenic product molecule serves as a probe, perfectly fitting in the enzymatic reaction active site for probing the enzymatic conformational dynamics. Interestingly, the product releasing dynamics shows the complex conformational behavior with multiple product releasing pathways. However, under magnetic force manipulation, the complex nature of the multiple product releasing pathways disappears and more simplistic conformations of the active site are populated.
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30
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Berezhkovskii AM, Szabo A, Rotbart T, Urbakh M, Kolomeisky AB. Dependence of the Enzymatic Velocity on the Substrate Dissociation Rate. J Phys Chem B 2016; 121:3437-3442. [PMID: 28423908 DOI: 10.1021/acs.jpcb.6b09055] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
Enzymes are biological catalysts that play a fundamental role in all living systems by supporting the selectivity and the speed for almost all cellular processes. While the general principles of enzyme functioning are known, the specific details of how they work at the microscopic level are not always available. Simple Michaelis-Menten kinetics assumes that the enzyme-substrate complex has only one conformation that decays as a single exponential. As a consequence, the enzymatic velocity decreases as the dissociation (off) rate constant of the complex increases. Recently, Reuveni et al. [ Proc. Natl. Acad. Sci. USA 2014 , 111 , 4391 - 4396 ] showed that it is possible for the enzymatic velocity to increase when the off rate becomes higher, if the enzyme-substrate complex has many conformations which dissociate with the same off rate constant. This was done using formal mathematical arguments, without specifying the nature of the dynamics of the enzyme-substrate complex. In order to provide a physical basis for this unexpected result, we derive an analytical expression for the enzymatic velocity assuming that the enzyme-substrate complex has multiple states and its conformational dynamics is described by rate equations with arbitrary rate constants. By applying our formalism to a complex with two conformations, we show that the unexpected off rate dependence of the velocity can be readily understood: If one of the conformations is unproductive, the system can escape from this "trap" by dissociating, thereby giving the enzyme another chance to form the productive enzyme-substrate complex. We also demonstrate that the nonmonotonic off rate dependence of the enzymatic velocity is possible not only when all off rate constants are identical, but even when they are different. We show that for typical experimentally determined rate constants, the nonmonotonic off rate dependence can occur for micromolar substrate concentrations. Finally, we discuss the relation of this work to the problem of optimizing the flux through singly occupied membrane channels and transporters.
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Affiliation(s)
- Alexander M Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health , Bethesda, Maryland 20892, United States
| | - Attila Szabo
- Laboratory of Chemical Physics, National institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health , Bethesda, Maryland 20892, United States
| | - T Rotbart
- School of Chemistry, Tel-Aviv University , Tel-Aviv 69978, Israel.,The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University , Tel Aviv 69978, Israel
| | - M Urbakh
- School of Chemistry, Tel-Aviv University , Tel-Aviv 69978, Israel.,The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University , Tel Aviv 69978, Israel
| | - Anatoly B Kolomeisky
- Department of Chemistry, Center for Theoretical Biological Physics, Rice University , Houston, Texas 77005, United States
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31
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Loring RF. Lattice model of spatial correlations in catalysis. J Chem Phys 2016; 145:134508. [DOI: 10.1063/1.4964282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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32
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Pérez-Rodríguez G, Gameiro D, Pérez-Pérez M, Lourenço A, Azevedo NF. Single Molecule Simulation of Diffusion and Enzyme Kinetics. J Phys Chem B 2016; 120:3809-20. [DOI: 10.1021/acs.jpcb.5b12544] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gael Pérez-Rodríguez
- ESEI:
Escuela Superior de Ingeniería Informática, University of Vigo, Edificio Politécnico, Campus Universitario As Lagoas s/n, 32004 Ourense, Spain
| | - Denise Gameiro
- LEPABE
− Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
| | - Martín Pérez-Pérez
- ESEI:
Escuela Superior de Ingeniería Informática, University of Vigo, Edificio Politécnico, Campus Universitario As Lagoas s/n, 32004 Ourense, Spain
| | - Anália Lourenço
- ESEI:
Escuela Superior de Ingeniería Informática, University of Vigo, Edificio Politécnico, Campus Universitario As Lagoas s/n, 32004 Ourense, Spain
- CEB
- Centre of Biological Engineering, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal
| | - Nuno F. Azevedo
- LEPABE
− Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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33
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Barel I, Reich NO, Brown FLH. Extracting enzyme processivity from kinetic assays. J Chem Phys 2015; 143:224115. [DOI: 10.1063/1.4937155] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Itay Barel
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Norbert O. Reich
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
| | - Frank L. H. Brown
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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34
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Rotbart T, Reuveni S, Urbakh M. Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:060101. [PMID: 26764608 DOI: 10.1103/physreve.92.060101] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2015] [Indexed: 05/27/2023]
Abstract
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
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Affiliation(s)
- Tal Rotbart
- School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel
| | - Shlomi Reuveni
- Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
| | - Michael Urbakh
- School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel
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35
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Affiliation(s)
- Andre C. Barato
- II. Institut
für Theoretische
Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut
für Theoretische
Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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36
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Wang Z, Lu HP. Probing Single-Molecule Protein Spontaneous Folding–Unfolding Conformational Fluctuation Dynamics: The Multiple-State and Multiple-Pathway Energy Landscape. J Phys Chem B 2015; 119:6366-78. [DOI: 10.1021/acs.jpcb.5b00735] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Zijian Wang
- Center for Photochemical
Sciences, Department of Chemistry, Bowling Green State University, Bowling
Green, Ohio 43403, United States
| | - H. Peter Lu
- Center for Photochemical
Sciences, Department of Chemistry, Bowling Green State University, Bowling
Green, Ohio 43403, United States
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37
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Xu B, Jiang W, Liu F, Yu Y, Dong J. Reactivity of Dinuclear Copper(II) Complexes with
N
-Salicylidene Glycine Schiff Bases as Carboxylesterase Models. INT J CHEM KINET 2015. [DOI: 10.1002/kin.20904] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Bin Xu
- School of Chemical and Pharmaceutical Engineering; Sichuan University of Science & Engineering; Sichuan Zigong 643000 People's Republic of China
- Key Laboratory of Green Catalysis of Sichuan Institute of High Education; Sicuan Zigong 643000 People's Republic of China
| | - Weidong Jiang
- School of Chemical and Pharmaceutical Engineering; Sichuan University of Science & Engineering; Sichuan Zigong 643000 People's Republic of China
- Key Laboratory of Green Catalysis of Sichuan Institute of High Education; Sicuan Zigong 643000 People's Republic of China
| | - Fuan Liu
- Key Laboratory of Green Catalysis of Sichuan Institute of High Education; Sicuan Zigong 643000 People's Republic of China
| | - Yongde Yu
- School of Chemical and Pharmaceutical Engineering; Sichuan University of Science & Engineering; Sichuan Zigong 643000 People's Republic of China
| | - Juan Dong
- School of Chemical and Pharmaceutical Engineering; Sichuan University of Science & Engineering; Sichuan Zigong 643000 People's Republic of China
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38
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Lervik A, Kjelstrup S, Qian H. Michaelis–Menten kinetics under non-isothermal conditions. Phys Chem Chem Phys 2015; 17:1317-24. [DOI: 10.1039/c4cp04334k] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We extend the celebrated Michaelis–Menten kinetics description of an enzymatic reaction taking into consideration the presence of a thermal driving force.
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Affiliation(s)
- Anders Lervik
- Department of Chemistry
- Norwegian University of Science and Technology
- Trondheim
- Norway
| | - Signe Kjelstrup
- Department of Chemistry
- Norwegian University of Science and Technology
- Trondheim
- Norway
- Process and Energy Laboratory
| | - Hong Qian
- Department of Applied Mathematics
- University of Washington
- Washington
- USA
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39
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Zhang Y, Song P, Fu Q, Ruan M, Xu W. Single-molecule chemical reaction reveals molecular reaction kinetics and dynamics. Nat Commun 2014; 5:4238. [PMID: 24963600 DOI: 10.1038/ncomms5238] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2013] [Accepted: 05/28/2014] [Indexed: 12/11/2022] Open
Abstract
Understanding the microscopic elementary process of chemical reactions, especially in condensed phase, is highly desirable for improvement of efficiencies in industrial chemical processes. Here we show an approach to gaining new insights into elementary reactions in condensed phase by combining quantum chemical calculations with a single-molecule analysis. Elementary chemical reactions in liquid-phase, revealed from quantum chemical calculations, are studied by tracking the fluorescence of single dye molecules undergoing a reversible redox process. Statistical analyses of single-molecule trajectories reveal molecular reaction kinetics and dynamics of elementary reactions. The reactivity dynamic fluctuations of single molecules are evidenced and probably arise from either or both of the low-frequency approach of the molecule to the internal surface of the SiO2 nanosphere or the molecule diffusion-induced memory effect. This new approach could be applied to other chemical reactions in liquid phase to gain more insight into their molecular reaction kinetics and the dynamics of elementary steps.
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Affiliation(s)
- Yuwei Zhang
- 1] State Key Laboratory of Electroanalytical Chemistry, Jilin Province Key Laboratory of Low Carbon Chemical Power, Changchun Institute of Applied Chemistry, Chinese Academy of Science, 5625 Renmin Street, Changchun 130022, China [2]
| | - Ping Song
- 1] State Key Laboratory of Electroanalytical Chemistry, Jilin Province Key Laboratory of Low Carbon Chemical Power, Changchun Institute of Applied Chemistry, Chinese Academy of Science, 5625 Renmin Street, Changchun 130022, China [2]
| | - Qiang Fu
- 1] State Key Laboratory of Electroanalytical Chemistry, Jilin Province Key Laboratory of Low Carbon Chemical Power, Changchun Institute of Applied Chemistry, Chinese Academy of Science, 5625 Renmin Street, Changchun 130022, China [2] Graduate University of Chinese Academy of Science, Beijing 100049, China
| | - Mingbo Ruan
- State Key Laboratory of Electroanalytical Chemistry, Jilin Province Key Laboratory of Low Carbon Chemical Power, Changchun Institute of Applied Chemistry, Chinese Academy of Science, 5625 Renmin Street, Changchun 130022, China
| | - Weilin Xu
- State Key Laboratory of Electroanalytical Chemistry, Jilin Province Key Laboratory of Low Carbon Chemical Power, Changchun Institute of Applied Chemistry, Chinese Academy of Science, 5625 Renmin Street, Changchun 130022, China
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Abstract
The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover--turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.
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Bruno WJ, Ullah G, Mak DOD, Pearson JE. Automated maximum likelihood separation of signal from baseline in noisy quantal data. Biophys J 2014; 105:68-79. [PMID: 23823225 DOI: 10.1016/j.bpj.2013.02.060] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2012] [Revised: 01/03/2013] [Accepted: 02/25/2013] [Indexed: 10/26/2022] Open
Abstract
Data recordings often include high-frequency noise and baseline fluctuations that are not generated by the system under investigation, which need to be removed before analyzing the signal for the system's behavior. In the absence of an automated method, experimentalists fall back on manual procedures for removing these fluctuations, which can be laborious and prone to subjective bias. We introduce a maximum likelihood formalism for separating signal from a drifting baseline plus noise, when the signal takes on integer multiples of some value, as in ion channel patch-clamp current traces. Parameters such as the quantal step size (e.g., current passing through a single channel), noise amplitude, and baseline drift rate can all be optimized automatically using the expectation-maximization algorithm, taking the number of open channels (or molecules in the on-state) at each time point as a hidden variable. Our goal here is to reconstruct the signal, not model the (possibly highly complex) underlying system dynamics. Thus, our likelihood function is independent of those dynamics. This may be thought of as restricting to the simplest possible hidden Markov model for the underlying channel current, in which successive measurements of the state of the channel(s) are independent. The resulting method is comparable to an experienced human in terms of results, but much faster. FORTRAN 90, C, R, and JAVA codes that implement the algorithm are available for download from our website.
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Affiliation(s)
- William J Bruno
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
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43
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Schwabe A, Maarleveld TR, Bruggeman FJ. Exploration of the spontaneous fluctuating activity of single enzyme molecules. FEBS Lett 2013; 587:2744-52. [PMID: 23850890 DOI: 10.1016/j.febslet.2013.07.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2013] [Revised: 07/01/2013] [Accepted: 07/02/2013] [Indexed: 11/30/2022]
Abstract
Single enzyme molecules display inevitable, stochastic fluctuations in their catalytic activity. In metabolism, for instance, the stochastic activity of individual enzymes is averaged out due to their high copy numbers per single cell. However, many processes inside cells rely on single enzyme activity, such as transcription, replication, translation, and histone modifications. Here we introduce the main theoretical concepts of stochastic single-enzyme activity starting from the Michaelis-Menten enzyme mechanism. Next, we discuss stochasticity of multi-substrate enzymes, of enzymes and receptors with multiple conformational states and finally, how fluctuations in receptor activity arise from fluctuations in signal concentration. This paper aims to introduce the exciting field of single-molecule enzyme kinetics and stochasticity to a wider audience of biochemists and systems biologists.
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Affiliation(s)
- Anne Schwabe
- Systems Bioinformatics, Amsterdam Institute for Molecules, Medicines and Systems, VU University Amsterdam, De Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands.
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Li CB, Komatsuzaki T. Aggregated markov model using time series of single molecule dwell times with minimum excessive information. PHYSICAL REVIEW LETTERS 2013; 111:058301. [PMID: 23952451 DOI: 10.1103/physrevlett.111.058301] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2012] [Indexed: 06/02/2023]
Abstract
Statistics of the dwell times, the stationary state distributions (SSDs), are often studied to infer the underlying kinetics from a single molecule finite-level time series. However, it is well known that the underlying kinetic scheme, a hidden Markov model (HMM), cannot be identified uniquely from the SSDs because some features of the underlying HMM are hidden by finite-level measurements. Here, we quantify the amount of excessive information in a given HMM that is not warranted by the measured SSDs and extract the HMM with minimum excessive information as the most objective representation of the data. The method is applied to a single molecule enzymatic turnover experiment, and the origin of dynamic disorder is discussed in terms of the network properties of the HMM.
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Affiliation(s)
- Chun-Biu Li
- Molecule and Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan
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Chaudhury S, Cao J, Sinitsyn NA. Universality of Poisson Indicator and Fano Factor of Transport Event Statistics in Ion Channels and Enzyme Kinetics. J Phys Chem B 2013. [DOI: 10.1021/jp3096659] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Srabanti Chaudhury
- Theoretical Division, Los Alamos National Laboratory, Los
Alamos, New Mexico, 87545 United States
- New Mexico Consortium,
Los Alamos, New Mexico, 87544 United States
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts,
02139 United States
| | - Nikolai A. Sinitsyn
- Theoretical Division, Los Alamos National Laboratory, Los
Alamos, New Mexico, 87545 United States
- New Mexico Consortium,
Los Alamos, New Mexico, 87544 United States
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46
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Wu J, Liu F, Ma J, Silbey RJ, Cao J. Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis. J Chem Phys 2012; 137:174111. [DOI: 10.1063/1.4762839] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Jarboe LR, Liu P, Kautharapu KB, Ingram LO. Optimization of enzyme parameters for fermentative production of biorenewable fuels and chemicals. Comput Struct Biotechnol J 2012; 3:e201210005. [PMID: 24688665 PMCID: PMC3962213 DOI: 10.5936/csbj.201210005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2012] [Revised: 10/21/2012] [Accepted: 10/24/2012] [Indexed: 12/23/2022] Open
Abstract
Microbial biocatalysts such as Escherichia coli and Saccharomyces cerevisiae have been extensively subjected to Metabolic Engineering for the fermentative production of biorenewable fuels and chemicals. This often entails the introduction of new enzymes, deletion of unwanted enzymes and efforts to fine-tune enzyme abundance in order to attain the desired strain performance. Enzyme performance can be quantitatively described in terms of the Michaelis-Menten type parameters Km, turnover number kcat and Ki, which roughly describe the affinity of an enzyme for its substrate, the speed of a reaction and the enzyme sensitivity to inhibition by regulatory molecules. Here we describe examples of where knowledge of these parameters have been used to select, evolve or engineer enzymes for the desired performance and enabled increased production of biorenewable fuels and chemicals. Examples include production of ethanol, isobutanol, 1-butanol and tyrosine and furfural tolerance. The Michaelis-Menten parameters can also be used to judge the cofactor dependence of enzymes and quantify their preference for NADH or NADPH. Similarly, enzymes can be selected, evolved or engineered for the preferred cofactor preference. Examples of exporter engineering and selection are also discussed in the context of production of malate, valine and limonene.
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Affiliation(s)
- Laura R Jarboe
- Chemical and Biological Engineering, Iowa State University, Ames, Iowa, USA ; Microbiology, Iowa State University, Ames, Iowa, USA
| | - Ping Liu
- Microbiology, Iowa State University, Ames, Iowa, USA
| | | | - Lonnie O Ingram
- Microbiology and Cell Science, University of Florida, Gainesville, Florida, USA
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Yang J, Pearson JE. Origins of concentration dependence of waiting times for single-molecule fluorescence binding. J Chem Phys 2012; 136:244506. [PMID: 22755586 DOI: 10.1063/1.4729947] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Binary fluorescence time series obtained from single-molecule imaging experiments can be used to infer protein binding kinetics, in particular, association and dissociation rate constants from waiting time statistics of fluorescence intensity changes. In many cases, rate constants inferred from fluorescence time series exhibit nonintuitive dependence on ligand concentration. Here, we examine several possible mechanistic and technical origins that may induce ligand dependence of rate constants. Using aggregated Markov models, we show under the condition of detailed balance that non-fluorescent bindings and missed events due to transient interactions, instead of conformation fluctuations, may underly the dependence of waiting times and thus apparent rate constants on ligand concentrations. In general, waiting times are rational functions of ligand concentration. The shape of concentration dependence is qualitatively affected by the number of binding sites in the single molecule and is quantitatively tuned by model parameters. We also show that ligand dependence can be caused by non-equilibrium conditions which result in violations of detailed balance and require an energy source. As to a different but significant mechanism, we examine the effect of ambient buffers that can substantially reduce the effective concentration of ligands that interact with the single molecules. To demonstrate the effects by these mechanisms, we applied our results to analyze the concentration dependence in a single-molecule experiment EGFR binding to fluorophore-labeled adaptor protein Grb2 by Morimatsu et al. [Proc. Natl. Acad. Sci. U.S.A. 104, 18013 (2007)].
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Affiliation(s)
- Jin Yang
- Chinese Academy of Sciences and Max Plank Society Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Shanghai 200031, China.
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Lim YR, Park SJ, Lee SY, Sung JY. Nonclassical Chemical Kinetics for Description of Chemical Fluctuation in a Dynamically Heterogeneous Biological System. B KOREAN CHEM SOC 2012. [DOI: 10.5012/bkcs.2012.33.3.963] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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50
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Lim YR, Park SJ, Park BJ, Cao J, Silbey RJ, Sung J. Reaction Event Counting Statistics of Biopolymer Reaction Systems with Dynamic Heterogeneity. J Chem Theory Comput 2012; 8:1415-25. [DOI: 10.1021/ct200785q] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yu Rim Lim
- Department of Chemistry, Chung-Ang
University, Seoul 156-756, Korea
| | - Seong Jun Park
- Department of Chemistry, Chung-Ang
University, Seoul 156-756, Korea
| | - Bo Jung Park
- Department of Chemistry, Chung-Ang
University, Seoul 156-756, Korea
| | - Jianshu Cao
- Department of Chemistry, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Robert J. Silbey
- Department of Chemistry, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Jaeyoung Sung
- Department of Chemistry, Chung-Ang
University, Seoul 156-756, Korea
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