The relationship between single-channel and whole-cell conductance in the T-type Ca2+ channel CaV3.1

Abstract

In T-type Ca(2+) channels, macroscopic I(Ba) is usually smaller than I(Ca), but at high Ca(2+) and Ba(2+), single-channel conductance (gamma) is equal. We investigated gamma as a function of divalent concentration and compared it to macroscopic currents using Ca(V)3.1 channels studied under similar experimental conditions (TEA(o) and K(i)). Single-channel current-voltage relationships were nonlinear in a way similar to macroscopic open-channel I/Vs, so divalent gamma was underestimated at depolarized voltages. To estimate divalent gamma, concentration dependence, i(Div), was measured at voltages <-50 mV. Data were well described by Langmuir isotherms with gamma(max)(Ca(2+)) of 9.5 +/- 0.4 pS and gamma(max)(Ba(2+)) of 10.3 +/- 0.5 pS. Apparent K(M) was lower for Ca(2+) (2.3 +/- 0.7 mM) than for Ba(2+) (7.9 +/- 1.3 mM). A subconductance state with an amplitude 70% that of the main state was observed, the relative occupancy of which increased with increasing Ca(2+). As predicted by gamma, macroscopic G(maxCa) was larger than G(maxBa) at 5 mM (G(max)Ca(2+)/Ba:(2+)1.43 +/- 0.14) and similar at 60 mM (G(max)Ca(2+)/Ba:(2+)1.10 +/- 0.02). However, over the range of activation, I(Ca) was larger than I(Ba) under both conditions. This was a consequence of the fact that V(rev) was more negative for I(Ba) than for I(Ca), so that the driving force determining I(Ba) was smaller than that determining I(Ca) over the range of potentials in standard current-voltage relationships.

FIGURE 1

(A) Family of representative whole-cell currents from the same cell in the presence of 5 mM Ba²⁺ (middle) and 5 mM Ca²⁺ (lower) in response to 5-mV voltage steps from a holding potential of −110 mV over the range −90–+40 mV. Cells were depolarized once every 5 s to ensure full recovery from inactivation. (B) Average ± SE of the current-voltage relationship in the presence of 5 mM Ba²⁺ (circles) and Ca²⁺ (squares) for five cells studied in the same way. Currents were normalized to the peak Ca²⁺ current in each cell.

FIGURE 2

Representative single T-type Ca²⁺ channel currents and ensemble averages. Capacity- and leak-corrected single-channel currents and the corresponding ensemble currents from a single cell-attached patch elicited with step depolarizations to the indicated potentials (left) in the presence of 20 mM Ca²⁺. Currents shown include 15 ms at the holding potential (−100 mV) and 100 ms at the depolarized potential. Currents were sampled at 20 kHz, filtered at 2 kHz, and then downsampled to 4 kHz offline. For graphical purposes, traces were additionally filtered by adjacently averaging by 3. The seal resistance of the patch was >100 GΩ.

FIGURE 3

Measured current amplitudes are the same when currents are elicited using depolarizations or tail-current protocols. (A) Capacity- and leak-corrected single-channel currents from a cell-attached patch elicited with a 50-mV step depolarization (−100 mV to −50 mV) with 20 mM Ca²⁺ as the permeant ion. Data were sampled at 20 kHz, filtered at 2 kHz, and downsampled to 4 kHz offline. (B) Capacity- and leak-corrected single-channel currents from the same patch as in A elicited with the tail-current protocol shown above. Patches were depolarized to 0 mV for 3 ms and subsequently hyperpolarized for 80 ms, in this case to −50 mV. Single-channel current amplitudes were determined from all-points histograms from selected segments of active traces. Selected segments were marked (dotted lines) from ∼100 sweeps per potential, concatenated, and used to generate the amplitude histogram. The data were binned into 30-fA bins and fit with a sum of two Gaussians. The signal/noise ratio was ∼3 at −30 mV and increased to ∼7 at −50 mV. (C) Amplitude histogram for currents elicited with 50-mV step depolarizations. The dotted black lines are the Gaussian fit of the closed and open states, and the solid line is the sum of the Gaussians. The open-channel current at −50 mV was measured to be −0.27 pA. The area under the curve bears no relationship to open and closed durations, because the data used to generate the amplitude histogram excluded much of the closed-state data. (D) The current-voltage relationship for the patch shown in A and B. The solid line is a linear fit to the data with a slope conductance of 5.9 ± 0.8 pS. The two points at −50 mV were calculated using the protocols from A and B.

FIGURE 4

Nonlinearity of the whole-cell and single-channel current-voltage relationships at positive potentials. (A) Family of capacity- and leak-corrected representative currents recorded during steps between −150 mV and 130 mV immediately after a 1-ms depolarization to 0 mV from a holding potential of −100 mV. Sweeps are shown for every 20 mV. (B) Representative whole-cell open-channel I/V relationship for the cell in A. For whole-cell experiments, the bath solution was the same as the 20-mM-Ca²⁺ single-channel pipette solution, and the pipette solution contained (in mM) 140 KCl, 1 CaCl₂, 10 EGTA, 5 MgCl₂, and 10 HEPES, titrated to pH 7.4 with KOH. Data were filtered at 100 kHz by an 8-pole lowpass Bessel filter and digitized at 200 kHz. Although the currents are rather large, the time to peak of the tail currents was within the same range as that of currents of much smaller amplitude (0.15 ms) indicating that voltage control was maintained (data not shown). (C) Single-channel current-voltage relationship. Currents shown are from eight different patches in 20 mM Ca²⁺. Tail protocols were used to elicit currents from −70 to −120 mV and 100-ms step depolarizations were used from 0 to −70 mV, where each symbol represents an individual determination from a single patch. Single-channel conductance was highly sensitive to the voltage range over which it is measured. The dotted line is a linear fit to the data between −20 mV and −60 mV (γ = 4.2 ± 0.3 pS) (solid squares). The solid line is a linear fit of the data between −60 mV and −120 mV (γ = 8.4 ± 0.8 pS) (solid circles).

FIGURE 5

Representative single-channel Ba²⁺ currents. (A) Voltage protocol used to elicit single-channel currents in B and C. Patches were held at −100 mV, depolarized to 0 mV for 3 ms, and then hyperpolarized to the test potential. Recordings were made during the final 15 ms of the 3-s interpulse interval, during the 3-ms depolarization to 0 mV, and for 80 ms at the test potential. (B) Capacity- and leak-corrected single-channel currents elicited with the tail protocol shown in A from a holding potential of −100 mV in 5 mM Ba²⁺ (upper) and 60 mM Ba²⁺ (lower). Top currents were sampled at 4 kHz and filtered at 2 kHz. Bottom currents were sampled at 20 kHz and filtered at 2 kHz and then downsampled to 4 kHz offline. The seal resistance was >100 GΩ in each patch.

FIGURE 6

(A) Single-channel currents as a function of potential measured using an amplitude histogram (open circles, n = 4) or QuB (solid squares, n = 5), as described in text, using the diagram of the model shown. (B) Current-voltage relationship for both the main conductance state (solid circles) and subconductance state (solid squares) obtained using QuB in the presence of 40 mM Ca²⁺ (n = 5). The solid line is a linear fit of the main-state data with a slope conductance of 9.0 ± 0.6 pS. The dotted line is a linear fit of the subconductance-state data with a slope conductance of 6.0 ± 1.0 pS. (Inset) Idealized currents in the presence of 40 mM Ca²⁺. Currents were sampled at 20 kHz, filtered at 2 kHz, and downsampled offline to 4 kHz. (C) The current-voltage relationship for both the main conductance state (open circles) and subconductance state (open squares) obtained using QuB in the presence of 115 mM Ca²⁺ (n = 4). The solid line is a linear fit of the main-state data with a slope conductance of 9.4 ± 1.5 pS. The dotted line is a linear fit of the subconductance-state data with a slope conductance of 6.8 ± 0.9pS. (Inset) Idealized currents in the presence of 115 mM Ca²⁺. Currents were sampled at 20 kHz, filtered at 2 kHz, and downsampled offline to 4 kHz. (D, left) The relative fractional occupancy of the subconductance states for 40 mM Ca²⁺ (solid squares) and 115 mM Ca²⁺ (open circles). Fractional occupancy was calculated as (occupancy of the subconductance state)/(occupancy of the subconductance state + occupancy of the main conductance state). (D, right) The grouped relative fractional occupancy of the subconductance state for 40 mM Ca²⁺ (n = 5) and 115 mM Ca²⁺ (n = 4). The data from each cell over a voltage range of −60 mV to −80 mV were averaged and the values from each cell were averaged and displayed as mean ± SE. *—Statistical significance as measured by a Student t-test (p = 0.03).

FIGURE 7

Divalent ion concentration dependence of single-channel conductance. Slope conductance over a range of Ca²⁺ concentrations (squares, n = 19) and Ba²⁺ concentrations (circles, n = 26) (5–115 mM). All of the conductance measurements were made using all-points histograms except 115 mM Ca²⁺. Conductance was determined by the linear regression to the currents from multiple patches at each concentration. Data are displayed as the estimate ± SE. For each concentration, there were at least three patches with current amplitudes at three potentials, except in two cases: for 5 mM Ba²⁺, there was only one patch with three potentials and in 5 mM Ca²⁺ there were only two patches with three potentials. The data are fit with a Langmuir isotherm function. For Ca²⁺, γ_max = 9.5 ± 0.4 pS and K_M = 2.3 ± 0.7 mM. For Ba²⁺, γ_max = 10.3 ± 0.5 pS; K_M = 7.9 ± 1.3 mM. (Inset) The concentration dependence is displayed on a semilogarithmic scale.

FIGURE 8

(A) Whole-cell current-voltage relationship in the presence of 5 mM divalent (same as Fig. 1 B) and I/V voltage protocol (inset). (B) The whole-cell current-voltage relationship in the presence of 60 mM Ca²⁺ (solid squares) and Ba²⁺ (open circles). The data are displayed as mean ± SE normalized to the peak current in Ca²⁺. In the cases where the error bars are not visible, it is because they are smaller than the size of the symbol. For whole-cell experiments, the bath solution was the same as the single-channel pipette solution containing 60 mM Ca²⁺ and 60 mM Ba²⁺, respectively. (C) Average whole-cell open-channel I/V relationship in 5 mM Ca²⁺ (solid squares) and 5 mM Ba²⁺ (open circles) and voltage protocol (inset). The data are displayed as mean ± SE normalized to the current in Ca²⁺ at −80 mV. In the cases where the error bars are not visible, it is because they are smaller than the size of the symbol. The half-solid circles are the Ba²⁺ data shifted 10 mV positive (as described in text). Data were filtered at 100 kHz by an 8-pole low-pass Bessel filter and digitized at 200 kHz. Currents were recorded at hyperpolarized potentials after depolarization to +60 mV for 1 ms. (Inset) Capacity- and leak-corrected representative currents in 5 mM Ba²⁺ (upper) and Ca²⁺ (lower). Traces were filtered offline to 20 kHz and the first 0.05 ms are not shown. (D) Average whole-cell open-channel I/V relationship in 60 mM Ca²⁺ (solid squares) and 60 mM Ba²⁺ (open circles). The data are displayed as the mean ± SE normalized to the Ca²⁺ at −80 mV. In the cases where the error bars are not visible, it is because they are smaller than the size of the symbol. The half-solid circles are the Ba²⁺ data shifted by 20 mV (as described in text). Currents were recorded at hyperpolarized potentials after a brief depolarization to +115 mV for 1 ms. Data were filtered at 100 kHz by an 8-pole low-pass Bessel filter and digitized at 200 kHz. (Inset) Capacity- and leak-corrected representative currents in 60 mM Ba²⁺ (upper) and Ca²⁺ (lower). Traces were filtered offline to 20 kHz and the first 0.06 ms are not shown.