The theory of ion transport through membrane channels

Cooper, Katelyn M.; Jakobsson, Eric; Wolynes, Peter G.

doi:10.1016/0079-6107(85)90012-4

Cited by 182 publications

(170 citation statements)

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“…The diffusion theory of chemical reactions was introduced, as far as I know, to the biophysical/channel literature by Kim Cooper, then a graduate student of the biophysicist Eric Jakobsson and physical chemist Peter Wolynes (Andersen & Koeppe, 1992;Barcilon et al, 1993;Chiu & Jakobsson, 1989;Cooper et al, 1985;Cooper et al, 1988a;Cooper et al, 1988b;Crouzy et al, 1994;Eisenberg et al, 1995;Läuger, 1991;Roux & Karplus, 1991a). Wolynes (Skinner & Wolynes, 1978;Wolynes, 1980) had an important role in popularizing and extending Kramers' approach to chemical reactions.…”

Section: Brief History Of Diffusion Theory Of Chemical Reactions Thementioning

confidence: 99%

“…I hasten to add that we were certainly neither alone nor the first to realize the significance of this problem. In the biological literature, see Andersen & Koeppe, 1992;Barcilon et al, 1993;Chiu & Jakobsson, 1989;Cooper, Jakobsson & Wolynes, 1985;Cooper et al, 1988a;Cooper, Gates & Eisenberg, 1988b;Crouzy, Woolf & Roux, 1994;Eisenberg et al, 1995;Läuger, 1991;Roux & Karplus, 1991a). In the chemical literature, the appropriate form for barrier theory in the presence of friction has been known for more than 50 years in chemistry as part of the diffusion theory of chemical reactions (Berne, Borkovec & Straub, 1988;Chandler, 1978;Cho et al, 1993;Coffey, Kalmykov & Wladron, 1996;Dresden, 1987;Eisenberg et al, 1995;Fleming & Hänggi, 1993;Fleming, Courtney & Balk, 1986;Friedman, 1985;Gardiner, 1985;Haar, 1998;Han, Lapointe & Lukens, 1993;Hänggi et al, 1990;Hynes, 1985;Hynes, 1986;Kramers, 1940;Laidler & King, 1983;Murthy & Singer, 1987;Nitzan & Schuss, 1993;Pollak, 1993;Pollak, 1996;Risken, 1984;Tyrrell & Harris, 1984).…”

Section: Traditional Explanations For the Mfementioning

confidence: 99%

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From Structure to Function in Open Ionic Channels

Eisenberg

1999

Journal of Membrane Biology

157

130

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We consider a simple working hypothesis that all permeation properties of open ionic channels can be predicted by understanding electrodiffusion in fixed structures, without invoking conformation changes, or changes in chemical bonds. We know, of course, that ions can bind to specific protein structures, and that this binding is not easily described by the traditional electrostatic equations of physics textbooks, that describe average electric fields, the so-called `mean field'. The question is which specific properties can be explained just by mean field electrostatics and which cannot. I believe the best way to uncover the specific chemical properties of channels is to invoke them as little as possible, seeking to explain with mean field electrostatics first. Then, when phenomena appear that cannot be described that way, by the mean field alone, we turn to chemically specific explanations, seeking the appropriate tools (of electrochemistry, Langevin, or molecular dynamics, for example) to understand them. In this spirit, we turn now to the structure of open ionic channels, apply the laws of electrodiffusion to them, and see how many of their properties we can predict just that way.Comment: Nearly final version of publicatio

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Section: Brief History Of Diffusion Theory Of Chemical Reactions Thementioning

confidence: 99%

Section: Traditional Explanations For the Mfementioning

confidence: 99%

From Structure to Function in Open Ionic Channels

Eisenberg

1999

Journal of Membrane Biology

157

130

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“…binding site ͉ first passage time ͉ membrane D iffusion of molecules through channels and pores of an otherwise impermeable membrane is an important issue in biological transport at the cellular level (1,2). Early considerations of channel transport have been concerned mainly with the effect of barriers inside channels (3).…”

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confidence: 99%

Molecular transport through channels and pores: Effects of in-channel interactions and blocking

Bauer¹,

Nadler²

2006

Proc. Natl. Acad. Sci. U.S.A.

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Facilitated translocation of molecules through channels and pores is of fundamental importance for transmembrane transport in biological systems. Several such systems have specific binding sites inside the channel, but a clear understanding of how the interaction between channel and molecules affects the flow is still missing. We present a generic analytical treatment of the problem that relates molecular flow to the first passage time across and the number of particles inside the channel. Both quantities depend in different ways on the channel properties. For the idealized case of noninteracting molecules, we find an increased flow whenever there is a binding site in the channel, despite an increased first passage time. In the more realistic case that molecules may block the channel, we find an increase of flow only up to a certain threshold value of the binding strength and a dependence on the sign of the concentration gradient, i.e., asymmetric transport. The optimal binding strength in that case is analyzed. In all cases the reason for transport facilitation is an increased occupation probability of a particle inside the channel that overcomes any increase in the first passage time because of binding.binding site ͉ first passage time ͉ membrane D iffusion of molecules through channels and pores of an otherwise impermeable membrane is an important issue in biological transport at the cellular level (1, 2). Early considerations of channel transport have been concerned mainly with the effect of barriers inside channels (3). However, various means of facilitated transport across a membrane have also been considered, e.g., shuttle mechanisms (4). In recent years it has been noted that there are several cases where the molecules transported interact strongly with regions inside the channel (5-13), apparently leading to an increase in transmembrane transport. However, a fundamental understanding and quantitative description of such an increased transport due to in-channel binding sites is still missing.From an intuitive point of view, it is not clear at all why a strong interaction with the channel should facilitate transport. Conversely, one could argue that a strong binding is associated with a longer residence time inside the channel, which reduces flow. Furthermore, molecules bound temporarily inside the channel may hamper transport of other molecules, especially when they are large (13,14), and block the channel. So, why do traps and͞or reaction sites within the channel facilitate molecular flow? These questions have to be addressed in the generic biological setting of a macroscopic concentration gradient across the membrane (see Fig. 1). An appropriate quantitative description should give the flow for a given concentration difference depending on the potential and other parameters describing the molecule-channel interaction. Physical insight can be gained if the flow can be related to other global properties of the system in question.Past efforts (15,16) to analyze this situation used the concepts of conditio...

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“…3 we compare τ 1 andt 1 . When the well depth U w is small, τ 1 underestimatest 1 , but when βU w reaches ∼5, there is very good agreement between τ 1 andt 1 .…”

Section: Illustrative Calculationsmentioning

confidence: 99%

“…Ion permeation through transmembrane channels has traditionally been modeled using two different approaches. [1][2][3][4] In one approach, the translocation of the permeant ion through the channel pore is modeled as continuous diffusion and the rate of ion transport is obtained from solving the steady-state diffusion equation. 2,4,5 In the other approach, the translocation of the permeant ion through the pore is modeled as hopping along a discrete set of internal binding sites and the rate of ion transport is obtained from solving a set of steady-state rate equations.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of two approaches for modeling ion permeation through a transmembrane channel with an internal binding site

Zhou¹

2011

The Journal of Chemical Physics

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Ion permeation through transmembrane channels has traditionally been modeled using two different approaches. In one approach, the translocation of the permeant ion through the channel pore is modeled as continuous diffusion and the rate of ion transport is obtained from solving the steady-state diffusion equation. In the other approach, the translocation of the permeant ion through the pore is modeled as hopping along a discrete set of internal binding sites and the rate of ion transport is obtained from solving a set of steady-state rate equations. In a recent work [Zhou, J. Phys. Chem. Lett. 1, 1973Lett. 1, (2010], the rate constants for binding to an internal site were further calculated by modeling binding as diffusion-influenced reactions. That work provided the foundation for bridging the two approaches. Here we show that, by representing a binding site as an energy well, the two approaches indeed give the same result for the rate of ion transport.

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The theory of ion transport through membrane channels

Cited by 182 publications

References 54 publications

From Structure to Function in Open Ionic Channels

From Structure to Function in Open Ionic Channels

Molecular transport through channels and pores: Effects of in-channel interactions and blocking

Equivalence of two approaches for modeling ion permeation through a transmembrane channel with an internal binding site

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