Kinetics of escape of ssDNA molecules from<i>α</i>-hemolysin nanopores: a dynamic disorder study

Kundu, Prasanta; Saha, Sajal; Gangopadhyay, Gautam

doi:10.1088/1742-5468/ab7f31

Cited by 3 publications

(6 citation statements)

References 27 publications

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“…Utilizing Zwanzig’s indirect approach, a detailed calculation then yields the Smoluchowski equation for the noise averaged survival probability with a quadratic sink, stated as follows where the time-dependent diffusion coefficient . We encountered similar equations in the recent studies of force unfolding of a protein molecule and the escape of ssDNA molecules from an α -hemolysin channel under the force clamp and voltage clamp conditions, respectively. Starting from eq , details of the steps to get an expression for the survival probability in the Laplace domain are outlined in these references.…”

Section: Single-enzyme Dynamics In Catalysissupporting

confidence: 53%

“…In the second case, we avoid the mechanistic details of product formation and delineate the structural transitions of the biocatalyst with the temporal fluctuations of the spatial distance between the different locations along a coarse-grained polymer chain . Such an idea appeared suitable in a number of recent and earlier studies, where excellent recovery of the observed results produced by the seemingly different experiments was established. − In accordance with our present view of the reaction, it is sufficient only to regard for substrate to product conversion, which in turn allows us to determine the probability of survival of the substrate molecule, S ( t ), that the latter survives up to time t . The first derivative of S ( t ) yields the waiting time distribution of the enzymatic turnovers.…”

Section: Introductionmentioning

confidence: 63%

“…We encountered similar equations in the recent studies of force unfolding of a protein molecule 22 and the escape of ssDNA molecules from an α-hemolysin channel 21 under the force clamp and voltage clamp conditions, respectively. Starting from eq 14, details of the steps to get an expression for the survival probability in the Laplace domain are outlined in these references.…”

Section: Single-enzyme Dynamics In Catalysismentioning

confidence: 98%

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A Revisit to Turnover Kinetics of IndividualEscherichia coliβ-Galactosidase Molecules

2021

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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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Section: Single-enzyme Dynamics In Catalysissupporting

confidence: 53%

Section: Introductionmentioning

confidence: 63%

Section: Single-enzyme Dynamics In Catalysismentioning

confidence: 98%

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A Revisit to Turnover Kinetics of IndividualEscherichia coliβ-Galactosidase Molecules

2021

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“…Hence, the choice of the intrinsic disorder to be dynamic, consistent with the previous attempts, 16−19 is better suited with the experimental results as observed here. We also recently explored the influence of dynamic disorder in DNA escape kinetics 39 and bacterial photosynthesis. 40,41 Application of our result to fit the nonexponential survival probability is depicted in Figure 3 where the different symbols are the data points and the solid lines are the estimates using eq 10.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…Hence, the choice of the intrinsic disorder to be dynamic, consistent with the previous attempts, − is better suited with the experimental results as observed here. We also recently explored the influence of dynamic disorder in DNA escape kinetics and bacterial photosynthesis. , …”

Section: Resultsmentioning

confidence: 99%

An Exactly Solvable Stochastic Kinetic Theory of Single-Molecule Force Experiments

2020

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The unfolding of a protein in single-molecule pulling experiments subjected to a constant force (force-clamp) and constant velocity (force-ramp) is analyzed by introducing an exactly solvable two-state kinetic model framed based on the general stochastic approach of discrete state and continuous time formulation. The effect of perturbation is interpreted in the presence of dynamic disorder, resulting from intrinsic conformational fluctuations, by deriving an exact analytical expression for the unfolding time distribution, which in turn allowed us to calculate the expressions for the quantities of experimental interest explicitly. In particular, the novelty of our method lies in the fact that it reduced the need for a lengthy calculation, contrary to the previous dynamic disorder studies, and provides a fairly concise but sufficient mathematical analysis, which becomes much easier to implement quantitatively. We tested our results against the measured data from a number of force unfolding experiments on various proteins, ubiquitin, titin, and filamin, and the force unzipping of DNA and observed excellent agreement in each case. This asserts the reliability of the present technique, which suggests a plausible extension of the stochastic kinetic theory in single-molecule force experiments beyond its present-day widespread implications.

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Stochastic Kinetic Approach to the Escape of DNA Hairpins from an α-Hemolysin Channel

2020

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Escape experiments probed the dynamics of DNA hairpins inside a membrane-embedded α-hemolysin channel, which revealed the orientation and voltage-dependent nature of the DNA–pore interactions. The mean escape times measured at different assisting voltages were strongly influenced by these interactions. Clearly, an escape process from the nanopore was stochastic in nature that occurred in milliseconds. In this paper, we present a new methodology for describing the experimental observations based on the stochastic kinetic approach of discrete-state and continuous-time formulations. Our model considers that a hairpin attains different states inside and out of the pore, and we derived the expression for the escape time distribution from which survival probability of the hairpin that still exists inside the nanopore is determined. On the other hand, the first moment of the above distribution readily yields the mean escape time. Importantly, we show that the recovery of the experimental results was possible taking into account the slow structural fluctuations of the combined DNA–pore system. Additional investigation tested the profound influence of conformational dynamics by considering a pure kinetic scheme, which satisfied the measured data only partially. Therefore, the single stochastic framework suggested here provides a powerful tool that leads to a significant improvement in the theoretical analysis of the experimental results over a range of applied voltages by removing the inadequacy of the original attempt constructed following a number of formulations in the absence of intrinsic fluctuations.

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Kinetics of escape of ssDNA molecules fromα-hemolysin nanopores: a dynamic disorder study

Cited by 3 publications

References 27 publications

A Revisit to Turnover Kinetics of IndividualEscherichia coliβ-Galactosidase Molecules

A Revisit to Turnover Kinetics of IndividualEscherichia coliβ-Galactosidase Molecules

An Exactly Solvable Stochastic Kinetic Theory of Single-Molecule Force Experiments

Stochastic Kinetic Approach to the Escape of DNA Hairpins from an α-Hemolysin Channel

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