Numerical framework models of single proton conduction through Gramicidin

Schumaker, Mark F.

doi:10.2741/1177

Cited by 6 publications

(7 citation statements)

References 32 publications

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“…Currents computed using the analytical model (from Eqs. (28)-(33) given later) are in excellent agreement with a numerical calculation that avoids the lumped state approximation (Schumaker, 2003).…”

Section: Grotthuss Conduction Modelsupporting

confidence: 77%

Framework Models of Ion Permeation Through Membrane Channels and the Generalized King–Altman Method

Mapes

Schumaker

2006

Bull. Math. Biol.

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A modern approach to studying the detailed dynamics of biomolecules is to simulate them on computers. Framework models have been developed to incorporate information from these simulations in order to calculate properties of the biomolecules on much longer time scales than can be achieved by the simulations. They also provide a simple way to think about the simulated dynamics. This article develops a method for the solution of framework models, which generalizes the King-Altman method of enzyme kinetics. The generalized method is used to construct solutions of two framework models which have been introduced previously, the single-particle and Grotthuss (proton conduction) models. The solution of the Grotthuss model is greatly simplified in comparison with direct integration. In addition, a new framework model is introduced, generalizing the shaking stack model of ion conduction through the potassium channel.

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Section: Grotthuss Conduction Modelsupporting

confidence: 77%

Framework Models of Ion Permeation Through Membrane Channels and the Generalized King–Altman Method

Mapes

Schumaker

2006

Bull. Math. Biol.

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“…it has been reported that the contribution of the access resistance to the recorded single-channel current is significant for proton permeation through the gA channel (Decker and Levitt, 1988;Cukierman, 2000;Schumaker et al, 2000;Schumaker, 2003;Braun-Sand et al, 2005). Therefore, the measured temperature dependence of earlier studies for the gA channel may be governed largely by the access resistance, similar to the voltage-gated proton channel.…”

Section: Temperature-dependent Q 10mentioning

confidence: 92%

Temperature dependence of proton permeation through a voltage-gated proton channel

Kuno

Ando

Morihata

et al. 2009

Journal of General Physiology

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Voltage-gated proton channels are found in many different types of cells, where they facilitate proton movement through the membrane. The mechanism of proton permeation through the channel is an issue of long-term interest, but it remains an open question. To address this issue, we examined the temperature dependence of proton permeation. Under whole cell recordings, rapid temperature changes within a few milliseconds were imposed. This method allowed for the measurement of current amplitudes immediately before and after a temperature jump, from which the ratios of these currents (Iratio) were determined. The use of Iratio for evaluating the temperature dependence minimized the contributions of factors other than permeation. Temperature jumps of various degrees (ΔT, −15 to 15°C) were applied over a wide temperature range (4–49°C), and the Q10s for the proton currents were evaluated from the Iratios. Q10 exhibited a high temperature dependence, varying from 2.2 at 10°C to 1.3 at 40°C. This implies that processes with different temperature dependencies underlie the observed Q10. A novel resistivity pulse method revealed that the access resistance with its low temperature dependence predominated in high temperature ranges. The measured temperature dependence of Q10 was decomposed into Q10 of the channel and of the access resistances. Finally, the Q10 for proton permeation through the voltage-gated proton channel itself was calculated and found to vary from 2.8 at 5°C to 2.2 at 45°C, as expected for an activation enthalpy of 64 kJ/mol. The thermodynamic features for proton permeation through proton-selective channels were discussed for the underlying mechanism.

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“…We applied a minimal model with a small number of states and transitions between them (a discretestate Markov model; DSMM), 42,43 which is similar to the lumped state model proposed by Schumaker et al for the hopand-turn mechanism. 41 The model is cyclic in its nature, and cyclic transitions among states yield proton currents. Accord-ingly, the hop-and-turn mechanism is decomposed into the elementary steps, and there should be a critical step for the preferred directional flux that is responsible for the rectification.…”

Section: Proton-hop and Water-turnover Model Under The Influence Of Tmentioning

confidence: 99%

“…for the hop-and-turn mechanism. 41 The model is cyclic in its nature, and cyclic transitions among states yield proton currents. Accordingly, the hop-and-turn mechanism is decomposed into the elementary steps, and there should be a critical step for the preferred directional flux that is responsible for the rectification.…”

Section: Rectified Proton Conduction In Symmetric Phmentioning

confidence: 99%

Rectified Proton Grotthuss Conduction Across a Long Water-Wire in the Test Nanotube of the Polytheonamide B Channel

et al. 2016

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A hydrogen-bonded water-chain in a nanotube is highly proton conductive, and examining the proton flux under electric fields is crucial to understanding the one-dimensional Grotthuss conduction. Here, we exploited a nanotube-forming natural product, the peptide polytheonamide B (pTB), to examine proton conduction mechanisms at a single-molecule level. The pTB nanotube has a length of ∼40 Å that spans the membrane and a uniform inner diameter of 4 Å that holds a single-file water-chain. Single-channel proton currents were measured using planar lipid bilayers in various proton concentrations and membrane potentials (±400 mV). We found, surprisingly, that the current-voltage curves were asymmetric with symmetric proton concentrations in both solutions across the membrane (rectification). The proton flux from the C-terminal to the N-terminal end was 1.6 times higher than that from the opposite. At lower proton concentrations, the degree of rectification was attenuated, but with the addition of a pH-buffer (dichloroacetate) that supplies protons near the entrance, the rectification emerged. These results indicate that the permeation processes inside the pore generate the rectification, which is masked at low concentrations by the diffusion-limited access of protons to the pore entrance. The permeation processes were characterized by a discrete-state Markov model, in which hops of a proton followed by water-chain turnovers were implemented. The optimized model revealed that the water-chain turnover exhibited unusual voltage dependence, and the distinct voltage-dependencies of the forward and backward transition rates yielded the rectification. The pTB nanotube serves as a rectified proton conductor, and the design principles can be exploited for proton-conducting materials.

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Numerical framework models of single proton conduction through Gramicidin

Cited by 6 publications

References 32 publications

Framework Models of Ion Permeation Through Membrane Channels and the Generalized King–Altman Method

Framework Models of Ion Permeation Through Membrane Channels and the Generalized King–Altman Method

Temperature dependence of proton permeation through a voltage-gated proton channel

Rectified Proton Grotthuss Conduction Across a Long Water-Wire in the Test Nanotube of the Polytheonamide B Channel

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