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A permeation theory for single-file ion channels: One- and two-step models
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10.1063/1.3580562
/content/aip/journal/jcp/134/16/10.1063/1.3580562
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/16/10.1063/1.3580562
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Figures

Image of FIG. 1.
FIG. 1.

Hodgkin and Keynes knock-on mechanism. Permeation is a one-step process—after Bernèche and Roux. (See Ref. 17.)

Image of FIG. 2.
FIG. 2.

Energetics of the knock-on model for a positive transmembrane voltage V. The permeation coordinate represents the fractional progress through outward permeation. qV is the electrical work done on the ions during a complete outward permeation transition. (1 − χ)qV is the increase in the transition state energy as a result of the transmembrane voltage V. E a is the activation energy for V = 0.

Image of FIG. 3.
FIG. 3.

Comparing the asymmetric knock-on model Eq. (3) with simulated single-channel channel Kv1.2 permeation data. The theoretical curve was fitted to all the nonzero current data resulting in χ = 0.95 and k a = 4.5 × 106 s−1 M−1. Simulation data (symbols) reproduced from Jensen et al. (See Ref. 14.)

Image of FIG. 4.
FIG. 4.

Energetics of the A/D model for positive membrane voltage V. The two states of the selectivity filter are labeled n (triple occupancy) and m (double occupancy). The permeation coordinate represents the fractional progress through outward permeation. qV is the electrical work done on all of the ions during a compete outward permeation event. (1 − χ)qV is the increase in state n's energy as a result of the transmembrane voltage V. E d is the dissociation energy for V = 0.

Image of FIG. 5.
FIG. 5.

A/D mechanism. Permeation is a two-step process. During the association step all three ions move together in a concerted manner as the entering ion shunts-on the two helper ions to form the triply occupied state n. During the dissociation step all three ions move together in a concerted manner as the two helper ions shunt-off the permeant ion to return the channel to state m.

Image of FIG. 6.
FIG. 6.

(a) Comparing the two-parameter symmetric A/D model Eq. (19) with single-channel MaxiK permeation data. Theoretical curves (solid lines) were fitted to the V > 0 experimental data using Eq. (19), resulting in k d = 2.2 × 108 s−1 and K d = 310 mM. Experimental data (symbols) and previous 15-parameter fit (dotted lines) reproduced (with permission) from Schroeder and Hansen. (See Ref. 45.) (b) Corresponding occupancy states plot of the positive-voltage data in Fig. 6(a). Within the A/D model, the experimental values of the scaled flux j* represent the occupancy θ n (degree of saturation) of the channel—see Eq. (16).

Image of FIG. 7.
FIG. 7.

Comparing the symmetric A/D model Eq. (19) with single-channel Shaker K+ channel permeation data. (a) Theoretical curves (solid lines) were fitted to the V > 0 experimental data resulting in K d = 150 mM, k d = 1.4 × 107 s−1. Experimental data (symbols) reproduced (with permission) from Heginbotham and MacKinnon. (See Ref. 37.) (b) Corresponding occupancy states plot of the positive-voltage data in Fig. 6(a). Solid circles represent the zero-volt conductances reported by Heginbotham and MacKinnon that have been fitted to Eq. (22).

Image of FIG. 8.
FIG. 8.

Two-step asymmetric “shunt-on pop-off” variant of the A/D permeation model proposed here based on the MD simulations of Jensen et al. (See Ref. 14.)

Image of FIG. 9.
FIG. 9.

Comparing the asymmetric A/D model Eq. (12) with single-channel Shaker K+ channel permeation data. (a) Theoretical curves (solid lines) were fitted to the experimental data resulting in K d = 89 mM, k d = 1.3 × 107 s−1, and χ = 0.67. Experimental data (symbols) reproduced (with permission) from Heginbotham and MacKinnon. (See Ref. 37.) (b) Corresponding occupancy states plot of the positive-voltage data in Fig. 9(a).

Image of FIG. 10.
FIG. 10.

Comparing the asymmetric A/D model Eq. (12) with single-channel Shaker K+ channel permeation data. (a) Theoretical curves (solid lines) were fitted to both positive and negative experimental data resulting in K d = 49 mM, k d = 9.5 × 106 s−1, and χ = 0.60. Experimental data (symbols) reproduced (with permission) from Heginbotham and MacKinnon. (See Ref. 37.) (b) Corresponding occupancy states plot of all the data in Fig. 10(a).

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/content/aip/journal/jcp/134/16/10.1063/1.3580562
2011-04-25
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A permeation theory for single-file ion channels: One- and two-step models
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/16/10.1063/1.3580562
10.1063/1.3580562
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