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. 2015 Sep;44(6):465-472.
doi: 10.1007/s00249-015-1049-2. Epub 2015 Jun 21.

Conductance hysteresis in the voltage-dependent anion channel

Shay M Rappaport #  1 , Oscar Teijido #  1 , David P Hoogerheide  1   2 , Tatiana K Rostovtseva  1 , Alexander M Berezhkovskii  1   3 , Sergey M Bezrukov  1
Affiliations

Conductance hysteresis in the voltage-dependent anion channel

Shay M Rappaport et al. Eur Biophys J. 2015 Sep.

Abstract

Hysteresis in the conductance of voltage-sensitive ion channels is observed when the transmembrane voltage is periodically varied with time. Although this phenomenon has been used in studies of gating of the voltage-dependent anion channel, VDAC, from the outer mitochondrial membrane for nearly four decades, full hysteresis curves have never been reported, because the focus was solely on the channel opening branches of the hysteresis loops. We studied the hysteretic response of a multichannel VDAC system to a triangular voltage ramp the frequency of which was varied over three orders of magnitude, from 0.5 mHz to 0.2 Hz. We found that in this wide frequency range the area encircled by the hysteresis curves changes by less than a factor of three, suggesting broad distribution of the characteristic times and strongly non-equilibrium behavior. At the same time, quasi-equilibrium two-state behavior is observed for hysteresis branches corresponding to VDAC opening. This enables calculation of the usual equilibrium gating parameters, gating charge and voltage of equipartitioning, which were found to be almost insensitive to the ramp frequency. To rationalize this peculiarity, we hypothesize that during voltage-induced closure and opening the system explores different regions of the complex free energy landscape, and, in the opening branch, follows quasi-equilibrium paths.

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Figures

Figure 1
Figure 1
Conductance of the multichannel membrane with the voltage ramp frequency ranging from 0.5 mHz to 0.2 Hz shows sensitivity of the hysteresis curves to the ramp frequency. A: “Raw” data on the ion current through a multichannel system of about 70 VDAC channels (upper panel) in response to a 0 mV to −60 mV voltage ramp of 20 mHz frequency (lower panel). B: Conductance hysteresis curves for different frequencies of the ramp. The arrows at the 0.2 Hz trace show the direction of the voltage change in the parts of the hysteresis loop corresponding to the channel closing and opening. The data are averaged over several ramp periods. C: The area encircled by the hysteresis curves as a function of the ramp frequency, calculated from three independent experiments on multi-channel membranes containing 70-180 channels, is shown by different symbols. The area does not display the tendency to decrease at low frequencies, suggesting strong deviations from equilibrium and the existence of a broad spectrum of relaxation times, including times exceeding 1/(0.5 mHz) = 2000 s. The solid line through the data is the best fit by A(f) = A0/f / f0 + f0 / f) with A0 and f0 used as adjustable parameters (see text).
Figure 2
Figure 2
Normalized hysteresis curves show that while the closure of the channels is highly frequency dependent, the normalized traces for the opening branches practically overlap. A: Conductance hysteresis curves of Fig. 1B after transformation according to Eq. (1). B: The gating parameters, the gating charge n and the voltage of the half-effect V0 corresponding to PO = 0.5, obtained from fitting the opening branches data to Eq. (2). The wavy arrows indicate that the triangles and squares give the values of V0 and n, respectively.
Figure 3
Figure 3
Two types of relaxation experiments. A: Conductance relaxation to two different voltages. The voltage protocol, shown at the bottom, is to start at −2.5 mV, then apply −50 mV for the three durations shown in the figure, and then return to −2.5 mV. Quite different relaxation rates towards closure and opening are clearly seen, as can be expected even in the case of a two-state model with voltage-dependent rate constants. B: Conductance relaxation to the same voltage. Experiments are started at −2.5 mV, then −30 mV is applied, in 25 seconds the voltage is switched to −50 mV, 25 seconds later the voltage is returned to −30 mV and then, in 25 seconds, to −2.5 mV. Dashed and solid lines are best fits by single exponentials with the equations displayed in the graph. They show about a two order of magnitude difference in the relaxation times. The data in panels A and B are averages over 3 and 4 separate experiments with membranes containing from 80 to 240 channels. The signal was filtered by a low-pass Bessel filter at 1.0 kHz and sampled at 5.0 kHz.
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