Comment on “Nonrenewal Statistics in the Catalytic Activity of Enzyme Molecules at Mesoscopic Concentrations”

Jeong, In-Chun; Song, Sanggeun; Kim, Dae Hyun; Park, Seong Jun; Kim, Jihyun; Sung, Jaeyoung

doi:10.1103/physrevlett.119.099801

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…In contrast, for a multi-step reaction process, shown in Fig 1C, the TCF of the product creation rate becomes an oscillatory function of time as the step number increases, so that the FSRR is a non-monotonic function with one or more peaks (see Eq S2-12). The oscillatory feature in the TCF of the product creation rate can be understood from the degradation-free mean product number, hn(t)i � , under the synchronized initial condition that the reaction event counting begins at the time when a reaction event is completed [55,59]. The TCF of the product creation rate is related to [55], enabling to calculate the rate correlation with hn(t)i � directly obtained from simulations as shown in Fig 1F. As the number, l, of steps involved in the creation process increases, reaction times are more narrowly distributed around the mean reaction time, hti(= hRi −1 ); in the large-l limit, the reaction time distribution approaches a Dirac delta function given by δ(t−hti).…”

Section: General Theorymentioning

confidence: 99%

“…As shown in Fig 2B and 2C, the frequency spectrum of the rate fluctuation is far more sensitive to the reaction dynamics, or the lifetime distribution of the enzyme-substrate complex, than the frequency spectrum of the product number fluctuation. It is worth mentioning that the reaction process of multiple enzymes is not a renewal process, even when the reaction process of individual enzyme is [59,67]. Nevertheless, given that the correlation between different enzymes is negligible, the FSRR, S ðnÞ R ðoÞ, of n enzymes is simply given by nS ð1Þ R ðoÞ, where S ð1Þ R ðoÞ denotes the FSRR of a single enzyme reaction, given by Eq 6.…”

Section: Application To Non-classical Enzyme Kinetic Modelsmentioning

confidence: 99%

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Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

et al. 2019

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Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

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Section: General Theorymentioning

confidence: 99%

Section: Application To Non-classical Enzyme Kinetic Modelsmentioning

confidence: 99%

Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

et al. 2019

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“…This result is in direct contradiction with the assertion made in ref 31 stating that the MM equation does not hold for a mesoscopic enzyme system. 32 In the presence of strong heterogeneity in K M , the mean enzyme reaction rate can deviate from the MM equation even in the steady state, 20 which can be analyzed with use of the method presented in refs 33 or 34.…”

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confidence: 99%

Nonclassical Kinetics of Clonal yet Heterogeneous Enzymes

Park

Song

Jeong

et al. 2017

J. Phys. Chem. Lett.

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Enzyme-to-enzyme variation in the catalytic rate is ubiquitous among single enzymes created from the same genetic information, which persists over the lifetimes of living cells. Despite advances in single-enzyme technologies, the lack of an enzyme reaction model accounting for the heterogeneous activity of single enzymes has hindered a quantitative understanding of the nonclassical stochastic outcome of single enzyme systems. Here we present a new statistical kinetics and exactly solvable models for clonal yet heterogeneous enzymes with possibly nonergodic state dynamics and state-dependent reactivity, which enable a quantitative understanding of modern single-enzyme experimental results for the mean and fluctuation in the number of product molecules created by single enzymes. We also propose a new experimental measure of the heterogeneity and nonergodicity for a system of enzymes.

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