Reaction-rate theory: fifty years after Kramers

Hänggi, Peter; Talkner, Peter; Borkovec, Michal

doi:10.1103/revmodphys.62.251

Cited by 5,860 publications

(5,688 citation statements)

References 571 publications

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“…In a viscous solvent, the variation of k app with temperature can be described by a Kramers-like model (Hänggi et al 1990;Kramers 1940) as follows:…”

Section: Ligand Effects On Membrane Protein Kinetic Stabilitymentioning

confidence: 99%

Kinetic stability of membrane proteins

2017

Biophys Rev

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Although membrane proteins constitute an important class of biomolecules involved in key cellular processes, study of the thermodynamic and kinetic stability of their structures is far behind that of soluble proteins. It is known that many membrane proteins become unstable when removed by detergent extraction from the lipid environment. In addition, most of them undergo irreversible denaturation, even under mild experimental conditions. This process was found to be associated with partial unfolding of the polypeptide chain exposing hydrophobic regions to water, and it was proposed that the formation of kinetically trapped conformations could be involved. In this review, we will describe some of the efforts toward understanding the irreversible inactivation of membrane proteins. Furthermore, its modulation by phospholipids, ligands, and temperature will be herein discussed.

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“…In a viscous solvent, the variation of k app with temperature can be described by a Kramers-like model (Hänggi et al 1990;Kramers 1940) as follows:…”

Section: Ligand Effects On Membrane Protein Kinetic Stabilitymentioning

confidence: 99%

Kinetic stability of membrane proteins

2017

Biophys Rev

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“…2. Whether or not a certain physicochemical pathway is viable depends chiefly on the height of the corresponding activation energy barrier [41]. Development of a thin liquid filament is associated with a lower barrier than formation of a protrusion with large diameter.…”

Section: Equation 10mentioning

confidence: 99%

“…As a result, d ts represents the most energetically unfavorable configuration. For ⌬E ts Ͼ 0 fission may occur as thermally activated barrier crossing, characterized by a rate constant k that follows an Arrhenius-type expression [41] k ϭ A exp͑Ϫ⌬E ts ⁄ RT͒…”

Section: Introductionmentioning

confidence: 99%

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

Konermann

2009

J. Am. Soc. Mass Spectrom.

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This work uses a minimalist model for deciphering the opposing effects of Coulomb repulsion and surface tension on the stability of electrosprayed droplets. Guided by previous observations, it is assumed that progeny droplets are ejected from the tip of liquid filaments that are formed as protrusions of an initially spherical parent. Nonspherical shapes are approximated as assemblies of multiple closely spaced beads. This strategy greatly facilitates the calculation of electrostatic and surface energies. For a droplet at the Rayleigh limit the model predicts that growth of a very thin filament is a spontaneous process with a negligible activation barrier. In contrast, significant barriers are encountered for the formation of larger diameter filaments. These different barrier heights favor highly asymmetric droplet fission because the dimensions of the filament determine those of the ejected droplet(s). Substantial charge accumulation occurs at the filament termini. This allows each progeny droplet to carry a significant fraction of charge, despite its very small volume. In the absence of a long connecting filament, relieving electrostatic stress through progeny droplet emission would be ineffective. The model predicts the prevalence of fission events leading to the formation of several progeny droplets, instead of just a single one. Ejection bursts are followed by collapse back to a spherical shape. The resulting charge depleted system is incapable of producing additional progeny droplets until solvent evaporation returns it to the Rayleigh limit. Despite the very simple nature of the model used here, all of these predictions agree with experimental data. E lectrospray ionization (ESI) mass spectrometry (MS) has evolved into one of the most versatile and widely used analytical techniques. The ESI process itself has been subject of numerous studies (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12] and references therein). Analyte solution is passed through a metal capillary to which high voltage has been applied, and solvent droplets emanate from the tip of a Taylor cone at the capillary outlet [11]. Each droplet carries a net charge due to protons or other cationic species that reside at the air/liquid interface. Solvent evaporation and droplet fission are fundamental elements of the ESI process. Evaporation increases the surface charge density to a point where fission occurs. The disintegration process triggered in this way is highly asymmetric, leading to the formation of several small progeny droplets that carry away only a small fraction of mass, but a disproportionately high amount of charge [13,14]. High-speed imaging is an important tool for gaining insights into the breakup mechanism [15,16]. More recently, the rapid solidification of charged nanodroplets using sol-gel techniques has provided a means to capture transient droplet shapes and study them by microscopy [17]. Also, molecular dynamics simulations represent an interesting approach in this area [9,10]. All those studies reveal that disintegrati...

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“…The rate, which describes the frequency of transitions per unit time in the frozen potential from the resting state to the firing state, is approximated by the Kramers rate expression [16] kðtÞ ¼ x r ðtÞx u ðtÞ 2p…”

Section: Firing Ratementioning

confidence: 99%

“…the times between adjacent firing events, are exponentially distributed. The respective rate was determined by Chow and White [5] as the Kramers rate [16] describing the noise activated escape from the resting state. Other nonlinear integrate-and-fire models as e.g.…”

Section: Introductionmentioning

confidence: 99%

Neuron firing in driven nonlinear integrate-and-fire models

Kostur

Schindler

Talkner

et al. 2007

Mathematical Biosciences

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Statistical properties of neuron firing are studied in the framework of a nonlinear leaky integrate-and-fire model that is driven by a slow periodic subthreshold signal. The firing events are characterized by first passage time densities. The experimentally better accessible interspike interval density generally depends on the sojourn times in a refractory state of the neuron. This aspect is not part of the integrate-and-fire model and must be modelled additionally. For a large class of refractory dynamics, a general expression for the interspike interval density is given and further evaluated for the two cases with an instantaneous resetting (i.e. no refractory state) and a refractory state possessing a deterministic lifetime. First passage time densities and interspike interval densities following from the proposed theory compare favorably with precise numerical simulations.

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Reaction-rate theory: fifty years after Kramers

Cited by 5,860 publications

References 571 publications

Kinetic stability of membrane proteins

Kinetic stability of membrane proteins

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

Neuron firing in driven nonlinear integrate-and-fire models

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