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Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 92, Issue 7, L52-L54, 1 April 2007

doi:10.1529/biophysj.106.102947

Biophysical Letters

Measuring Extracellular Ion Gradients from Single Channels with Ion-Selective Microelectrodes

Mark A. Messerli, Erica D. Corson and Peter J.S. Smith^,  

BioCurrents Research Center, Program in Molecular Physiology, Marine Biological Laboratory, Woods Hole, Massachusetts

Address reprint requests and inquiries to Peter J. S. Smith, Fax: 508-540-6902.

Ion-selective microelectrodes (ISMs) have been used to measure steady and dynamic changes in extracellular ion concentration at the surface of single cells and tissues 1,2. In many cases the combined activity of a population of a single type of channel or transporter leads to the majority of the extracellular ion concentration change for a specific ion. In theory, ISMs possess the sensitivity and time response for measuring localized changes in ion concentration due to flux through a single ion channel. We have used a combination of extracellular ion gradient modeling, measurement, and fitting to prove the feasibility and explore the applicability of this hypothesis.

[K⁺] changes at the external side of the Ca²⁺-activated K⁺ channel, mSlo, were calculated assuming diffusion from a point source. The equation below describes diffusion into a hemisphere due to restricted diffusion imposed by the plasma membrane

Activation of the mSlo channel at membrane potentials more positive than the K⁺ equilibrium potential () will give rise to K⁺ efflux. Modeling was therefore constrained to the resulting increase in [K⁺] at the extracellular side of the channel. This increase is dependent on channel conductance to the permeant ion(s), the electrochemical driving force(s) on the permeant ion(s), channel open time, and distance from the channel. Single-channel conductance of 272 pS was determined during initial characterization of mSlo in Xenopus oocytes 3.

Figure 1AC, shows the change in [K⁺] that occurs for ranges of the three remaining parameters. A modified form of the Goldman-Hodgkin-Katz equation was used to determine the number of K⁺ ions that would leave the cell through the channel under different depolarizing potentials. The in Xenopus oocytes is ∼−88mV under normal conditions. The peak change in [K⁺] 2μm from the channel is only 0.06μM when the membrane potential is driven to −80mV. Depolarizing the membrane potential further away from the −40, 0, +40, and +80mV leads to an average [K⁺] increase of 0.9, 2.4, 4.9, and 8.1μM, respectively, for a channel with an open time of 100ms. The profile of the [K⁺] changes as a function of open time, appearing as a spike for channel events shorter than 30ms but reaching a relative steady-state plateau for events longer than 100ms, as shown in Figure 1B. These profiles were generated for a [K⁺] at 2μm from the channel with a +40mV membrane potential. Under these conditions the [K⁺]_ext rises >4μM for even a brief 10-ms event. Diffusion of K⁺ away from the channel leads to dilution of the [K⁺] as displayed in Figure 1C. The voltage response of the detecting ISM is dependent on the background [K⁺]. Larger voltages will occur for the same rise in [K⁺] with lower background [K⁺] as displayed in Figure 1D. In normal OR-2, 3mM K⁺, the voltage response will peak at <0.1mV, at 2μm from the channel with +40mV membrane potential. However, the voltage response of the ISM increases 10- to 30-fold for a proportional decrease in background [K⁺]. Modeling in Figure 1D assumes an ISM with an instantaneous response. In a flow exchange system, a K⁺ ISM measured a 193±4μV difference for a [K⁺] change from 100 to 101μM. Peak-to-peak noise was 45μV.

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Figure 1

Models of [K⁺]_ext changes near an activated mSlo channel with varying driving force on K⁺ (A) open time (B) distance from the channel (C) and when measured with an ideal K⁺ ISM in varying background [K⁺] (D).

Measurements of single-channel events were performed on Xenopus oocytes expressing the mSlo channel. Oocytes were injected with 50nL of increasing dilutions of mSlo RNA to obtain low channel density, ∼1 channel per 50μm², thereby increasing the probability of capturing isolated channel events. Recordings were collected from oocytes in 0.1mM K⁺ OR-2. The coelomic envelope was left intact during recordings to maintain the integrity of the plasma membrane and provide structural support.

K⁺ ISMs were used to measure the increase in [K⁺]_ext next to the surface of the plasma membrane of oocytes overexpressing the mSlo channel and water-injected controls. The mSlo channels are activated by cytosolic Ca²⁺ and depolarization; higher cytosolic Ca²⁺ leads to channel activation at less positive potentials 3. Due to enhanced difficulty with reliably controlling the cytosolic [Ca²⁺], we activated the channels under resting cytosolic [Ca²⁺] with more positive depolarizing potentials. Voltage and current passing electrodes impaled the oocyte at the equator whereas the K⁺ ISM was placed near the animal pole. The ISM was advanced far enough to induce dimpling of the coelomic envelope and then was backed up until the coelomic envelope was no longer dimpled. Depolarization of the plasma membrane caused a large brief electrical transient followed by a slow increase in the [K⁺]-dependent voltage recorded by the ISM next to water-injected controls as well as mSlo RNA-injected oocytes. Figure 2A shows the large increase in the [K⁺]-dependent voltage recorded by an ISM next to an oocyte overexpressing mSlo and depolarized to +40mV. The background [K⁺] recovered over a similar time course upon repolarization to resting membrane potential. This large increase in [K⁺]_ext upon depolarization is likely due to K⁺ efflux through the five different types of endogenous K⁺ channels normally expressed in Xenopus oocytes and activated at this potential 4. K⁺ efflux through endogenous channels raised the local background [K⁺] from 0.1 to >0.3mM. Despite the threefold increase in background [K⁺], upon depolarization, relatively rapid transient changes in [K⁺] were still detected only in depolarized mSlo expressing oocytes. The larger events are underlined in Fig. 2. The first cluster of events in Fig. 2 is magnified in the inset. No such transients were measured on the [K⁺]-dependent voltage acquired during repolarization of mSlo expressing oocytes or in control oocytes. The transients are not due to current-generated voltages that peak at only 2.3μV, 1μm from the channel, under these conditions. In support of this statement, a current-passing K⁺-selective ISM was used to generate local, transient [K⁺] increases. Near the source a second K⁺ ISM measured 1–1.5mV [K⁺]-dependent voltage increases, but no corresponding voltage changes were measured with open barreled electrodes.

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Figure 2

Raw voltage output of a K⁺-selective microelectrode near a depolarized Xenopus oocyte expressing the mSlo channel. The inset shows amplification of the 60- to 100-s region with an overlay of the model for the slow rise in [K⁺] (red).

The large conductance mSlo channels produce a signal that is separable from the lower conductance endogenous K⁺ channels. To perform a direct comparison of the measured mSlo activity to the modeled mSlo channels we removed the large basal increase in [K⁺]. A seven-parameter exponential fit model, was used to find a close match to the large slow increase in [K⁺]_ext. Three single-channel events were isolated for further analysis by subtracting the modeled slow rise from the raw recording and are shown in Figure 3AC. Events 1 and 2 are isolated from other mSlo events whereas event 3 is sandwiched between two other events. A best-fit alignment between the model and the measured [K⁺]-dependent voltage output of the ISM was performed by varying ion channel model parameters and ISM response times and minimizing the sum of the squares of the differences between the two as they were shifted in time with respect to each other. A 2-s duration profile was used for each of the three modeled events. Distance of the ISM from the ion channel was incremented by 0.01μm, whereas the channel open time and ISM response time were incremented by 1 and 5ms, respectively. The black profile shows the [K⁺]-dependent voltage measured by the ISM whereas the overlaid red profile shows a best-fit alignment of the model. The ISM was modeled with varying response times to perform the best-fit alignment because the actual response time of the electrode was not determined during recordings. Table 1 shows the best-fit parameters for each event.

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Figure 3

(A–C) Raw recordings (black) with overlaid best-fit models (red) of increased [K⁺]_ext from single mSlo channels. (D–F) Best-fit models (red) and instantaneous electrode response time models (black) of single-channel events from panels A–C.

According to these parameters, channel events 1 and 2 are slightly >1μm from the ISM whereas channel event 3 is 2.3μm away. The diffusion profile contains information regarding the absolute distance from the ISM but not the vector position of the channel from the ISM. Future work with three closely positioned ISMs could be used to determine the exact position of the channel with respect to the ISMs.

The relatively slow response time of the measuring system is the weakest aspect of this detection method. As a result, shorter duration and lower conductance channel events were missed during these recordings. Also, the signals shown in Figure 3AC, are attenuated. Assuming an instantaneous ISM response time, the profiles for the three events would be much easier to distinguish as shown in Figure 3DF. Although ISMs with instantaneous responses are only theoretically possible, ISMs with response times between 5 and 25ms have been reported 5,6 and will be critical for accurately monitoring signals from channels with smaller conductance and shorter open time. If response time can be improved to this level then ion gradients from single channels with 50 and 20 pS conductance will produce [K⁺]-dependent voltages above 320 and 125μV, respectively, after 20ms open time at 1μm from the cell with a +40mV membrane potential. Our emphasis here has been on the modeling and detection of single channels. However, in practice, ion channel densities range from <1 to >10,000μm⁻²7, indicating that substantially larger ion gradients will be established and more complex signal extraction methods will be needed to functionally map and characterize channels with extracellular ISMs.