Unraveling mechanisms from waiting time distributions in single-nanoparticle catalysis.
28 May 2019-Journal of Chemical Physics (AIP Publishing LLCAIP Publishing)-Vol. 150, Iss: 20, pp 204119-204119
TL;DR: This work provides a mechanistic origin of the coupling between the kinetics of catalytic turnovers and surface restructuring dynamics and yields a systematic way to compute catalytic rates from distributions of waiting times between product turnovers in the presence of surface restructuring.
Abstract: The catalytic conversion of substrates to products at the surface of a single nanoparticle cluster can now be resolved at the molecular scale and the waiting time between individual product turnovers measured with precision. The distribution of waiting times and, in particular, their means and variances can thus be obtained experimentally. Here, we show how theoretical modeling based on the chemical master equation (CME) provides a powerful tool to extract catalytic mechanisms and rate parameters from such experimental data. Conjecturing a family of mechanisms that both include and exclude surface restructuring, we obtain the mean and variance of their waiting times from the CME. A detailed analysis of the link between mechanism topology and waiting time dispersion, then, allows us to select several candidate mechanisms, with branched topologies, that can reproduce experimental data. From these, the least complex model that best matches experimental data is chosen as the minimum model. The CME modeling extracts the Langmuir-Hinshelwood mechanism for product formation and two-pathway mechanism for product dissociation, with substantial off-pathway state fluctuations due to surface restructuring dynamics, as the minimal model consistent with data. Our work, thus, provides a mechanistic origin of the coupling between the kinetics of catalytic turnovers and surface restructuring dynamics and yields a systematic way to compute catalytic rates from distributions of waiting times between product turnovers in the presence of surface restructuring.
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TL;DR: In this paper, the size and temperature-dependent structural transitions in gold nanoparticles were revealed with morphology statistics obtained by high-resolution electron microscopic observations for thousands of particles annealed in a helium heat bath.
Abstract: Size- and temperature-dependent structural transitions in gold nanoparticles were revealed with morphology statistics obtained by high-resolution electron microscopic observations for thousands of particles annealed in a helium heat bath. We found that gold nanoparticles over a wide size range, 3-14 nm, undergo a structural transformation from icosahedral to decahedral morphology just below the melting points. It was also clarified that the formation of bulk crystalline structures from the decahedral morphology requires the melt-freeze process due to an insurmountable high free-energy barrier.
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TL;DR: In this paper, the authors define minimal conformational regulation schemes capable of bearing peculiar regulatory properties like cooperativity or substrate inhibition, either in the ensemble or single-molecule case.
Abstract: In searching non-standard ways of conformational regulation, various Michaelis–Menten-like schemes attract relentless attention, resulting in sometimes too sophisticated considerations. With the example of monomeric enzymes possessing an only binding site, we define the minimal schemes capable of bearing peculiar regulatory properties like “cooperativity” or substrate inhibition. The simplest ways of calculating the enzymatic reaction velocity are exemplified, either in the ensemble or single-molecule case.
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TL;DR: In this article , a standard symmetrical random walk with Poissonian resetting in a chain with terminal sinks is considered, and the expressions for probabilities of occupation of chain nodes are obtained for arbitrary values of chain length N, rate k of jumps to adjacent nodes, sink intensities q 0, q N and placements of resetting node n r and starting node n 0.
Abstract: A standard symmetrical random walk with Poissonian resetting in a chain with terminal sinks is considered. The expressions for probabilities of occupation of chain nodes are obtained for arbitrary values of chain length N, rate k of jumps to adjacent nodes, sink intensities q 0, q N and placements of resetting node n r and starting node n 0. These expressions are used for calculating the dependences of the prime characteristics of the process (unconditional and conditional mean first passage/exit times and splitting probabilities W 0, W N ) on resetting rate r. Among a rich variety of process scenarios, the possibility of inverting the ratio W 0/W N with r growing is of special interest. This provides an effective mechanism of controlling the process outcome.
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TL;DR: This study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.
Abstract: The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that "molecular noise" - intrinsic stochasticity at the molecular scale - leads to significant deviations from classical results and to unexpected effects like "molecular memory", i.e., the breakdown of statistical independence between turnover events. Here we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.
2 citations
TL;DR: In this paper, the authors show that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes.
Abstract: The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis–Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that “molecular noise”—intrinsic stochasticity at the molecular scale—leads to significant deviations from classical results and to unexpected effects like “molecular memory,” i.e., the breakdown of statistical independence between turnover events. Here, we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady-states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.
1 citations
References
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TL;DR: In this article, a survey of elementary applications of probability theory can be found, including the following: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Advanced applications: 11. Discrete prior probabilities, the entropy principle 12. Simple applications of decision theory 15.
Abstract: Foreword Preface Part I. Principles and Elementary Applications: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Physics of 'random experiments' Part II. Advanced Applications: 11. Discrete prior probabilities, the entropy principle 12. Ignorance priors and transformation groups 13. Decision theory: historical background 14. Simple applications of decision theory 15. Paradoxes of probability theory 16. Orthodox methods: historical background 17. Principles and pathology of orthodox statistics 18. The Ap distribution and rule of succession 19. Physical measurements 20. Model comparison 21. Outliers and robustness 22. Introduction to communication theory References Appendix A. Other approaches to probability theory Appendix B. Mathematical formalities and style Appendix C. Convolutions and cumulants.
4,641 citations
TL;DR: A molecular memory phenomenon, in which an enzymatic turnover was not independent of its previous turnovers because of a slow fluctuated of protein conformation, was evidenced by spontaneous spectral fluctuation of FAD.
Abstract: Enzymatic turnovers of single cholesterol oxidase molecules were observed in real time by monitoring the emission from the enzyme's fluorescent active site, flavin adenine dinucleotide (FAD). Statistical analyses of single-molecule trajectories revealed a significant and slow fluctuation in the rate of cholesterol oxidation by FAD. The static disorder and dynamic disorder of reaction rates, which are essentially indistinguishable in ensemble-averaged experiments, were determined separately by the real-time single-molecule approach. A molecular memory phenomenon, in which an enzymatic turnover was not independent of its previous turnovers because of a slow fluctuation of protein conformation, was evidenced by spontaneous spectral fluctuation of FAD.
1,352 citations
TL;DR: It is proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.
Abstract: Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual b-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.
735 citations
TL;DR: This study uses single-molecule fluorescence microscopy to study the size-dependent catalytic activity and dynamics of spherical Au-nanoparticles under ambient solution conditions and provides estimates on the activation energies and time scales of spontaneous dynamic surface restructuring that are fundamental to heterogeneous catalysis in both the nano- and the macro-scale.
Abstract: Nanoparticles are important catalysts for petroleum processing, energy conversion, and pollutant removal. As compared to their bulk counterparts, their often superior or new catalytic properties result from their nanometer size, which gives them increased surface-to-volume ratios and chemical potentials. The size of nanoparticles is thus pivotal for their catalytic properties. Here, we use single-molecule fluorescence microscopy to study the size-dependent catalytic activity and dynamics of spherical Au-nanoparticles under ambient solution conditions. By monitoring the catalysis of individual Au-nanoparticles of three different sizes in real time with single-turnover resolution, we observe clear size-dependent activities in both the catalytic product formation reaction and the product dissociation reaction. Within a model of classical thermodynamics, these size-dependent activities of Au-nanoparticles can be accounted for by the changes in the adsorption free energies of the substrate resazurin and the product resorufin because of the nanosize effect. We also observe size-dependent differential selectivity of the Au-nanoparticles between two parallel product dissociation pathways, with larger nanoparticles less selective between the two pathways. The particle size also strongly influences the surface-restructuring-coupled catalytic dynamics; both the catalysis-induced and the spontaneous dynamic surface restructuring occur more readily for smaller Au-nanoparticles due to their higher surface energies. Using a simple thermodynamic model, we analyze the catalysis- and size-dependent dynamic surface restructuring quantitatively; the results provide estimates on the activation energies and time scales of spontaneous dynamic surface restructuring that are fundamental to heterogeneous catalysis in both the nano- and the macro-scale. This study further exemplifies the power of the single-molecule approach in probing the intricate workings of nanoscale catalysts.
492 citations
TL;DR: The results exemplify the power of the single-molecule approach in revealing the interplay of catalysis, heterogeneous reactivity and surface structural dynamics in nanocatalysis.
Abstract: Nanoparticles are important catalysts for many chemical transformations. However, owing to their structural dispersions, heterogeneous distribution of surface sites and surface restructuring dynamics, nanoparticles are intrinsically heterogeneous and challenging to characterize in ensemble measurements. Using a single-nanoparticle single-turnover approach, we study the redox catalysis of individual colloidal Au nanoparticles in solution, using single-molecule detection of fluorogenic reactions. We find that for product generation, all Au nanoparticles follow a Langmuir-Hinshelwood mechanism but with heterogeneous reactivity; and for product dissociation, three nanoparticle subpopulations are present that show heterogeneous reactivity between multiple dissociation pathways with distinct kinetics. Correlation analyses of single-turnover waiting times further reveal activity fluctuations of individual Au nanoparticles, attributable to both catalysis-induced and spontaneous dynamic surface restructuring that occurs at different timescales at the surface catalytic and product docking sites. The results exemplify the power of the single-molecule approach in revealing the interplay of catalysis, heterogeneous reactivity and surface structural dynamics in nanocatalysis.
383 citations