1
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Kanehira Y, Kogikoski S, Titov E, Tapio K, Mostafa A, Bald I. Watching a Single Enzyme at Work Using Single-Molecule Surface-Enhanced Raman Scattering and DNA Origami-Based Plasmonic Antennas. ACS NANO 2024; 18:20191-20200. [PMID: 39074854 PMCID: PMC11308918 DOI: 10.1021/acsnano.4c03384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 07/12/2024] [Accepted: 07/18/2024] [Indexed: 07/31/2024]
Abstract
The detection of a single-enzyme catalytic reaction by surfaced-enhanced Raman scattering (SERS) is presented by utilizing DNA origami-based plasmonic antennas. A single horseradish peroxidase (HRP) was accommodated on a DNA origami nanofork plasmonic antenna (DONA) containing gold nanoparticles, enabling the tracing of single-molecule SERS signals during the peroxide reduction reaction. This allows monitoring of the structure of a single enzymatic catalytic center and products under suitable liquid conditions. Herein, we demonstrate the chemical changes of HRP and the appearance of tetramethylbenzidine (TMB), which works as a hydrogen donor before and after the catalytic reaction. The results show that the iron in HRP adopts Fe4+ and low spin states with the introduction of H2O2, indicating compound-I formation. Density functional theory (DFT) calculations were performed for later catalytic steps to rationalize the experimental Raman/SERS spectra. The presented data provide several possibilities for tracking single biomolecules in situ during a chemical reaction and further developing plasmon-enhanced biocatalysis.
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Affiliation(s)
- Yuya Kanehira
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
| | - Sergio Kogikoski
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
| | - Evgenii Titov
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
| | - Kosti Tapio
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
| | - Amr Mostafa
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
| | - Ilko Bald
- Institute
of Chemistry, University of Potsdam, 14476 Potsdam, Germany
- Dynamics
of Molecules and Clusters Department, J.
Heyrovský Institute of Physical Chemistry of the CAS, Dolejškova 3, 18223 Prague, Czech Republic
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2
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Ye R, Sun X, Mao X, Alfonso FS, Baral S, Liu C, Coates GW, Chen P. Optical sequencing of single synthetic polymers. Nat Chem 2024; 16:210-217. [PMID: 37945834 DOI: 10.1038/s41557-023-01363-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Accepted: 10/06/2023] [Indexed: 11/12/2023]
Abstract
Microscopic sequences of synthetic polymers play crucial roles in the polymer properties, but are generally unknown and inaccessible to traditional measurements. Here we report real-time optical sequencing of single synthetic copolymer chains under living polymerization conditions. We achieve this by carrying out multi-colour imaging of polymer growth by single catalysts at single-monomer resolution using CREATS (coupled reaction approach toward super-resolution imaging). CREATS makes a reaction effectively fluorogenic, enabling single-molecule localization microscopy of chemical reactions at higher reactant concentrations. Our data demonstrate that the chain propagation kinetics of surface-grafted polymerization contains temporal fluctuations with a defined memory time (which can be attributed to neighbouring monomer interactions) and chain-length dependence (due to surface electrostatic effects). Furthermore, the microscopic sequences of individual copolymers reveal their tendency to form block copolymers, and, more importantly, quantify the size distribution of individual blocks for comparison with theoretically random copolymers. Such sequencing capability paves the way for single-chain-level structure-function correlation studies of synthetic polymers.
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Affiliation(s)
- Rong Ye
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
- Department of Chemical Engineering and Catalysis Science and Technology Institute, University of Michigan, Ann Arbor, MI, USA
| | - Xiangcheng Sun
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
- Department of Chemical Engineering, Rochester Institute of Technology, Rochester, NY, USA
| | - Xianwen Mao
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
- Department of Materials Science and Engineering, Institute of Functional Intelligent Materials, and Centre for Advanced 2D Materials, National University of Singapore, Singapore, Singapore
| | - Felix S Alfonso
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
| | - Susil Baral
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
- Department of Chemistry, Illinois State University, Normal, IL, USA
| | - Chunming Liu
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
- School of Polymer Science and Polymer Engineering and Department of Chemistry, University of Akron, Akron, OH, USA
| | - Geoffrey W Coates
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
| | - Peng Chen
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA.
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3
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Defaveri L, Barkai E, Kessler DA. Stretched-exponential relaxation in weakly confined Brownian systems through large deviation theory. Phys Rev E 2024; 109:L022102. [PMID: 38491584 DOI: 10.1103/physreve.109.l022102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 12/15/2023] [Indexed: 03/18/2024]
Abstract
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the droplet radius with an r^{2/3} potential. Here, we study a Brownian particle under the influence of a general confining, albeit weak, potential field that grows with distance as a sublinear power law. We find that for this memoryless model, observables display stretched-exponential relaxation. The probability density function of the system is studied using a rate-function ansatz. We obtain analytically the stretched-exponential exponent along with an anomalous power-law scaling of length with time. The rate function exhibits a point of nonanalyticity, indicating a dynamical phase transition. In particular, the rate function is double valued both to the left and right of this point, leading to four different rate functions, depending on the choice of initial conditions and symmetry.
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Affiliation(s)
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - David A Kessler
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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4
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Kundu P, Saha S, Gangopadhyay G. A minimal kinetic model for the interpretation of complex catalysis in single enzyme molecules. Phys Chem Chem Phys 2023; 26:463-476. [PMID: 38078459 DOI: 10.1039/d3cp01720f] [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: 12/22/2023]
Abstract
Multi-exponential waiting-time distribution and randomness parameter greater than unity ascribe dynamic disorder in single-enzyme catalysis corroborated to the interplay of transforming conformers [English et al., Nat. Chem. Biol., 2006, 2, 87]. The associated multi-state model of enzymatic turnovers with statically heterogeneous catalytic rates misdescribes the non-linear uprising of the randomness parameter from unity in relation to the attributes of the fall-offs of the waiting-time distribution at different substrate concentrations. To resolve this crucial issue, we first employ a comprehensive stochastic reaction scenario and further rationalize and work out the minimal indispensable dynamic-disorder model that ensures the foregoing relationship upon comparison with the data. We elucidate that specific disregard for the transition rate coefficients in the multi-state model on account of the especially slow conformational transitions is the underlying reason for not achieving interrelation between the observables.
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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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5
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Orrit M. Dynamic Heterogeneity in the Optical Signals from Single Nano-Objects. J Phys Chem B 2023; 127:3982-3989. [PMID: 37115719 PMCID: PMC10184125 DOI: 10.1021/acs.jpcb.2c09055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
In contrast to ensemble-averaged measurements, single-molecule experiments directly display the heterogeneity of molecular properties in space and time. In many complex systems, spatial heterogeneity is regularly accompanied by temporal or dynamic heterogeneity; if a property differs from molecule to molecule, it will often vary in time for one and the same molecule. In this short paper, we discuss a few examples of complex systems where dynamical heterogeneity was observed in single-molecule or single-particle optical signals. For single biomolecules, the first demonstration of dynamic heterogeneity in a single enzyme was provided by Xie and colleagues. Other examples are found in glassy systems, and very recently in the magnetic relaxation of single superparamagnetic nanoparticles. The ubiquity of this phenomenon suggests that, rather than an exception, dynamic heterogeneity is the rule in complex systems with multiple degrees of freedom.
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Affiliation(s)
- Michel Orrit
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, Netherlands
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6
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Ahmadi M, Thomas PJ, Buecherl L, Winstead C, Myers CJ, Zheng H. A Comparison of Weighted Stochastic Simulation Methods for the Analysis of Genetic Circuits. ACS Synth Biol 2023; 12:287-304. [PMID: 36583529 DOI: 10.1021/acssynbio.2c00553] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Rare events are of particular interest in synthetic biology because rare biochemical events may be catastrophic to a biological system by, for example, triggering irreversible events such as off-target drug delivery. To estimate the probability of rare events efficiently, several weighted stochastic simulation methods have been developed. Under optimal parameters and model conditions, these methods can greatly improve simulation efficiency in comparison to traditional stochastic simulation. Unfortunately, the optimal parameters and conditions cannot be deduced a priori. This paper presents a critical survey of weighted stochastic simulation methods. It shows that the methods considered here cannot consistently, efficiently, and exactly accomplish the task of rare event simulation without resorting to a computationally expensive calibration procedure, which undermines their overall efficiency. The results suggest that further development is needed before these methods can be deployed for general use in biological simulations.
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Affiliation(s)
- Mohammad Ahmadi
- Department of Computer Science and Engineering, University of South Florida, Tampa, Florida33620-9951, United States
| | - Payton J Thomas
- Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah84112, United States
| | - Lukas Buecherl
- Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, Boulder, Colorado80309-0401, United States
| | - Chris Winstead
- Department of Electrical and Computer Engineering, Utah State University, Logan, Utah84322-1400, United States
| | - Chris J Myers
- Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, Boulder, Colorado80309-0401, United States
| | - Hao Zheng
- Department of Computer Science and Engineering, University of South Florida, Tampa, Florida33620-9951, United States
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7
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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: 3] [Impact Index Per Article: 1.5] [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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8
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Bonomo OL, Pal A, Reuveni S. Mitigating long queues and waiting times with service resetting. PNAS NEXUS 2022; 1:pgac070. [PMID: 36741459 PMCID: PMC9896945 DOI: 10.1093/pnasnexus/pgac070] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Accepted: 05/25/2022] [Indexed: 02/07/2023]
Abstract
What determines the average length of a queue, which stretches in front of a service station? The answer to this question clearly depends on the average rate at which jobs arrive at the queue and on the average rate of service. Somewhat less obvious is the fact that stochastic fluctuations in service and arrival times are also important, and that these are a major source of backlogs and delays. Strategies that could mitigate fluctuations-induced delays are, thus in high demand as queue structures appear in various natural and man-made systems. Here, we demonstrate that a simple service resetting mechanism can reverse the deleterious effects of large fluctuations in service times, thus turning a marked drawback into a favorable advantage. This happens when stochastic fluctuations are intrinsic to the server, and we show that service resetting can then dramatically cut down average queue lengths and waiting times. Remarkably, this strategy is also useful in extreme situations where the variance, and possibly even mean, of the service time diverge-as resetting can then prevent queues from "blowing up." We illustrate these results on the M/G/1 queue in which service times are general and arrivals are assumed to be Markovian. However, the main results and conclusions coming from our analysis are not specific to this particular model system. Thus, the results presented herein can be carried over to other queueing systems: in telecommunications, via computing, and all the way to molecular queues that emerge in enzymatic and metabolic cycles of living organisms.
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Affiliation(s)
- Ofek Lauber Bonomo
- School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel,Center for the Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel,The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Arnab Pal
- School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel,Center for the Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel,The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai 600113, Tamil Nadu, India,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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9
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Adhikari S, Orrit M. Progress and perspectives in single-molecule optical spectroscopy. J Chem Phys 2022; 156:160903. [PMID: 35489995 DOI: 10.1063/5.0087003] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We review some of the progress of single-molecule optical experiments in the past 20 years and propose some perspectives for the coming years. We particularly focus on methodological advances in fluorescence, super-resolution, photothermal contrast, and interferometric scattering and briefly discuss a few of the applications. These advances have enabled the exploration of new emitters and quantum optics; the chemistry and biology of complex heterogeneous systems, nanoparticles, and plasmonics; and the detection and study of non-fluorescing and non-absorbing nano-objects. We conclude by proposing some ideas for future experiments. The field will move toward more and better signals of a broader variety of objects and toward a sharper view of the surprising complexity of the nanoscale world of single (bio-)molecules, nanoparticles, and their nano-environments.
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Affiliation(s)
- Subhasis Adhikari
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2333 CA Leiden, The Netherlands
| | - Michel Orrit
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2333 CA Leiden, The Netherlands
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10
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A single-molecule stochastic theory of protein-ligand binding in the presence of multiple unfolding/folding and ligand binding pathways. Biophys Chem 2022; 285:106803. [DOI: 10.1016/j.bpc.2022.106803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Revised: 03/17/2022] [Accepted: 03/17/2022] [Indexed: 11/19/2022]
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11
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Li J, Xie J, Godec A, Weninger KR, Liu C, Smith JC, Hong L. Non-ergodicity of a globular protein extending beyond its functional timescale. Chem Sci 2022; 13:9668-9677. [PMID: 36091909 PMCID: PMC9400594 DOI: 10.1039/d2sc03069a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 07/18/2022] [Indexed: 11/21/2022] Open
Abstract
Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble. Here, by performing single-molecule fluorescence resonance energy transfer (smFRET) experiments and molecular dynamics (MD) simulations of a multi-domain globular protein, cytoplasmic protein-tyrosine phosphatase (SHP2), we demonstrate that the functional inter-domain motion is observationally non-ergodic over the time spans 10−12 to 10−7 s and 10−1 to 102 s. The difference between observational non-ergodicity and simple non-convergence is discussed. In comparison, a single-strand DNA of similar size behaves ergodically with an energy landscape resembling a one-dimensional linear chain. The observed non-ergodicity results from the hierarchical connectivity of the high-dimensional energy landscape of the protein molecule. As the characteristic time for the protein to conduct its dephosphorylation function is ∼10 s, our findings suggest that, due to the non-ergodicity, individual, seemingly identical protein molecules can be dynamically and functionally different. Internal motions of folded proteins have been assumed to be ergodic, i.e., that the dynamics of a single protein molecule averaged over a very long time resembles that of an ensemble.![]()
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Affiliation(s)
- Jun Li
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - JingFei Xie
- Interdisciplinary Research Center on Biology and Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 201203, China
- University of the Chinese Academy of Sciences, Beijing 100049, China
| | - Aljaž Godec
- Mathematical BioPhysics Group, Max Planck Institute for Biophysical Chemistry, Göttingen 37077, Germany
| | - Keith R. Weninger
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Cong Liu
- Interdisciplinary Research Center on Biology and Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, Chinese Academy of Sciences, Shanghai 201203, China
| | - Jeremy C. Smith
- UT/ORNL Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Liang Hong
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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12
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Moses ME, Lund PM, Bohr SSR, Iversen JF, Kæstel-Hansen J, Kallenbach AS, Iversen L, Christensen SM, Hatzakis NS. Single-Molecule Study of Thermomyces lanuginosus Lipase in a Detergency Application System Reveals Diffusion Pattern Remodeling by Surfactants and Calcium. ACS APPLIED MATERIALS & INTERFACES 2021; 13:33704-33712. [PMID: 34235926 DOI: 10.1021/acsami.1c08809] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Lipases comprise one of the major enzyme classes in biotechnology with applications within, e.g., baking, brewing, biocatalysis, and the detergent industry. Understanding the mechanisms of lipase function and regulation is therefore important to facilitate the optimization of their function by protein engineering. Advances in single-molecule studies in model systems have provided deep mechanistic insights on lipase function, such as the existence of functional states, their dependence on regulatory cues, and their correlation to activity. However, it is unclear how these observations translate to enzyme behavior in applied settings. Here, single-molecule tracking of individual Thermomyces lanuginosus lipase (TLL) enzymes in a detergency application system allowed real-time direct observation of spatiotemporal localization, and thus diffusional behavior, of TLL enzymes on a lard substrate. Parallelized imaging of thousands of individual enzymes allowed us to observe directly the existence and quantify the abundance and interconversion kinetics between three diffusional states that we recently provided evidence to correlate with function. We observe redistribution of the enzyme's diffusional pattern at the lipid-water interface as well as variations in binding efficiency in response to surfactants and calcium, demonstrating that detergency effectors can drive the sampling of lipase functional states. Our single-molecule results combined with ensemble activity assays and enzyme surface binding efficiency readouts allowed us to deconvolute how application conditions can significantly alter protein functional dynamics and/or surface binding, both of which underpin enzyme performance. We anticipate that our results will inspire further efforts to decipher and integrate the dynamic nature of lipases, and other enzymes, in the design of new biotechnological solutions.
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Affiliation(s)
- Matias E Moses
- Novozymes A/S, Biologiens Vej 2, DK-2800 Kgs. Lyngby, Denmark
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Philip M Lund
- Novozymes A/S, Biologiens Vej 2, DK-2800 Kgs. Lyngby, Denmark
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Søren S-R Bohr
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Josephine F Iversen
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Jacob Kæstel-Hansen
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Amalie S Kallenbach
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
| | - Lars Iversen
- Novozymes A/S, Biologiens Vej 2, DK-2800 Kgs. Lyngby, Denmark
| | | | - Nikos S Hatzakis
- Department of Chemistry & Nano-science Center, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark
- Novo Nordisk Foundation Centre for Protein Research, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3B, DK-2200 Copenhagen N, Denmark
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13
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Kundu P, Saha S, Gangopadhyay G. A Revisit to Turnover Kinetics of Individual Escherichia coli β-Galactosidase Molecules. J Phys Chem B 2021; 125:8010-8020. [PMID: 34270240 DOI: 10.1021/acs.jpcb.1c04299] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Single-molecule experiments on β-galactosidase from Escherichia coli that catalyzes the hydrolysis of resorufin-β-d-galactopyranoside revealed important observations like fluctuating catalytic rate, memory effects arising from temporal correlations between the enzymatic turnovers and nonexponential waiting time distributions. The root cause of the observed results is intrinsic fluctuations among the different conformers of the active species, during the course of the reaction, thereby imparting dynamic disorder in the system under investigation. Originally, a multistate stochastic kinetic theory was employed that, despite satisfying the measured waiting time distributions and the mean waiting times at different substrate concentrations, yields a constant estimate of the randomness parameter. Inevitably, this manifests a strong disagreement with the substrate-concentration-dependent time variations of the said distribution, which at the same time misinterprets the measured magnitudes of the randomness parameter at lower concentrations. Here, we suggest a dual approach to the single-enzyme reaction, independently, making important improvements over the parent study and the recently suggested two-state stochastic analyses followed by quantitative rationalization of the experimental data. In the first case, an off-pathway mechanism satisfied the Michaelis-Menten equation under the circumstance of prevailing disorder while tested against the single-molecule data. However, recovery of randomness data in the lower-concentration regime, albeit primarily marks a significant refinement, a qualitative agreement at the growing concentrations seems to be reasoned by an account of switching among the limited numbers of discrete conformers. Consequently, in the second case, we circumvented the conventional way of approaching the enzyme catalysis and mapped the dynamics of structural transitions of the biocatalyst with the temporal fluctuations of the spatial distance between the different locations along a coarse-grained polymer chain. Exploiting a general mechanism for dynamic disorder, a reaction-diffusion formalism yielded an analytical expression for the waiting time distribution of the enzymatic turnovers, from which the mean waiting time and the randomness parameter were readily determined. Application of our results to the findings of the experiment on single β-galactosidase shows a quantitative agreement in each case. This soundly validates the usefulness of accounting for a more rigorous microscopic description pertinent to the conformational multiplicity in rationalizing the real-time data over the routine state-based sketch of the reaction system.
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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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14
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Subramanian S, Jones HB, Frustaci S, Winter S, van der Kamp MW, Arcus VL, Pudney CR, Vollmer F. Sensing Enzyme Activation Heat Capacity at the Single-Molecule Level Using Gold-Nanorod-Based Optical Whispering Gallery Modes. ACS APPLIED NANO MATERIALS 2021; 4:4576-4583. [PMID: 34085031 PMCID: PMC8165693 DOI: 10.1021/acsanm.1c00176] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 03/16/2021] [Indexed: 06/12/2023]
Abstract
Here, we report a label-free gold nanoparticle-based single-molecule optical platform to study the immobilization, activity, and thermodynamics of single enzymes. The sensor uses plasmonic gold nanoparticles coupled to optical whispering gallery modes (WGMs) to probe enzyme conformational dynamics during turnover at a microsecond time resolution. Using a glucosidase enzyme as the model system, we explore the temperature dependence of the enzyme turnover at the single-molecule (SM) level. A recent physical model for understanding enzyme temperature dependencies (macromolecular rate theory; MMRT) has emerged as a powerful tool to study the relationship between enzyme turnover and thermodynamics. Using WGMs, SM enzyme measurements enable us to accurately track turnover as a function of conformational changes and therefore to quantitatively probe the key feature of the MMRT model, the activation heat capacity, at the ultimate level of SM. Our data shows that WGMs are extraordinarily sensitive to protein conformational change and can discern both multiple steps with turnover as well as microscopic conformational substates within those steps. The temperature dependence studies show that the MMRT model can be applied to a range of steps within turnover at the SM scale that is associated with conformational change. Our study validates the notion that MMRT captures differences in dynamics between states. The WGM sensors provide a platform for the quantitative analysis of SM activation heat capacity, applying MMRT to the label-free sensing of microsecond substates of active enzymes.
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Affiliation(s)
- Sivaraman Subramanian
- Living
Systems Institute, Department of Physics & Astronomy, University of Exeter, Exeter EX4 4QD, U.K.
| | - Hannah B.L. Jones
- Department
of Biology and Biochemistry, Centre for Biosensors, Bioelectronics
and Biodevices, University of Bath, Bath BA2 7AY, U.K.
| | - Simona Frustaci
- Living
Systems Institute, Department of Physics & Astronomy, University of Exeter, Exeter EX4 4QD, U.K.
| | - Samuel Winter
- Department
of Biology and Biochemistry, Centre for Biosensors, Bioelectronics
and Biodevices, University of Bath, Bath BA2 7AY, U.K.
| | | | - Vickery L. Arcus
- Te
Aka Ma̅tuatua - School of Science, University of Waikato, Hamilton 3240, New Zealand
| | - Christopher R. Pudney
- Department
of Biology and Biochemistry, Centre for Biosensors, Bioelectronics
and Biodevices, University of Bath, Bath BA2 7AY, U.K.
| | - Frank Vollmer
- Living
Systems Institute, Department of Physics & Astronomy, University of Exeter, Exeter EX4 4QD, U.K.
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15
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Fischer T, Xu Q, Zhao K, Gärtner W, Slavov C, Wachtveitl J. Effect of the PHY Domain on the Photoisomerization Step of the Forward P r →P fr Conversion of a Knotless Phytochrome. Chemistry 2020; 26:17261-17266. [PMID: 32812681 PMCID: PMC7839672 DOI: 10.1002/chem.202003138] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Revised: 08/04/2020] [Indexed: 01/26/2023]
Abstract
Phytochrome photoreceptors operate via photoisomerization of a bound bilin chromophore. Their typical architecture consists of GAF, PAS and PHY domains. Knotless phytochromes lack the PAS domain, while retaining photoconversion abilities, with some being able to photoconvert with just the GAF domain. Therefore, we investigated the ultrafast photoisomerization of the Pr state of a knotless phytochrome to reveal the effect of the PHY domain and its "tongue" region on the transduction of the light signal. We show that the PHY domain does not affect the initial conformational dynamics of the chromophore. However, it significantly accelerates the consecutively induced reorganizational dynamics of the protein, necessary for the progression of the photoisomerization. Consequently, the PHY domain keeps the bilin and its binding pocket in a more reactive conformation, which decreases the extent of protein reorganization required for the chromophore isomerization. Thereby, less energy is lost along nonproductive reaction pathways, resulting in increased efficiency.
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Affiliation(s)
- Tobias Fischer
- Institute of Physical and Theoretical ChemistryGoethe University Frankfurt am MainMax-von-Laue Straße 760438FrankfurtGermany
| | - Qianzhao Xu
- Institute of Analytical ChemistryUniversity of LeipzigLinnéstr. 304103LeipzigGermany
| | - Kai‐Hong Zhao
- Key State Laboratory of Agriculture MicrobiologyHuazhong Agriculture University WuhanShizishan Street, Hongshan DistrictWuhan430070P. R. China
| | - Wolfgang Gärtner
- Institute of Analytical ChemistryUniversity of LeipzigLinnéstr. 304103LeipzigGermany
| | - Chavdar Slavov
- Institute of Physical and Theoretical ChemistryGoethe University Frankfurt am MainMax-von-Laue Straße 760438FrankfurtGermany
| | - Josef Wachtveitl
- Institute of Physical and Theoretical ChemistryGoethe University Frankfurt am MainMax-von-Laue Straße 760438FrankfurtGermany
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16
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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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17
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The interplay between chromophore and protein determines the extended excited state dynamics in a single-domain phytochrome. Proc Natl Acad Sci U S A 2020; 117:16356-16362. [PMID: 32591422 DOI: 10.1073/pnas.1921706117] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Phytochromes are a diverse family of bilin-binding photoreceptors that regulate a wide range of physiological processes. Their photochemical properties make them attractive for applications in optogenetics and superresolution microscopy. Phytochromes undergo reversible photoconversion triggered by the Z ⇄ E photoisomerization about the double bond in the bilin chromophore. However, it is not fully understood at the molecular level how the protein framework facilitates the complex photoisomerization dynamics. We have studied a single-domain bilin-binding photoreceptor All2699g1 (Nostoc sp. PCC 7120) that exhibits photoconversion between the red light-absorbing (Pr) and far red-absorbing (Pfr) states just like canonical phytochromes. We present the crystal structure and examine the photoisomerization mechanism of the Pr form as well as the formation of the primary photoproduct Lumi-R using time-resolved spectroscopy and hybrid quantum mechanics/molecular mechanics simulations. We show that the unusually long excited state lifetime (broad lifetime distribution centered at ∼300 picoseconds) is due to the interactions between the isomerizing pyrrole ring D and an adjacent conserved Tyr142. The decay kinetics shows a strongly distributed character which is imposed by the nonexponential protein dynamics. Our findings offer a mechanistic insight into how the quantum efficiency of the bilin photoisomerization is tuned by the protein environment, thereby providing a structural framework for engineering bilin-based optical agents for imaging and optogenetics applications.
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18
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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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19
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Structural Kinetics of MsbA Investigated by Stopped-Flow Time-Resolved Small-Angle X-Ray Scattering. Structure 2019; 28:348-354.e3. [PMID: 31899087 DOI: 10.1016/j.str.2019.12.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Revised: 10/06/2019] [Accepted: 12/02/2019] [Indexed: 12/19/2022]
Abstract
Recent structures of full-length ATP-binding cassette (ABC) transporter MsbA in different states indicate large conformational changes during the reaction cycle that involve transient dimerization of its nucleotide-binding domains (NBDs). However, a detailed molecular understanding of the structural changes and associated kinetics of MsbA upon ATP binding and hydrolysis is still missing. Here, we employed time-resolved small-angle X-ray scattering, initiated by stopped-flow mixing, to investigate the kinetics and accompanying structural changes of NBD dimerization (upon ATP binding) and subsequent dissociation (upon ATP hydrolysis) in the context of isolated NBDs as well as full-length MsbA in lipid nanodiscs. Our data allowed us to structurally characterize the major states involved in the process and determine time constants for NBD dimerization and dissociation. In the full-length protein, these structural transitions occur on much faster time scales, indicating close-proximity effects and structural coupling of the transmembrane domains with the NBDs.
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20
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Pradhan B, Engelhard C, Van Mulken S, Miao X, Canters GW, Orrit M. Single electron transfer events and dynamical heterogeneity in the small protein azurin from Pseudomonas aeruginosa. Chem Sci 2019; 11:763-771. [PMID: 34123050 PMCID: PMC8146731 DOI: 10.1039/c9sc05405g] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 11/25/2019] [Indexed: 01/07/2023] Open
Abstract
Monitoring the fluorescence of single-dye-labeled azurin molecules, we observed the reaction of azurin with hexacyanoferrate under controlled redox potential yielding data on the timing of individual (forward and backward) electron transfer (ET) events. Change-point analysis of the time traces demonstrates significant fluctuations of ET rates and of mid-point potential E 0. These fluctuations are a signature of dynamical heterogeneity, here observed on a 14 kDa protein, the smallest to date. By correlating changes in forward and backward reaction rates we found that 6% of the observed change events could be explained by a change in midpoint potential, while for 25% a change of the donor-acceptor coupling could explain the data. The remaining 69% are driven by variations in complex association constants or structural changes that cause forward and back ET rates to vary independently. Thus, the observed spread in individual ET rates could be related in a unique way to variations in molecular parameters. The relevance for the understanding of metabolic processes is briefly discussed.
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Affiliation(s)
- Biswajit Pradhan
- Huygens-Kamerlingh Onnes Laboratory, Leiden University 2300 RA Leiden Netherlands
| | | | | | - Xueyan Miao
- School of Public Health, Guilin Medical University 541004 Guilin China
| | - Gerard W Canters
- Huygens-Kamerlingh Onnes Laboratory, Leiden University 2300 RA Leiden Netherlands
| | - Michel Orrit
- Huygens-Kamerlingh Onnes Laboratory, Leiden University 2300 RA Leiden Netherlands
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21
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Bohr SSR, Lund PM, Kallenbach AS, Pinholt H, Thomsen J, Iversen L, Svendsen A, Christensen SM, Hatzakis NS. Direct observation of Thermomyces lanuginosus lipase diffusional states by Single Particle Tracking and their remodeling by mutations and inhibition. Sci Rep 2019; 9:16169. [PMID: 31700110 PMCID: PMC6838188 DOI: 10.1038/s41598-019-52539-1] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Accepted: 10/08/2019] [Indexed: 12/11/2022] Open
Abstract
Lipases are interfacially activated enzymes that catalyze the hydrolysis of ester bonds and constitute prime candidates for industrial and biotechnological applications ranging from detergent industry, to chiral organic synthesis. As a result, there is an incentive to understand the mechanisms underlying lipase activity at the molecular level, so as to be able to design new lipase variants with tailor-made functionalities. Our understanding of lipase function primarily relies on bulk assay averaging the behavior of a high number of enzymes masking structural dynamics and functional heterogeneities. Recent advances in single molecule techniques based on fluorogenic substrate analogues revealed the existence of lipase functional states, and furthermore so how they are remodeled by regulatory cues. Single particle studies of lipases on the other hand directly observed diffusional heterogeneities and suggested lipases to operate in two different modes. Here to decipher how mutations in the lid region controls Thermomyces lanuginosus lipase (TLL) diffusion and function we employed a Single Particle Tracking (SPT) assay to directly observe the spatiotemporal localization of TLL and rationally designed mutants on native substrate surfaces. Parallel imaging of thousands of individual TLL enzymes and HMM analysis allowed us to observe and quantify the diffusion, abundance and microscopic transition rates between three linearly interconverting diffusional states for each lipase. We proposed a model that correlate diffusion with function that allowed us to predict that lipase regulation, via mutations in lid region or product inhibition, primarily operates via biasing transitions to the active states.
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Affiliation(s)
- Søren S-R Bohr
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark
| | - Philip M Lund
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark
| | - Amalie S Kallenbach
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark
| | - Henrik Pinholt
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark
| | - Johannes Thomsen
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark
| | - Lars Iversen
- Novozymes A/S, Krogshøjsvej 36, DK 2880, Bagværd, Denmark
| | - Allan Svendsen
- Novozymes A/S, Krogshøjsvej 36, DK 2880, Bagværd, Denmark
| | | | - Nikos S Hatzakis
- Department of Chemistry & Nanoscience Center, Thorvaldsensvej 40, University of Copenhagen, Frederiksberg C, 1871, Denmark.
- NovoNordisk center for protein research, Novo Nordisk Foundation Centre for Protein Research, University of Copenhagen, Blegdamsvej 3B, 2200, Copenhagen, Denmark.
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22
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Panigrahy M, Kumar A, Chowdhury S, Dua A. Unraveling mechanisms from waiting time distributions in single-nanoparticle catalysis. J Chem Phys 2019; 150:204119. [DOI: 10.1063/1.5087974] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Manmath Panigrahy
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
| | - Ashutosh Kumar
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
| | - Sutirtha Chowdhury
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
| | - Arti Dua
- Department of Chemistry, Indian Institute of Technology, Madras, Chennai 600036, India
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23
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Menges JA, Clasen A, Jourdain M, Beckmann J, Hoffmann C, König J, Jung G. Surface Preparation for Single-Molecule Chemistry. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2019; 35:2506-2516. [PMID: 30664351 DOI: 10.1021/acs.langmuir.8b03603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Immobilization procedures, intended to enable prolonged observation of single molecules by fluorescence microscopy, may generate heterogeneous microenvironments, thus inducing heterogeneity in the molecular behavior. On that account, we propose a straightforward surface preparation procedure for studying chemical reactions on the single-molecule level. Sensor fluorophores were developed, which exhibit dual-emissive characteristics in a homogeneously catalyzed showcase reaction. These molecules undergo a shift of fluorescence wavelength of about 100 nm upon Pd(0)-induced deallylation in the Tsuji-Trost reaction, allowing for separate visualization of the starting material and product. Whereas a simultaneous immobilization of dye and inert silane leads to strongly polydisperse reaction kinetics, a consecutive immobilization routine with deposition of dye molecules as the last step provides substrates underlying the kinetics of ensemble experiments. Also, the found kinetics are unaffected by the chemical variation of inert silanes, nearly uniform, and therefore well reproducible. Additional parameters like photostability, signal-to-noise ratio, dye-molecule density, and spatial distribution of dye molecules are, as well, hardly affected by surface modification in the successive immobilization scheme.
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Affiliation(s)
- Johannes A Menges
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Anne Clasen
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Matthias Jourdain
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Julian Beckmann
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Caroline Hoffmann
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Julien König
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
| | - Gregor Jung
- Biophysical Chemistry , Saarland University , Building B2.2 , 66123 Saarbrücken , Germany
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24
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Matyushov DV. Fluctuation relations, effective temperature, and ageing of enzymes: The case of protein electron transfer. J Mol Liq 2018. [DOI: 10.1016/j.molliq.2018.06.087] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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25
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Kienle DF, Falatach RM, Kaar JL, Schwartz DK. Correlating Structural and Functional Heterogeneity of Immobilized Enzymes. ACS NANO 2018; 12:8091-8103. [PMID: 30067333 DOI: 10.1021/acsnano.8b02956] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Many nanobiotechnology applications rely on stable and efficient integration of functional biomacromolecules with synthetic nanomaterials. Unfortunately, the reasons for the ubiquitous loss of activity of immobilized enzymes remain poorly understood due to the difficulty in distinguishing between distinct molecular-level mechanisms. Here, we employ complementary single-molecule fluorescence methods that independently measure the impact of immobilization on the structure and function ( i. e., substrate binding kinetics) of nitroreductase (NfsB). Stochastic statistical modeling methods were used to unambiguously quantify the effects of immobilized NfsB structural dynamics on function, allowing us to explicitly separate effects due to conformation and accessibility. Interestingly, we found that nonspecifically tethered NfsB exhibited enhanced stability compared to site-specifically tethered NfsB; however, the folded state of site-specifically tethered NfsB had faster substrate binding rates, suggesting improved active site accessibility. This demonstrated an unexpected intrinsic trade-off associated with competing bioconjugation methods, suggesting that it may be necessary to balance conformational stability versus active site accessibility. This nuanced view of the impact of immobilization will facilitate a rational approach to the integration of enzymes with synthetic nanomaterials.
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Affiliation(s)
- Daniel F Kienle
- Department of Chemical and Biological Engineering , University of Colorado , Boulder , Colorado 80309 , United States
| | - Rebecca M Falatach
- Department of Chemical and Biological Engineering , University of Colorado , Boulder , Colorado 80309 , United States
| | - Joel L Kaar
- Department of Chemical and Biological Engineering , University of Colorado , Boulder , Colorado 80309 , United States
| | - Daniel K Schwartz
- Department of Chemical and Biological Engineering , University of Colorado , Boulder , Colorado 80309 , United States
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26
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Wang Y, Zijlstra P. Plasmon-Enhanced Single-Molecule Enzymology. ACS PHOTONICS 2018; 5:3073-3081. [PMID: 30148184 PMCID: PMC6105035 DOI: 10.1021/acsphotonics.8b00327] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2018] [Indexed: 05/06/2023]
Abstract
We present a numerical study on plasmon-enhanced single-molecule enzymology. We combine Brownian dynamics and electromagnetic simulations to calculate the enhancement of fluorescence signals of fluorogenic substrate converted by an enzyme conjugated to a plasmonic particle. We simulate the Brownian motion of a fluorescent product away from the active site of the enzyme, and calculate the photon detection rate taking into account modifications of the excitation and emission processes by coupling to the plasmon. We show that plasmon enhancement can boost the signal-to-noise ratio (SNR) of single turnovers by up to 100 fold compared to confocal microscopy. This enhancement factor is a trade-off between the reduced residence time in the near-field of the particle, and the enhanced emission intensity due to coupling to the plasmon. The enhancement depends on the size, shape and material of the particle and the photophysical properties of the fluorescent product. Our study provides guidelines on how to enhance the SNR of single-molecule enzyme studies and may aid in further understanding and quantifying static and dynamic heterogeneity.
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27
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Robin T, Reuveni S, Urbakh M. Single-molecule theory of enzymatic inhibition. Nat Commun 2018; 9:779. [PMID: 29472579 PMCID: PMC5823943 DOI: 10.1038/s41467-018-02995-6] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2017] [Accepted: 01/12/2018] [Indexed: 12/19/2022] Open
Abstract
The classical theory of enzymatic inhibition takes a deterministic, bulk based approach to quantitatively describe how inhibitors affect the progression of enzymatic reactions. Catalysis at the single-enzyme level is, however, inherently stochastic which could lead to strong deviations from classical predictions. To explore this, we take the single-enzyme perspective and rebuild the theory of enzymatic inhibition from the bottom up. We find that accounting for multi-conformational enzyme structure and intrinsic randomness should strongly change our view on the uncompetitive and mixed modes of inhibition. There, stochastic fluctuations at the single-enzyme level could make inhibitors act as activators; and we state—in terms of experimentally measurable quantities—a mathematical condition for the emergence of this surprising phenomenon. Our findings could explain why certain molecules that inhibit enzymatic activity when substrate concentrations are high, elicit a non-monotonic dose response when substrate concentrations are low. Single molecule approaches demonstrated that enzymatic catalysis is stochastic which could lead to deviations from classical predictions. Here authors rebuild the theory of enzymatic inhibition to show that stochastic fluctuations on the single enzyme level could make inhibitors act as activators.
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Affiliation(s)
- Tal Robin
- School of Chemistry and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801, Tel Aviv, Israel
| | - Shlomi Reuveni
- School of Chemistry and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801, Tel Aviv, Israel. .,Department of Systems Biology, HMS, Harvard University, 200 Longwood Avenue, Boston, MA, 02115, USA.
| | - Michael Urbakh
- School of Chemistry and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, 6997801, Tel Aviv, Israel
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28
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Rodríguez-Padrón D, Puente-Santiago AR, Caballero A, Balu AM, Romero AA, Luque R. Highly efficient direct oxygen electro-reduction by partially unfolded laccases immobilized on waste-derived magnetically separable nanoparticles. NANOSCALE 2018; 10:3961-3968. [PMID: 29424377 DOI: 10.1039/c8nr00512e] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A biocatalytic system based on laccase functionalized waste-derived iron oxide nanoparticles (LAC-DA-Fe2O3) was designed by a mechanochemical approach and employed in the electrocatalytic reduction of oxygen. Full characterization of the obtained bioconjugates revealed that the protein adopted a partially unfolded state. The mentioned configuration, together with the geometry coordination changes along the T1 center can be further related to a high bioelectrocatalytic response. A current density up to 2.9 mA cm-2 has been achieved, which is among the highest values reported in literature for laccase functionalized nanomaterials.
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Affiliation(s)
- Daily Rodríguez-Padrón
- Departamento de Química Orgánica, Grupo FQM-383, Universidad de Córdoba, Campus de Rabanales, Edificio Marie Curie (C-3), Ctra Nnal IV-A, Km 396, E14014, Córdoba, Spain.
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29
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Slow domain reconfiguration causes power-law kinetics in a two-state enzyme. Proc Natl Acad Sci U S A 2018; 115:513-518. [PMID: 29298911 DOI: 10.1073/pnas.1714401115] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.
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30
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Monitoring the Activity of Immobilized Lipase with Quinizarin Diester Fluoro-Chromogenic Probe. Molecules 2017; 22:molecules22122136. [PMID: 29207517 PMCID: PMC6149872 DOI: 10.3390/molecules22122136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Revised: 11/23/2017] [Accepted: 12/01/2017] [Indexed: 11/25/2022] Open
Abstract
Quinizarin diester is used as a fluoro-chromogenic substrate of the activity of lipase supported in poly(methylmetacrylate) beads (CALB, Novozym® 435) dispersed in organic solvents. The monoester and diester of quinizarin are both non-fluorescent species contrasting with the enzymatic product quinizarin that shows optical absorption in the visible region and strong fluorescence signal. The enzymatic conversion is accomplished by spectroscopic measurements and it follows a sigmoid curve from which the mean reaction time of the enzymatic process can be determined. This parameter indicates the enzyme activity of the immobilized lipase. Its dependency with the amount of lipase allowed the determination of the ratio of the catalytic rate and the Michaelis constant (kc/Km) and the experimental value found was (1.0 ± 0.1) × 10−2 mg−1/min in the case of quinizarin diacetate.
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31
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Alaghemandi M, Koller V, Green JR. Nonexponential kinetics of ion pair dissociation in electrofreezing water. Phys Chem Chem Phys 2017; 19:26396-26402. [PMID: 28944386 DOI: 10.1039/c7cp04572g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Temporally- or spatially-heterogeneous environments can participate in many kinetic processes, from chemical reactions and self-assembly to the forced dissociation of biomolecules. Here, we simulate the molecular dynamics of a model ion pair forced to dissociate in an explicit, aqueous solution. Triggering dissociation with an external electric field causes the surrounding water to electrofreeze and the ion pair population to decay nonexponentially. To further probe the role of the aqueous environment in the kinetics, we also simulate dissociation events under a purely mechanical force on the ion pair. In this case, regardless of whether the surrounding water is a liquid or already electrofrozen, the ion pair population decays exponentially with a well-defined rate constant that is specific to the medium and applied force. These simulation data, and the rate parameters we extract, suggest the disordered kinetics in an electrofreezing medium are a result of the comparable time scales of two concurrent processes, electrofreezing and dissociation.
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Affiliation(s)
- Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125, USA.
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32
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Perlík V, Šanda F. Vibrational relaxation beyond the linear damping limit in two-dimensional optical spectra of molecular aggregates. J Chem Phys 2017; 147:084104. [DOI: 10.1063/1.4999680] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Václav Perlík
- Institute of Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 121 16, Czech Republic
| | - František Šanda
- Institute of Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, Prague 121 16, Czech Republic
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33
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Kitagawa K, Blum SA. Structure–Reactivity Studies of Intermediates for Mechanistic Information by Subensemble Fluorescence Microscopy. ACS Catal 2017. [DOI: 10.1021/acscatal.7b00627] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kazuhiro Kitagawa
- Department of Chemistry, University of California, Irvine, California 92697−2025, United States
| | - Suzanne A. Blum
- Department of Chemistry, University of California, Irvine, California 92697−2025, United States
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34
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Chen H, Thill P, Cao J. Transitions in genetic toggle switches driven by dynamic disorder in rate coefficients. J Chem Phys 2017; 144:175104. [PMID: 27155656 DOI: 10.1063/1.4948461] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes with the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.
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Affiliation(s)
- Hang Chen
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Peter Thill
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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35
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Haddadian EJ, Zhang H, Freed KF, Douglas JF. Comparative Study of the Collective Dynamics of Proteins and Inorganic Nanoparticles. Sci Rep 2017; 7:41671. [PMID: 28176808 PMCID: PMC5296861 DOI: 10.1038/srep41671] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2015] [Accepted: 12/14/2016] [Indexed: 12/16/2022] Open
Abstract
Molecular dynamics simulations of ubiquitin in water/glycerol solutions are used to test the suggestion by Karplus and coworkers that proteins in their biologically active state should exhibit a dynamics similar to 'surface-melted' inorganic nanoparticles (NPs). Motivated by recent studies indicating that surface-melted inorganic NPs are in a 'glassy' state that is an intermediate dynamical state between a solid and liquid, we probe the validity and significance of this proposed analogy. In particular, atomistic simulations of ubiquitin in solution based on CHARMM36 force field and pre-melted Ni NPs (Voter-Chen Embedded Atom Method potential) indicate a common dynamic heterogeneity, along with other features of glass-forming (GF) liquids such as collective atomic motion in the form of string-like atomic displacements, potential energy fluctuations and particle displacements with long range correlations ('colored' or 'pink' noise), and particle displacement events having a power law scaling in magnitude, as found in earthquakes. On the other hand, we find the dynamics of ubiquitin to be even more like a polycrystalline material in which the α-helix and β-sheet regions of the protein are similar to crystal grains so that the string-like collective atomic motion is concentrated in regions between the α-helix and β-sheet domains.
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Affiliation(s)
- Esmael J Haddadian
- Biological Sciences Collegiate Division, University of Chicago, Chicago, IL 60637, USA
| | - Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Alberta, T6G 1H9 Canada
| | - Karl F Freed
- Department of Chemistry, James Franck Institute, and Computation Institute, University of Chicago, Chicago, IL 60637, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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36
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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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37
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Münninghoff JAW, Elemans JAAW. Chemistry at the square nanometer: reactivity at liquid/solid interfaces revealed with an STM. Chem Commun (Camb) 2017; 53:1769-1788. [DOI: 10.1039/c6cc07862a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
An overview is given of single molecule reactivity at a liquid/solid interface employing a scanning tunneling microscope.
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38
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Hwang W, Lee IB, Hong SC, Hyeon C. Decoding Single Molecule Time Traces with Dynamic Disorder. PLoS Comput Biol 2016; 12:e1005286. [PMID: 28027304 PMCID: PMC5226833 DOI: 10.1371/journal.pcbi.1005286] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Revised: 01/11/2017] [Accepted: 12/07/2016] [Indexed: 12/11/2022] Open
Abstract
Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm—Variational Bayes-double chain Markov model (VB-DCMM)—to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na+ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA. We have developed a new algorithm to better decode single molecule data with dynamic disorder. Our new algorithm, which represents a substantial improvement over other methodologies, can detect the presence of dynamic disorder in each trajectory and quantify the kinetic characteristics of underlying energy landscape. As a model system, we applied our algorithm to the single molecule FRET time traces of H-DNA. While duplex-triplex transitions of H-DNA are conventionally interpreted in terms of two-state kinetics, slowly varying dynamic patterns corresponding to hidden internal states can also be identified from the individual time traces. Our algorithm reveals that at least 4 distinct internal states are required to correctly interpret the data.
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Affiliation(s)
- Wonseok Hwang
- Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Il-Buem Lee
- Department of Physics, Korea University, Seoul, Republic of Korea
| | - Seok-Cheol Hong
- Korea Institute for Advanced Study, Seoul, Republic of Korea
- Department of Physics, Korea University, Seoul, Republic of Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul, Republic of Korea
- * E-mail:
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39
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Kätelhön E, Sepunaru L, Karyakin AA, Compton RG. Can Nanoimpacts Detect Single-Enzyme Activity? Theoretical Considerations and an Experimental Study of Catalase Impacts. ACS Catal 2016. [DOI: 10.1021/acscatal.6b02633] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Enno Kätelhön
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Lior Sepunaru
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Arkady A. Karyakin
- Chemistry
Faculty, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Richard G. Compton
- Department
of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
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40
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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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41
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Manhart M, Kion-Crosby W, Morozov AV. Path statistics, memory, and coarse-graining of continuous-time random walks on networks. J Chem Phys 2016; 143:214106. [PMID: 26646868 DOI: 10.1063/1.4935968] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.
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Affiliation(s)
- Michael Manhart
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Willow Kion-Crosby
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Alexandre V Morozov
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
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42
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Lupo KM, Hinton DA, Ng JD, Padilla NA, Goldsmith RH. Probing Heterogeneity and Bonding at Silica Surfaces through Single-Molecule Investigation of Base-Mediated Linkage Failure. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:9171-9179. [PMID: 27541852 DOI: 10.1021/acs.langmuir.6b02456] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The nature of silica surfaces is relevant to many chemical systems, including heterogeneous catalysis and chromatographies utilizing functionalized-silica stationary phases. Surface linkages must be robust to achieve wide and reliable applicability. However, silyl ether-silica support linkages are known to be susceptible to detachment when exposed to basic conditions. We use single-molecule spectroscopy to examine the rate of surface linkage failure upon exposure to base at a variety of deposition conditions. Kinetic analysis elucidates the role of thermal annealing and addition of blocking layers in increasing stability. Critically, it was found that successful surface modification strategies alter the rate at which base molecules approach the silica surface as opposed to reducing surface linkage reactivity. Our results also demonstrate that the innate structural diversity of the silica surface is likely the cause of observed heterogeneity in surface-linkage disruption kinetics.
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Affiliation(s)
- Katherine M Lupo
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Daniel A Hinton
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - James D Ng
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Nicolas A Padilla
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Randall H Goldsmith
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
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43
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Kumar A, Chatterjee S, Nandi M, Dua A. Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes. J Chem Phys 2016; 145:085103. [DOI: 10.1063/1.4961540] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Berg MA, Darvin JR. Measuring a hidden coordinate: Rate-exchange kinetics from 3D correlation functions. J Chem Phys 2016; 145:054119. [DOI: 10.1063/1.4960186] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mark A. Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - Jason R. Darvin
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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45
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Reuveni S. Optimal Stochastic Restart Renders Fluctuations in First Passage Times Universal. PHYSICAL REVIEW LETTERS 2016; 116:170601. [PMID: 27176510 DOI: 10.1103/physrevlett.116.170601] [Citation(s) in RCA: 95] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Indexed: 05/27/2023]
Abstract
Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT) processes seem to have very little in common but it is actually quite the other way around. Here we show that the relative standard deviation associated with the FPT of an optimally restarted process, i.e., one that is restarted at a constant (nonzero) rate which brings the mean FPT to a minimum, is always unity. We interpret, further generalize, and discuss this finding and the implications arising from it.
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Affiliation(s)
- Shlomi Reuveni
- Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
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46
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Ng JD, Upadhyay SP, Marquard AN, Lupo KM, Hinton DA, Padilla NA, Bates DM, Goldsmith RH. Single-Molecule Investigation of Initiation Dynamics of an Organometallic Catalyst. J Am Chem Soc 2016; 138:3876-83. [PMID: 26944030 DOI: 10.1021/jacs.6b00357] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The action of molecular catalysts comprises multiple microscopic kinetic steps whose nature is of central importance in determining catalyst activity and selectivity. Single-molecule microscopy enables the direct examination of these steps, including elucidation of molecule-to-molecule variability. Such molecular diversity is particularly important for the behavior of molecular catalysts supported at surfaces. We present the first combined investigation of the initiation dynamics of an operational palladium cross-coupling catalyst at the bulk and single-molecule levels, including under turnover conditions. Base-initiated kinetics reveal highly heterogeneous behavior indicative of diverse catalyst population. Unexpectedly, this distribution becomes more heterogeneous at increasing base concentration. We model this behavior with a two-step saturation mechanism and identify specific microscopic steps where chemical variability must exist in order to yield observed behavior. Critically, we reveal how structural diversity at a surface translates into heterogeneity in catalyst behavior, while demonstrating how single-molecule experiments can contribute to understanding of molecular catalysts.
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Affiliation(s)
- James D Ng
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Sunil P Upadhyay
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Angela N Marquard
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Katherine M Lupo
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Daniel A Hinton
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Nicolas A Padilla
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Desiree M Bates
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Randall H Goldsmith
- Department of Chemistry, The University of Wisconsin-Madison , 1101 University Avenue, Madison, Wisconsin 53706, United States
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47
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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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48
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Bian Y, Wang Z, Chen A, Zhao N. Fluctuating bottleneck model studies on kinetics of DNA escape from α-hemolysin nanopores. J Chem Phys 2015; 143:184908. [PMID: 26567685 DOI: 10.1063/1.4935118] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
We have proposed a fluctuation bottleneck (FB) model to investigate the non-exponential kinetics of DNA escape from nanometer-scale pores. The basic idea is that the escape rate is proportional to the fluctuating cross-sectional area of DNA escape channel, the radius r of which undergoes a subdiffusion dynamics subjected to fractional Gaussian noise with power-law memory kernel. Such a FB model facilitates us to obtain the analytical result of the averaged survival probability as a function of time, which can be directly compared to experimental results. Particularly, we have applied our theory to address the escape kinetics of DNA through α-hemolysin nanopores. We find that our theoretical framework can reproduce the experimental results very well in the whole time range with quite reasonable estimation for the intrinsic parameters of the kinetics processes. We believe that FB model has caught some key features regarding the long time kinetics of DNA escape through a nanopore and it might provide a sound starting point to study much wider problems involving anomalous dynamics in confined fluctuating channels.
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Affiliation(s)
- Yukun Bian
- Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
| | - Zilin Wang
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Anpu Chen
- College of Chemistry, Sichuan University, Chengdu 610064, China
| | - Nanrong Zhao
- College of Chemistry, Sichuan University, Chengdu 610064, China
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49
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Govind Rao V, Dhital B, Lu HP. Probing Driving Force and Electron Accepting State Density Dependent Interfacial Electron Transfer Dynamics: Suppressed Fluorescence Blinking of Single Molecules on Indium Tin Oxide Semiconductor. J Phys Chem B 2015; 120:1685-97. [DOI: 10.1021/acs.jpcb.5b08807] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vishal Govind Rao
- Department
of Chemistry and
Center for Photochemical Sciences, Bowling Green State University, Bowling
Green, Ohio 43403, United States
| | - Bharat Dhital
- Department
of Chemistry and
Center for Photochemical Sciences, Bowling Green State University, Bowling
Green, Ohio 43403, United States
| | - H. Peter Lu
- Department
of Chemistry and
Center for Photochemical Sciences, Bowling Green State University, Bowling
Green, Ohio 43403, United States
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50
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Verma SD, Vanden Bout DA, Berg MA. When is a single molecule heterogeneous? A multidimensional answer and its application to dynamics near the glass transition. J Chem Phys 2015; 143:024110. [DOI: 10.1063/1.4926463] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Affiliation(s)
- Sachin Dev Verma
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
| | - David A. Vanden Bout
- Department of Chemistry and Biochemistry, University of Texas, Austin, Texas 78712, USA
| | - Mark A. Berg
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA
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