Brownian motion in a field of force and the diffusion model of chemical reactions

Kramers, H. A.

doi:10.1016/s0031-8914(40)90098-2

Cited by 8,331 publications

(6,038 citation statements)

References 9 publications

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“…The force-dependent kinetics of the linkers then imposes a strong nonlinear coupling between the kinetics and the position of the membrane. The detachment rate is assumed to follow a Kramer's-like kinetics (25) appropriate to thermally induced processes,…”

Section: Methodsmentioning

confidence: 99%

Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

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Casademunt

Brugués

et al. 2015

Biophysical Journal

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We propose a model for membrane-cortex adhesion that couples membrane deformations, hydrodynamics, and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active acto-myosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.

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Section: Methodsmentioning

confidence: 99%

Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

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Casademunt

Brugués

et al. 2015

Biophysical Journal

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“…Also human movement may be characterized as (the result of) a diffusion process, because it can often be captured in the form of common stochastic differential equations, that is, a dynamical system (or differential forms) comprising both deterministic and stochastic components. The unique link between these deterministic and stochastic components and the first two cumulants of the corresponding probability distribution is well documented (Gardiner 2004;Kramers 1940;Moyal 1949;Risken 1989;Stratonovich 1963) and has provided a theoretical framework for understanding the interaction between deterministic and random features (Haken 1983). …”

Section: General Principlesmentioning

confidence: 99%

Deterministic and stochastic features of rhythmic human movement

2005

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The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method's merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.

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“…This phenomenon, referred to broadly as dynamic disorder, 27,28 has been inferred previously from ensemble measurements 29 and quantitatively verified by recent single-molecule experiments. 14,[18][19][20][21][22][23][24][25] Dynamic disorder is not described within the framework of conventional transition state theory 30 and Kramers' theory 31,32 of condensed phase chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

Fluctuating Enzymes: Lessons from Single-Molecule Studies

et al. 2005

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Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

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Brownian motion in a field of force and the diffusion model of chemical reactions

Cited by 8,331 publications

References 9 publications

Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

Deterministic and stochastic features of rhythmic human movement

Fluctuating Enzymes: Lessons from Single-Molecule Studies

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